diff --git a/test/enzyme-indexmanipulations-flip-twist/flip.jl b/test/enzyme-indexmanipulations-flip-twist/flip.jl
new file mode 100644
index 000000000..1349fbc62
--- /dev/null
+++ b/test/enzyme-indexmanipulations-flip-twist/flip.jl
@@ -0,0 +1,22 @@
+using Test, TestExtras
+using TensorKit
+using Enzyme, EnzymeTestUtils
+using Random
+
+spacelist = ad_spacelist(fast_tests)
+eltypes = (Float64, ComplexF64)
+
+@timedtestset "Enzyme - Index Manipulations (flip):" begin
+    @timedtestset "$(TensorKit.type_repr(sectortype(eltype(V)))) ($T) TA ($TA)" for V in spacelist, T in eltypes, TA in (Duplicated,)
+        atol = default_tol(T)
+        rtol = default_tol(T)
+        has_braiding = BraidingStyle(sectortype(eltype(V))) isa HasBraiding
+        if has_braiding
+            A = randn(T, V[1] ⊗ V[2] ← (V[3] ⊗ V[4] ⊗ V[5])')
+            EnzymeTestUtils.test_reverse(flip, TA, (A, TA), (1, Const); atol, rtol, fkwargs = (inv = false,))
+            EnzymeTestUtils.test_reverse(flip, TA, (A, TA), [1, 3]; atol, rtol, fkwargs = (inv = true,))
+            EnzymeTestUtils.test_reverse(flip, TA, (A, TA), (1, Const); atol, rtol)
+            EnzymeTestUtils.test_reverse(flip, TA, (A, TA), ([1, 3], Const); atol, rtol)
+        end
+    end
+end
diff --git a/test/enzyme-indexmanipulations-flip-twist/twist.jl b/test/enzyme-indexmanipulations-flip-twist/twist.jl
new file mode 100644
index 000000000..ec8f9cb11
--- /dev/null
+++ b/test/enzyme-indexmanipulations-flip-twist/twist.jl
@@ -0,0 +1,24 @@
+using Test, TestExtras
+using TensorKit
+using TensorOperations
+using VectorInterface: Zero, One
+using Enzyme, EnzymeTestUtils
+using Random
+
+spacelist = ad_spacelist(fast_tests)
+eltypes = (Float64, ComplexF64)
+
+@timedtestset "Enzyme - Index Manipulations (twist):" begin
+    @timedtestset "$(TensorKit.type_repr(sectortype(eltype(V)))) ($T)" for V in spacelist, T in eltypes, TA in (Duplicated,)
+        atol = default_tol(T)
+        rtol = default_tol(T)
+        A = randn(T, V[1] ⊗ V[2] ← (V[3] ⊗ V[4] ⊗ V[5])')
+        has_braiding = BraidingStyle(sectortype(eltype(V))) isa HasBraiding
+        if has_braiding && !(T <: Real && !(sectorscalartype(sectortype(A)) <: Real))
+            EnzymeTestUtils.test_reverse(twist!, TA, (copy(A), TA), (1, Const); atol, rtol, fkwargs = (inv = false,))
+            EnzymeTestUtils.test_reverse(twist!, TA, (copy(A), TA), ([1, 3], Const); atol, rtol, fkwargs = (inv = true,))
+            EnzymeTestUtils.test_reverse(twist!, TA, (copy(A), TA), (1, Const); atol, rtol)
+            EnzymeTestUtils.test_reverse(twist!, TA, (copy(A), TA), ([1, 3], Const); atol, rtol)
+        end
+    end
+end
diff --git a/test/enzyme-indexmanipulations/braid.jl b/test/enzyme-indexmanipulations-transform/braid.jl
similarity index 78%
rename from test/enzyme-indexmanipulations/braid.jl
rename to test/enzyme-indexmanipulations-transform/braid.jl
index 28d1e52ba..ae5f055ad 100644
--- a/test/enzyme-indexmanipulations/braid.jl
+++ b/test/enzyme-indexmanipulations-transform/braid.jl
@@ -11,12 +11,12 @@ is_ci = get(ENV, "CI", "false") == "true"
 Tαs = is_ci ? (Active,) : (Active, Const)
 Tβs = is_ci ? (Active,) : (Active, Const)
 
-@timedtestset "Enzyme - Index Manipulations (braid!):" begin
-    @timedtestset "$(TensorKit.type_repr(sectortype(eltype(V)))) ($T) Tα $Tα Tβ $Tβ" for V in spacelist, T in eltypes, Tα in Tαs, Tβ in Tβs
-        atol = default_tol(T)
-        rtol = default_tol(T)
-        Vstr = TensorKit.type_repr(sectortype(eltype(V)))
-        A = randn(T, V[1] ⊗ V[2] ← V[4] ⊗ V[5])
+@timedtestset "Enzyme - Index Manipulations (braid!) $(TensorKit.type_repr(sectortype(eltype(V)))) ($T) Tα $Tα Tβ $Tβ" for V in spacelist, T in eltypes, Tα in Tαs, Tβ in Tβs
+    atol = default_tol(T)
+    rtol = default_tol(T)
+    has_braiding = BraidingStyle(sectortype(eltype(V))) isa HasBraiding
+    if has_braiding
+        A = randn(T, V[1] ⊗ V[2] ← (V[3] ⊗ V[4] ⊗ V[5])')
         α = randn(T)
         β = randn(T)
         p = randcircshift(numout(A), numin(A))
diff --git a/test/enzyme-indexmanipulations/permute.jl b/test/enzyme-indexmanipulations-transform/permute.jl
similarity index 72%
rename from test/enzyme-indexmanipulations/permute.jl
rename to test/enzyme-indexmanipulations-transform/permute.jl
index a7f6126d6..d78ec1e41 100644
--- a/test/enzyme-indexmanipulations/permute.jl
+++ b/test/enzyme-indexmanipulations-transform/permute.jl
@@ -11,14 +11,15 @@ is_ci = get(ENV, "CI", "false") == "true"
 Tαs = is_ci ? (Active,) : (Active, Const)
 Tβs = is_ci ? (Active,) : (Active, Const)
 
-@timedtestset "Enzyme - Index Manipulations (permute!):" begin
-    @timedtestset "$(TensorKit.type_repr(sectortype(eltype(V)))) ($T)" for V in spacelist, T in eltypes
+if VERSION >= v"1.11.0-rc" # segfault issues on 1.10
+    @timedtestset "Enzyme - Index Manipulations (permute!): $(TensorKit.type_repr(sectortype(eltype(V)))) ($T)" for V in spacelist, T in eltypes
+        println(TensorKit.type_repr(sectortype(eltype(V))))
         atol = default_tol(T)
         rtol = default_tol(T)
         symmetricbraiding = BraidingStyle(sectortype(eltype(V))) isa SymmetricBraiding
 
         symmetricbraiding && @timedtestset "permute! Tα $Tα, Tβ $Tβ" for Tα in Tαs, Tβ in Tβs
-            A = randn(T, V[1] ⊗ V[2] ← V[4] ⊗ V[5])
+            A = randn(T, V[1] ⊗ V[2] ← (V[3] ⊗ V[4] ⊗ V[5])')
             α = randn(T)
             β = randn(T)
             p = randindextuple(numind(A))
diff --git a/test/enzyme-indexmanipulations-transform/transpose.jl b/test/enzyme-indexmanipulations-transform/transpose.jl
new file mode 100644
index 000000000..9e6703eb1
--- /dev/null
+++ b/test/enzyme-indexmanipulations-transform/transpose.jl
@@ -0,0 +1,35 @@
+using Test, TestExtras
+using TensorKit
+using TensorOperations
+using VectorInterface: Zero, One
+using Enzyme, EnzymeTestUtils
+using Random
+
+spacelist = ad_spacelist(fast_tests)
+eltypes = (Float64, ComplexF64)
+
+is_ci = get(ENV, "CI", "false") == "true"
+
+Tαs = is_ci ? (Active,) : (Active, Const)
+Tβs = is_ci ? (Active,) : (Active, Const)
+
+@timedtestset "Enzyme - Index Manipulations (transpose!) $(TensorKit.type_repr(sectortype(eltype(V)))) ($T)" for V in spacelist, T in eltypes
+    atol = default_tol(T)
+    rtol = default_tol(T)
+    A = randn(T, V[1] ⊗ V[2] ← (V[3] ⊗ V[4] ⊗ V[5])')
+    α = randn(T)
+    β = randn(T)
+
+    # repeat a couple times to get some distribution of arrows
+    p = randcircshift(numout(A), numin(A))
+    C = randn!(transpose(A, p))
+    !is_ci && EnzymeTestUtils.test_reverse(TensorKit.transpose!, Duplicated, (copy(C), Duplicated), (A, Duplicated), (p, Const), (One(), Const), (Zero(), Const); atol, rtol)
+    @testset for Tα in Tαs, Tβ in Tβs
+        EnzymeTestUtils.test_reverse(TensorKit.transpose!, Duplicated, (copy(C), Duplicated), (A, Duplicated), (p, Const), (α, Tα), (β, Tβ); atol, rtol)
+        if !(T <: Real) && !is_ci
+            EnzymeTestUtils.test_reverse(TensorKit.transpose!, Duplicated, (copy(C), Duplicated), (real(A), Duplicated), (p, Const), (α, Tα), (β, Tβ); atol, rtol)
+            EnzymeTestUtils.test_reverse(TensorKit.transpose!, Duplicated, (copy(C), Duplicated), (A, Duplicated), (p, Const), (real(α), Tα), (β, Tβ); atol, rtol)
+            EnzymeTestUtils.test_reverse(TensorKit.transpose!, Duplicated, (copy(C), Duplicated), (real(A), Duplicated), (p, Const), (real(α), Tα), (β, Tβ); atol, rtol)
+        end
+    end
+end
diff --git a/test/enzyme-indexmanipulations/insertunit.jl b/test/enzyme-indexmanipulations-unit/insertunit.jl
similarity index 95%
rename from test/enzyme-indexmanipulations/insertunit.jl
rename to test/enzyme-indexmanipulations-unit/insertunit.jl
index 15e02d22c..69c299b0e 100644
--- a/test/enzyme-indexmanipulations/insertunit.jl
+++ b/test/enzyme-indexmanipulations-unit/insertunit.jl
@@ -10,7 +10,7 @@ eltypes = (Float64, ComplexF64)
     @timedtestset verbose = true "$(TensorKit.type_repr(sectortype(eltype(V)))) ($T)" for V in spacelist, T in eltypes, TA in (Duplicated,)
         atol = default_tol(T)
         rtol = default_tol(T)
-        A = randn(T, V[1] ⊗ V[2] ← V[4] ⊗ V[5])
+        A = randn(T, V[1] ⊗ V[2] ← (V[3] ⊗ V[4] ⊗ V[5])')
         @testset for insertunit in (insertleftunit, insertrightunit)
             EnzymeTestUtils.test_reverse(insertunit, TA, (A, TA), (Val(1), Const); atol, rtol)
             EnzymeTestUtils.test_reverse(insertunit, TA, (A, TA), (Val(4), Const); atol, rtol)
diff --git a/test/enzyme-indexmanipulations/removeunit.jl b/test/enzyme-indexmanipulations-unit/removeunit.jl
similarity index 92%
rename from test/enzyme-indexmanipulations/removeunit.jl
rename to test/enzyme-indexmanipulations-unit/removeunit.jl
index 2249483be..3e64cb2cd 100644
--- a/test/enzyme-indexmanipulations/removeunit.jl
+++ b/test/enzyme-indexmanipulations-unit/removeunit.jl
@@ -10,7 +10,7 @@ eltypes = (Float64, ComplexF64)
     @timedtestset verbose = true "$(TensorKit.type_repr(sectortype(eltype(V)))) ($T)" for V in spacelist, T in eltypes, TB in (Duplicated,)
         atol = default_tol(T)
         rtol = default_tol(T)
-        A = randn(T, V[1] ⊗ V[2] ← V[4] ⊗ V[5])
+        A = randn(T, V[1] ⊗ V[2] ← (V[3] ⊗ V[4] ⊗ V[5])')
         for i in 1:2
             B = insertleftunit(A, i; dual = rand(Bool))
             EnzymeTestUtils.test_reverse(removeunit, TB, (B, TB), (Val(i), Const); atol, rtol, fkwargs = (copy = false,))
diff --git a/test/enzyme-indexmanipulations/flip.jl b/test/enzyme-indexmanipulations/flip.jl
deleted file mode 100644
index 8afe4e914..000000000
--- a/test/enzyme-indexmanipulations/flip.jl
+++ /dev/null
@@ -1,19 +0,0 @@
-using Test, TestExtras
-using TensorKit
-using Enzyme, EnzymeTestUtils
-using Random
-
-spacelist = ad_spacelist(fast_tests)
-eltypes = (Float64, ComplexF64)
-
-@timedtestset "Enzyme - Index Manipulations (flip):" begin
-    @timedtestset "$(TensorKit.type_repr(sectortype(eltype(V)))) ($T) TA ($TA)" for V in spacelist, T in eltypes, TA in (Duplicated,)
-        atol = default_tol(T)
-        rtol = default_tol(T)
-        A = randn(T, V[1] ⊗ V[2] ← V[4] ⊗ V[5])
-        EnzymeTestUtils.test_reverse(flip, TA, (A, TA), (1, Const); atol, rtol, fkwargs = (inv = false,))
-        EnzymeTestUtils.test_reverse(flip, TA, (A, TA), [1, 3]; atol, rtol, fkwargs = (inv = true,))
-        EnzymeTestUtils.test_reverse(flip, TA, (A, TA), (1, Const); atol, rtol)
-        EnzymeTestUtils.test_reverse(flip, TA, (A, TA), ([1, 3], Const); atol, rtol)
-    end
-end
diff --git a/test/enzyme-indexmanipulations/transpose.jl b/test/enzyme-indexmanipulations/transpose.jl
deleted file mode 100644
index bff2cb379..000000000
--- a/test/enzyme-indexmanipulations/transpose.jl
+++ /dev/null
@@ -1,37 +0,0 @@
-using Test, TestExtras
-using TensorKit
-using TensorOperations
-using VectorInterface: Zero, One
-using Enzyme, EnzymeTestUtils
-using Random
-
-spacelist = ad_spacelist(fast_tests)
-eltypes = (Float64, ComplexF64)
-
-is_ci = get(ENV, "CI", "false") == "true"
-
-Tαs = is_ci ? (Active,) : (Active, Const)
-Tβs = is_ci ? (Active,) : (Active, Const)
-
-@timedtestset "Enzyme - Index Manipulations (transpose!):" begin
-    @timedtestset "$(TensorKit.type_repr(sectortype(eltype(V)))) ($T)" for V in spacelist, T in eltypes
-        atol = default_tol(T)
-        rtol = default_tol(T)
-        A = randn(T, V[1] ⊗ V[2] ← V[4] ⊗ V[5])
-        α = randn(T)
-        β = randn(T)
-
-        # repeat a couple times to get some distribution of arrows
-        p = randcircshift(numout(A), numin(A))
-        C = randn!(transpose(A, p))
-        EnzymeTestUtils.test_reverse(TensorKit.transpose!, Duplicated, (C, Duplicated), (A, Duplicated), (p, Const), (One(), Const), (Zero(), Const); atol, rtol)
-        @testset for Tα in Tαs, Tβ in Tβs
-            EnzymeTestUtils.test_reverse(TensorKit.transpose!, Duplicated, (C, Duplicated), (A, Duplicated), (p, Const), (α, Tα), (β, Tβ); atol, rtol)
-            if !(T <: Real) && !is_ci
-                EnzymeTestUtils.test_reverse(TensorKit.transpose!, Duplicated, (C, Duplicated), (real(A), Duplicated), (p, Const), (α, Tα), (β, Tβ); atol, rtol)
-                EnzymeTestUtils.test_reverse(TensorKit.transpose!, Duplicated, (C, Duplicated), (A, Duplicated), (p, Const), (real(α), Tα), (β, Tβ); atol, rtol)
-                EnzymeTestUtils.test_reverse(TensorKit.transpose!, Duplicated, (C, Duplicated), (real(A), Duplicated), (p, Const), (real(α), Tα), (β, Tβ); atol, rtol)
-            end
-        end
-    end
-end
diff --git a/test/enzyme-indexmanipulations/twist.jl b/test/enzyme-indexmanipulations/twist.jl
deleted file mode 100644
index c939c76d2..000000000
--- a/test/enzyme-indexmanipulations/twist.jl
+++ /dev/null
@@ -1,23 +0,0 @@
-using Test, TestExtras
-using TensorKit
-using TensorOperations
-using VectorInterface: Zero, One
-using Enzyme, EnzymeTestUtils
-using Random
-
-spacelist = ad_spacelist(fast_tests)
-eltypes = (Float64, ComplexF64)
-
-@timedtestset "Enzyme - Index Manipulations (twist):" begin
-    @timedtestset "$(TensorKit.type_repr(sectortype(eltype(V)))) ($T)" for V in spacelist, T in eltypes, TA in (Duplicated,)
-        atol = default_tol(T)
-        rtol = default_tol(T)
-        A = randn(T, V[1] ⊗ V[2] ← V[4] ⊗ V[5])
-        if !(T <: Real && !(sectorscalartype(sectortype(A)) <: Real))
-            EnzymeTestUtils.test_reverse(twist!, TA, (A, TA), (1, Const); atol, rtol, fkwargs = (inv = false,))
-            EnzymeTestUtils.test_reverse(twist!, TA, (A, TA), ([1, 3], Const); atol, rtol, fkwargs = (inv = true,))
-            EnzymeTestUtils.test_reverse(twist!, TA, (A, TA), (1, Const); atol, rtol)
-            EnzymeTestUtils.test_reverse(twist!, TA, (A, TA), ([1, 3], Const); atol, rtol)
-        end
-    end
-end