Alternating group of order 4!/2 as a permutation group

[Subgroup generated by [()] of (Alternating group of order 4!/2 as a permutation group), Subgroup generated by [(1,2)(3,4)] of (Alternating group of order 4!/2 as a permutation group), Subgroup generated by [(1,3)(2,4)] of (Alternating group of order 4!/2 as a permutation group), Subgroup generated by [(1,4)(2,3)] of (Alternating group of order 4!/2 as a permutation group), Subgroup generated by [(2,4,3)] of (Alternating group of order 4!/2 as a permutation group), Subgroup generated by [(1,2,3)] of (Alternating group of order 4!/2 as a permutation group), Subgroup generated by [(1,4,2)] of (Alternating group of order 4!/2 as a permutation group), Subgroup generated by [(1,3,4)] of (Alternating group of order 4!/2 as a permutation group), Subgroup generated by [(1,2)(3,4), (1,3)(2,4)] of (Alternating group of order 4!/2 as a permutation group), Subgroup generated by [(2,4,3), (1,2)(3,4), (1,3)(2,4)] of (Alternating group of order 4!/2 as a permutation group)]

[(), (1,3)(2,4), (1,2)(3,4), (1,4)(2,3), (2,4,3), (1,3,4), (1,2,3), (1,4,2), (2,3,4), (1,3,2), (1,2,4), (1,4,3)]

[((), 1), ((1,3)(2,4), 2), ((1,2)(3,4), 2), ((1,4)(2,3), 2), ((2,4,3), 3), ((1,3,4), 3), ((1,2,3), 3), ((1,4,2), 3), ((2,3,4), 3), ((1,3,2), 3), ((1,2,4), 3), ((1,4,3), 3)]

(1,3)(2,4)

Subgroup generated by [(1,3)(2,4)] of (Alternating group of order 4!/2 as a permutation group)
[(), (1,3)(2,4)]

[(), (1,2)(3,4)]