Subgroup structure of alternating group:A6

This article discusses the subgroup structure of alternating group:A6, which is the alternating group on the set $$\{ 1, 2,3,4,5,6\}$$. The group has order 360.

Table classifying subgroups up to permutation automorphisms
Note that alternating groups are simple (with an exception for degree 1,2,4), so in particular $$A_6$$ is simple. Hence no proper nontrivial subgroup is normal or subnormal.

The below lists subgroups up to automorphisms arising from permutations, i.e., automorphisms arising from conjugation in symmetric group:S6. This is not the same as the classification up to automorphisms because of the presence of other automorphisms, a phenomenon unique to degree six.