Subgroup structure of alternating groups

This article gives specific information, namely, subgroup structure, about a family of groups, namely: alternating group.
View subgroup structure of group families | View other specific information about alternating group

$n$	Alternating group	Order	Subgroup structure page
3	cyclic group:Z3	3	subgroup structure of cyclic group:Z3
4	alternating group:A4	12	subgroup structure of alternating group:A4
5	alternating group:A5	60	subgroup structure of alternating group:A5
6	alternating group:A6	360	subgroup structure of alternating group:A6
7	alternating group:A7	2520	subgroup structure of alternating group:A7
8	alternating group:A8	20160	subgroup structure of alternating group:A8
9	alternating group:A9	181440	subgroup structure of alternating group:A9
10	alternating group:A10	1814400	subgroup structure of alternating group:A10

Key statistics

We start at $n=3$, because the group is trivial for smaller $n$.

$n$	$n!/2$ (order of alternating group)	Alternating group of degree $n$	Number of subgroups	Number of conjugacy classes of subgroups	Number of automorphism classes of subgroups	Number of normal subgroups	Number of characteristic subgroups
3	3	cyclic group:Z3	2	2	2	2	2
4	12	alternating group:A4	10	5	5	3	3
5	60	alternating group:A5	59	9	9	2	2
6	360	alternating group:A6	501	22	16	2	2
7	2520	alternating group:A7	3786	40	37	2	2
8	20160	alternating group:A8	48337	137	112	2	2