# Subgroup structure of alternating groups

## Contents

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