Subgroups — A₆ #67188

Order 360.

22 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	A₅	—	6	2	no	maximal
2	#157	—	10	1	no	maximal
3	S₄	—	15	2	no	maximal
4	C₃⋊D₃	—	10	1	no	—
5	A₄	—	15	2	no	—
6	D₅	—	36	1	no	—
7	C₃²	—	10	1	no	Sylow
8	D₄	—	45	1	no	Sylow
9	D₃	—	60	2	no	—
10	C₅	—	36	1	no	Sylow
11	C₂²	—	15	2	no	—
12	C₄	—	45	1	no	—
13	C₃	—	20	2	no	—
14	C₂	—	45	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, hypocenter	G	C₁
LCS	G
UCS	C₁

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.