Subgroups — C₂×A₅ #1225

Order 120.

22 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	A₅	C₂	1	1	yes	maximal, characteristic, direct product factor
2	C₂×A₄	—	5	1	no	maximal, Hall
3	C₂×D₅	—	6	1	no	maximal
4	C₂×D₃	—	10	1	no	maximal
5	A₄	—	5	1	no	—
6	C₂×C₅	—	6	1	no	—
7	D₅	—	6	1	no	—
8	D₅	—	6	1	no	—
9	C₂³	—	5	1	no	Sylow
10	C₂×C₃	—	10	1	no	—
11	D₃	—	10	1	no	—
12	D₃	—	10	1	no	—
13	C₅	—	6	1	no	Sylow
14	C₂²	—	5	1	no	—
15	C₂²	—	15	1	no	—
16	C₂²	—	15	1	no	—
17	C₃	—	10	1	no	Sylow
18	C₂	—	15	1	no	—
19	C₂	—	15	1	no	—
20	C₂	A₅	1	1	yes	maximal normal, characteristic, direct product factor

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. A₅	C₂	direct (N × H)
20. C₂	A₅	direct (N × H)

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