Subgroups — C₃×A₅ #4374

Order 180.

21 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	A₅	C₃	1	1	yes	maximal, characteristic, direct product factor
2	C₃×A₄	—	5	1	no	maximal, Hall
3	C₃×D₅	—	6	1	no	maximal
4	C₃×D₃	—	10	1	no	maximal
5	C₃×C₅	—	6	1	no	—
6	C₂²×C₃	—	5	1	no	—
7	A₄	—	5	1	no	—
8	A₄	—	5	2	no	—
9	D₅	—	6	1	no	—
10	C₃²	—	10	1	no	Sylow
11	C₂×C₃	—	15	1	no	—
12	D₃	—	10	1	no	—
13	C₅	—	6	1	no	Sylow
14	C₂²	—	5	1	no	Sylow
15	C₃	—	10	1	no	—
16	C₃	—	20	1	no	—
17	C₃	A₅	1	1	yes	maximal normal, characteristic, direct product factor
18	C₂	—	15	1	no	—

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

N	H ≅ G/N	type
1. A₅	C₃	direct (N × H)
17. C₃	A₅	direct (N × H)

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