Subgroups — C₃²×D₂₀ #67162

Order 360.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×D₅	C₂	1	2	yes	maximal, complemented
2	C₃²×C₄×C₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×D₂₀	C₃	1	4	yes	maximal, direct product factor
4	C₂×C₃²×C₅	C₂²	1	1	yes	characteristic
5	C₃²×D₅	—	2	2	no	—
6	C₃²×D₄	—	5	1	no	maximal, Hall
7	C₂×C₃×D₅	C₂×C₃	1	8	yes	complemented
8	C₃×C₄×C₅	C₂×C₃	1	4	yes	complemented
9	C₃²×C₅	D₄	1	1	yes	characteristic, complemented, Hall
10	D₂₀	C₃²	1	1	yes	characteristic, direct product factor, Hall
11	C₂²×C₃²	—	5	2	no	—
12	C₃²×C₄	D₅	1	1	yes	characteristic, complemented
13	C₂×C₃×C₅	C₂²×C₃	1	4	yes	—
14	C₃×D₅	—	2	8	no	—
15	C₃×D₄	—	5	4	no	—
16	C₂×D₅	C₂×C₃²	1	2	yes	complemented
17	C₄×C₅	C₂×C₃²	1	1	yes	characteristic, complemented
18	C₂×C₃²	—	10	2	no	—
19	C₂×C₃²	C₂×D₅	1	1	yes	characteristic
20	C₃×C₅	C₃×D₄	1	4	yes	complemented
21	C₂²×C₃	—	5	8	no	—
22	C₃×C₄	C₃×D₅	1	4	yes	complemented
23	C₂×C₅	C₂²×C₃²	1	1	yes	characteristic
24	D₅	—	2	2	no	—
25	C₃²	D₂₀	1	1	yes	characteristic, direct product factor, Sylow
26	D₄	—	5	1	no	Sylow
27	C₂×C₃	—	10	8	no	—
28	C₂×C₃	C₂×C₃×D₅	1	4	yes	—
29	C₅	C₃²×D₄	1	1	yes	characteristic, complemented, Sylow
30	C₂²	—	5	2	no	—
31	C₄	C₃²×D₅	1	1	yes	characteristic, complemented
32	C₃	C₃×D₂₀	1	4	yes	direct product factor
33	C₂	—	10	2	no	—
34	C₂	C₂×C₃²×D₅	1	1	yes	characteristic

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

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