Subgroups — C₃²×Dic₁₀ #67160

Order 360.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₄×C₅	C₂	1	1	yes	maximal, characteristic
2	C₃²×Dic₅	C₂	1	2	yes	maximal
3	C₃×Dic₁₀	C₃	1	4	yes	maximal, direct product factor
4	C₂×C₃²×C₅	C₂²	1	1	yes	characteristic
5	C₃²×Q₈	—	5	1	no	maximal, Hall
6	C₃×C₄×C₅	C₂×C₃	1	4	yes	—
7	C₃×Dic₅	C₂×C₃	1	8	yes	—
8	C₃²×C₅	Q₈	1	1	yes	characteristic, complemented, Hall
9	Dic₁₀	C₃²	1	1	yes	characteristic, direct product factor, Hall
10	C₃²×C₄	—	5	2	no	—
11	C₃²×C₄	D₅	1	1	yes	characteristic
12	C₂×C₃×C₅	C₂²×C₃	1	4	yes	—
13	C₃×Q₈	—	5	4	no	—
14	C₄×C₅	C₂×C₃²	1	1	yes	characteristic
15	Dic₅	C₂×C₃²	1	2	yes	—
16	C₂×C₃²	C₂×D₅	1	1	yes	characteristic
17	C₃×C₅	C₃×Q₈	1	4	yes	complemented
18	C₃×C₄	—	5	8	no	—
19	C₃×C₄	C₃×D₅	1	4	yes	—
20	C₂×C₅	C₂²×C₃²	1	1	yes	characteristic
21	C₃²	Dic₁₀	1	1	yes	characteristic, direct product factor, Sylow
22	Q₈	—	5	1	no	Sylow
23	C₂×C₃	C₂×C₃×D₅	1	4	yes	—
24	C₅	C₃²×Q₈	1	1	yes	characteristic, complemented, Sylow
25	C₄	—	5	2	no	—
26	C₄	C₃²×D₅	1	1	yes	characteristic
27	C₃	C₃×Dic₁₀	1	4	yes	direct product factor
28	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.