Subgroups — #3948

Order 160.

42 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₁₀	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×C₈	C₂	1	1	yes	maximal, characteristic
3	C₄⋊Dic₅	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×C₅	C₂²	1	1	yes	characteristic
5	C₂×Dic₅	—	2	1	no	—
6	C₂×Dic₅	—	2	1	no	—
7	Dic₁₀	—	2	1	no	—
8	Dic₁₀	C₄	1	2	yes	complemented
9	C₅×C₈	—	2	1	no	—
10	#103	—	5	1	no	maximal, Sylow
11	C₂²×C₅	D₄	1	1	yes	characteristic
12	C₄×C₅	C₂×C₄	1	1	yes	characteristic
13	C₄×C₅	D₄	1	1	yes	characteristic
14	Dic₅	—	2	2	no	—
15	Dic₅	—	4	1	no	—
16	C₂×Q₈	—	5	1	no	—
17	C₂×C₈	D₅	1	1	yes	characteristic
18	C₄⋊C₄	—	5	1	no	—
19	C₂×C₅	C₂²⋊C₄	1	1	yes	characteristic
20	C₂×C₅	SD₁₆	1	1	yes	characteristic
21	C₂×C₅	Q₁₆	1	1	yes	characteristic
22	Q₈	—	5	2	no	—
23	Q₈	—	10	1	no	—
24	C₂×C₄	—	10	1	no	—
25	C₂×C₄	—	10	1	no	—
26	C₂×C₄	C₂×D₅	1	1	yes	characteristic
27	C₈	—	2	1	no	—
28	C₅	#103	1	1	yes	characteristic, complemented, Sylow
29	C₂²	D₂₀	1	1	yes	characteristic
30	C₄	—	10	2	no	—
31	C₄	—	20	1	no	—
32	C₄	C₄×D₅	1	1	yes	characteristic
33	C₄	C₂²⋊D₅	1	1	yes	characteristic
34	C₂	#677	1	1	yes	characteristic
35	C₂	Dic₂₀	1	1	yes	characteristic
36	C₂	#685	1	1	yes	characteristic

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

N	H ≅ G/N	type
8. Dic₁₀	C₄	semidirect
28. C₅	#103	semidirect

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