Subgroups — #3946

Order 160.

38 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₈	C₂	1	1	yes	maximal, characteristic
2	C₄×Dic₅	C₂	1	1	yes	maximal, characteristic
3	C₂×#168	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×C₅	C₂²	1	1	yes	characteristic
5	C₂×Dic₅	C₄	1	1	yes	characteristic
6	C₂×Dic₅	C₄	1	1	yes	characteristic
7	C₅×C₈	—	2	1	no	—
8	#168	—	2	1	no	—
9	C₄⋊C₈	—	5	1	no	maximal, Sylow
10	C₂²×C₅	C₂×C₄	1	1	yes	characteristic
11	C₄×C₅	D₄	1	1	yes	characteristic
12	C₄×C₅	Q₈	1	1	yes	characteristic
13	Dic₅	—	2	1	no	—
14	Dic₅	C₈	1	2	yes	complemented
15	C₂×C₈	—	5	1	no	—
16	C₂×C₈	D₅	1	1	yes	characteristic
17	C₄²	—	5	1	no	—
18	C₂×C₅	C₄⋊C₄	1	1	yes	characteristic
19	C₂×C₅	C₂×C₈	1	1	yes	characteristic
20	C₂×C₅	M₁₆	1	1	yes	characteristic
21	C₂×C₄	—	5	1	no	—
22	C₂×C₄	—	5	1	no	—
23	C₂×C₄	C₂×D₅	1	1	yes	characteristic
24	C₈	—	2	1	no	—
25	C₈	—	10	1	no	—
26	C₅	C₄⋊C₈	1	1	yes	characteristic, complemented, Sylow
27	C₂²	C₄×D₅	1	1	yes	characteristic
28	C₄	—	5	2	no	—
29	C₄	—	10	1	no	—
30	C₄	Dic₁₀	1	1	yes	characteristic
31	C₄	C₂²⋊D₅	1	1	yes	characteristic
32	C₂	C₈×D₅	1	1	yes	characteristic
33	C₂	#676	1	1	yes	characteristic
34	C₂	#683	1	1	yes	characteristic

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

N	H ≅ G/N	type
14. Dic₅	C₈	semidirect
26. C₅	C₄⋊C₈	semidirect

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