Subgroups — #4090

Order 160.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×Q₈	C₂	1	1	yes	maximal, characteristic
2	C₂×Dic₁₀	C₂	1	1	yes	maximal, characteristic
3	#683	C₂	1	4	yes	maximal
4	C₄×Dic₅	C₂	1	1	yes	maximal, characteristic
5	C₅×Q₈	—	2	2	no	—
6	C₂×C₄×C₅	C₂²	1	2	yes	—
7	C₂×C₄×C₅	C₂²	1	1	yes	characteristic
8	C₂×Dic₅	C₂²	1	2	yes	—
9	C₂×Dic₅	C₂²	1	2	yes	—
10	Dic₁₀	—	2	2	no	—
11	C₄⋊Q₈	—	5	1	no	maximal, Sylow
12	C₂²×C₅	C₂³	1	1	yes	characteristic
13	C₄×C₅	—	2	2	no	—
14	C₄×C₅	D₄	1	2	yes	—
15	Dic₅	—	2	2	no	—
16	Dic₅	Q₈	1	4	yes	complemented
17	C₂×Q₈	—	5	1	no	—
18	C₂×Q₈	D₅	1	1	yes	characteristic
19	C₄⋊C₄	—	5	4	no	—
20	C₄²	—	5	1	no	—
21	C₂×C₅	C₂×D₄	1	1	yes	characteristic
22	C₂×C₅	C₂×Q₈	1	2	yes	—
23	Q₈	—	2	2	no	—
24	Q₈	—	10	2	no	—
25	C₂×C₄	—	5	2	no	—
26	C₂×C₄	—	5	2	no	—
27	C₂×C₄	C₂×D₅	1	2	yes	—
28	C₂×C₄	C₂×D₅	1	1	yes	characteristic
29	C₅	C₄⋊Q₈	1	1	yes	characteristic, complemented, Sylow
30	C₂²	C₂²×D₅	1	1	yes	characteristic
31	C₄	—	2	2	no	—
32	C₄	—	5	4	no	—
33	C₄	—	10	2	no	—
34	C₄	C₂²⋊D₅	1	2	yes	—
35	C₂	Q₈×D₅	1	2	yes	—
36	C₂	C₂×C₂²⋊D₅	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂²×D₅
commutator, socle, prime radical, cosocle	C₂²×C₅	C₂³
Fitting	C₂×C₅×Q₈	C₂
hypercenter	C₂×Q₈	D₅
hypocenter	C₅	C₄⋊Q₈
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂² ◁ C₂×Q₈

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

N	H ≅ G/N	type
16. Dic₅	Q₈	semidirect
29. C₅	C₄⋊Q₈	semidirect

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