Subgroups — C₅×C₂²⋊Q₈ #4108

Order 160.

74 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, complemented
2	C₂²×C₄×C₅	C₂	1	1	yes	maximal, characteristic
3	C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×C₄⋊C₄	C₂	1	2	yes	maximal, complemented
5	C₅×C₂²⋊C₄	C₂	1	2	yes	maximal
6	C₂³×C₅	C₂²	1	1	yes	characteristic
7	C₅×Q₈	—	2	2	no	—
8	C₂×C₄×C₅	—	2	2	no	—
9	C₂×C₄×C₅	C₂²	1	2	yes	—
10	C₂×C₄×C₅	C₂²	1	2	yes	—
11	C₂×C₄×C₅	C₂²	1	1	yes	characteristic
12	C₂×C₄×C₅	C₂²	1	1	yes	characteristic
13	C₂²⋊Q₈	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
14	C₂²×C₅	—	2	1	no	—
15	C₂²×C₅	—	2	1	no	—
16	C₂²×C₅	Q₈	1	2	yes	complemented
17	C₂²×C₅	C₂³	1	1	yes	characteristic
18	C₄×C₅	—	2	1	no	—
19	C₄×C₅	—	2	2	no	—
20	C₄×C₅	—	2	2	no	—
21	C₄×C₅	D₄	1	2	yes	—
22	C₂×Q₈	C₂×C₅	1	1	yes	characteristic, complemented
23	C₂²×C₄	C₂×C₅	1	1	yes	characteristic
24	C₄⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
25	C₄⋊C₄	C₂×C₅	1	2	yes	complemented
26	C₂²⋊C₄	C₂×C₅	1	2	yes	—
27	C₂×C₅	—	2	2	no	—
28	C₂×C₅	C₂×D₄	1	1	yes	characteristic
29	C₂×C₅	C₂×Q₈	1	1	yes	characteristic
30	C₂×C₅	#41	1	1	yes	characteristic
31	C₂³	C₂²×C₅	1	1	yes	characteristic
32	Q₈	—	2	2	no	—
33	C₂×C₄	—	2	2	no	—
34	C₂×C₄	C₂²×C₅	1	2	yes	—
35	C₂×C₄	C₂²×C₅	1	2	yes	—
36	C₂×C₄	C₂²×C₅	1	1	yes	characteristic
37	C₂×C₄	C₂²×C₅	1	1	yes	characteristic
38	C₅	C₂²⋊Q₈	1	1	yes	characteristic, direct product factor, Sylow
39	C₂²	—	2	1	no	—
40	C₂²	—	2	1	no	—
41	C₂²	C₅×Q₈	1	2	yes	complemented
42	C₂²	C₂³×C₅	1	1	yes	characteristic
43	C₄	—	2	1	no	—
44	C₄	—	2	2	no	—
45	C₄	—	2	2	no	—
46	C₄	C₅×D₄	1	2	yes	—
47	C₂	—	2	2	no	—
48	C₂	C₂×C₅×D₄	1	1	yes	characteristic
49	C₂	C₂×C₅×Q₈	1	1	yes	characteristic
50	C₂	C₅×#41	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅	C₂³
commutator, Frattini, cosocle	C₂²	C₂³×C₅
prime radical	C₂³×C₅	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×Q₈	C₂	semidirect
3. C₅×C₄⋊C₄	C₂	semidirect
4. C₅×C₄⋊C₄	C₂	semidirect
13. C₂²⋊Q₈	C₅	direct (N × H)
16. C₂²×C₅	Q₈	semidirect
22. C₂×Q₈	C₂×C₅	semidirect
24. C₄⋊C₄	C₂×C₅	semidirect
25. C₄⋊C₄	C₂×C₅	semidirect
38. C₅	C₂²⋊Q₈	direct (N × H)
41. C₂²	C₅×Q₈	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×Q₈	2
C₂²×C₄×C₅	2
C₅×C₄⋊C₄	2
C₅×C₂²⋊C₄	2
C₂²⋊Q₈	5

Subgroups — C5×C22⋊Q8 #4108

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₂²⋊Q₈ #4108