Subgroups — C₅×#493 #65656

Order 320.

162 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×D₈	C₂	1	4	yes	maximal, complemented
2	C₅×#127	C₂	1	2	yes	maximal, complemented
3	C₄×C₅×C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×D₄	—	2	4	no	—
5	C₂×C₅×D₄	C₂²	1	4	yes	—
6	C₅×D₈	—	2	8	no	—
7	C₂×C₅×C₈	C₂²	1	2	yes	—
8	C₄²×C₅	C₂²	1	1	yes	characteristic
9	#493	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
10	C₂³×C₅	—	2	4	no	—
11	C₅×D₄	—	2	8	no	—
12	C₅×D₄	—	4	8	no	—
13	C₂×C₄×C₅	D₄	1	2	yes	—
14	C₂×C₄×C₅	C₂³	1	1	yes	characteristic
15	C₅×C₈	D₄	1	4	yes	complemented
16	C₂×D₈	C₂×C₅	1	4	yes	complemented
17	#127	C₂×C₅	1	2	yes	complemented
18	C₄×C₈	C₂×C₅	1	1	yes	characteristic, complemented
19	C₂²×C₅	—	4	4	no	—
20	C₂²×C₅	—	4	8	no	—
21	C₂²×C₅	C₂×D₄	1	1	yes	characteristic
22	C₄×C₅	D₈	1	4	yes	complemented
23	C₄×C₅	C₂×D₄	1	2	yes	—
24	C₂×D₄	—	2	4	no	—
25	C₂×D₄	C₂²×C₅	1	4	yes	—
26	D₈	—	2	8	no	—
27	C₂×C₈	C₂²×C₅	1	2	yes	—
28	C₄²	C₂²×C₅	1	1	yes	characteristic
29	C₂×C₅	—	8	4	no	—
30	C₂×C₅	#127	1	1	yes	characteristic
31	C₂×C₅	C₂×D₈	1	2	yes	—
32	C₂³	—	2	4	no	—
33	D₄	—	2	8	no	—
34	D₄	—	4	8	no	—
35	C₂×C₄	C₅×D₄	1	2	yes	—
36	C₂×C₄	C₂³×C₅	1	1	yes	characteristic
37	C₈	C₅×D₄	1	4	yes	complemented
38	C₅	#493	1	1	yes	characteristic, direct product factor, Sylow
39	C₂²	—	4	4	no	—
40	C₂²	—	4	8	no	—
41	C₂²	C₂×C₅×D₄	1	1	yes	characteristic
42	C₄	C₅×D₈	1	4	yes	complemented
43	C₄	C₂×C₅×D₄	1	2	yes	—
44	C₂	—	8	4	no	—
45	C₂	C₅×#127	1	1	yes	characteristic
46	C₂	C₂×C₅×D₈	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₅	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂³×C₅
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×D₈	C₂	semidirect
2. C₅×#127	C₂	semidirect
3. C₄×C₅×C₈	C₂	semidirect
9. #493	C₅	direct (N × H)
15. C₅×C₈	D₄	semidirect
16. C₂×D₈	C₂×C₅	semidirect
17. #127	C₂×C₅	semidirect
18. C₄×C₈	C₂×C₅	semidirect
22. C₄×C₅	D₈	semidirect
37. C₈	C₅×D₄	semidirect
38. C₅	#493	direct (N × H)
42. C₄	C₅×D₈	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×D₈	2
C₅×#127	2
C₄×C₅×C₈	2
#493	5

Subgroups — C5×#493 #65656

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#493 #65656