Subgroups — C₅×#474 #65637

Order 320.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×C₅×D₄	C₂	1	1	yes	maximal, characteristic
3	C₅×#107	C₂	1	2	yes	maximal, complemented
4	C₅×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#102	C₂	1	2	yes	maximal
6	C₂×C₅×Q₈	—	2	1	no	—
7	C₂×C₅×D₄	C₂²	1	1	yes	characteristic
8	C₂²×C₄×C₅	—	2	1	no	—
9	C₂×C₅×C₈	C₂²	1	2	yes	—
10	C₅×C₄⋊C₄	—	2	1	no	—
11	C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
12	C₅×C₄⋊C₄	C₂²	1	2	yes	—
13	C₅×C₂²⋊C₄	—	2	1	no	—
14	C₄²×C₅	C₂²	1	1	yes	characteristic
15	#474	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
16	C₂³×C₅	—	2	1	no	—
17	C₅×Q₈	—	4	2	no	—
18	C₅×D₄	—	2	1	no	—
19	C₅×D₄	Q₈	1	2	yes	complemented
20	C₂×C₄×C₅	—	2	1	no	—
21	C₂×C₄×C₅	—	2	2	no	—
22	C₂×C₄×C₅	—	4	2	no	—
23	C₂×C₄×C₅	D₄	1	1	yes	characteristic
24	C₂×C₄×C₅	D₄	1	1	yes	characteristic
25	C₂×C₄×C₅	C₂³	1	1	yes	characteristic
26	C₅×C₈	—	2	2	no	—
27	C₄⋊Q₈	C₂×C₅	1	1	yes	characteristic, complemented
28	C₄×D₄	C₂×C₅	1	1	yes	characteristic
29	#107	C₂×C₅	1	2	yes	complemented
30	C₄⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
31	#102	C₂×C₅	1	2	yes	—
32	C₂²×C₅	—	2	2	no	—
33	C₂²×C₅	—	4	1	no	—
34	C₂²×C₅	—	4	1	no	—
35	C₂²×C₅	C₂×D₄	1	1	yes	characteristic
36	C₄×C₅	—	2	1	no	—
37	C₄×C₅	—	4	1	no	—
38	C₄×C₅	—	4	2	no	—
39	C₄×C₅	D₈	1	2	yes	—
40	C₄×C₅	C₂×Q₈	1	1	yes	characteristic
41	C₄×C₅	#41	1	1	yes	characteristic
42	C₂×Q₈	—	2	1	no	—
43	C₂×D₄	C₂²×C₅	1	1	yes	characteristic
44	C₂²×C₄	—	2	1	no	—
45	C₂×C₈	C₂²×C₅	1	2	yes	—
46	C₄⋊C₄	—	2	1	no	—
47	C₄⋊C₄	C₂²×C₅	1	2	yes	—
48	C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
49	C₂²⋊C₄	—	2	1	no	—
50	C₄²	C₂²×C₅	1	1	yes	characteristic
51	C₂×C₅	—	4	2	no	—
52	C₂×C₅	C₂²⋊Q₈	1	1	yes	characteristic
53	C₂×C₅	C₂×D₈	1	1	yes	characteristic
54	C₂×C₅	#137	1	1	yes	characteristic
55	C₂³	—	2	1	no	—
56	Q₈	—	4	2	no	—
57	D₄	—	2	1	no	—
58	D₄	C₅×Q₈	1	2	yes	complemented
59	C₂×C₄	—	2	1	no	—
60	C₂×C₄	—	2	2	no	—
61	C₂×C₄	—	4	2	no	—
62	C₂×C₄	C₅×D₄	1	1	yes	characteristic
63	C₂×C₄	C₅×D₄	1	1	yes	characteristic
64	C₂×C₄	C₂³×C₅	1	1	yes	characteristic
65	C₈	—	2	2	no	—
66	C₅	#474	1	1	yes	characteristic, direct product factor, Sylow
67	C₂²	—	2	2	no	—
68	C₂²	—	4	1	no	—
69	C₂²	—	4	1	no	—
70	C₂²	C₂×C₅×D₄	1	1	yes	characteristic
71	C₄	—	2	1	no	—
72	C₄	—	4	1	no	—
73	C₄	—	4	2	no	—
74	C₄	C₅×D₈	1	2	yes	—
75	C₄	C₂×C₅×Q₈	1	1	yes	characteristic
76	C₄	C₅×#41	1	1	yes	characteristic
77	C₂	—	4	2	no	—
78	C₂	C₅×C₂²⋊Q₈	1	1	yes	characteristic
79	C₂	C₂×C₅×D₈	1	1	yes	characteristic
80	C₂	C₅×#137	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂³×C₅
prime radical	C₂×C₅×D₄	C₂²
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. C₅×C₄⋊Q₈	C₂	semidirect
3. C₅×#107	C₂	semidirect
4. C₅×C₄⋊C₈	C₂	semidirect
15. #474	C₅	direct (N × H)
19. C₅×D₄	Q₈	semidirect
27. C₄⋊Q₈	C₂×C₅	semidirect
29. #107	C₂×C₅	semidirect
30. C₄⋊C₈	C₂×C₅	semidirect
58. D₄	C₅×Q₈	semidirect
66. C₅	#474	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×C₄⋊Q₈	2
C₄×C₅×D₄	2
C₅×#107	2
C₅×C₄⋊C₈	2
C₅×#102	2
#474	5

Subgroups — C5×#474 #65637

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#474 #65637