Subgroups — C₈×D₂₀ #64975

Order 320.

134 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₈×D₅	C₂	1	2	yes	maximal, complemented
2	C₄×D₂₀	C₂	1	1	yes	maximal, characteristic
3	C₄×C₅×C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	#3952	C₂	1	2	yes	maximal, complemented
5	C₄⋊#168	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₂₀	C₄	1	1	yes	characteristic
7	C₂×C₄×D₅	C₂²	1	2	yes	—
8	C₂×C₅×C₈	C₂²	1	1	yes	characteristic
9	C₂×C₅×C₈	C₂²	1	1	yes	characteristic
10	C₄²×C₅	C₂²	1	1	yes	characteristic
11	#685	C₄	1	2	yes	—
12	C₄⋊Dic₅	C₄	1	1	yes	characteristic
13	C₂×#168	C₂²	1	2	yes	—
14	C₈×D₅	—	2	4	no	—
15	C₈×D₄	—	5	1	no	maximal, Sylow
16	C₂²×D₅	C₂×C₄	1	2	yes	—
17	C₂×C₄×C₅	C₂×C₄	1	1	yes	characteristic
18	C₂×C₄×C₅	C₂×C₄	1	1	yes	characteristic
19	C₂×C₄×C₅	C₂³	1	1	yes	characteristic
20	C₂×Dic₅	C₂×C₄	1	2	yes	—
21	D₂₀	C₈	1	4	yes	direct product factor
22	C₄×D₅	—	2	2	no	—
23	C₄×D₅	—	2	2	no	—
24	C₅×C₈	—	2	1	no	—
25	C₅×C₈	D₄	1	2	yes	complemented
26	#168	—	2	2	no	—
27	C₂²×C₈	—	5	2	no	—
28	C₄×D₄	—	5	1	no	—
29	C₄⋊C₈	—	5	1	no	—
30	C₂²⋊C₈	—	5	2	no	—
31	C₄×C₈	D₅	1	1	yes	characteristic, complemented
32	C₂²×C₅	C₂²×C₄	1	1	yes	characteristic
33	C₂×D₅	—	2	2	no	—
34	C₂×D₅	—	2	2	no	—
35	C₂×D₅	C₂×C₈	1	4	yes	complemented
36	C₄×C₅	—	2	1	no	—
37	C₄×C₅	C₂×C₈	1	2	yes	complemented
38	C₄×C₅	C₂×D₄	1	1	yes	characteristic
39	C₄×C₅	#41	1	1	yes	characteristic
40	Dic₅	—	2	2	no	—
41	C₂×D₄	—	5	1	no	—
42	C₂²×C₄	—	5	2	no	—
43	C₂×C₈	—	5	2	no	—
44	C₂×C₈	—	10	4	no	—
45	C₂×C₈	C₂×D₅	1	1	yes	characteristic
46	C₂×C₈	C₂×D₅	1	1	yes	characteristic
47	C₄⋊C₄	—	5	1	no	—
48	C₂²⋊C₄	—	5	2	no	—
49	C₄²	C₂×D₅	1	1	yes	characteristic
50	C₂×C₅	C₄×D₄	1	1	yes	characteristic
51	C₂×C₅	C₂²×C₈	1	1	yes	characteristic
52	C₂×C₅	#131	1	1	yes	characteristic
53	D₅	—	2	4	no	—
54	C₂³	—	5	2	no	—
55	D₄	—	5	4	no	—
56	C₂×C₄	—	5	2	no	—
57	C₂×C₄	—	10	2	no	—
58	C₂×C₄	—	10	2	no	—
59	C₂×C₄	C₄×D₅	1	1	yes	characteristic
60	C₂×C₄	C₄×D₅	1	1	yes	characteristic
61	C₂×C₄	C₂²×D₅	1	1	yes	characteristic
62	C₈	—	2	1	no	—
63	C₈	—	10	2	no	—
64	C₈	D₂₀	1	2	yes	direct product factor
65	C₅	C₈×D₄	1	1	yes	characteristic, complemented, Sylow
66	C₂²	—	5	4	no	—
67	C₂²	—	10	2	no	—
68	C₂²	—	10	2	no	—
69	C₂²	C₂×C₄×D₅	1	1	yes	characteristic
70	C₄	—	2	1	no	—
71	C₄	—	10	2	no	—
72	C₄	C₈×D₅	1	2	yes	complemented
73	C₄	C₂×D₂₀	1	1	yes	characteristic
74	C₄	#709	1	1	yes	characteristic
75	C₂	—	10	4	no	—
76	C₂	C₄×D₂₀	1	1	yes	characteristic
77	C₂	C₂×C₈×D₅	1	1	yes	characteristic
78	C₂	#4047	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂×D₅
commutator	C₂×C₅	C₂²×C₈
Frattini	C₂×C₄	C₂²×D₅
Fitting	C₄×C₅×C₈	C₂
socle	C₂²×C₅	C₂²×C₄
prime radical	C₂×D₂₀	C₄
cosocle	C₂×C₄×C₅	C₂³
hypercenter	C₄×C₈	D₅
hypocenter	C₅	C₈×D₄
LCS	G ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₈ ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
1. C₂×C₈×D₅	C₂	semidirect
3. C₄×C₅×C₈	C₂	semidirect
4. #3952	C₂	semidirect
5. C₄⋊#168	C₂	semidirect
21. D₂₀	C₈	direct (N × H)
25. C₅×C₈	D₄	semidirect
31. C₄×C₈	D₅	semidirect
35. C₂×D₅	C₂×C₈	semidirect
37. C₄×C₅	C₂×C₈	semidirect
64. C₈	D₂₀	direct (N × H)
65. C₅	C₈×D₄	semidirect
72. C₄	C₈×D₅	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₈×D₅	2
C₄×D₂₀	2
C₄×C₅×C₈	2
#3952	2
C₄⋊#168	2
C₈×D₄	5

Subgroups — C8×D20 #64975

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈×D₂₀ #64975