Subgroups — #65185

Order 320.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#4055	C₂	1	2	yes	maximal
2	C₂×Dic₂₀	C₂	1	1	yes	maximal, characteristic, complemented
3	#4047	C₂	1	1	yes	maximal, characteristic
4	C₅×#108	C₂	1	1	yes	maximal, characteristic, complemented
5	#3956	C₂	1	2	yes	maximal, complemented
6	#709	C₂²	1	1	yes	characteristic
7	C₂×Dic₁₀	C₂²	1	2	yes	—
8	C₅×M₁₆	C₂²	1	2	yes	—
9	C₂×C₅×C₈	C₂²	1	1	yes	characteristic
10	#681	C₂²	1	1	yes	characteristic
11	Dic₂₀	—	2	2	no	—
12	Dic₂₀	—	2	1	no	—
13	Dic₂₀	—	2	1	no	—
14	#677	—	2	2	no	—
15	#676	—	2	1	no	—
16	C₈×D₅	—	2	1	no	—
17	#473	—	5	1	no	maximal, Sylow
18	C₂×C₄×C₅	C₂³	1	1	yes	characteristic
19	C₂²⋊D₅	—	2	1	no	—
20	C₂×Dic₅	—	2	2	no	—
21	D₂₀	D₄	1	1	yes	characteristic
22	C₄×D₅	—	2	1	no	—
23	Dic₁₀	—	2	2	no	—
24	Dic₁₀	—	2	2	no	—
25	Dic₁₀	D₄	1	1	yes	characteristic
26	C₅×C₈	—	2	2	no	—
27	C₅×C₈	D₄	1	1	yes	characteristic
28	C₅×C₈	D₄	1	1	yes	characteristic
29	#168	—	2	1	no	—
30	#137	—	5	2	no	—
31	C₂×Q₁₆	—	5	1	no	—
32	#131	—	5	1	no	—
33	#108	D₅	1	1	yes	characteristic, complemented
34	#101	—	5	2	no	—
35	C₂²×C₅	#41	1	1	yes	characteristic
36	C₂×D₅	—	2	1	no	—
37	C₄×C₅	C₂×D₄	1	1	yes	characteristic
38	C₄×C₅	C₂×D₄	1	1	yes	characteristic
39	Dic₅	—	2	1	no	—
40	Dic₅	—	4	2	no	—
41	#41	—	5	1	no	—
42	C₂×Q₈	—	5	2	no	—
43	Q₁₆	—	10	2	no	—
44	Q₁₆	—	10	1	no	—
45	Q₁₆	—	10	1	no	—
46	SD₁₆	—	10	2	no	—
47	M₁₆	—	5	1	no	—
48	M₁₆	—	10	1	no	—
49	M₁₆	C₂×D₅	1	2	yes	—
50	C₂×C₈	—	10	1	no	—
51	C₂×C₈	C₂×D₅	1	1	yes	characteristic
52	C₂×C₅	—	2	1	no	—
53	C₂×C₅	#121	1	1	yes	characteristic
54	D₅	—	4	1	no	—
55	Q₈	—	5	1	no	—
56	Q₈	—	10	2	no	—
57	Q₈	—	10	2	no	—
58	D₄	—	5	1	no	—
59	D₄	—	10	1	no	—
60	C₂×C₄	—	10	1	no	—
61	C₂×C₄	—	10	2	no	—
62	C₂×C₄	C₂²×D₅	1	1	yes	characteristic
63	C₈	—	2	2	no	—
64	C₈	—	10	1	no	—
65	C₈	D₂₀	1	1	yes	characteristic
66	C₈	D₂₀	1	1	yes	characteristic
67	C₅	#473	1	1	yes	characteristic, complemented, Sylow
68	C₂²	—	10	1	no	—
69	C₂²	#713	1	1	yes	characteristic
70	C₄	—	10	1	no	—
71	C₄	—	20	2	no	—
72	C₄	C₂×D₂₀	1	1	yes	characteristic
73	C₄	D₄×D₅	1	1	yes	characteristic
74	C₂	—	2	1	no	—
75	C₂	—	20	1	no	—
76	C₂	#4041	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#4041
commutator, cosocle	C₂×C₄×C₅	C₂³
Frattini	C₂×C₄	C₂²×D₅
Fitting	C₅×#108	C₂
socle	C₂×C₅	#121
prime radical	#709	C₂²
hypercenter	#108	D₅
hypocenter	C₅	#473
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ #108

Complements

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

N	H ≅ G/N	type
2. C₂×Dic₂₀	C₂	semidirect
4. C₅×#108	C₂	semidirect
5. #3956	C₂	semidirect
33. #108	D₅	semidirect
67. C₅	#473	semidirect

Maximal subgroups

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

subgroup	index
#4055	2
C₂×Dic₂₀	2
#4047	2
C₅×#108	2
#3956	2
#473	5