Subgroups — #65432

Order 320.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#131	C₂	1	1	yes	maximal, characteristic
2	#4097	C₂	1	2	yes	maximal
3	C₂×Dic₂₀	C₂	1	1	yes	maximal, characteristic, complemented
4	#3956	C₂	1	2	yes	maximal, complemented
5	#3951	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#41	C₂²	1	1	yes	characteristic
7	C₂×Dic₁₀	C₂²	1	2	yes	—
8	C₅×M₁₆	—	2	1	no	—
9	C₅×M₁₆	C₂²	1	1	yes	characteristic
10	C₂×C₅×C₈	—	2	1	no	—
11	C₂×C₅×C₈	C₂²	1	1	yes	characteristic
12	#689	—	2	2	no	—
13	#687	—	2	2	no	—
14	#681	C₂²	1	2	yes	—
15	Dic₂₀	—	2	1	no	—
16	Dic₂₀	—	2	1	no	—
17	#473	—	5	1	no	maximal, Sylow
18	C₅×Q₈	D₄	1	1	yes	characteristic
19	C₅×D₄	—	2	1	no	—
20	C₅×D₄	D₄	1	1	yes	characteristic
21	C₂×C₄×C₅	—	2	1	no	—
22	C₂×C₄×C₅	C₂³	1	1	yes	characteristic
23	C₂×Dic₅	—	2	2	no	—
24	Dic₁₀	—	2	2	no	—
25	Dic₁₀	—	2	2	no	—
26	C₅×C₈	—	2	1	no	—
27	C₅×C₈	D₄	1	1	yes	characteristic
28	C₅×C₈	D₄	1	1	yes	characteristic
29	#168	—	2	2	no	—
30	#137	—	5	2	no	—
31	C₂×Q₁₆	—	5	1	no	—
32	#131	D₅	1	1	yes	characteristic
33	#108	—	5	1	no	—
34	#101	—	5	2	no	—
35	C₂²×C₅	—	2	1	no	—
36	C₂²×C₅	#41	1	1	yes	characteristic
37	C₄×C₅	—	2	1	no	—
38	C₄×C₅	C₂×D₄	1	1	yes	characteristic
39	C₄×C₅	C₂×D₄	1	1	yes	characteristic
40	Dic₅	—	4	2	no	—
41	#41	C₂×D₅	1	1	yes	characteristic
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	—	2	1	no	—
48	M₁₆	—	5	2	no	—
49	M₁₆	C₂×D₅	1	1	yes	characteristic
50	C₂×C₈	—	2	1	no	—
51	C₂×C₈	C₂×D₅	1	1	yes	characteristic
52	C₂×C₅	—	2	1	no	—
53	C₂×C₅	—	4	1	no	—
54	C₂×C₅	#121	1	1	yes	characteristic
55	Q₈	—	10	2	no	—
56	Q₈	—	10	2	no	—
57	Q₈	D₂₀	1	1	yes	characteristic
58	D₄	—	2	1	no	—
59	D₄	D₂₀	1	1	yes	characteristic
60	C₂×C₄	—	2	1	no	—
61	C₂×C₄	—	10	2	no	—
62	C₂×C₄	C₂²×D₅	1	1	yes	characteristic
63	C₈	—	2	1	no	—
64	C₈	—	10	2	no	—
65	C₈	C₂²⋊D₅	1	1	yes	characteristic
66	C₈	C₂²⋊D₅	1	1	yes	characteristic
67	C₅	#473	1	1	yes	characteristic, complemented, Sylow
68	C₂²	—	2	1	no	—
69	C₂²	#709	1	1	yes	characteristic
70	C₄	—	2	1	no	—
71	C₄	—	20	2	no	—
72	C₄	C₂×D₂₀	1	1	yes	characteristic
73	C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
74	C₂	—	2	1	no	—
75	C₂	—	4	1	no	—
76	C₂	#4076	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#4076
commutator, cosocle	C₂×C₄×C₅	C₂³
Frattini	C₂×C₄	C₂²×D₅
Fitting	C₅×#131	C₂
socle	C₂×C₅	#121
prime radical	C₅×#41	C₂²
hypercenter	#131	D₅
hypocenter	C₅	#473
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ #131

Complements

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

N	H ≅ G/N	type
3. C₂×Dic₂₀	C₂	semidirect
4. #3956	C₂	semidirect
5. #3951	C₂	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
C₅×#131	2
#4097	2
C₂×Dic₂₀	2
#3956	2
#3951	2
#473	5