Subgroups — #65431

Order 320.

108 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, complemented
2	#4095	C₂	1	2	yes	maximal, complemented
3	C₂×D₄₀	C₂	1	1	yes	maximal, characteristic, complemented
4	#3955	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×D₂₀	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	#688	—	2	2	no	—
13	#686	—	2	2	no	—
14	#681	C₂²	1	2	yes	—
15	D₄₀	—	2	1	no	—
16	D₄₀	—	2	1	no	—
17	#472	—	5	1	no	maximal, Sylow
18	C₂²×D₅	—	2	2	no	—
19	C₅×Q₈	D₄	1	1	yes	characteristic
20	C₅×D₄	—	2	1	no	—
21	C₅×D₄	D₄	1	1	yes	characteristic
22	C₂×C₄×C₅	—	2	1	no	—
23	C₂×C₄×C₅	C₂³	1	1	yes	characteristic
24	D₂₀	—	2	2	no	—
25	D₂₀	—	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	AGL(1,ℤ/8)	—	5	2	no	—
31	C₂×D₈	—	5	1	no	—
32	#131	D₅	1	1	yes	characteristic, complemented
33	#108	—	5	1	no	—
34	#100	—	5	2	no	—
35	C₂²×C₅	—	2	1	no	—
36	C₂²×C₅	#41	1	1	yes	characteristic
37	C₂×D₅	—	4	2	no	—
38	C₂×D₅	—	8	2	no	—
39	C₄×C₅	—	2	1	no	—
40	C₄×C₅	C₂×D₄	1	1	yes	characteristic
41	C₄×C₅	C₂×D₄	1	1	yes	characteristic
42	#41	C₂×D₅	1	1	yes	characteristic
43	C₂×D₄	—	5	2	no	—
44	SD₁₆	—	10	2	no	—
45	D₈	—	10	2	no	—
46	D₈	—	10	1	no	—
47	D₈	—	10	1	no	—
48	M₁₆	—	2	1	no	—
49	M₁₆	—	5	2	no	—
50	M₁₆	C₂×D₅	1	1	yes	characteristic
51	C₂×C₈	—	2	1	no	—
52	C₂×C₈	C₂×D₅	1	1	yes	characteristic
53	C₂×C₅	—	2	1	no	—
54	C₂×C₅	—	4	1	no	—
55	C₂×C₅	#121	1	1	yes	characteristic
56	D₅	—	8	2	no	—
57	C₂³	—	10	2	no	—
58	Q₈	D₂₀	1	1	yes	characteristic
59	D₄	—	2	1	no	—
60	D₄	—	10	2	no	—
61	D₄	—	10	2	no	—
62	D₄	D₂₀	1	1	yes	characteristic
63	C₂×C₄	—	2	1	no	—
64	C₂×C₄	C₂²×D₅	1	1	yes	characteristic
65	C₈	—	2	1	no	—
66	C₈	—	10	2	no	—
67	C₈	C₂²⋊D₅	1	1	yes	characteristic
68	C₈	C₂²⋊D₅	1	1	yes	characteristic
69	C₅	#472	1	1	yes	characteristic, complemented, Sylow
70	C₂²	—	2	1	no	—
71	C₂²	—	20	2	no	—
72	C₂²	—	40	2	no	—
73	C₂²	#709	1	1	yes	characteristic
74	C₄	—	2	1	no	—
75	C₄	C₂×D₂₀	1	1	yes	characteristic
76	C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
77	C₂	—	2	1	no	—
78	C₂	—	4	1	no	—
79	C₂	—	40	2	no	—
80	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
hypercenter	#131	D₅
hypocenter	C₅	#472
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
1. C₅×#131	C₂	semidirect
2. #4095	C₂	semidirect
3. C₂×D₄₀	C₂	semidirect
4. #3955	C₂	semidirect
5. #3951	C₂	semidirect
32. #131	D₅	semidirect
69. C₅	#472	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
#4095	2
C₂×D₄₀	2
#3955	2
#3951	2
#472	5