Subgroups — #65449

Order 320.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×D₈	C₂	1	1	yes	maximal, characteristic, complemented
2	#4078	C₂	1	2	yes	maximal, complemented
3	#4047	C₂	1	1	yes	maximal, characteristic, complemented
4	#3965	C₂	1	2	yes	maximal, complemented
5	#3951	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₅×D₄	C₂²	1	2	yes	—
7	#709	C₂²	1	1	yes	characteristic
8	C₅×D₈	—	2	1	no	—
9	C₅×D₈	—	2	1	no	—
10	C₂×C₅×C₈	C₂²	1	1	yes	characteristic
11	#687	—	2	2	no	—
12	#686	—	2	2	no	—
13	#681	C₂²	1	2	yes	—
14	#681	C₂²	1	1	yes	characteristic
15	#676	—	2	1	no	—
16	C₈×D₅	—	2	1	no	—
17	#472	—	5	1	no	maximal, Sylow
18	C₂³×C₅	—	2	2	no	—
19	C₅×D₄	—	2	2	no	—
20	C₅×D₄	—	2	2	no	—
21	C₂×C₄×C₅	C₂³	1	1	yes	characteristic
22	C₂²⋊D₅	—	2	1	no	—
23	D₂₀	D₄	1	1	yes	characteristic
24	C₄×D₅	—	2	1	no	—
25	Dic₁₀	D₄	1	1	yes	characteristic
26	C₅×C₈	D₄	1	1	yes	characteristic
27	C₅×C₈	D₄	1	1	yes	characteristic
28	#168	—	2	1	no	—
29	#168	—	2	2	no	—
30	AGL(1,ℤ/8)	—	5	2	no	—
31	C₂×D₈	D₅	1	1	yes	characteristic, complemented
32	#131	—	5	1	no	—
33	#108	—	5	1	no	—
34	#100	—	5	2	no	—
35	C₂²×C₅	—	4	2	no	—
36	C₂²×C₅	—	8	2	no	—
37	C₂²×C₅	#41	1	1	yes	characteristic
38	C₂×D₅	—	2	1	no	—
39	C₄×C₅	C₂×D₄	1	1	yes	characteristic
40	C₄×C₅	C₂×D₄	1	1	yes	characteristic
41	Dic₅	—	2	1	no	—
42	#41	—	5	1	no	—
43	C₂×D₄	C₂×D₅	1	2	yes	—
44	SD₁₆	—	10	2	no	—
45	D₈	—	2	1	no	—
46	D₈	—	2	1	no	—
47	D₈	—	10	2	no	—
48	M₁₆	—	5	1	no	—
49	M₁₆	—	5	2	no	—
50	M₁₆	—	10	1	no	—
51	C₂×C₈	—	10	1	no	—
52	C₂×C₈	C₂×D₅	1	1	yes	characteristic
53	C₂×C₅	—	2	1	no	—
54	C₂×C₅	—	8	2	no	—
55	C₂×C₅	#121	1	1	yes	characteristic
56	D₅	—	4	1	no	—
57	C₂³	—	2	2	no	—
58	Q₈	—	5	1	no	—
59	D₄	—	2	2	no	—
60	D₄	—	2	2	no	—
61	D₄	—	5	1	no	—
62	D₄	—	10	1	no	—
63	C₂×C₄	—	10	1	no	—
64	C₂×C₄	C₂²×D₅	1	1	yes	characteristic
65	C₈	—	10	2	no	—
66	C₈	—	10	1	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	—	4	2	no	—
71	C₂²	—	8	2	no	—
72	C₂²	—	10	1	no	—
73	C₂²	#711	1	1	yes	characteristic
74	C₄	—	10	1	no	—
75	C₄	D₄×D₅	1	1	yes	characteristic
76	C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
77	C₂	—	2	1	no	—
78	C₂	—	8	2	no	—
79	C₂	—	20	1	no	—
80	C₂	#4084	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#4084
commutator, cosocle	C₂×C₄×C₅	C₂³
Frattini	C₂×C₄	C₂²×D₅
Fitting	C₂×C₅×D₈	C₂
socle	C₂×C₅	#121
hypercenter	C₂×D₈	D₅
hypocenter	C₅	#472
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×D₈

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×D₈	C₂	semidirect
2. #4078	C₂	semidirect
3. #4047	C₂	semidirect
4. #3965	C₂	semidirect
5. #3951	C₂	semidirect
31. C₂×D₈	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
C₂×C₅×D₈	2
#4078	2
#4047	2
#3965	2
#3951	2
#472	5