Subgroups — #65176

Order 320.

114 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₂₀	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₈×D₅	C₂	1	1	yes	maximal, characteristic
3	#4043	C₂	1	2	yes	maximal
4	C₅×#107	C₂	1	1	yes	maximal, characteristic, complemented
5	#3942	C₂	1	2	yes	maximal, complemented
6	C₂×C₄×D₅	C₂²	1	1	yes	characteristic
7	C₂×Dic₁₀	C₂²	1	2	yes	—
8	C₂×C₅×C₈	C₂²	1	1	yes	characteristic
9	C₅×C₄⋊C₄	C₂²	1	2	yes	—
10	#685	—	2	2	no	—
11	C₄⋊Dic₅	—	2	2	no	—
12	C₂×#168	C₂²	1	1	yes	characteristic
13	Dic₂₀	—	2	2	no	—
14	C₈×D₅	—	2	2	no	—
15	#467	—	5	1	no	maximal, Sylow
16	C₂²×D₅	D₄	1	1	yes	characteristic
17	C₂×C₄×C₅	—	2	2	no	—
18	C₂×C₄×C₅	C₂³	1	1	yes	characteristic
19	C₂×Dic₅	—	2	2	no	—
20	C₂×Dic₅	D₄	1	1	yes	characteristic
21	C₄×D₅	—	2	1	no	—
22	C₄×D₅	—	2	1	no	—
23	Dic₁₀	—	2	2	no	—
24	Dic₁₀	—	2	2	no	—
25	C₅×C₈	D₄	1	2	yes	—
26	#168	—	2	1	no	—
27	C₂×Q₁₆	—	5	1	no	—
28	C₂²×C₈	—	5	1	no	—
29	C₂²⋊Q₈	—	5	2	no	—
30	#107	D₅	1	1	yes	characteristic, complemented
31	#103	—	5	2	no	—
32	C₂²×C₅	C₂×D₄	1	1	yes	characteristic
33	C₂×D₅	—	2	1	no	—
34	C₂×D₅	—	2	1	no	—
35	C₂×D₅	Q₁₆	1	2	yes	complemented
36	C₄×C₅	—	4	2	no	—
37	C₄×C₅	C₂×D₄	1	1	yes	characteristic
38	C₄×C₅	#41	1	1	yes	characteristic
39	Dic₅	—	2	1	no	—
40	Dic₅	—	4	2	no	—
41	C₂×Q₈	—	5	2	no	—
42	C₂²×C₄	—	5	1	no	—
43	Q₁₆	—	10	2	no	—
44	C₂×C₈	—	5	1	no	—
45	C₂×C₈	—	10	2	no	—
46	C₂×C₈	C₂×D₅	1	1	yes	characteristic
47	C₄⋊C₄	—	10	2	no	—
48	C₄⋊C₄	C₂×D₅	1	2	yes	—
49	C₂²⋊C₄	—	10	2	no	—
50	C₂×C₅	#121	1	1	yes	characteristic
51	C₂×C₅	C₂×Q₁₆	1	1	yes	characteristic
52	C₂×C₅	#135	1	1	yes	characteristic
53	D₅	—	2	2	no	—
54	C₂³	—	5	1	no	—
55	Q₈	—	10	2	no	—
56	Q₈	—	10	2	no	—
57	C₂×C₄	—	2	2	no	—
58	C₂×C₄	—	5	1	no	—
59	C₂×C₄	—	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	—	10	1	no	—
64	C₈	D₂₀	1	2	yes	—
65	C₅	#467	1	1	yes	characteristic, complemented, Sylow
66	C₂²	—	5	2	no	—
67	C₂²	—	10	1	no	—
68	C₂²	—	10	1	no	—
69	C₂²	D₄×D₅	1	1	yes	characteristic
70	C₄	—	4	2	no	—
71	C₄	—	10	1	no	—
72	C₄	—	20	2	no	—
73	C₄	C₂×D₂₀	1	1	yes	characteristic
74	C₄	#713	1	1	yes	characteristic
75	C₂	—	10	2	no	—
76	C₂	#4041	1	1	yes	characteristic
77	C₂	#4058	1	1	yes	characteristic
78	C₂	D₅×Q₁₆	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₅
commutator, cosocle	C₂×C₄×C₅	C₂³
Frattini	C₂×C₄	C₂²×D₅
Fitting	C₅×#107	C₂
socle	C₂²×C₅	C₂×D₄
prime radical	C₂²×D₅	D₄
hypercenter	#107	D₅
hypocenter	C₅	#467
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #107

Complements

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

N	H ≅ G/N	type
1. C₂×Dic₂₀	C₂	semidirect
4. C₅×#107	C₂	semidirect
5. #3942	C₂	semidirect
30. #107	D₅	semidirect
35. C₂×D₅	Q₁₆	semidirect
65. C₅	#467	semidirect

Maximal subgroups

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

subgroup	index
C₂×Dic₂₀	2
C₂×C₈×D₅	2
#4043	2
C₅×#107	2
#3942	2
#467	5