Subgroups — #10602147

Order 640.

116 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#499	C₂	1	1	yes	maximal, characteristic
2	#64972	C₂	1	1	yes	maximal, characteristic
3	#64710	C₂	1	2	yes	maximal
4	#64709	C₂	1	2	yes	maximal
5	C₄×#672	C₂	1	1	yes	maximal, characteristic
6	C₅×#125	—	2	1	no	—
7	#4016	—	2	1	no	—
8	C₅×#107	C₂²	1	2	yes	—
9	C₅×#106	—	2	1	no	—
10	C₄×C₅×C₈	C₂²	1	1	yes	characteristic
11	#3950	C₂²	1	2	yes	—
12	#3949	—	2	1	no	—
13	C₂×#672	C₂²	1	1	yes	characteristic
14	C₂×#672	C₂²	1	1	yes	characteristic
15	#2253	—	5	1	no	maximal, Sylow
16	C₂×C₅×C₈	D₄	1	1	yes	characteristic
17	C₂×C₅×C₈	C₂³	1	1	yes	characteristic
18	C₅×C₄⋊C₄	—	2	2	no	—
19	C₅×C₄⋊C₄	—	4	2	no	—
20	C₄²×C₅	D₄	1	1	yes	characteristic
21	C₄⋊Dic₅	—	2	2	no	—
22	#683	—	4	2	no	—
23	#672	Q₈	1	2	yes	—
24	#672	Q₈	1	2	yes	—
25	#499	—	5	1	no	—
26	#499	D₅	1	1	yes	characteristic
27	#367	—	5	2	no	—
28	#366	—	5	2	no	—
29	C₄×C₁₆	—	5	1	no	—
30	C₂×C₄×C₅	—	4	2	no	—
31	C₂×C₄×C₅	D₈	1	2	yes	—
32	C₂×C₄×C₅	C₂×D₄	1	1	yes	characteristic
33	C₂×Dic₅	—	4	2	no	—
34	C₅×C₈	Q₁₆	1	2	yes	—
35	C₅×C₈	C₂×Q₈	1	1	yes	characteristic
36	C₅×C₈	C₂×Q₈	1	1	yes	characteristic
37	#125	—	2	1	no	—
38	#125	—	10	1	no	—
39	C₂×C₁₆	—	5	1	no	—
40	C₂×C₁₆	—	5	1	no	—
41	#107	—	5	2	no	—
42	#107	C₂×D₅	1	2	yes	—
43	#106	—	2	1	no	—
44	#106	—	10	1	no	—
45	C₄×C₈	C₂×D₅	1	1	yes	characteristic
46	C₂²×C₅	C₂×D₈	1	1	yes	characteristic
47	C₄×C₅	—	2	2	no	—
48	C₄×C₅	—	8	2	no	—
49	C₄×C₅	C₄⋊Q₈	1	1	yes	characteristic
50	C₄×C₅	C₂×Q₁₆	1	1	yes	characteristic
51	Dic₅	—	8	2	no	—
52	C₂×C₈	C₂²⋊D₅	1	1	yes	characteristic
53	C₂×C₈	C₂²×D₅	1	1	yes	characteristic
54	C₄⋊C₄	—	2	2	no	—
55	C₄⋊C₄	—	4	2	no	—
56	C₄⋊C₄	—	10	2	no	—
57	C₄⋊C₄	—	20	2	no	—
58	C₄²	C₂²⋊D₅	1	1	yes	characteristic
59	C₁₆	—	5	2	no	—
60	C₁₆	—	5	2	no	—
61	C₂×C₅	#500	1	1	yes	characteristic
62	C₂×C₅	#508	1	2	yes	—
63	C₂×C₄	—	4	2	no	—
64	C₂×C₄	—	20	2	no	—
65	C₂×C₄	#686	1	2	yes	—
66	C₂×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
67	C₈	#689	1	2	yes	—
68	C₈	Q₈×D₅	1	1	yes	characteristic
69	C₈	Q₈×D₅	1	1	yes	characteristic
70	C₅	#2253	1	1	yes	characteristic, complemented, Sylow
71	C₂²	C₂×#686	1	1	yes	characteristic
72	C₄	—	2	2	no	—
73	C₄	—	8	2	no	—
74	C₄	—	40	2	no	—
75	C₄	C₂×#689	1	1	yes	characteristic
76	C₄	#4090	1	1	yes	characteristic
77	C₂	#65367	1	1	yes	characteristic
78	C₂	#65483	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×#686
commutator, cosocle	C₂×C₅×C₈	C₂³
Frattini	C₂×C₈	C₂²×D₅
Fitting	C₅×#499	C₂
socle, prime radical	C₂²×C₅	C₂×D₈
hypercenter	#499	D₅
hypocenter	C₅	#2253
LCS	G ▷ C₂×C₅×C₈ ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #499

Complements

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

N	H ≅ G/N	type
70. C₅	#2253	semidirect

Maximal subgroups

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

subgroup	index
C₅×#499	2
#64972	2
#64710	2
#64709	2
C₄×#672	2
#2253	5