Subgroups — #10602104

Order 640.

132 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#494	C₂	1	1	yes	maximal, characteristic
2	#64972	C₂	1	1	yes	maximal, characteristic
3	#64784	C₂	1	4	yes	maximal
4	#64681	C₂	1	1	yes	maximal, characteristic
5	C₂×C₅×Q₁₆	—	2	1	no	—
6	C₂×C₅×Q₁₆	C₂²	1	2	yes	—
7	C₅×C₄⋊Q₈	—	2	1	no	—
8	#4016	—	2	1	no	—
9	C₄×C₅×C₈	C₂²	1	1	yes	characteristic
10	#3950	C₂²	1	2	yes	—
11	#3949	—	2	1	no	—
12	C₂×#672	C₂²	1	2	yes	—
13	#2245	—	5	1	no	maximal, Sylow
14	C₂×C₅×Q₈	—	2	2	no	—
15	C₅×Q₁₆	—	2	4	no	—
16	C₅×Q₁₆	—	4	2	no	—
17	C₂×C₅×C₈	D₄	1	1	yes	characteristic
18	C₂×C₅×C₈	C₂³	1	1	yes	characteristic
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	—	2	2	no	—
24	#499	—	5	1	no	—
25	#494	D₅	1	1	yes	characteristic
26	#358	—	5	4	no	—
27	#346	—	5	1	no	—
28	C₅×Q₈	—	4	2	no	—
29	C₅×Q₈	—	4	2	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	SD₁₆	1	2	yes	—
35	C₅×C₈	#41	1	2	yes	—
36	C₂×Q₁₆	—	2	1	no	—
37	C₂×Q₁₆	C₂×D₅	1	2	yes	—
38	C₄⋊Q₈	—	2	1	no	—
39	#125	—	10	1	no	—
40	C₂×C₁₆	—	5	2	no	—
41	#107	—	5	2	no	—
42	#106	—	10	1	no	—
43	C₄×C₈	C₂×D₅	1	1	yes	characteristic
44	C₂²×C₅	C₂×D₈	1	1	yes	characteristic
45	C₄×C₅	—	2	2	no	—
46	C₄×C₅	—	8	2	no	—
47	C₄×C₅	#124	1	1	yes	characteristic
48	C₄×C₅	C₂×SD₁₆	1	1	yes	characteristic
49	Dic₅	—	8	2	no	—
50	C₂×Q₈	—	2	2	no	—
51	Q₁₆	—	2	4	no	—
52	Q₁₆	—	4	2	no	—
53	C₂×C₈	C₂²⋊D₅	1	1	yes	characteristic
54	C₂×C₈	C₂²×D₅	1	1	yes	characteristic
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	—	10	2	no	—
60	C₂×C₅	#486	1	1	yes	characteristic
61	C₂×C₅	#510	1	2	yes	—
62	Q₈	—	4	2	no	—
63	Q₈	—	4	2	no	—
64	C₂×C₄	—	4	2	no	—
65	C₂×C₄	—	20	2	no	—
66	C₂×C₄	#686	1	2	yes	—
67	C₂×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
68	C₈	#687	1	2	yes	—
69	C₈	#711	1	2	yes	—
70	C₅	#2245	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×#687	1	1	yes	characteristic
76	C₄	#4082	1	1	yes	characteristic
77	C₂	#65359	1	1	yes	characteristic
78	C₂	#65468	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×#686
commutator, cosocle	C₂×C₅×C₈	C₂³
Frattini	C₂×C₈	C₂²×D₅
Fitting	C₅×#494	C₂
socle, prime radical	C₂²×C₅	C₂×D₈
hypercenter	#494	D₅
hypocenter	C₅	#2245
LCS	G ▷ C₂×C₅×C₈ ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #494

Complements

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

N	H ≅ G/N	type
70. C₅	#2245	semidirect

Maximal subgroups

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

subgroup	index
C₅×#494	2
#64972	2
#64784	2
#64681	2
#2245	5