Subgroups — #10602082

Order 640.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#493	C₂	1	1	yes	maximal, characteristic
2	#64972	C₂	1	1	yes	maximal, characteristic, complemented
3	#64782	C₂	1	4	yes	maximal, complemented
4	#64681	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅×D₈	—	2	1	no	—
6	C₂×C₅×D₈	C₂²	1	2	yes	—
7	C₅×#127	—	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	#2244	—	5	1	no	maximal, Sylow
14	C₂×C₅×D₄	—	2	2	no	—
15	C₂×C₅×D₄	—	4	2	no	—
16	C₅×D₈	—	2	4	no	—
17	C₅×D₈	—	4	2	no	—
18	C₂×C₅×C₈	D₄	1	1	yes	characteristic
19	C₂×C₅×C₈	C₂³	1	1	yes	characteristic
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	#493	D₅	1	1	yes	characteristic
26	#357	—	5	4	no	—
27	#346	—	5	1	no	—
28	C₂³×C₅	—	4	2	no	—
29	C₅×D₄	—	4	2	no	—
30	C₅×D₄	—	4	2	no	—
31	C₅×D₄	—	8	4	no	—
32	C₂×C₄×C₅	D₈	1	2	yes	—
33	C₂×C₄×C₅	C₂×D₄	1	1	yes	characteristic
34	C₂×Dic₅	—	4	2	no	—
35	C₅×C₈	SD₁₆	1	2	yes	—
36	C₅×C₈	#41	1	2	yes	—
37	C₂×D₈	—	2	1	no	—
38	C₂×D₈	C₂×D₅	1	2	yes	—
39	#127	—	2	1	no	—
40	#125	—	10	1	no	—
41	C₂×C₁₆	—	5	2	no	—
42	#107	—	5	2	no	—
43	#106	—	10	1	no	—
44	C₄×C₈	C₂×D₅	1	1	yes	characteristic
45	C₂²×C₅	—	8	2	no	—
46	C₂²×C₅	—	8	4	no	—
47	C₂²×C₅	C₂×D₈	1	1	yes	characteristic
48	C₄×C₅	—	2	2	no	—
49	C₄×C₅	#124	1	1	yes	characteristic
50	C₄×C₅	C₂×SD₁₆	1	1	yes	characteristic
51	Dic₅	—	8	2	no	—
52	C₂×D₄	—	2	2	no	—
53	C₂×D₄	—	4	2	no	—
54	D₈	—	2	4	no	—
55	D₈	—	4	2	no	—
56	C₂×C₈	C₂²⋊D₅	1	1	yes	characteristic
57	C₂×C₈	C₂²×D₅	1	1	yes	characteristic
58	C₄⋊C₄	—	10	2	no	—
59	C₄⋊C₄	—	20	2	no	—
60	C₄²	C₂²⋊D₅	1	1	yes	characteristic
61	C₁₆	—	10	2	no	—
62	C₂×C₅	—	16	2	no	—
63	C₂×C₅	#486	1	1	yes	characteristic
64	C₂×C₅	#509	1	2	yes	—
65	C₂³	—	4	2	no	—
66	D₄	—	4	2	no	—
67	D₄	—	4	2	no	—
68	D₄	—	8	4	no	—
69	C₂×C₄	—	20	2	no	—
70	C₂×C₄	#686	1	2	yes	—
71	C₂×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
72	C₈	#687	1	2	yes	—
73	C₈	#711	1	2	yes	—
74	C₅	#2244	1	1	yes	characteristic, complemented, Sylow
75	C₂²	—	8	2	no	—
76	C₂²	—	8	4	no	—
77	C₂²	C₂×#686	1	1	yes	characteristic
78	C₄	—	2	2	no	—
79	C₄	—	40	2	no	—
80	C₄	C₂×#687	1	1	yes	characteristic
81	C₄	#4082	1	1	yes	characteristic
82	C₂	—	16	2	no	—
83	C₂	#65359	1	1	yes	characteristic
84	C₂	#65436	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×#686
commutator, cosocle	C₂×C₅×C₈	C₂³
Frattini	C₂×C₈	C₂²×D₅
Fitting, prime radical	C₅×#493	C₂
socle	C₂²×C₅	C₂×D₈
hypercenter	#493	D₅
hypocenter	C₅	#2244
LCS	G ▷ C₂×C₅×C₈ ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #493

Complements

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

N	H ≅ G/N	type
2. #64972	C₂	semidirect
3. #64782	C₂	semidirect
4. #64681	C₂	semidirect
74. C₅	#2244	semidirect

Maximal subgroups

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

subgroup	index
C₅×#493	2
#64972	2
#64782	2
#64681	2
#2244	5