Subgroups — #10602145

Order 640.

152 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, complemented
2	#64984	C₂	1	1	yes	maximal, characteristic
3	#64711	C₂	1	4	yes	maximal, complemented
4	#64681	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#125	—	2	1	no	—
6	C₂×D₄₀	—	2	1	no	—
7	C₂×D₄₀	C₂²	1	2	yes	—
8	#4020	—	2	1	no	—
9	C₅×#107	C₂²	1	2	yes	—
10	C₅×#106	—	2	1	no	—
11	C₄×C₅×C₈	C₂²	1	1	yes	characteristic
12	C₂×#672	C₂²	1	2	yes	—
13	#2244	—	5	1	no	maximal, Sylow
14	C₂×D₂₀	—	2	2	no	—
15	C₂×D₂₀	—	4	2	no	—
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	D₄₀	—	2	4	no	—
22	D₄₀	—	4	2	no	—
23	#672	—	2	2	no	—
24	#499	D₅	1	1	yes	characteristic, complemented
25	#493	—	5	1	no	—
26	#357	—	5	4	no	—
27	#346	—	5	1	no	—
28	C₂²×D₅	—	4	2	no	—
29	C₂×C₄×C₅	—	4	2	no	—
30	C₂×C₄×C₅	D₈	1	2	yes	—
31	C₂×C₄×C₅	C₂×D₄	1	1	yes	characteristic
32	D₂₀	—	4	2	no	—
33	D₂₀	—	4	2	no	—
34	D₂₀	—	8	4	no	—
35	C₅×C₈	SD₁₆	1	2	yes	—
36	C₅×C₈	#41	1	2	yes	—
37	C₂×D₈	—	5	2	no	—
38	C₂×D₈	—	10	1	no	—
39	#127	—	10	1	no	—
40	#125	—	2	1	no	—
41	C₂×C₁₆	—	5	2	no	—
42	#107	C₂×D₅	1	2	yes	—
43	#106	—	2	1	no	—
44	C₄×C₈	C₂×D₅	1	1	yes	characteristic
45	C₂²×C₅	C₂×D₈	1	1	yes	characteristic
46	C₂×D₅	—	8	2	no	—
47	C₂×D₅	—	8	4	no	—
48	C₄×C₅	—	2	2	no	—
49	C₄×C₅	—	8	2	no	—
50	C₄×C₅	#124	1	1	yes	characteristic
51	C₄×C₅	C₂×SD₁₆	1	1	yes	characteristic
52	C₂×D₄	—	10	2	no	—
53	C₂×D₄	—	20	2	no	—
54	D₈	—	10	4	no	—
55	D₈	—	20	2	no	—
56	C₂×C₈	C₂²⋊D₅	1	1	yes	characteristic
57	C₂×C₈	C₂²×D₅	1	1	yes	characteristic
58	C₄⋊C₄	—	2	2	no	—
59	C₄⋊C₄	—	4	2	no	—
60	C₄²	C₂²⋊D₅	1	1	yes	characteristic
61	C₁₆	—	10	2	no	—
62	C₂×C₅	#486	1	1	yes	characteristic
63	C₂×C₅	#509	1	2	yes	—
64	D₅	—	16	2	no	—
65	C₂³	—	20	2	no	—
66	D₄	—	20	2	no	—
67	D₄	—	20	2	no	—
68	D₄	—	40	4	no	—
69	C₂×C₄	—	4	2	no	—
70	C₂×C₄	#686	1	2	yes	—
71	C₂×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
72	C₈	#688	1	2	yes	—
73	C₈	#713	1	2	yes	—
74	C₅	#2244	1	1	yes	characteristic, complemented, Sylow
75	C₂²	—	40	2	no	—
76	C₂²	—	40	4	no	—
77	C₂²	C₂×#686	1	1	yes	characteristic
78	C₄	—	2	2	no	—
79	C₄	—	8	2	no	—
80	C₄	C₂×#688	1	1	yes	characteristic
81	C₄	#4093	1	1	yes	characteristic
82	C₂	—	80	2	no	—
83	C₂	#65377	1	1	yes	characteristic
84	C₂	#65482	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	C₂²×C₅	C₂×D₈
prime radical	#64984	C₂
hypercenter	#499	D₅
hypocenter	C₅	#2244
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
1. C₅×#499	C₂	semidirect
3. #64711	C₂	semidirect
4. #64681	C₂	semidirect
24. #499	D₅	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×#499	2
#64984	2
#64711	2
#64681	2
#2244	5