Subgroups — #10599873

Order 640.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#64984	C₂	1	1	yes	maximal, characteristic
2	#64972	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#346	C₂	1	1	yes	maximal, characteristic, complemented
4	#64729	C₂	1	4	yes	maximal, complemented
5	C₂×D₄₀	—	2	1	no	—
6	C₂×D₄₀	C₂²	1	2	yes	—
7	#4020	—	2	1	no	—
8	#4016	—	2	1	no	—
9	C₂×C₅×C₁₆	C₂²	1	2	yes	—
10	C₄×C₅×C₈	C₂²	1	1	yes	characteristic
11	#3950	C₂²	1	2	yes	—
12	#3949	—	2	1	no	—
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	C₄²×C₅	D₄	1	1	yes	characteristic
19	C₄⋊Dic₅	—	2	2	no	—
20	#683	—	4	2	no	—
21	D₄₀	—	2	4	no	—
22	D₄₀	—	4	2	no	—
23	C₅×C₁₆	—	2	2	no	—
24	#499	—	5	1	no	—
25	#493	—	5	1	no	—
26	#357	—	5	4	no	—
27	#346	D₅	1	1	yes	characteristic, complemented
28	C₂²×D₅	—	4	2	no	—
29	C₂×C₄×C₅	D₈	1	2	yes	—
30	C₂×C₄×C₅	C₂×D₄	1	1	yes	characteristic
31	C₂×Dic₅	—	4	2	no	—
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	—	10	1	no	—
41	C₂×C₁₆	C₂×D₅	1	2	yes	—
42	#107	—	5	2	no	—
43	#106	—	10	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	#124	1	1	yes	characteristic
50	C₄×C₅	C₂×SD₁₆	1	1	yes	characteristic
51	Dic₅	—	8	2	no	—
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	D₂₀	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	D₂₀	1	1	yes	characteristic
61	C₁₆	—	2	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	—	20	2	no	—
70	C₂×C₄	D₄₀	1	2	yes	—
71	C₂×C₄	C₂×D₂₀	1	1	yes	characteristic
72	C₈	#677	1	2	yes	—
73	C₈	#709	1	2	yes	—
74	C₅	#2244	1	1	yes	characteristic, complemented, Sylow
75	C₂²	—	40	4	no	—
76	C₂²	—	40	2	no	—
77	C₂²	C₂×D₄₀	1	1	yes	characteristic
78	C₄	—	2	2	no	—
79	C₄	—	40	2	no	—
80	C₄	#4021	1	1	yes	characteristic
81	C₄	C₂×#677	1	1	yes	characteristic
82	C₂	—	80	2	no	—
83	C₂	#64983	1	1	yes	characteristic
84	C₂	#65197	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×D₄₀
commutator, cosocle	C₂×C₅×C₈	C₂³
Frattini	C₂×C₈	C₂²×D₅
Fitting	C₅×#346	C₂
socle	C₂²×C₅	C₂×D₈
prime radical	#64984	C₂
hypercenter	#346	D₅
hypocenter	C₅	#2244
LCS	G ▷ C₂×C₅×C₈ ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #346

Complements

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

N	H ≅ G/N	type
2. #64972	C₂	semidirect
3. C₅×#346	C₂	semidirect
4. #64729	C₂	semidirect
27. #346	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
#64984	2
#64972	2
C₅×#346	2
#64729	2
#2244	5