Subgroups — #10598607

Order 640.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#65161	C₂	1	1	yes	maximal, characteristic
2	#64886	C₂	1	1	yes	maximal, characteristic, complemented
3	#64881	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₄₀	C₄	1	1	yes	characteristic
5	#4039	—	2	1	no	—
6	C₄⋊#170	—	2	1	no	—
7	C₂×#674	—	2	1	no	—
8	C₅×#107	C₄	1	1	yes	characteristic
9	C₈×Dic₅	C₂²	1	1	yes	characteristic
10	#3941	—	2	1	no	—
11	#1333	—	5	1	no	maximal, Sylow
12	C₂×D₂₀	—	2	1	no	—
13	C₂×C₄×D₅	—	4	1	no	—
14	C₂×#170	—	4	1	no	—
15	C₂×C₅×C₈	C₂×C₄	1	1	yes	characteristic
16	C₅×C₄⋊C₄	—	2	1	no	—
17	#685	—	4	1	no	—
18	C₄×Dic₅	D₄	1	1	yes	characteristic
19	C₂×#168	D₄	1	1	yes	characteristic
20	D₄₀	—	2	1	no	—
21	D₄₀	C₈	1	2	yes	complemented
22	#674	—	2	2	no	—
23	C₄×D₈	—	5	1	no	—
24	#346	—	5	1	no	—
25	#334	—	5	1	no	—
26	C₂²×D₅	—	4	1	no	—
27	C₂×C₄×C₅	—	4	1	no	—
28	C₂×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
29	C₂×Dic₅	D₈	1	1	yes	characteristic
30	C₂×Dic₅	SD₁₆	1	1	yes	characteristic
31	D₂₀	—	2	2	no	—
32	D₂₀	—	4	1	no	—
33	C₄×D₅	—	8	2	no	—
34	#170	—	8	1	no	—
35	C₅×C₈	C₂×C₈	1	1	yes	characteristic
36	C₅×C₈	M₁₆	1	1	yes	characteristic
37	#168	—	2	1	no	—
38	C₂×D₈	—	5	1	no	—
39	C₄×D₄	—	10	1	no	—
40	C₂×C₁₆	—	10	1	no	—
41	#107	AGL(1,𝔽₅)	1	1	yes	characteristic
42	C₄⋊C₈	—	10	1	no	—
43	#102	—	10	1	no	—
44	C₄×C₈	—	5	1	no	—
45	C₂²×C₅	#102	1	1	yes	characteristic
46	C₂×D₅	—	4	2	no	—
47	C₂×D₅	—	8	1	no	—
48	C₂×D₅	—	8	1	no	—
49	C₄×C₅	—	8	1	no	—
50	C₄×C₅	C₂²⋊C₈	1	1	yes	characteristic
51	C₄×C₅	#104	1	1	yes	characteristic
52	Dic₅	—	2	1	no	—
53	Dic₅	—	2	1	no	—
54	C₂×D₄	—	10	1	no	—
55	C₂²×C₄	—	20	1	no	—
56	D₈	—	5	2	no	—
57	D₈	—	10	1	no	—
58	C₂×C₈	—	5	1	no	—
59	C₂×C₈	—	20	1	no	—
60	C₂×C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
61	C₄⋊C₄	—	2	1	no	—
62	C₂²⋊C₄	—	20	1	no	—
63	C₄²	—	5	1	no	—
64	C₁₆	—	10	2	no	—
65	C₂×C₅	D₄⋊C₈	1	1	yes	characteristic
66	C₂×C₅	#360	1	1	yes	characteristic
67	C₂×C₅	#361	1	1	yes	characteristic
68	D₅	—	8	2	no	—
69	C₂³	—	20	1	no	—
70	D₄	—	10	2	no	—
71	D₄	—	20	1	no	—
72	C₂×C₄	—	4	1	no	—
73	C₂×C₄	—	5	1	no	—
74	C₂×C₄	—	5	1	no	—
75	C₂×C₄	—	40	2	no	—
76	C₂×C₄	C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic
77	C₈	—	10	1	no	—
78	C₈	—	40	1	no	—
79	C₈	D₅⋊C₈	1	1	yes	characteristic
80	C₈	#700	1	1	yes	characteristic
81	C₅	#1333	1	1	yes	characteristic, complemented, Sylow
82	C₂²	—	20	2	no	—
83	C₂²	—	40	1	no	—
84	C₂²	—	40	1	no	—
85	C₂²	#4007	1	1	yes	characteristic
86	C₄	—	8	1	no	—
87	C₄	—	10	1	no	—
88	C₄	—	10	1	no	—
89	C₄	#4003	1	1	yes	characteristic
90	C₄	#4010	1	1	yes	characteristic
91	C₂	—	40	2	no	—
92	C₂	#64871	1	1	yes	characteristic
93	C₂	#64906	1	1	yes	characteristic
94	C₂	#64907	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#4007
commutator	C₅×C₈	C₂×C₈
Frattini	C₂×C₈	C₂×AGL(1,𝔽₅)
Fitting	C₅×#107	C₄
socle	C₂²×C₅	#102
prime radical	C₂×D₄₀	C₄
cosocle	C₈×Dic₅	C₂²
hypercenter	#107	AGL(1,𝔽₅)
hypocenter	C₅	#1333
LCS	G ▷ C₅×C₈ ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #107

Complements

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

N	H ≅ G/N	type
2. #64886	C₂	semidirect
3. #64881	C₂	semidirect
21. D₄₀	C₈	semidirect
81. C₅	#1333	semidirect

Maximal subgroups

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

subgroup	index
#65161	2
#64886	2
#64881	2
#1333	5