Subgroups — #10587852⋊C₃ #13132012

Order 1680.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₇₀⋊C₃	C₂	1	1	yes	maximal, characteristic
2	ΓL(1,𝔽₈)×Dic₁₀	C₂	1	1	yes	maximal, characteristic
3	C₅×ΓL(1,𝔽₈)⋊C₈	C₂	1	1	yes	maximal, characteristic
4	#10587852	C₃	1	1	yes	maximal, characteristic, complemented, Hall
5	C₄×C₅×ΓL(1,𝔽₈)	C₂²	1	1	yes	characteristic
6	ΓL(1,𝔽₈)⋊Dic₅	—	2	1	no	—
7	Dic₅×ΓL(1,𝔽₈)	—	2	1	no	—
8	#1144⋊C₃	—	5	1	no	maximal, Hall
9	Dic₇₀	C₂×C₃	1	1	yes	characteristic
10	C₇×Dic₁₀	C₂×C₃	1	1	yes	characteristic
11	C₅×C₇⋊C₈	C₂×C₃	1	1	yes	characteristic
12	C₃×Dic₂₀	—	7	1	no	maximal, Hall
13	C₂×C₅×ΓL(1,𝔽₈)	D₄	1	1	yes	characteristic
14	Q₈×ΓL(1,𝔽₈)	—	5	1	no	—
15	ΓL(1,𝔽₈)⋊Q₈	—	5	1	no	—
16	ΓL(1,𝔽₈)⋊C₈	D₅	1	1	yes	characteristic
17	C₄×C₅×C₇	C₂²×C₃	1	1	yes	characteristic
18	Dic₃₅	—	2	1	no	—
19	C₇×Dic₅	—	2	1	no	—
20	C₃×Dic₁₀	—	7	1	no	—
21	C₃×Dic₁₀	—	7	1	no	—
22	C₃×C₅×C₈	—	7	1	no	—
23	#1144	—	5	1	no	Hall
24	C₅×ΓL(1,𝔽₈)	Q₁₆	1	1	yes	characteristic, complemented, Hall
25	C₄×ΓL(1,𝔽₈)	—	10	1	no	—
26	C₄×ΓL(1,𝔽₈)	C₂×D₅	1	1	yes	characteristic
27	ΓL(1,𝔽₈)⋊C₄	—	10	1	no	—
28	Dic₂₀	—	7	1	no	Hall
29	C₂×C₅×C₇	C₃×D₄	1	1	yes	characteristic
30	C₃×C₄×C₅	—	7	1	no	—
31	C₃×Dic₅	—	14	1	no	—
32	C₃×Dic₅	—	14	1	no	—
33	C₇×Q₈	—	5	1	no	—
34	Dic₁₄	—	5	1	no	—
35	C₇⋊C₈	C₃×D₅	1	1	yes	characteristic
36	C₃×Q₁₆	—	35	1	no	Hall
37	C₂×ΓL(1,𝔽₈)	D₂₀	1	1	yes	characteristic
38	Dic₁₀	—	7	1	no	—
39	Dic₁₀	AGL(1,𝔽₇)	1	1	yes	characteristic
40	C₅×C₈	—	7	1	no	—
41	C₅×C₇	C₃×Q₁₆	1	1	yes	characteristic, complemented, Hall
42	C₂×C₃×C₅	—	7	1	no	—
43	C₄×C₇	—	10	1	no	—
44	C₄×C₇	C₂×C₃×D₅	1	1	yes	characteristic
45	Dic₇	—	10	1	no	—
46	C₃×Q₈	—	35	1	no	—
47	C₃×Q₈	—	35	1	no	—
48	C₃×C₈	—	7	1	no	—
49	ΓL(1,𝔽₈)	Dic₂₀	1	1	yes	characteristic, complemented, Hall
50	C₄×C₅	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic
51	Dic₅	—	2	1	no	—
52	Dic₅	—	14	1	no	—
53	Q₁₆	—	35	1	no	Sylow
54	C₃×C₅	—	7	1	no	Hall
55	C₂×C₇	C₃×D₂₀	1	1	yes	characteristic
56	C₃×C₄	—	7	1	no	—
57	C₃×C₄	—	70	1	no	—
58	C₃×C₄	—	70	1	no	—
59	C₂×C₅	(C₂²⋊D₇)⋊C₃	1	1	yes	characteristic
60	Q₈	—	5	1	no	—
61	Q₈	—	35	1	no	—
62	C₈	—	7	1	no	—
63	C₇	C₃×Dic₂₀	1	1	yes	characteristic, complemented, Sylow
64	C₂×C₃	—	7	1	no	—
65	C₅	#1144⋊C₃	1	1	yes	characteristic, complemented, Sylow
66	C₄	—	10	1	no	—
67	C₄	—	70	1	no	—
68	C₄	D₅×AGL(1,𝔽₇)	1	1	yes	characteristic
69	C₃	—	7	1	no	Sylow
70	C₂	#63307⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#63307⋊C₃
commutator, Fitting, cosocle	C₄×C₅×C₇	C₂²×C₃
Frattini, hypercenter	C₄	D₅×AGL(1,𝔽₇)
socle	C₂×C₅×C₇	C₃×D₄
prime radical	C₂×C₅×ΓL(1,𝔽₈)	D₄
hypocenter	C₅×C₇	C₃×Q₁₆
LCS	G ▷ C₄×C₅×C₇ ▷ C₂×C₅×C₇ ▷ C₅×C₇
UCS	C₁ ◁ C₂ ◁ C₄

Complements

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

N	H ≅ G/N	type
4. #10587852	C₃	semidirect
24. C₅×ΓL(1,𝔽₈)	Q₁₆	semidirect
41. C₅×C₇	C₃×Q₁₆	semidirect
49. ΓL(1,𝔽₈)	Dic₂₀	semidirect
63. C₇	C₃×Dic₂₀	semidirect
65. C₅	#1144⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
Dic₇₀⋊C₃	2
ΓL(1,𝔽₈)×Dic₁₀	2
C₅×ΓL(1,𝔽₈)⋊C₈	2
#10587852	3
#1144⋊C₃	5
C₃×Dic₂₀	7

Subgroups — #10587852⋊C3 #13132012

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #10587852⋊C₃ #13132012