Subgroups — C₇×#4020 #11765118

Order 1120.

216 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×D₂₀	C₂	1	6	yes	maximal, complemented
2	C₄²×C₅×C₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₇×D₅	C₂²	1	4	yes	—
4	C₂×C₄×C₅×C₇	C₂²	1	3	yes	—
5	C₇×D₂₀	—	2	12	no	—
6	C₇×#127	—	5	1	no	maximal, Hall
7	#4020	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂²×C₅×C₇	C₂³	1	1	yes	characteristic
9	C₂×C₇×D₅	—	2	12	no	—
10	C₄×C₅×C₇	D₄	1	6	yes	complemented
11	C₂×C₇×D₄	—	5	6	no	—
12	C₄²×C₇	D₅	1	1	yes	characteristic, complemented
13	C₂×D₂₀	C₂×C₇	1	6	yes	complemented
14	C₄²×C₅	C₂×C₇	1	1	yes	characteristic, complemented
15	C₂×C₅×C₇	C₂×D₄	1	3	yes	—
16	C₇×D₅	—	4	4	no	—
17	C₂³×C₇	—	5	4	no	—
18	C₇×D₄	—	10	12	no	—
19	C₂×C₄×C₇	C₂×D₅	1	3	yes	—
20	C₂²×D₅	C₂²×C₇	1	4	yes	—
21	C₂×C₄×C₅	C₂²×C₇	1	3	yes	—
22	D₂₀	—	2	12	no	—
23	C₅×C₇	#127	1	1	yes	characteristic, complemented, Hall
24	#127	—	5	1	no	Sylow
25	C₂²×C₇	—	10	12	no	—
26	C₂²×C₇	C₂²×D₅	1	1	yes	characteristic
27	C₄×C₇	D₂₀	1	6	yes	complemented
28	C₂²×C₅	C₂³×C₇	1	1	yes	characteristic
29	C₂×D₅	—	2	12	no	—
30	C₄×C₅	C₇×D₄	1	6	yes	complemented
31	C₂×D₄	—	5	6	no	—
32	C₄²	C₇×D₅	1	1	yes	characteristic, complemented
33	C₂×C₇	—	20	4	no	—
34	C₂×C₇	C₂×D₂₀	1	3	yes	—
35	C₂×C₅	C₂×C₇×D₄	1	3	yes	—
36	D₅	—	4	4	no	—
37	C₂³	—	5	4	no	—
38	D₄	—	10	12	no	—
39	C₂×C₄	C₂×C₇×D₅	1	3	yes	—
40	C₇	#4020	1	1	yes	characteristic, direct product factor, Sylow
41	C₅	C₇×#127	1	1	yes	characteristic, complemented, Sylow
42	C₂²	—	10	12	no	—
43	C₂²	C₂²×C₇×D₅	1	1	yes	characteristic
44	C₄	C₇×D₂₀	1	6	yes	complemented
45	C₂	—	20	4	no	—
46	C₂	C₂×C₇×D₂₀	1	3	yes	—

	subgroup	G/H
center	C₂²×C₇	C₂²×D₅
commutator, cosocle	C₂²×C₅	C₂³×C₇
Frattini	C₂²	C₂²×C₇×D₅
Fitting	C₄²×C₅×C₇	C₂
socle	C₂²×C₅×C₇	C₂³
hypercenter	C₄²×C₇	D₅
hypocenter	C₅	C₇×#127
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₇ ◁ C₄²×C₇

Complements

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

N	H ≅ G/N	type
1. C₂×C₇×D₂₀	C₂	semidirect
2. C₄²×C₅×C₇	C₂	semidirect
7. #4020	C₇	direct (N × H)
10. C₄×C₅×C₇	D₄	semidirect
12. C₄²×C₇	D₅	semidirect
13. C₂×D₂₀	C₂×C₇	semidirect
14. C₄²×C₅	C₂×C₇	semidirect
23. C₅×C₇	#127	semidirect
27. C₄×C₇	D₂₀	semidirect
30. C₄×C₅	C₇×D₄	semidirect
32. C₄²	C₇×D₅	semidirect
40. C₇	#4020	direct (N × H)
41. C₅	C₇×#127	semidirect
44. C₄	C₇×D₂₀	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₇×D₂₀	2
C₄²×C₅×C₇	2
C₇×#127	5
#4020	7

Subgroups — C7×#4020 #11765118

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#4020 #11765118