Subgroups — C₅⋊(C₅⋊(ΓL(1,𝔽₈)⋊D₇)) #20301278

Order 7350.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²×C₇×ΓL(1,𝔽₈)	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅⋊(C₅⋊(C₇⋊D₇))	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₅⋊(ΓL(1,𝔽₈)⋊D₇)	—	5	6	no	maximal
4	C₅²×C₇²	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	C₃×C₅⋊D₃₅	—	7	1	no	maximal
6	C₅⋊(C₅⋊AGL(1,𝔽₇))	—	7	1	no	maximal
7	C₅×C₇×ΓL(1,𝔽₈)	D₅	1	6	yes	complemented
8	C₃×C₅²×C₇	—	7	1	no	—
9	C₅²×ΓL(1,𝔽₈)	D₇	1	1	yes	characteristic, complemented
10	C₅⋊(C₇⋊D₇)	—	5	6	no	—
11	C₅⋊D₃₅	—	7	1	no	—
12	C₅⋊D₃₅	—	7	1	no	—
13	C₅⋊D₃₅	—	21	2	no	—
14	ΓL(1,𝔽₈)⋊D₇	—	25	1	no	Hall
15	C₅×C₇²	C₃×D₅	1	6	yes	complemented
16	C₃×D₃₅	—	35	6	no	—
17	C₅⋊AGL(1,𝔽₇)	—	35	6	no	—
18	C₅²×C₇	—	3	2	no	—
19	C₅²×C₇	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
20	C₅²×C₇	C₃×D₇	1	1	yes	characteristic, complemented
21	C₃×C₅⋊D₅	—	49	1	no	Hall
22	C₇×ΓL(1,𝔽₈)	C₅⋊D₅	1	1	yes	characteristic, complemented, Hall
23	C₃×C₅×C₇	—	7	6	no	—
24	C₅×ΓL(1,𝔽₈)	D₃₅	1	6	yes	complemented
25	C₇⋊D₇	—	25	1	no	Hall
26	C₃×C₅²	—	7	1	no	Hall
27	D₃₅	—	35	6	no	—
28	D₃₅	—	35	6	no	—
29	D₃₅	—	105	12	no	—
30	C₅⋊D₅	—	49	1	no	Hall
31	C₇²	C₃×C₅⋊D₅	1	1	yes	characteristic, complemented, Sylow
32	C₃×D₇	—	175	1	no	—
33	AGL(1,𝔽₇)	—	175	1	no	—
34	C₅×C₇	—	3	12	no	—
35	C₅×C₇	C₅⋊AGL(1,𝔽₇)	1	6	yes	complemented
36	C₅×C₇	C₃×D₃₅	1	6	yes	complemented
37	C₃×D₅	—	245	6	no	—
38	C₅²	ΓL(1,𝔽₈)⋊D₇	1	1	yes	characteristic, complemented, Sylow
39	C₃×C₇	—	7	1	no	—
40	ΓL(1,𝔽₈)	C₅⋊D₃₅	1	1	yes	characteristic, complemented
41	C₃×C₅	—	7	6	no	—
42	D₇	—	525	2	no	—
43	D₇	—	175	1	no	—
44	D₇	—	175	1	no	—
45	D₅	—	245	6	no	—
46	C₇	—	3	2	no	—
47	C₇	C₅⋊(C₅⋊AGL(1,𝔽₇))	1	1	yes	characteristic, complemented
48	C₇	C₃×C₅⋊D₃₅	1	1	yes	characteristic, complemented
49	C₂×C₃	—	1225	1	no	Hall
50	C₅	C₅⋊(ΓL(1,𝔽₈)⋊D₇)	1	6	yes	complemented
51	C₃	—	7	1	no	Sylow
52	C₂	—	1225	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₅²×C₇²	C₂×C₃
LCS	G ▷ C₅²×C₇²
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₅²×C₇×ΓL(1,𝔽₈)	C₂	semidirect
2. C₅⋊(C₅⋊(C₇⋊D₇))	C₃	semidirect
4. C₅²×C₇²	C₂×C₃	semidirect
7. C₅×C₇×ΓL(1,𝔽₈)	D₅	semidirect
9. C₅²×ΓL(1,𝔽₈)	D₇	semidirect
15. C₅×C₇²	C₃×D₅	semidirect
19. C₅²×C₇	AGL(1,𝔽₇)	semidirect
20. C₅²×C₇	C₃×D₇	semidirect
22. C₇×ΓL(1,𝔽₈)	C₅⋊D₅	semidirect
24. C₅×ΓL(1,𝔽₈)	D₃₅	semidirect
31. C₇²	C₃×C₅⋊D₅	semidirect
35. C₅×C₇	C₅⋊AGL(1,𝔽₇)	semidirect
36. C₅×C₇	C₃×D₃₅	semidirect
38. C₅²	ΓL(1,𝔽₈)⋊D₇	semidirect
40. ΓL(1,𝔽₈)	C₅⋊D₃₅	semidirect
47. C₇	C₅⋊(C₅⋊AGL(1,𝔽₇))	semidirect
48. C₇	C₃×C₅⋊D₃₅	semidirect
50. C₅	C₅⋊(ΓL(1,𝔽₈)⋊D₇)	semidirect

Subgroups — C5⋊(C5⋊(ΓL(1,𝔽8)⋊D7)) #20301278

Conjugacy classes of subgroups

Complements

Subgroups — C₅⋊(C₅⋊(ΓL(1,𝔽₈)⋊D₇)) #20301278