Subgroups — C₂₉×C₅⋊(C₅⋊AGL(1,𝔽₇)) #44478593

Order 30450.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²×ΓL(1,𝔽₈)×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₂₉×C₅⋊D₃₅	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₂₉×C₅⋊AGL(1,𝔽₇)	—	5	6	no	maximal
4	C₅²×C₇×C₂₉	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	C₃×C₂₉×C₅⋊D₅	—	7	1	no	maximal, Hall
6	C₅×ΓL(1,𝔽₈)×C₂₉	D₅	1	6	yes	complemented
7	C₃×C₅²×C₂₉	—	7	1	no	Hall
8	C₂₉×D₃₅	—	5	6	no	—
9	C₂₉×C₅⋊D₅	—	7	1	no	Hall
10	C₂₉×AGL(1,𝔽₇)	—	25	1	no	Hall
11	C₅⋊(C₅⋊AGL(1,𝔽₇))	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₅×C₇×C₂₉	C₃×D₅	1	6	yes	complemented
13	C₃×D₅×C₂₉	—	35	6	no	—
14	C₅²×C₂₉	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented, Hall
15	ΓL(1,𝔽₈)×C₂₉	C₅⋊D₅	1	1	yes	characteristic, complemented, Hall
16	C₅²×ΓL(1,𝔽₈)	C₂×C₂₉	1	1	yes	characteristic, complemented, Hall
17	C₃×C₅×C₂₉	—	7	6	no	—
18	D₇×C₂₉	—	25	1	no	Hall
19	C₅⋊D₃₅	C₃×C₂₉	1	1	yes	characteristic, complemented, Hall
20	D₅×C₂₉	—	35	6	no	—
21	C₅⋊AGL(1,𝔽₇)	—	5	6	no	—
22	C₇×C₂₉	C₃×C₅⋊D₅	1	1	yes	characteristic, complemented, Hall
23	C₅²×C₇	C₂×C₃×C₂₉	1	1	yes	characteristic, complemented, Hall
24	C₂×C₃×C₂₉	—	175	1	no	Hall
25	C₃×C₅⋊D₅	—	7	1	no	Hall
26	C₅×C₂₉	C₅⋊AGL(1,𝔽₇)	1	6	yes	complemented
27	C₅×ΓL(1,𝔽₈)	D₅×C₂₉	1	6	yes	complemented
28	C₃×C₂₉	—	7	1	no	Hall
29	C₃×C₅²	—	7	1	no	Hall
30	D₃₅	—	5	6	no	—
31	C₂×C₂₉	—	175	1	no	Hall
32	C₅⋊D₅	—	7	1	no	Hall
33	AGL(1,𝔽₇)	—	25	1	no	Hall
34	C₅×C₇	C₃×D₅×C₂₉	1	6	yes	complemented
35	C₃×D₅	—	35	6	no	—
36	C₂₉	C₅⋊(C₅⋊AGL(1,𝔽₇))	1	1	yes	characteristic, direct product factor, Sylow
37	C₅²	C₂₉×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented, Sylow
38	ΓL(1,𝔽₈)	C₂₉×C₅⋊D₅	1	1	yes	characteristic, complemented, Hall
39	C₃×C₅	—	7	6	no	—
40	D₇	—	25	1	no	Hall
41	D₅	—	35	6	no	—
42	C₇	C₃×C₂₉×C₅⋊D₅	1	1	yes	characteristic, complemented, Sylow
43	C₂×C₃	—	175	1	no	Hall
44	C₅	C₂₉×C₅⋊AGL(1,𝔽₇)	1	6	yes	complemented
45	C₃	—	7	1	no	Sylow
46	C₂	—	175	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₂₉	C₅⋊(C₅⋊AGL(1,𝔽₇))
commutator, cosocle, hypocenter	C₅²×C₇	C₂×C₃×C₂₉
Frattini	C₁	G
Fitting, socle	C₅²×C₇×C₂₉	C₂×C₃
LCS	G ▷ C₅²×C₇
UCS	C₁ ◁ C₂₉

Complements

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

N	H ≅ G/N	type
1. C₅²×ΓL(1,𝔽₈)×C₂₉	C₂	semidirect
2. C₂₉×C₅⋊D₃₅	C₃	semidirect
4. C₅²×C₇×C₂₉	C₂×C₃	semidirect
6. C₅×ΓL(1,𝔽₈)×C₂₉	D₅	semidirect
11. C₅⋊(C₅⋊AGL(1,𝔽₇))	C₂₉	direct (N × H)
12. C₅×C₇×C₂₉	C₃×D₅	semidirect
14. C₅²×C₂₉	AGL(1,𝔽₇)	semidirect
15. ΓL(1,𝔽₈)×C₂₉	C₅⋊D₅	semidirect
16. C₅²×ΓL(1,𝔽₈)	C₂×C₂₉	semidirect
19. C₅⋊D₃₅	C₃×C₂₉	semidirect
22. C₇×C₂₉	C₃×C₅⋊D₅	semidirect
23. C₅²×C₇	C₂×C₃×C₂₉	semidirect
26. C₅×C₂₉	C₅⋊AGL(1,𝔽₇)	semidirect
27. C₅×ΓL(1,𝔽₈)	D₅×C₂₉	semidirect
34. C₅×C₇	C₃×D₅×C₂₉	semidirect
36. C₂₉	C₅⋊(C₅⋊AGL(1,𝔽₇))	direct (N × H)
37. C₅²	C₂₉×AGL(1,𝔽₇)	semidirect
38. ΓL(1,𝔽₈)	C₂₉×C₅⋊D₅	semidirect
42. C₇	C₃×C₂₉×C₅⋊D₅	semidirect
44. C₅	C₂₉×C₅⋊AGL(1,𝔽₇)	semidirect

Maximal subgroups

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

subgroup	index
C₅²×ΓL(1,𝔽₈)×C₂₉	2
C₂₉×C₅⋊D₃₅	3
C₂₉×C₅⋊AGL(1,𝔽₇)	5
C₃×C₂₉×C₅⋊D₅	7
C₅⋊(C₅⋊AGL(1,𝔽₇))	29

Subgroups — C29×C5⋊(C5⋊AGL(1,𝔽7)) #44478593

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×C₅⋊(C₅⋊AGL(1,𝔽₇)) #44478593