Subgroups — C₂₉×C₇⋊(C₇⋊AGL(1,𝔽₅)) #43249347

Order 28420.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇²×D₅×C₂₉	C₂	1	1	yes	maximal, characteristic
2	C₅×C₇²×C₂₉	C₄	1	1	yes	characteristic, complemented, Hall
3	C₂₉×C₇⋊Dic₇	—	5	1	no	maximal, Hall
4	C₂₉×C₇⋊AGL(1,𝔽₅)	—	7	8	no	maximal
5	C₂×C₇²×C₂₉	—	5	1	no	—
6	C₇×D₅×C₂₉	D₇	1	8	yes	—
7	C₇²×C₂₉	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
8	C₅×C₇×C₂₉	Dic₇	1	8	yes	complemented
9	C₇⋊(C₇⋊AGL(1,𝔽₅))	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
10	Dic₇×C₂₉	—	35	8	no	—
11	AGL(1,𝔽₅)×C₂₉	—	49	1	no	Hall
12	C₇²×D₅	C₂×C₂₉	1	1	yes	characteristic
13	C₂×C₇×C₂₉	—	5	8	no	—
14	D₅×C₂₉	C₇⋊D₇	1	1	yes	characteristic
15	C₅×C₇²	C₄×C₂₉	1	1	yes	characteristic, complemented, Hall
16	C₇×C₂₉	C₇⋊AGL(1,𝔽₅)	1	8	yes	complemented
17	C₇⋊Dic₇	—	5	1	no	Hall
18	C₅×C₂₉	C₇⋊Dic₇	1	1	yes	characteristic, complemented, Hall
19	C₇⋊AGL(1,𝔽₅)	—	7	8	no	—
20	C₄×C₂₉	—	245	1	no	Hall
21	C₂×C₇²	—	5	1	no	—
22	C₇×D₅	D₇×C₂₉	1	8	yes	—
23	C₂×C₂₉	—	5	1	no	—
24	C₇²	AGL(1,𝔽₅)×C₂₉	1	1	yes	characteristic, complemented, Sylow
25	C₅×C₇	Dic₇×C₂₉	1	8	yes	complemented
26	C₂₉	C₇⋊(C₇⋊AGL(1,𝔽₅))	1	1	yes	characteristic, direct product factor, Sylow
27	Dic₇	—	35	8	no	—
28	AGL(1,𝔽₅)	—	49	1	no	Hall
29	C₂×C₇	—	5	8	no	—
30	D₅	C₂₉×C₇⋊D₇	1	1	yes	characteristic
31	C₇	C₂₉×C₇⋊AGL(1,𝔽₅)	1	8	yes	complemented
32	C₅	C₂₉×C₇⋊Dic₇	1	1	yes	characteristic, complemented, Sylow
33	C₄	—	245	1	no	Sylow
34	C₂	—	5	1	no	—

	subgroup	G/H
center, hypercenter	C₂₉	C₇⋊(C₇⋊AGL(1,𝔽₅))
commutator, hypocenter	C₅×C₇²	C₄×C₂₉
Frattini	C₁	G
Fitting, socle	C₅×C₇²×C₂₉	C₄
prime radical	C₇²×D₅×C₂₉	C₂
cosocle	C₇²×D₅	C₂×C₂₉
LCS	G ▷ C₅×C₇²
UCS	C₁ ◁ C₂₉

Complements

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

N	H ≅ G/N	type
2. C₅×C₇²×C₂₉	C₄	semidirect
7. C₇²×C₂₉	AGL(1,𝔽₅)	semidirect
8. C₅×C₇×C₂₉	Dic₇	semidirect
9. C₇⋊(C₇⋊AGL(1,𝔽₅))	C₂₉	direct (N × H)
15. C₅×C₇²	C₄×C₂₉	semidirect
16. C₇×C₂₉	C₇⋊AGL(1,𝔽₅)	semidirect
18. C₅×C₂₉	C₇⋊Dic₇	semidirect
24. C₇²	AGL(1,𝔽₅)×C₂₉	semidirect
25. C₅×C₇	Dic₇×C₂₉	semidirect
26. C₂₉	C₇⋊(C₇⋊AGL(1,𝔽₅))	direct (N × H)
31. C₇	C₂₉×C₇⋊AGL(1,𝔽₅)	semidirect
32. C₅	C₂₉×C₇⋊Dic₇	semidirect

Maximal subgroups

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

subgroup	index
C₇²×D₅×C₂₉	2
C₂₉×C₇⋊Dic₇	5
C₂₉×C₇⋊AGL(1,𝔽₅)	7
C₇⋊(C₇⋊AGL(1,𝔽₅))	29

Subgroups — C29×C7⋊(C7⋊AGL(1,𝔽5)) #43249347

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×C₇⋊(C₇⋊AGL(1,𝔽₅)) #43249347