Subgroups — C₇²×AGL(1,𝔽₅)×C₂₉ #43249339

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	C₄×C₇²×C₂₉	—	5	1	no	maximal, Hall
4	C₇×AGL(1,𝔽₅)×C₂₉	C₇	1	8	yes	maximal, direct product factor
5	C₂×C₇²×C₂₉	—	5	1	no	—
6	C₇×D₅×C₂₉	C₂×C₇	1	8	yes	—
7	C₇²×C₂₉	AGL(1,𝔽₅)	1	1	yes	characteristic, direct product factor, Hall
8	C₅×C₇×C₂₉	C₄×C₇	1	8	yes	complemented
9	C₇²×AGL(1,𝔽₅)	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₄×C₇×C₂₉	—	5	8	no	—
11	AGL(1,𝔽₅)×C₂₉	C₇²	1	1	yes	characteristic, direct product factor, Hall
12	C₇²×D₅	C₂×C₂₉	1	1	yes	characteristic
13	C₂×C₇×C₂₉	—	5	8	no	—
14	D₅×C₂₉	C₂×C₇²	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	direct product factor
17	C₄×C₇²	—	5	1	no	Hall
18	C₅×C₂₉	C₄×C₇²	1	1	yes	characteristic, complemented, Hall
19	C₇×AGL(1,𝔽₅)	C₇×C₂₉	1	8	yes	direct product factor
20	C₄×C₂₉	—	5	1	no	Hall
21	C₂×C₇²	—	5	1	no	—
22	C₇×D₅	C₂×C₇×C₂₉	1	8	yes	—
23	C₂×C₂₉	—	5	1	no	—
24	C₇²	AGL(1,𝔽₅)×C₂₉	1	1	yes	characteristic, direct product factor, Sylow
25	C₅×C₇	C₄×C₇×C₂₉	1	8	yes	complemented
26	C₂₉	C₇²×AGL(1,𝔽₅)	1	1	yes	characteristic, direct product factor, Sylow
27	C₄×C₇	—	5	8	no	—
28	AGL(1,𝔽₅)	C₇²×C₂₉	1	1	yes	characteristic, direct product factor, Hall
29	C₂×C₇	—	5	8	no	—
30	D₅	C₂×C₇²×C₂₉	1	1	yes	characteristic
31	C₇	C₇×AGL(1,𝔽₅)×C₂₉	1	8	yes	direct product factor
32	C₅	C₄×C₇²×C₂₉	1	1	yes	characteristic, complemented, Sylow
33	C₄	—	5	1	no	Sylow
34	C₂	—	5	1	no	—

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

Complements

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

N	H ≅ G/N	type
2. C₅×C₇²×C₂₉	C₄	semidirect
4. C₇×AGL(1,𝔽₅)×C₂₉	C₇	direct (N × H)
7. C₇²×C₂₉	AGL(1,𝔽₅)	direct (N × H)
8. C₅×C₇×C₂₉	C₄×C₇	semidirect
9. C₇²×AGL(1,𝔽₅)	C₂₉	direct (N × H)
11. AGL(1,𝔽₅)×C₂₉	C₇²	direct (N × H)
15. C₅×C₇²	C₄×C₂₉	semidirect
16. C₇×C₂₉	C₇×AGL(1,𝔽₅)	direct (N × H)
18. C₅×C₂₉	C₄×C₇²	semidirect
19. C₇×AGL(1,𝔽₅)	C₇×C₂₉	direct (N × H)
24. C₇²	AGL(1,𝔽₅)×C₂₉	direct (N × H)
25. C₅×C₇	C₄×C₇×C₂₉	semidirect
26. C₂₉	C₇²×AGL(1,𝔽₅)	direct (N × H)
28. AGL(1,𝔽₅)	C₇²×C₂₉	direct (N × H)
31. C₇	C₇×AGL(1,𝔽₅)×C₂₉	direct (N × H)
32. C₅	C₄×C₇²×C₂₉	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
C₄×C₇²×C₂₉	5
C₇×AGL(1,𝔽₅)×C₂₉	7
C₇²×AGL(1,𝔽₅)	29

Subgroups — C72×AGL(1,𝔽5)×C29 #43249339

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇²×AGL(1,𝔽₅)×C₂₉ #43249339