Subgroups — C₃×C₅×D₇×C₂₉ #20259019

Order 6090.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₇×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×D₇×C₂₉	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×D₇×C₂₉	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₅×C₇×C₂₉	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃×C₅×C₂₉	—	7	1	no	maximal, Hall
6	C₃×C₇×C₂₉	C₂×C₅	1	1	yes	characteristic, complemented, Hall
7	C₃×C₅×C₂₉	D₇	1	1	yes	characteristic, direct product factor, Hall
8	D₇×C₂₉	C₃×C₅	1	1	yes	characteristic, direct product factor, Hall
9	C₂×C₅×C₂₉	—	7	1	no	Hall
10	C₃×C₅×D₇	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₇×C₂₉	C₂×C₃×C₅	1	1	yes	characteristic, complemented, Hall
12	C₂×C₃×C₂₉	—	7	1	no	Hall
13	C₅×C₂₉	C₃×D₇	1	1	yes	characteristic, direct product factor, Hall
14	C₃×C₅×C₇	C₂×C₂₉	1	1	yes	characteristic, complemented, Hall
15	C₃×C₂₉	C₅×D₇	1	1	yes	characteristic, direct product factor, Hall
16	C₅×D₇	C₃×C₂₉	1	1	yes	characteristic, direct product factor, Hall
17	C₂×C₂₉	—	7	1	no	Hall
18	C₃×D₇	C₅×C₂₉	1	1	yes	characteristic, direct product factor, Hall
19	C₅×C₇	C₂×C₃×C₂₉	1	1	yes	characteristic, complemented, Hall
20	C₂×C₃×C₅	—	7	1	no	Hall
21	C₂₉	C₃×C₅×D₇	1	1	yes	characteristic, direct product factor, Sylow
22	C₃×C₇	C₂×C₅×C₂₉	1	1	yes	characteristic, complemented, Hall
23	C₃×C₅	D₇×C₂₉	1	1	yes	characteristic, direct product factor, Hall
24	D₇	C₃×C₅×C₂₉	1	1	yes	characteristic, direct product factor, Hall
25	C₂×C₅	—	7	1	no	Hall
26	C₇	C₂×C₃×C₅×C₂₉	1	1	yes	characteristic, complemented, Sylow
27	C₂×C₃	—	7	1	no	Hall
28	C₅	C₃×D₇×C₂₉	1	1	yes	characteristic, direct product factor, Sylow
29	C₃	C₅×D₇×C₂₉	1	1	yes	characteristic, direct product factor, Sylow
30	C₂	—	7	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₅×C₂₉	D₇
commutator, hypocenter	C₇	C₂×C₃×C₅×C₂₉
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₇×C₂₉	C₂
LCS	G ▷ C₇
UCS	C₁ ◁ C₃×C₅×C₂₉

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×C₇×C₂₉	C₂	semidirect
2. C₅×D₇×C₂₉	C₃	direct (N × H)
3. C₃×D₇×C₂₉	C₅	direct (N × H)
4. C₅×C₇×C₂₉	C₂×C₃	semidirect
6. C₃×C₇×C₂₉	C₂×C₅	semidirect
7. C₃×C₅×C₂₉	D₇	direct (N × H)
8. D₇×C₂₉	C₃×C₅	direct (N × H)
10. C₃×C₅×D₇	C₂₉	direct (N × H)
11. C₇×C₂₉	C₂×C₃×C₅	semidirect
13. C₅×C₂₉	C₃×D₇	direct (N × H)
14. C₃×C₅×C₇	C₂×C₂₉	semidirect
15. C₃×C₂₉	C₅×D₇	direct (N × H)
16. C₅×D₇	C₃×C₂₉	direct (N × H)
18. C₃×D₇	C₅×C₂₉	direct (N × H)
19. C₅×C₇	C₂×C₃×C₂₉	semidirect
21. C₂₉	C₃×C₅×D₇	direct (N × H)
22. C₃×C₇	C₂×C₅×C₂₉	semidirect
23. C₃×C₅	D₇×C₂₉	direct (N × H)
24. D₇	C₃×C₅×C₂₉	direct (N × H)
26. C₇	C₂×C₃×C₅×C₂₉	semidirect
28. C₅	C₃×D₇×C₂₉	direct (N × H)
29. C₃	C₅×D₇×C₂₉	direct (N × H)

Subgroups — C3×C5×D7×C29 #20259019

Conjugacy classes of subgroups

Complements

Subgroups — C₃×C₅×D₇×C₂₉ #20259019