Subgroups — C₃×C₅×D₇×C₁₅₁ #44540243

Order 31710.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₇×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×D₇×C₁₅₁	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×D₇×C₁₅₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₅×C₇×C₁₅₁	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃×C₅×C₁₅₁	—	7	1	no	maximal, Hall
6	C₃×C₇×C₁₅₁	C₂×C₅	1	1	yes	characteristic, complemented, Hall
7	C₃×C₅×C₁₅₁	D₇	1	1	yes	characteristic, direct product factor, Hall
8	D₇×C₁₅₁	C₃×C₅	1	1	yes	characteristic, direct product factor, Hall
9	C₂×C₅×C₁₅₁	—	7	1	no	Hall
10	C₇×C₁₅₁	C₂×C₃×C₅	1	1	yes	characteristic, complemented, Hall
11	C₂×C₃×C₁₅₁	—	7	1	no	Hall
12	C₅×C₁₅₁	C₃×D₇	1	1	yes	characteristic, direct product factor, Hall
13	C₃×C₁₅₁	C₅×D₇	1	1	yes	characteristic, direct product factor, Hall
14	C₂×C₁₅₁	—	7	1	no	Hall
15	C₃×C₅×D₇	C₁₅₁	1	1	yes	maximal, characteristic, direct product factor, Hall
16	C₁₅₁	C₃×C₅×D₇	1	1	yes	characteristic, direct product factor, Sylow
17	C₃×C₅×C₇	C₂×C₁₅₁	1	1	yes	characteristic, complemented, Hall
18	C₅×D₇	C₃×C₁₅₁	1	1	yes	characteristic, direct product factor, Hall
19	C₃×D₇	C₅×C₁₅₁	1	1	yes	characteristic, direct product factor, Hall
20	C₅×C₇	C₂×C₃×C₁₅₁	1	1	yes	characteristic, complemented, Hall
21	C₂×C₃×C₅	—	7	1	no	Hall
22	C₃×C₇	C₂×C₅×C₁₅₁	1	1	yes	characteristic, complemented, Hall
23	C₃×C₅	D₇×C₁₅₁	1	1	yes	characteristic, direct product factor, Hall
24	D₇	C₃×C₅×C₁₅₁	1	1	yes	characteristic, direct product factor, Hall
25	C₂×C₅	—	7	1	no	Hall
26	C₇	C₂×C₃×C₅×C₁₅₁	1	1	yes	characteristic, complemented, Sylow
27	C₂×C₃	—	7	1	no	Hall
28	C₅	C₃×D₇×C₁₅₁	1	1	yes	characteristic, direct product factor, Sylow
29	C₃	C₅×D₇×C₁₅₁	1	1	yes	characteristic, direct product factor, Sylow
30	C₂	—	7	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₅×C₁₅₁	D₇
commutator, cosocle, hypocenter	C₇	C₂×C₃×C₅×C₁₅₁
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₇×C₁₅₁	C₂
LCS	G ▷ C₇
UCS	C₁ ◁ C₃×C₅×C₁₅₁

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×C₇×C₁₅₁	C₂	semidirect
2. C₅×D₇×C₁₅₁	C₃	direct (N × H)
3. C₃×D₇×C₁₅₁	C₅	direct (N × H)
4. C₅×C₇×C₁₅₁	C₂×C₃	semidirect
6. C₃×C₇×C₁₅₁	C₂×C₅	semidirect
7. C₃×C₅×C₁₅₁	D₇	direct (N × H)
8. D₇×C₁₅₁	C₃×C₅	direct (N × H)
10. C₇×C₁₅₁	C₂×C₃×C₅	semidirect
12. C₅×C₁₅₁	C₃×D₇	direct (N × H)
13. C₃×C₁₅₁	C₅×D₇	direct (N × H)
15. C₃×C₅×D₇	C₁₅₁	direct (N × H)
16. C₁₅₁	C₃×C₅×D₇	direct (N × H)
17. C₃×C₅×C₇	C₂×C₁₅₁	semidirect
18. C₅×D₇	C₃×C₁₅₁	direct (N × H)
19. C₃×D₇	C₅×C₁₅₁	direct (N × H)
20. C₅×C₇	C₂×C₃×C₁₅₁	semidirect
22. C₃×C₇	C₂×C₅×C₁₅₁	semidirect
23. C₃×C₅	D₇×C₁₅₁	direct (N × H)
24. D₇	C₃×C₅×C₁₅₁	direct (N × H)
26. C₇	C₂×C₃×C₅×C₁₅₁	semidirect
28. C₅	C₃×D₇×C₁₅₁	direct (N × H)
29. C₃	C₅×D₇×C₁₅₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₅×C₇×C₁₅₁	2
C₅×D₇×C₁₅₁	3
C₃×D₇×C₁₅₁	5
C₂×C₃×C₅×C₁₅₁	7
C₃×C₅×D₇	151

Subgroups — C3×C5×D7×C151 #44540243

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×D₇×C₁₅₁ #44540243