Subgroups — C₁₅₁×D₁₀₅ #44540255

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	D₃₅×C₁₅₁	—	3	1	no	maximal, Hall
3	D₂₁×C₁₅₁	—	5	1	no	maximal, Hall
4	C₅×C₇×C₁₅₁	D₃	1	1	yes	characteristic, complemented, Hall
5	D₁₅×C₁₅₁	—	7	1	no	maximal, Hall
6	C₃×C₇×C₁₅₁	D₅	1	1	yes	characteristic, complemented, Hall
7	C₃×C₅×C₁₅₁	D₇	1	1	yes	characteristic, complemented, Hall
8	D₇×C₁₅₁	—	15	1	no	Hall
9	D₅×C₁₅₁	—	21	1	no	Hall
10	C₇×C₁₅₁	D₁₅	1	1	yes	characteristic, complemented, Hall
11	D₃×C₁₅₁	—	35	1	no	Hall
12	C₅×C₁₅₁	D₂₁	1	1	yes	characteristic, complemented, Hall
13	C₃×C₁₅₁	D₃₅	1	1	yes	characteristic, complemented, Hall
14	C₂×C₁₅₁	—	105	1	no	Hall
15	D₁₀₅	C₁₅₁	1	1	yes	maximal, characteristic, direct product factor, Hall
16	C₁₅₁	D₁₀₅	1	1	yes	characteristic, direct product factor, Sylow
17	C₃×C₅×C₇	C₂×C₁₅₁	1	1	yes	characteristic, complemented, Hall
18	D₃₅	—	3	1	no	Hall
19	D₂₁	—	5	1	no	Hall
20	C₅×C₇	D₃×C₁₅₁	1	1	yes	characteristic, complemented, Hall
21	D₁₅	—	7	1	no	Hall
22	C₃×C₇	D₅×C₁₅₁	1	1	yes	characteristic, complemented, Hall
23	C₃×C₅	D₇×C₁₅₁	1	1	yes	characteristic, complemented, Hall
24	D₇	—	15	1	no	Hall
25	D₅	—	21	1	no	Hall
26	C₇	D₁₅×C₁₅₁	1	1	yes	characteristic, complemented, Sylow
27	D₃	—	35	1	no	Hall
28	C₅	D₂₁×C₁₅₁	1	1	yes	characteristic, complemented, Sylow
29	C₃	D₃₅×C₁₅₁	1	1	yes	characteristic, complemented, Sylow
30	C₂	—	105	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₅₁	D₁₀₅
commutator, cosocle, hypocenter	C₃×C₅×C₇	C₂×C₁₅₁
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₇×C₁₅₁	C₂
LCS	G ▷ C₃×C₅×C₇
UCS	C₁ ◁ C₁₅₁

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×C₇×C₁₅₁	C₂	semidirect
4. C₅×C₇×C₁₅₁	D₃	semidirect
6. C₃×C₇×C₁₅₁	D₅	semidirect
7. C₃×C₅×C₁₅₁	D₇	semidirect
10. C₇×C₁₅₁	D₁₅	semidirect
12. C₅×C₁₅₁	D₂₁	semidirect
13. C₃×C₁₅₁	D₃₅	semidirect
15. D₁₀₅	C₁₅₁	direct (N × H)
16. C₁₅₁	D₁₀₅	direct (N × H)
17. C₃×C₅×C₇	C₂×C₁₅₁	semidirect
20. C₅×C₇	D₃×C₁₅₁	semidirect
22. C₃×C₇	D₅×C₁₅₁	semidirect
23. C₃×C₅	D₇×C₁₅₁	semidirect
26. C₇	D₁₅×C₁₅₁	semidirect
28. C₅	D₂₁×C₁₅₁	semidirect
29. C₃	D₃₅×C₁₅₁	semidirect

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
D₃₅×C₁₅₁	3
D₂₁×C₁₅₁	5
D₁₅×C₁₅₁	7
D₁₀₅	151

Subgroups — C151×D105 #44540255

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₅₁×D₁₀₅ #44540255