Subgroups — C₃×C₇×D₇₅₅ #44540246

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	C₇×D₇₅₅	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₇×D₁₅₁	—	5	1	no	maximal, Hall
4	C₅×C₇×C₁₅₁	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	C₃×D₇₅₅	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₃×C₇×C₁₅₁	D₅	1	1	yes	characteristic, complemented, Hall
7	C₃×C₅×C₁₅₁	C₂×C₇	1	1	yes	characteristic, complemented, Hall
8	C₇×D₁₅₁	—	5	1	no	Hall
9	D₇₅₅	C₃×C₇	1	1	yes	characteristic, direct product factor, Hall
10	C₇×C₁₅₁	C₃×D₅	1	1	yes	characteristic, complemented, Hall
11	C₃×D₁₅₁	—	5	1	no	Hall
12	C₅×C₁₅₁	C₂×C₃×C₇	1	1	yes	characteristic, complemented, Hall
13	C₃×C₁₅₁	C₇×D₅	1	1	yes	characteristic, complemented, Hall
14	D₁₅₁	—	5	1	no	Hall
15	C₃×C₇×D₅	—	151	1	no	maximal, Hall
16	C₁₅₁	C₃×C₇×D₅	1	1	yes	characteristic, complemented, Sylow
17	C₃×C₅×C₇	D₁₅₁	1	1	yes	characteristic, complemented, Hall
18	C₇×D₅	—	151	1	no	Hall
19	C₂×C₃×C₇	—	755	1	no	Hall
20	C₅×C₇	C₃×D₁₅₁	1	1	yes	characteristic, complemented, Hall
21	C₃×D₅	—	151	1	no	Hall
22	C₃×C₇	D₇₅₅	1	1	yes	characteristic, direct product factor, Hall
23	C₃×C₅	C₇×D₁₅₁	1	1	yes	characteristic, complemented, Hall
24	C₂×C₇	—	755	1	no	Hall
25	D₅	—	151	1	no	Hall
26	C₇	C₃×D₇₅₅	1	1	yes	characteristic, direct product factor, Sylow
27	C₂×C₃	—	755	1	no	Hall
28	C₅	C₃×C₇×D₁₅₁	1	1	yes	characteristic, complemented, Sylow
29	C₃	C₇×D₇₅₅	1	1	yes	characteristic, direct product factor, Sylow
30	C₂	—	755	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₇	D₇₅₅
commutator, cosocle, hypocenter	C₅×C₁₅₁	C₂×C₃×C₇
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₇×C₁₅₁	C₂
LCS	G ▷ C₅×C₁₅₁
UCS	C₁ ◁ C₃×C₇

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×C₇×C₁₅₁	C₂	semidirect
2. C₇×D₇₅₅	C₃	direct (N × H)
4. C₅×C₇×C₁₅₁	C₂×C₃	semidirect
5. C₃×D₇₅₅	C₇	direct (N × H)
6. C₃×C₇×C₁₅₁	D₅	semidirect
7. C₃×C₅×C₁₅₁	C₂×C₇	semidirect
9. D₇₅₅	C₃×C₇	direct (N × H)
10. C₇×C₁₅₁	C₃×D₅	semidirect
12. C₅×C₁₅₁	C₂×C₃×C₇	semidirect
13. C₃×C₁₅₁	C₇×D₅	semidirect
16. C₁₅₁	C₃×C₇×D₅	semidirect
17. C₃×C₅×C₇	D₁₅₁	semidirect
20. C₅×C₇	C₃×D₁₅₁	semidirect
22. C₃×C₇	D₇₅₅	direct (N × H)
23. C₃×C₅	C₇×D₁₅₁	semidirect
26. C₇	C₃×D₇₅₅	direct (N × H)
28. C₅	C₃×C₇×D₁₅₁	semidirect
29. C₃	C₇×D₇₅₅	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
C₇×D₇₅₅	3
C₃×C₇×D₁₅₁	5
C₃×D₇₅₅	7
C₃×C₇×D₅	151

Subgroups — C3×C7×D755 #44540246

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₇×D₇₅₅ #44540246