Subgroups — C₃×C₁₇×D₉₁ #22604635

Order 9282.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×C₁₃×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₇×D₉₁	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₇×C₁₃×C₁₇	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₃×C₁₇×D₁₃	—	7	1	no	maximal, Hall
5	C₃×D₇×C₁₇	—	13	1	no	maximal, Hall
6	C₃×C₁₃×C₁₇	D₇	1	1	yes	characteristic, complemented, Hall
7	C₃×D₉₁	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₁₇×D₁₃	—	7	1	no	Hall
9	C₃×C₇×C₁₇	D₁₃	1	1	yes	characteristic, complemented, Hall
10	C₃×C₇×C₁₃	C₂×C₁₇	1	1	yes	characteristic, complemented, Hall
11	D₇×C₁₇	—	13	1	no	Hall
12	C₁₃×C₁₇	C₃×D₇	1	1	yes	characteristic, complemented, Hall
13	D₉₁	C₃×C₁₇	1	1	yes	characteristic, direct product factor, Hall
14	C₇×C₁₇	C₃×D₁₃	1	1	yes	characteristic, complemented, Hall
15	C₂×C₃×C₁₇	—	91	1	no	Hall
16	C₇×C₁₃	C₂×C₃×C₁₇	1	1	yes	characteristic, complemented, Hall
17	C₃×D₁₃	—	7	1	no	Hall
18	C₃×C₁₇	D₉₁	1	1	yes	characteristic, direct product factor, Hall
19	C₃×D₇	—	13	1	no	Hall
20	C₃×C₁₃	D₇×C₁₇	1	1	yes	characteristic, complemented, Hall
21	C₂×C₁₇	—	91	1	no	Hall
22	D₁₃	—	7	1	no	Hall
23	C₃×C₇	C₁₇×D₁₃	1	1	yes	characteristic, complemented, Hall
24	C₁₇	C₃×D₉₁	1	1	yes	characteristic, direct product factor, Sylow
25	D₇	—	13	1	no	Hall
26	C₁₃	C₃×D₇×C₁₇	1	1	yes	characteristic, complemented, Sylow
27	C₇	C₃×C₁₇×D₁₃	1	1	yes	characteristic, complemented, Sylow
28	C₂×C₃	—	91	1	no	Hall
29	C₃	C₁₇×D₉₁	1	1	yes	characteristic, direct product factor, Sylow
30	C₂	—	91	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₁₇	D₉₁
commutator, hypocenter	C₇×C₁₃	C₂×C₃×C₁₇
Frattini	C₁	G
Fitting, socle	C₃×C₇×C₁₃×C₁₇	C₂
LCS	G ▷ C₇×C₁₃
UCS	C₁ ◁ C₃×C₁₇

Complements

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

N	H ≅ G/N	type
1. C₃×C₇×C₁₃×C₁₇	C₂	semidirect
2. C₁₇×D₉₁	C₃	direct (N × H)
3. C₇×C₁₃×C₁₇	C₂×C₃	semidirect
6. C₃×C₁₃×C₁₇	D₇	semidirect
7. C₃×D₉₁	C₁₇	direct (N × H)
9. C₃×C₇×C₁₇	D₁₃	semidirect
10. C₃×C₇×C₁₃	C₂×C₁₇	semidirect
12. C₁₃×C₁₇	C₃×D₇	semidirect
13. D₉₁	C₃×C₁₇	direct (N × H)
14. C₇×C₁₇	C₃×D₁₃	semidirect
16. C₇×C₁₃	C₂×C₃×C₁₇	semidirect
18. C₃×C₁₇	D₉₁	direct (N × H)
20. C₃×C₁₃	D₇×C₁₇	semidirect
23. C₃×C₇	C₁₇×D₁₃	semidirect
24. C₁₇	C₃×D₉₁	direct (N × H)
26. C₁₃	C₃×D₇×C₁₇	semidirect
27. C₇	C₃×C₁₇×D₁₃	semidirect
29. C₃	C₁₇×D₉₁	direct (N × H)

Subgroups — C3×C17×D91 #22604635

Conjugacy classes of subgroups

Complements

Subgroups — C₃×C₁₇×D₉₁ #22604635