Subgroups — C₃×C₆₁×D₉₁ #45686553

Order 33306.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×C₁₃×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₆₁×D₉₁	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₇×C₁₃×C₆₁	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₃×D₁₃×C₆₁	—	7	1	no	maximal, Hall
5	C₃×D₇×C₆₁	—	13	1	no	maximal, Hall
6	C₃×C₁₃×C₆₁	D₇	1	1	yes	characteristic, complemented, Hall
7	D₁₃×C₆₁	—	7	1	no	Hall
8	C₃×C₇×C₆₁	D₁₃	1	1	yes	characteristic, complemented, Hall
9	D₇×C₆₁	—	13	1	no	Hall
10	C₁₃×C₆₁	C₃×D₇	1	1	yes	characteristic, complemented, Hall
11	C₃×D₉₁	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₇×C₆₁	C₃×D₁₃	1	1	yes	characteristic, complemented, Hall
13	C₂×C₃×C₆₁	—	91	1	no	Hall
14	C₃×C₇×C₁₃	C₂×C₆₁	1	1	yes	characteristic, complemented, Hall
15	C₃×C₆₁	D₉₁	1	1	yes	characteristic, direct product factor, Hall
16	D₉₁	C₃×C₆₁	1	1	yes	characteristic, direct product factor, Hall
17	C₂×C₆₁	—	91	1	no	Hall
18	C₇×C₁₃	C₂×C₃×C₆₁	1	1	yes	characteristic, complemented, Hall
19	C₃×D₁₃	—	7	1	no	Hall
20	C₆₁	C₃×D₉₁	1	1	yes	characteristic, direct product factor, Sylow
21	C₃×D₇	—	13	1	no	Hall
22	C₃×C₁₃	D₇×C₆₁	1	1	yes	characteristic, complemented, Hall
23	D₁₃	—	7	1	no	Hall
24	C₃×C₇	D₁₃×C₆₁	1	1	yes	characteristic, complemented, Hall
25	D₇	—	13	1	no	Hall
26	C₁₃	C₃×D₇×C₆₁	1	1	yes	characteristic, complemented, Sylow
27	C₇	C₃×D₁₃×C₆₁	1	1	yes	characteristic, complemented, Sylow
28	C₂×C₃	—	91	1	no	Hall
29	C₃	C₆₁×D₉₁	1	1	yes	characteristic, direct product factor, Sylow
30	C₂	—	91	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₆₁	D₉₁
commutator, cosocle, hypocenter	C₇×C₁₃	C₂×C₃×C₆₁
Frattini	C₁	G
Fitting, socle	C₃×C₇×C₁₃×C₆₁	C₂
LCS	G ▷ C₇×C₁₃
UCS	C₁ ◁ C₃×C₆₁

Complements

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

N	H ≅ G/N	type
1. C₃×C₇×C₁₃×C₆₁	C₂	semidirect
2. C₆₁×D₉₁	C₃	direct (N × H)
3. C₇×C₁₃×C₆₁	C₂×C₃	semidirect
6. C₃×C₁₃×C₆₁	D₇	semidirect
8. C₃×C₇×C₆₁	D₁₃	semidirect
10. C₁₃×C₆₁	C₃×D₇	semidirect
11. C₃×D₉₁	C₆₁	direct (N × H)
12. C₇×C₆₁	C₃×D₁₃	semidirect
14. C₃×C₇×C₁₃	C₂×C₆₁	semidirect
15. C₃×C₆₁	D₉₁	direct (N × H)
16. D₉₁	C₃×C₆₁	direct (N × H)
18. C₇×C₁₃	C₂×C₃×C₆₁	semidirect
20. C₆₁	C₃×D₉₁	direct (N × H)
22. C₃×C₁₃	D₇×C₆₁	semidirect
24. C₃×C₇	D₁₃×C₆₁	semidirect
26. C₁₃	C₃×D₇×C₆₁	semidirect
27. C₇	C₃×D₁₃×C₆₁	semidirect
29. C₃	C₆₁×D₉₁	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×C₇×C₁₃×C₆₁	2
C₆₁×D₉₁	3
C₃×D₁₃×C₆₁	7
C₃×D₇×C₆₁	13
C₃×D₉₁	61

Subgroups — C3×C61×D91 #45686553

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₆₁×D₉₁ #45686553