Subgroups — C₃×C₆₁×D₉₅ #46851908

Order 34770.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₁₉×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₆₁×D₉₅	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×D₁₉×C₆₁	—	5	1	no	maximal, Hall
4	C₅×C₁₉×C₆₁	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	C₃×C₁₉×C₆₁	D₅	1	1	yes	characteristic, complemented, Hall
6	D₁₉×C₆₁	—	5	1	no	Hall
7	C₃×D₅×C₆₁	—	19	1	no	maximal, Hall
8	C₁₉×C₆₁	C₃×D₅	1	1	yes	characteristic, complemented, Hall
9	C₃×C₅×C₆₁	D₁₉	1	1	yes	characteristic, complemented, Hall
10	D₅×C₆₁	—	19	1	no	Hall
11	C₃×D₉₅	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₂×C₃×C₆₁	—	95	1	no	Hall
13	C₅×C₆₁	C₃×D₁₉	1	1	yes	characteristic, complemented, Hall
14	C₃×C₅×C₁₉	C₂×C₆₁	1	1	yes	characteristic, complemented, Hall
15	D₉₅	C₃×C₆₁	1	1	yes	characteristic, direct product factor, Hall
16	C₃×C₆₁	D₉₅	1	1	yes	characteristic, direct product factor, Hall
17	C₂×C₆₁	—	95	1	no	Hall
18	C₃×D₁₉	—	5	1	no	Hall
19	C₅×C₁₉	C₂×C₃×C₆₁	1	1	yes	characteristic, complemented, Hall
20	C₆₁	C₃×D₉₅	1	1	yes	characteristic, direct product factor, Sylow
21	C₃×C₁₉	D₅×C₆₁	1	1	yes	characteristic, complemented, Hall
22	D₁₉	—	5	1	no	Hall
23	C₃×D₅	—	19	1	no	Hall
24	C₁₉	C₃×D₅×C₆₁	1	1	yes	characteristic, complemented, Sylow
25	C₃×C₅	D₁₉×C₆₁	1	1	yes	characteristic, complemented, Hall
26	D₅	—	19	1	no	Hall
27	C₂×C₃	—	95	1	no	Hall
28	C₅	C₃×D₁₉×C₆₁	1	1	yes	characteristic, complemented, Sylow
29	C₃	C₆₁×D₉₅	1	1	yes	characteristic, direct product factor, Sylow
30	C₂	—	95	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₆₁	D₉₅
commutator, cosocle, hypocenter	C₅×C₁₉	C₂×C₃×C₆₁
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₁₉×C₆₁	C₂
LCS	G ▷ C₅×C₁₉
UCS	C₁ ◁ C₃×C₆₁

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×C₁₉×C₆₁	C₂	semidirect
2. C₆₁×D₉₅	C₃	direct (N × H)
4. C₅×C₁₉×C₆₁	C₂×C₃	semidirect
5. C₃×C₁₉×C₆₁	D₅	semidirect
8. C₁₉×C₆₁	C₃×D₅	semidirect
9. C₃×C₅×C₆₁	D₁₉	semidirect
11. C₃×D₉₅	C₆₁	direct (N × H)
13. C₅×C₆₁	C₃×D₁₉	semidirect
14. C₃×C₅×C₁₉	C₂×C₆₁	semidirect
15. D₉₅	C₃×C₆₁	direct (N × H)
16. C₃×C₆₁	D₉₅	direct (N × H)
19. C₅×C₁₉	C₂×C₃×C₆₁	semidirect
20. C₆₁	C₃×D₉₅	direct (N × H)
21. C₃×C₁₉	D₅×C₆₁	semidirect
24. C₁₉	C₃×D₅×C₆₁	semidirect
25. C₃×C₅	D₁₉×C₆₁	semidirect
28. C₅	C₃×D₁₉×C₆₁	semidirect
29. C₃	C₆₁×D₉₅	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×C₁₉×C₆₁	2
C₆₁×D₉₅	3
C₃×D₁₉×C₆₁	5
C₃×D₅×C₆₁	19
C₃×D₉₅	61

Subgroups — C3×C61×D95 #46851908

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₆₁×D₉₅ #46851908