Subgroups — C₃×C₂₉×D₁₈₅ #44565714

Order 32190.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₂₉×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₂₉×D₁₈₅	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₂₉×D₃₇	—	5	1	no	maximal, Hall
4	C₅×C₂₉×C₃₇	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	C₃×C₂₉×C₃₇	D₅	1	1	yes	characteristic, complemented, Hall
6	C₂₉×D₃₇	—	5	1	no	Hall
7	C₃×D₁₈₅	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂₉×C₃₇	C₃×D₅	1	1	yes	characteristic, complemented, Hall
9	C₃×D₅×C₂₉	—	37	1	no	maximal, Hall
10	C₃×C₅×C₃₇	C₂×C₂₉	1	1	yes	characteristic, complemented, Hall
11	C₃×C₅×C₂₉	D₃₇	1	1	yes	characteristic, complemented, Hall
12	D₁₈₅	C₃×C₂₉	1	1	yes	characteristic, direct product factor, Hall
13	D₅×C₂₉	—	37	1	no	Hall
14	C₃×D₃₇	—	5	1	no	Hall
15	C₅×C₃₇	C₂×C₃×C₂₉	1	1	yes	characteristic, complemented, Hall
16	C₂×C₃×C₂₉	—	185	1	no	Hall
17	C₅×C₂₉	C₃×D₃₇	1	1	yes	characteristic, complemented, Hall
18	C₃×C₃₇	D₅×C₂₉	1	1	yes	characteristic, complemented, Hall
19	C₃×C₂₉	D₁₈₅	1	1	yes	characteristic, direct product factor, Hall
20	D₃₇	—	5	1	no	Hall
21	C₂×C₂₉	—	185	1	no	Hall
22	C₃₇	C₃×D₅×C₂₉	1	1	yes	characteristic, complemented, Sylow
23	C₃×D₅	—	37	1	no	Hall
24	C₂₉	C₃×D₁₈₅	1	1	yes	characteristic, direct product factor, Sylow
25	C₃×C₅	C₂₉×D₃₇	1	1	yes	characteristic, complemented, Hall
26	D₅	—	37	1	no	Hall
27	C₂×C₃	—	185	1	no	Hall
28	C₅	C₃×C₂₉×D₃₇	1	1	yes	characteristic, complemented, Sylow
29	C₃	C₂₉×D₁₈₅	1	1	yes	characteristic, direct product factor, Sylow
30	C₂	—	185	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₂₉	D₁₈₅
commutator, cosocle, hypocenter	C₅×C₃₇	C₂×C₃×C₂₉
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₂₉×C₃₇	C₂
LCS	G ▷ C₅×C₃₇
UCS	C₁ ◁ C₃×C₂₉

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×C₂₉×C₃₇	C₂	semidirect
2. C₂₉×D₁₈₅	C₃	direct (N × H)
4. C₅×C₂₉×C₃₇	C₂×C₃	semidirect
5. C₃×C₂₉×C₃₇	D₅	semidirect
7. C₃×D₁₈₅	C₂₉	direct (N × H)
8. C₂₉×C₃₇	C₃×D₅	semidirect
10. C₃×C₅×C₃₇	C₂×C₂₉	semidirect
11. C₃×C₅×C₂₉	D₃₇	semidirect
12. D₁₈₅	C₃×C₂₉	direct (N × H)
15. C₅×C₃₇	C₂×C₃×C₂₉	semidirect
17. C₅×C₂₉	C₃×D₃₇	semidirect
18. C₃×C₃₇	D₅×C₂₉	semidirect
19. C₃×C₂₉	D₁₈₅	direct (N × H)
22. C₃₇	C₃×D₅×C₂₉	semidirect
24. C₂₉	C₃×D₁₈₅	direct (N × H)
25. C₃×C₅	C₂₉×D₃₇	semidirect
28. C₅	C₃×C₂₉×D₃₇	semidirect
29. C₃	C₂₉×D₁₈₅	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×C₂₉×C₃₇	2
C₂₉×D₁₈₅	3
C₃×C₂₉×D₃₇	5
C₃×D₁₈₅	29
C₃×D₅×C₂₉	37

Subgroups — C3×C29×D185 #44565714

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₂₉×D₁₈₅ #44565714