Subgroups — C₃×D₅×C₂₉×C₃₇ #44565713

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	D₅×C₂₉×C₃₇	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₂×C₃×C₂₉×C₃₇	—	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, direct product factor, Hall
6	C₂×C₂₉×C₃₇	—	5	1	no	Hall
7	C₃×D₅×C₃₇	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂₉×C₃₇	C₃×D₅	1	1	yes	characteristic, direct product factor, Hall
9	C₃×D₅×C₂₉	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₃×C₅×C₃₇	C₂×C₂₉	1	1	yes	characteristic, complemented, Hall
11	C₃×C₅×C₂₉	C₂×C₃₇	1	1	yes	characteristic, complemented, Hall
12	D₅×C₃₇	C₃×C₂₉	1	1	yes	characteristic, direct product factor, Hall
13	D₅×C₂₉	C₃×C₃₇	1	1	yes	characteristic, direct product factor, Hall
14	C₂×C₃×C₃₇	—	5	1	no	Hall
15	C₅×C₃₇	C₂×C₃×C₂₉	1	1	yes	characteristic, complemented, Hall
16	C₂×C₃×C₂₉	—	5	1	no	Hall
17	C₅×C₂₉	C₂×C₃×C₃₇	1	1	yes	characteristic, complemented, Hall
18	C₃×C₃₇	D₅×C₂₉	1	1	yes	characteristic, direct product factor, Hall
19	C₃×C₂₉	D₅×C₃₇	1	1	yes	characteristic, direct product factor, Hall
20	C₂×C₃₇	—	5	1	no	Hall
21	C₂×C₂₉	—	5	1	no	Hall
22	C₃₇	C₃×D₅×C₂₉	1	1	yes	characteristic, direct product factor, Sylow
23	C₃×D₅	C₂₉×C₃₇	1	1	yes	characteristic, direct product factor, Hall
24	C₂₉	C₃×D₅×C₃₇	1	1	yes	characteristic, direct product factor, Sylow
25	C₃×C₅	C₂×C₂₉×C₃₇	1	1	yes	characteristic, complemented, Hall
26	D₅	C₃×C₂₉×C₃₇	1	1	yes	characteristic, direct product factor, Hall
27	C₂×C₃	—	5	1	no	Hall
28	C₅	C₂×C₃×C₂₉×C₃₇	1	1	yes	characteristic, complemented, Sylow
29	C₃	D₅×C₂₉×C₃₇	1	1	yes	characteristic, direct product factor, Sylow
30	C₂	—	5	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₂₉×C₃₇	D₅
commutator, cosocle, hypocenter	C₅	C₂×C₃×C₂₉×C₃₇
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₂₉×C₃₇	C₂
LCS	G ▷ C₅
UCS	C₁ ◁ C₃×C₂₉×C₃₇

Complements

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

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

Subgroups — C3×D5×C29×C37 #44565713

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₅×C₂₉×C₃₇ #44565713