Subgroups — C₅×C₂₉×D₁₁₁ #44565718

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	C₅×C₂₉×D₃₇	—	3	1	no	maximal, Hall
3	C₂₉×D₁₁₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₅×C₂₉×C₃₇	D₃	1	1	yes	characteristic, complemented, Hall
5	C₃×C₂₉×C₃₇	C₂×C₅	1	1	yes	characteristic, complemented, Hall
6	C₂₉×D₃₇	—	3	1	no	Hall
7	C₅×D₁₁₁	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂₉×C₃₇	C₅×D₃	1	1	yes	characteristic, complemented, Hall
9	C₅×D₃×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	C₅×D₃₇	—	3	1	no	Hall
13	C₂×C₅×C₂₉	—	111	1	no	Hall
14	D₁₁₁	C₅×C₂₉	1	1	yes	characteristic, direct product factor, Hall
15	C₅×C₃₇	D₃×C₂₉	1	1	yes	characteristic, complemented, Hall
16	D₃×C₂₉	—	37	1	no	Hall
17	C₅×C₂₉	D₁₁₁	1	1	yes	characteristic, direct product factor, Hall
18	C₃×C₃₇	C₂×C₅×C₂₉	1	1	yes	characteristic, complemented, Hall
19	C₃×C₂₉	C₅×D₃₇	1	1	yes	characteristic, complemented, Hall
20	D₃₇	—	3	1	no	Hall
21	C₂×C₂₉	—	111	1	no	Hall
22	C₃₇	C₅×D₃×C₂₉	1	1	yes	characteristic, complemented, Sylow
23	C₅×D₃	—	37	1	no	Hall
24	C₂₉	C₅×D₁₁₁	1	1	yes	characteristic, direct product factor, Sylow
25	C₃×C₅	C₂₉×D₃₇	1	1	yes	characteristic, complemented, Hall
26	C₂×C₅	—	111	1	no	Hall
27	D₃	—	37	1	no	Hall
28	C₅	C₂₉×D₁₁₁	1	1	yes	characteristic, direct product factor, Sylow
29	C₃	C₅×C₂₉×D₃₇	1	1	yes	characteristic, complemented, Sylow
30	C₂	—	111	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅×C₂₉	D₁₁₁
commutator, cosocle, hypocenter	C₃×C₃₇	C₂×C₅×C₂₉
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₂₉×C₃₇	C₂
LCS	G ▷ C₃×C₃₇
UCS	C₁ ◁ C₅×C₂₉

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×C₂₉×C₃₇	C₂	semidirect
3. C₂₉×D₁₁₁	C₅	direct (N × H)
4. C₅×C₂₉×C₃₇	D₃	semidirect
5. C₃×C₂₉×C₃₇	C₂×C₅	semidirect
7. C₅×D₁₁₁	C₂₉	direct (N × H)
8. C₂₉×C₃₇	C₅×D₃	semidirect
10. C₃×C₅×C₃₇	C₂×C₂₉	semidirect
11. C₃×C₅×C₂₉	D₃₇	semidirect
14. D₁₁₁	C₅×C₂₉	direct (N × H)
15. C₅×C₃₇	D₃×C₂₉	semidirect
17. C₅×C₂₉	D₁₁₁	direct (N × H)
18. C₃×C₃₇	C₂×C₅×C₂₉	semidirect
19. C₃×C₂₉	C₅×D₃₇	semidirect
22. C₃₇	C₅×D₃×C₂₉	semidirect
24. C₂₉	C₅×D₁₁₁	direct (N × H)
25. C₃×C₅	C₂₉×D₃₇	semidirect
28. C₅	C₂₉×D₁₁₁	direct (N × H)
29. C₃	C₅×C₂₉×D₃₇	semidirect

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
C₅×C₂₉×D₃₇	3
C₂₉×D₁₁₁	5
C₅×D₁₁₁	29
C₅×D₃×C₂₉	37

Subgroups — C5×C29×D111 #44565718

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₂₉×D₁₁₁ #44565718