Subgroups — C₃×C₃₁×D₈₅ #30629029

Order 15810.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₁₇×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃₁×D₈₅	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₃₁×D₁₇	—	5	1	no	maximal, Hall
4	C₅×C₁₇×C₃₁	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	C₃×C₁₇×C₃₁	D₅	1	1	yes	characteristic, complemented, Hall
6	C₃₁×D₁₇	—	5	1	no	Hall
7	C₃×D₅×C₃₁	—	17	1	no	maximal, Hall
8	C₁₇×C₃₁	C₃×D₅	1	1	yes	characteristic, complemented, Hall
9	C₃×D₈₅	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₃×C₅×C₃₁	D₁₇	1	1	yes	characteristic, complemented, Hall
11	D₅×C₃₁	—	17	1	no	Hall
12	C₃×C₅×C₁₇	C₂×C₃₁	1	1	yes	characteristic, complemented, Hall
13	C₂×C₃×C₃₁	—	85	1	no	Hall
14	D₈₅	C₃×C₃₁	1	1	yes	characteristic, direct product factor, Hall
15	C₅×C₃₁	C₃×D₁₇	1	1	yes	characteristic, complemented, Hall
16	C₃×D₁₇	—	5	1	no	Hall
17	C₃×C₃₁	D₈₅	1	1	yes	characteristic, direct product factor, Hall
18	C₅×C₁₇	C₂×C₃×C₃₁	1	1	yes	characteristic, complemented, Hall
19	C₂×C₃₁	—	85	1	no	Hall
20	C₃×C₁₇	D₅×C₃₁	1	1	yes	characteristic, complemented, Hall
21	D₁₇	—	5	1	no	Hall
22	C₃₁	C₃×D₈₅	1	1	yes	characteristic, direct product factor, Sylow
23	C₃×D₅	—	17	1	no	Hall
24	C₁₇	C₃×D₅×C₃₁	1	1	yes	characteristic, complemented, Sylow
25	C₃×C₅	C₃₁×D₁₇	1	1	yes	characteristic, complemented, Hall
26	D₅	—	17	1	no	Hall
27	C₂×C₃	—	85	1	no	Hall
28	C₅	C₃×C₃₁×D₁₇	1	1	yes	characteristic, complemented, Sylow
29	C₃	C₃₁×D₈₅	1	1	yes	characteristic, direct product factor, Sylow
30	C₂	—	85	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₃₁	D₈₅
commutator, cosocle, hypocenter	C₅×C₁₇	C₂×C₃×C₃₁
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₁₇×C₃₁	C₂
LCS	G ▷ C₅×C₁₇
UCS	C₁ ◁ C₃×C₃₁

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×C₁₇×C₃₁	C₂	semidirect
2. C₃₁×D₈₅	C₃	direct (N × H)
4. C₅×C₁₇×C₃₁	C₂×C₃	semidirect
5. C₃×C₁₇×C₃₁	D₅	semidirect
8. C₁₇×C₃₁	C₃×D₅	semidirect
9. C₃×D₈₅	C₃₁	direct (N × H)
10. C₃×C₅×C₃₁	D₁₇	semidirect
12. C₃×C₅×C₁₇	C₂×C₃₁	semidirect
14. D₈₅	C₃×C₃₁	direct (N × H)
15. C₅×C₃₁	C₃×D₁₇	semidirect
17. C₃×C₃₁	D₈₅	direct (N × H)
18. C₅×C₁₇	C₂×C₃×C₃₁	semidirect
20. C₃×C₁₇	D₅×C₃₁	semidirect
22. C₃₁	C₃×D₈₅	direct (N × H)
24. C₁₇	C₃×D₅×C₃₁	semidirect
25. C₃×C₅	C₃₁×D₁₇	semidirect
28. C₅	C₃×C₃₁×D₁₇	semidirect
29. C₃	C₃₁×D₈₅	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×C₁₇×C₃₁	2
C₃₁×D₈₅	3
C₃×C₃₁×D₁₇	5
C₃×D₅×C₃₁	17
C₃×D₈₅	31

Subgroups — C3×C31×D85 #30629029

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₃₁×D₈₅ #30629029