Subgroups — C₃×C₅×D₈₅₁ #38784277

Order 25530.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₂₃×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×D₈₅₁	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×D₈₅₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₅×C₂₃×C₃₇	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	C₃×C₂₃×C₃₇	C₂×C₅	1	1	yes	characteristic, complemented, Hall
6	D₈₅₁	C₃×C₅	1	1	yes	characteristic, direct product factor, Hall
7	C₃×C₅×D₃₇	—	23	1	no	maximal, Hall
8	C₂₃×C₃₇	C₂×C₃×C₅	1	1	yes	characteristic, complemented, Hall
9	C₃×C₅×D₂₃	—	37	1	no	maximal, Hall
10	C₃×C₅×C₃₇	D₂₃	1	1	yes	characteristic, complemented, Hall
11	C₅×D₃₇	—	23	1	no	Hall
12	C₃×C₅×C₂₃	D₃₇	1	1	yes	characteristic, complemented, Hall
13	C₅×D₂₃	—	37	1	no	Hall
14	C₃×D₃₇	—	23	1	no	Hall
15	C₅×C₃₇	C₃×D₂₃	1	1	yes	characteristic, complemented, Hall
16	C₃×D₂₃	—	37	1	no	Hall
17	C₅×C₂₃	C₃×D₃₇	1	1	yes	characteristic, complemented, Hall
18	C₃×C₃₇	C₅×D₂₃	1	1	yes	characteristic, complemented, Hall
19	D₃₇	—	23	1	no	Hall
20	C₃×C₂₃	C₅×D₃₇	1	1	yes	characteristic, complemented, Hall
21	D₂₃	—	37	1	no	Hall
22	C₃₇	C₃×C₅×D₂₃	1	1	yes	characteristic, complemented, Sylow
23	C₂×C₃×C₅	—	851	1	no	Hall
24	C₂₃	C₃×C₅×D₃₇	1	1	yes	characteristic, complemented, Sylow
25	C₃×C₅	D₈₅₁	1	1	yes	characteristic, direct product factor, Hall
26	C₂×C₅	—	851	1	no	Hall
27	C₂×C₃	—	851	1	no	Hall
28	C₅	C₃×D₈₅₁	1	1	yes	characteristic, direct product factor, Sylow
29	C₃	C₅×D₈₅₁	1	1	yes	characteristic, direct product factor, Sylow
30	C₂	—	851	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₅	D₈₅₁
commutator, cosocle, hypocenter	C₂₃×C₃₇	C₂×C₃×C₅
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₂₃×C₃₇	C₂
LCS	G ▷ C₂₃×C₃₇
UCS	C₁ ◁ C₃×C₅

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×C₂₃×C₃₇	C₂	semidirect
2. C₅×D₈₅₁	C₃	direct (N × H)
3. C₃×D₈₅₁	C₅	direct (N × H)
4. C₅×C₂₃×C₃₇	C₂×C₃	semidirect
5. C₃×C₂₃×C₃₇	C₂×C₅	semidirect
6. D₈₅₁	C₃×C₅	direct (N × H)
8. C₂₃×C₃₇	C₂×C₃×C₅	semidirect
10. C₃×C₅×C₃₇	D₂₃	semidirect
12. C₃×C₅×C₂₃	D₃₇	semidirect
15. C₅×C₃₇	C₃×D₂₃	semidirect
17. C₅×C₂₃	C₃×D₃₇	semidirect
18. C₃×C₃₇	C₅×D₂₃	semidirect
20. C₃×C₂₃	C₅×D₃₇	semidirect
22. C₃₇	C₃×C₅×D₂₃	semidirect
24. C₂₃	C₃×C₅×D₃₇	semidirect
25. C₃×C₅	D₈₅₁	direct (N × H)
28. C₅	C₃×D₈₅₁	direct (N × H)
29. C₃	C₅×D₈₅₁	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×C₂₃×C₃₇	2
C₅×D₈₅₁	3
C₃×D₈₅₁	5
C₃×C₅×D₃₇	23
C₃×C₅×D₂₃	37

Subgroups — C3×C5×D851 #38784277

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×D₈₅₁ #38784277