Subgroups — C₃×C₄₇×D₈₅ #37561789

Order 23970.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₁₇×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₄₇×D₈₅	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×D₁₇×C₄₇	—	5	1	no	maximal, Hall
4	C₅×C₁₇×C₄₇	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	C₃×C₁₇×C₄₇	D₅	1	1	yes	characteristic, complemented, Hall
6	D₁₇×C₄₇	—	5	1	no	Hall
7	C₃×D₅×C₄₇	—	17	1	no	maximal, Hall
8	C₁₇×C₄₇	C₃×D₅	1	1	yes	characteristic, complemented, Hall
9	C₃×C₅×C₄₇	D₁₇	1	1	yes	characteristic, complemented, Hall
10	C₃×D₈₅	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Hall
11	D₅×C₄₇	—	17	1	no	Hall
12	C₂×C₃×C₄₇	—	85	1	no	Hall
13	C₃×C₅×C₁₇	C₂×C₄₇	1	1	yes	characteristic, complemented, Hall
14	C₅×C₄₇	C₃×D₁₇	1	1	yes	characteristic, complemented, Hall
15	D₈₅	C₃×C₄₇	1	1	yes	characteristic, direct product factor, Hall
16	C₃×C₄₇	D₈₅	1	1	yes	characteristic, direct product factor, Hall
17	C₃×D₁₇	—	5	1	no	Hall
18	C₂×C₄₇	—	85	1	no	Hall
19	C₅×C₁₇	C₂×C₃×C₄₇	1	1	yes	characteristic, complemented, Hall
20	C₃×C₁₇	D₅×C₄₇	1	1	yes	characteristic, complemented, Hall
21	C₄₇	C₃×D₈₅	1	1	yes	characteristic, direct product factor, Sylow
22	D₁₇	—	5	1	no	Hall
23	C₃×D₅	—	17	1	no	Hall
24	C₁₇	C₃×D₅×C₄₇	1	1	yes	characteristic, complemented, Sylow
25	C₃×C₅	D₁₇×C₄₇	1	1	yes	characteristic, complemented, Hall
26	D₅	—	17	1	no	Hall
27	C₂×C₃	—	85	1	no	Hall
28	C₅	C₃×D₁₇×C₄₇	1	1	yes	characteristic, complemented, Sylow
29	C₃	C₄₇×D₈₅	1	1	yes	characteristic, direct product factor, Sylow
30	C₂	—	85	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₄₇	D₈₅
commutator, cosocle, hypocenter	C₅×C₁₇	C₂×C₃×C₄₇
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₁₇×C₄₇	C₂
LCS	G ▷ C₅×C₁₇
UCS	C₁ ◁ C₃×C₄₇

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×C₁₇×C₄₇	C₂	semidirect
2. C₄₇×D₈₅	C₃	direct (N × H)
4. C₅×C₁₇×C₄₇	C₂×C₃	semidirect
5. C₃×C₁₇×C₄₇	D₅	semidirect
8. C₁₇×C₄₇	C₃×D₅	semidirect
9. C₃×C₅×C₄₇	D₁₇	semidirect
10. C₃×D₈₅	C₄₇	direct (N × H)
13. C₃×C₅×C₁₇	C₂×C₄₇	semidirect
14. C₅×C₄₇	C₃×D₁₇	semidirect
15. D₈₅	C₃×C₄₇	direct (N × H)
16. C₃×C₄₇	D₈₅	direct (N × H)
19. C₅×C₁₇	C₂×C₃×C₄₇	semidirect
20. C₃×C₁₇	D₅×C₄₇	semidirect
21. C₄₇	C₃×D₈₅	direct (N × H)
24. C₁₇	C₃×D₅×C₄₇	semidirect
25. C₃×C₅	D₁₇×C₄₇	semidirect
28. C₅	C₃×D₁₇×C₄₇	semidirect
29. C₃	C₄₇×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×C₄₇	2
C₄₇×D₈₅	3
C₃×D₁₇×C₄₇	5
C₃×D₅×C₄₇	17
C₃×D₈₅	47

Subgroups — C3×C47×D85 #37561789

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₄₇×D₈₅ #37561789