Subgroups — C₃×D₅₁₈₅ #44527438

Order 31110.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₁₇×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₅₁₈₅	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×D₁₀₃₇	—	5	1	no	maximal, Hall
4	C₅×C₁₇×C₆₁	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	C₃×C₁₇×C₆₁	D₅	1	1	yes	characteristic, complemented, Hall
6	D₁₀₃₇	—	5	1	no	Hall
7	C₃×D₃₀₅	—	17	1	no	maximal, Hall
8	C₁₇×C₆₁	C₃×D₅	1	1	yes	characteristic, complemented, Hall
9	C₃×C₅×C₆₁	D₁₇	1	1	yes	characteristic, complemented, Hall
10	D₃₀₅	—	17	1	no	Hall
11	C₃×D₈₅	—	61	1	no	maximal, Hall
12	C₃×D₆₁	—	85	1	no	Hall
13	C₅×C₆₁	C₃×D₁₇	1	1	yes	characteristic, complemented, Hall
14	C₃×C₅×C₁₇	D₆₁	1	1	yes	characteristic, complemented, Hall
15	C₃×C₆₁	D₈₅	1	1	yes	characteristic, complemented, Hall
16	D₈₅	—	61	1	no	Hall
17	D₆₁	—	85	1	no	Hall
18	C₃×D₁₇	—	305	1	no	Hall
19	C₅×C₁₇	C₃×D₆₁	1	1	yes	characteristic, complemented, Hall
20	C₆₁	C₃×D₈₅	1	1	yes	characteristic, complemented, Sylow
21	C₃×C₁₇	D₃₀₅	1	1	yes	characteristic, complemented, Hall
22	D₁₇	—	305	1	no	Hall
23	C₃×D₅	—	1037	1	no	Hall
24	C₁₇	C₃×D₃₀₅	1	1	yes	characteristic, complemented, Sylow
25	C₃×C₅	D₁₀₃₇	1	1	yes	characteristic, complemented, Hall
26	D₅	—	1037	1	no	Hall
27	C₂×C₃	—	5185	1	no	Hall
28	C₅	C₃×D₁₀₃₇	1	1	yes	characteristic, complemented, Sylow
29	C₃	D₅₁₈₅	1	1	yes	characteristic, direct product factor, Sylow
30	C₂	—	5185	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃	D₅₁₈₅
commutator, cosocle, hypocenter	C₅×C₁₇×C₆₁	C₂×C₃
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₁₇×C₆₁	C₂
LCS	G ▷ C₅×C₁₇×C₆₁
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×C₁₇×C₆₁	C₂	semidirect
2. D₅₁₈₅	C₃	direct (N × H)
4. C₅×C₁₇×C₆₁	C₂×C₃	semidirect
5. C₃×C₁₇×C₆₁	D₅	semidirect
8. C₁₇×C₆₁	C₃×D₅	semidirect
9. C₃×C₅×C₆₁	D₁₇	semidirect
13. C₅×C₆₁	C₃×D₁₇	semidirect
14. C₃×C₅×C₁₇	D₆₁	semidirect
15. C₃×C₆₁	D₈₅	semidirect
19. C₅×C₁₇	C₃×D₆₁	semidirect
20. C₆₁	C₃×D₈₅	semidirect
21. C₃×C₁₇	D₃₀₅	semidirect
24. C₁₇	C₃×D₃₀₅	semidirect
25. C₃×C₅	D₁₀₃₇	semidirect
28. C₅	C₃×D₁₀₃₇	semidirect
29. C₃	D₅₁₈₅	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×C₆₁	2
D₅₁₈₅	3
C₃×D₁₀₃₇	5
C₃×D₃₀₅	17
C₃×D₈₅	61

Subgroups — C3×D5185 #44527438

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₅₁₈₅ #44527438