Subgroups — C₅×D₃×C₁₇×C₆₁ #44527439

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	C₂×C₅×C₁₇×C₆₁	—	3	1	no	maximal, Hall
3	D₃×C₁₇×C₆₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₅×C₁₇×C₆₁	D₃	1	1	yes	characteristic, direct product factor, Hall
5	C₃×C₁₇×C₆₁	C₂×C₅	1	1	yes	characteristic, complemented, Hall
6	C₂×C₁₇×C₆₁	—	3	1	no	Hall
7	C₅×D₃×C₆₁	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₁₇×C₆₁	C₅×D₃	1	1	yes	characteristic, direct product factor, Hall
9	C₃×C₅×C₆₁	C₂×C₁₇	1	1	yes	characteristic, complemented, Hall
10	C₂×C₅×C₆₁	—	3	1	no	Hall
11	C₅×D₃×C₁₇	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Hall
12	D₃×C₆₁	C₅×C₁₇	1	1	yes	characteristic, direct product factor, Hall
13	C₅×C₆₁	D₃×C₁₇	1	1	yes	characteristic, direct product factor, Hall
14	C₃×C₅×C₁₇	C₂×C₆₁	1	1	yes	characteristic, complemented, Hall
15	C₃×C₆₁	C₂×C₅×C₁₇	1	1	yes	characteristic, complemented, Hall
16	C₂×C₅×C₁₇	—	3	1	no	Hall
17	C₂×C₆₁	—	3	1	no	Hall
18	D₃×C₁₇	C₅×C₆₁	1	1	yes	characteristic, direct product factor, Hall
19	C₅×C₁₇	D₃×C₆₁	1	1	yes	characteristic, direct product factor, Hall
20	C₆₁	C₅×D₃×C₁₇	1	1	yes	characteristic, direct product factor, Sylow
21	C₃×C₁₇	C₂×C₅×C₆₁	1	1	yes	characteristic, complemented, Hall
22	C₂×C₁₇	—	3	1	no	Hall
23	C₅×D₃	C₁₇×C₆₁	1	1	yes	characteristic, direct product factor, Hall
24	C₁₇	C₅×D₃×C₆₁	1	1	yes	characteristic, direct product factor, Sylow
25	C₃×C₅	C₂×C₁₇×C₆₁	1	1	yes	characteristic, complemented, Hall
26	C₂×C₅	—	3	1	no	Hall
27	D₃	C₅×C₁₇×C₆₁	1	1	yes	characteristic, direct product factor, Hall
28	C₅	D₃×C₁₇×C₆₁	1	1	yes	characteristic, direct product factor, Sylow
29	C₃	C₂×C₅×C₁₇×C₆₁	1	1	yes	characteristic, complemented, Sylow
30	C₂	—	3	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅×C₁₇×C₆₁	D₃
commutator, cosocle, hypocenter	C₃	C₂×C₅×C₁₇×C₆₁
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₁₇×C₆₁	C₂
LCS	G ▷ C₃
UCS	C₁ ◁ C₅×C₁₇×C₆₁

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×C₁₇×C₆₁	C₂	semidirect
3. D₃×C₁₇×C₆₁	C₅	direct (N × H)
4. C₅×C₁₇×C₆₁	D₃	direct (N × H)
5. C₃×C₁₇×C₆₁	C₂×C₅	semidirect
7. C₅×D₃×C₆₁	C₁₇	direct (N × H)
8. C₁₇×C₆₁	C₅×D₃	direct (N × H)
9. C₃×C₅×C₆₁	C₂×C₁₇	semidirect
11. C₅×D₃×C₁₇	C₆₁	direct (N × H)
12. D₃×C₆₁	C₅×C₁₇	direct (N × H)
13. C₅×C₆₁	D₃×C₁₇	direct (N × H)
14. C₃×C₅×C₁₇	C₂×C₆₁	semidirect
15. C₃×C₆₁	C₂×C₅×C₁₇	semidirect
18. D₃×C₁₇	C₅×C₆₁	direct (N × H)
19. C₅×C₁₇	D₃×C₆₁	direct (N × H)
20. C₆₁	C₅×D₃×C₁₇	direct (N × H)
21. C₃×C₁₇	C₂×C₅×C₆₁	semidirect
23. C₅×D₃	C₁₇×C₆₁	direct (N × H)
24. C₁₇	C₅×D₃×C₆₁	direct (N × H)
25. C₃×C₅	C₂×C₁₇×C₆₁	semidirect
27. D₃	C₅×C₁₇×C₆₁	direct (N × H)
28. C₅	D₃×C₁₇×C₆₁	direct (N × H)
29. C₃	C₂×C₅×C₁₇×C₆₁	semidirect

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
C₂×C₅×C₁₇×C₆₁	3
D₃×C₁₇×C₆₁	5
C₅×D₃×C₆₁	17
C₅×D₃×C₁₇	61

Subgroups — C5×D3×C17×C61 #44527439

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₃×C₁₇×C₆₁ #44527439