Subgroups — C₃×D₅×C₁₇×C₆₁ #44527435

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	D₅×C₁₇×C₆₁	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₂×C₃×C₁₇×C₆₁	—	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, direct product factor, Hall
6	C₂×C₁₇×C₆₁	—	5	1	no	Hall
7	C₃×D₅×C₆₁	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₁₇×C₆₁	C₃×D₅	1	1	yes	characteristic, direct product factor, Hall
9	C₃×C₅×C₆₁	C₂×C₁₇	1	1	yes	characteristic, complemented, Hall
10	D₅×C₆₁	C₃×C₁₇	1	1	yes	characteristic, direct product factor, Hall
11	C₃×D₅×C₁₇	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₂×C₃×C₆₁	—	5	1	no	Hall
13	C₅×C₆₁	C₂×C₃×C₁₇	1	1	yes	characteristic, complemented, Hall
14	C₃×C₅×C₁₇	C₂×C₆₁	1	1	yes	characteristic, complemented, Hall
15	C₃×C₆₁	D₅×C₁₇	1	1	yes	characteristic, direct product factor, Hall
16	D₅×C₁₇	C₃×C₆₁	1	1	yes	characteristic, direct product factor, Hall
17	C₂×C₆₁	—	5	1	no	Hall
18	C₂×C₃×C₁₇	—	5	1	no	Hall
19	C₅×C₁₇	C₂×C₃×C₆₁	1	1	yes	characteristic, complemented, Hall
20	C₆₁	C₃×D₅×C₁₇	1	1	yes	characteristic, direct product factor, Sylow
21	C₃×C₁₇	D₅×C₆₁	1	1	yes	characteristic, direct product factor, Hall
22	C₂×C₁₇	—	5	1	no	Hall
23	C₃×D₅	C₁₇×C₆₁	1	1	yes	characteristic, direct product factor, Hall
24	C₁₇	C₃×D₅×C₆₁	1	1	yes	characteristic, direct product factor, Sylow
25	C₃×C₅	C₂×C₁₇×C₆₁	1	1	yes	characteristic, complemented, Hall
26	D₅	C₃×C₁₇×C₆₁	1	1	yes	characteristic, direct product factor, Hall
27	C₂×C₃	—	5	1	no	Hall
28	C₅	C₂×C₃×C₁₇×C₆₁	1	1	yes	characteristic, complemented, Sylow
29	C₃	D₅×C₁₇×C₆₁	1	1	yes	characteristic, direct product factor, Sylow
30	C₂	—	5	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₁₇×C₆₁	D₅
commutator, cosocle, hypocenter	C₅	C₂×C₃×C₁₇×C₆₁
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₁₇×C₆₁	C₂
LCS	G ▷ C₅
UCS	C₁ ◁ C₃×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
2. D₅×C₁₇×C₆₁	C₃	direct (N × H)
4. C₅×C₁₇×C₆₁	C₂×C₃	semidirect
5. C₃×C₁₇×C₆₁	D₅	direct (N × H)
7. C₃×D₅×C₆₁	C₁₇	direct (N × H)
8. C₁₇×C₆₁	C₃×D₅	direct (N × H)
9. C₃×C₅×C₆₁	C₂×C₁₇	semidirect
10. D₅×C₆₁	C₃×C₁₇	direct (N × H)
11. C₃×D₅×C₁₇	C₆₁	direct (N × H)
13. C₅×C₆₁	C₂×C₃×C₁₇	semidirect
14. C₃×C₅×C₁₇	C₂×C₆₁	semidirect
15. C₃×C₆₁	D₅×C₁₇	direct (N × H)
16. D₅×C₁₇	C₃×C₆₁	direct (N × H)
19. C₅×C₁₇	C₂×C₃×C₆₁	semidirect
20. C₆₁	C₃×D₅×C₁₇	direct (N × H)
21. C₃×C₁₇	D₅×C₆₁	direct (N × H)
23. C₃×D₅	C₁₇×C₆₁	direct (N × H)
24. C₁₇	C₃×D₅×C₆₁	direct (N × H)
25. C₃×C₅	C₂×C₁₇×C₆₁	semidirect
26. D₅	C₃×C₁₇×C₆₁	direct (N × H)
28. C₅	C₂×C₃×C₁₇×C₆₁	semidirect
29. C₃	D₅×C₁₇×C₆₁	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
D₅×C₁₇×C₆₁	3
C₂×C₃×C₁₇×C₆₁	5
C₃×D₅×C₆₁	17
C₃×D₅×C₁₇	61

Subgroups — C3×D5×C17×C61 #44527435

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₅×C₁₇×C₆₁ #44527435