Subgroups — C₃×C₅×D₁₇×C₃₇ #34038263

Order 18870.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₁₇×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×D₁₇×C₃₇	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×D₁₇×C₃₇	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₅×C₁₇×C₃₇	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	C₃×C₁₇×C₃₇	C₂×C₅	1	1	yes	characteristic, complemented, Hall
6	D₁₇×C₃₇	C₃×C₅	1	1	yes	characteristic, direct product factor, Hall
7	C₂×C₃×C₅×C₃₇	—	17	1	no	maximal, Hall
8	C₁₇×C₃₇	C₂×C₃×C₅	1	1	yes	characteristic, complemented, Hall
9	C₃×C₅×C₃₇	D₁₇	1	1	yes	characteristic, direct product factor, Hall
10	C₃×C₅×D₁₇	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂×C₅×C₃₇	—	17	1	no	Hall
12	C₃×C₅×C₁₇	C₂×C₃₇	1	1	yes	characteristic, complemented, Hall
13	C₂×C₃×C₃₇	—	17	1	no	Hall
14	C₅×C₃₇	C₃×D₁₇	1	1	yes	characteristic, direct product factor, Hall
15	C₅×D₁₇	C₃×C₃₇	1	1	yes	characteristic, direct product factor, Hall
16	C₃×C₃₇	C₅×D₁₇	1	1	yes	characteristic, direct product factor, Hall
17	C₃×D₁₇	C₅×C₃₇	1	1	yes	characteristic, direct product factor, Hall
18	C₅×C₁₇	C₂×C₃×C₃₇	1	1	yes	characteristic, complemented, Hall
19	C₂×C₃₇	—	17	1	no	Hall
20	C₃×C₁₇	C₂×C₅×C₃₇	1	1	yes	characteristic, complemented, Hall
21	C₃₇	C₃×C₅×D₁₇	1	1	yes	characteristic, direct product factor, Sylow
22	D₁₇	C₃×C₅×C₃₇	1	1	yes	characteristic, direct product factor, Hall
23	C₂×C₃×C₅	—	17	1	no	Hall
24	C₁₇	C₂×C₃×C₅×C₃₇	1	1	yes	characteristic, complemented, Sylow
25	C₃×C₅	D₁₇×C₃₇	1	1	yes	characteristic, direct product factor, Hall
26	C₂×C₅	—	17	1	no	Hall
27	C₂×C₃	—	17	1	no	Hall
28	C₅	C₃×D₁₇×C₃₇	1	1	yes	characteristic, direct product factor, Sylow
29	C₃	C₅×D₁₇×C₃₇	1	1	yes	characteristic, direct product factor, Sylow
30	C₂	—	17	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₅×C₃₇	D₁₇
commutator, cosocle, hypocenter	C₁₇	C₂×C₃×C₅×C₃₇
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₁₇×C₃₇	C₂
LCS	G ▷ C₁₇
UCS	C₁ ◁ C₃×C₅×C₃₇

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×C₁₇×C₃₇	C₂	semidirect
2. C₅×D₁₇×C₃₇	C₃	direct (N × H)
3. C₃×D₁₇×C₃₇	C₅	direct (N × H)
4. C₅×C₁₇×C₃₇	C₂×C₃	semidirect
5. C₃×C₁₇×C₃₇	C₂×C₅	semidirect
6. D₁₇×C₃₇	C₃×C₅	direct (N × H)
8. C₁₇×C₃₇	C₂×C₃×C₅	semidirect
9. C₃×C₅×C₃₇	D₁₇	direct (N × H)
10. C₃×C₅×D₁₇	C₃₇	direct (N × H)
12. C₃×C₅×C₁₇	C₂×C₃₇	semidirect
14. C₅×C₃₇	C₃×D₁₇	direct (N × H)
15. C₅×D₁₇	C₃×C₃₇	direct (N × H)
16. C₃×C₃₇	C₅×D₁₇	direct (N × H)
17. C₃×D₁₇	C₅×C₃₇	direct (N × H)
18. C₅×C₁₇	C₂×C₃×C₃₇	semidirect
20. C₃×C₁₇	C₂×C₅×C₃₇	semidirect
21. C₃₇	C₃×C₅×D₁₇	direct (N × H)
22. D₁₇	C₃×C₅×C₃₇	direct (N × H)
24. C₁₇	C₂×C₃×C₅×C₃₇	semidirect
25. C₃×C₅	D₁₇×C₃₇	direct (N × H)
28. C₅	C₃×D₁₇×C₃₇	direct (N × H)
29. C₃	C₅×D₁₇×C₃₇	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×C₃₇	2
C₅×D₁₇×C₃₇	3
C₃×D₁₇×C₃₇	5
C₂×C₃×C₅×C₃₇	17
C₃×C₅×D₁₇	37

Subgroups — C3×C5×D17×C37 #34038263

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×D₁₇×C₃₇ #34038263