Subgroups — C₅×C₁₇×D₁₁₁ #34038270

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×C₁₇×D₃₇	—	3	1	no	maximal, Hall
3	C₁₇×D₁₁₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₅×C₁₇×C₃₇	D₃	1	1	yes	characteristic, complemented, Hall
5	C₃×C₁₇×C₃₇	C₂×C₅	1	1	yes	characteristic, complemented, Hall
6	C₁₇×D₃₇	—	3	1	no	Hall
7	C₅×D₁₁₁	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₁₇×C₃₇	C₅×D₃	1	1	yes	characteristic, complemented, Hall
9	C₃×C₅×C₃₇	C₂×C₁₇	1	1	yes	characteristic, complemented, Hall
10	C₅×D₃×C₁₇	—	37	1	no	maximal, Hall
11	C₅×D₃₇	—	3	1	no	Hall
12	C₃×C₅×C₁₇	D₃₇	1	1	yes	characteristic, complemented, Hall
13	D₁₁₁	C₅×C₁₇	1	1	yes	characteristic, direct product factor, Hall
14	C₅×C₃₇	D₃×C₁₇	1	1	yes	characteristic, complemented, Hall
15	C₂×C₅×C₁₇	—	111	1	no	Hall
16	C₃×C₃₇	C₂×C₅×C₁₇	1	1	yes	characteristic, complemented, Hall
17	D₃×C₁₇	—	37	1	no	Hall
18	C₅×C₁₇	D₁₁₁	1	1	yes	characteristic, direct product factor, Hall
19	D₃₇	—	3	1	no	Hall
20	C₃×C₁₇	C₅×D₃₇	1	1	yes	characteristic, complemented, Hall
21	C₃₇	C₅×D₃×C₁₇	1	1	yes	characteristic, complemented, Sylow
22	C₂×C₁₇	—	111	1	no	Hall
23	C₅×D₃	—	37	1	no	Hall
24	C₁₇	C₅×D₁₁₁	1	1	yes	characteristic, direct product factor, Sylow
25	C₃×C₅	C₁₇×D₃₇	1	1	yes	characteristic, complemented, Hall
26	C₂×C₅	—	111	1	no	Hall
27	D₃	—	37	1	no	Hall
28	C₅	C₁₇×D₁₁₁	1	1	yes	characteristic, direct product factor, Sylow
29	C₃	C₅×C₁₇×D₃₇	1	1	yes	characteristic, complemented, Sylow
30	C₂	—	111	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅×C₁₇	D₁₁₁
commutator, cosocle, hypocenter	C₃×C₃₇	C₂×C₅×C₁₇
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₁₇×C₃₇	C₂
LCS	G ▷ C₃×C₃₇
UCS	C₁ ◁ C₅×C₁₇

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×C₁₇×C₃₇	C₂	semidirect
3. C₁₇×D₁₁₁	C₅	direct (N × H)
4. C₅×C₁₇×C₃₇	D₃	semidirect
5. C₃×C₁₇×C₃₇	C₂×C₅	semidirect
7. C₅×D₁₁₁	C₁₇	direct (N × H)
8. C₁₇×C₃₇	C₅×D₃	semidirect
9. C₃×C₅×C₃₇	C₂×C₁₇	semidirect
12. C₃×C₅×C₁₇	D₃₇	semidirect
13. D₁₁₁	C₅×C₁₇	direct (N × H)
14. C₅×C₃₇	D₃×C₁₇	semidirect
16. C₃×C₃₇	C₂×C₅×C₁₇	semidirect
18. C₅×C₁₇	D₁₁₁	direct (N × H)
20. C₃×C₁₇	C₅×D₃₇	semidirect
21. C₃₇	C₅×D₃×C₁₇	semidirect
24. C₁₇	C₅×D₁₁₁	direct (N × H)
25. C₃×C₅	C₁₇×D₃₇	semidirect
28. C₅	C₁₇×D₁₁₁	direct (N × H)
29. C₃	C₅×C₁₇×D₃₇	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×C₃₇	2
C₅×C₁₇×D₃₇	3
C₁₇×D₁₁₁	5
C₅×D₁₁₁	17
C₅×D₃×C₁₇	37

Subgroups — C5×C17×D111 #34038270

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₁₇×D₁₁₁ #34038270