Subgroups — C₅×C₁₇×D₁₈₅ #44537795

Order 31450.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²×C₁₇×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₇×D₁₈₅	C₅	1	1	yes	maximal, characteristic, direct product factor
3	C₅×C₁₇×D₃₇	—	5	1	no	maximal
4	C₅×C₁₇×C₃₇	—	2	2	no	—
5	C₅×C₁₇×C₃₇	D₅	1	1	yes	characteristic, complemented
6	C₅×C₁₇×C₃₇	C₂×C₅	1	1	yes	characteristic, complemented
7	C₅×D₁₈₅	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₁₇×D₃₇	—	5	1	no	Hall
9	C₅²×C₃₇	C₂×C₁₇	1	1	yes	characteristic, complemented, Hall
10	C₅×D₅×C₁₇	—	37	1	no	maximal, Hall
11	C₁₇×C₃₇	C₅×D₅	1	1	yes	characteristic, complemented, Hall
12	C₅²×C₁₇	D₃₇	1	1	yes	characteristic, complemented, Hall
13	D₁₈₅	C₅×C₁₇	1	1	yes	characteristic, direct product factor
14	C₅×D₃₇	—	5	1	no	—
15	C₅×C₃₇	—	2	2	no	—
16	C₅×C₃₇	D₅×C₁₇	1	1	yes	characteristic, complemented
17	C₅×C₃₇	C₂×C₅×C₁₇	1	1	yes	characteristic, complemented
18	C₂×C₅×C₁₇	—	185	1	no	—
19	D₅×C₁₇	—	37	1	no	—
20	C₅×C₁₇	—	2	2	no	—
21	C₅×C₁₇	C₅×D₃₇	1	1	yes	characteristic, complemented
22	C₅×C₁₇	D₁₈₅	1	1	yes	characteristic, direct product factor
23	D₃₇	—	5	1	no	Hall
24	C₅×D₅	—	37	1	no	Hall
25	C₃₇	C₅×D₅×C₁₇	1	1	yes	characteristic, complemented, Sylow
26	C₂×C₁₇	—	185	1	no	Hall
27	C₅²	C₁₇×D₃₇	1	1	yes	characteristic, complemented, Sylow
28	C₁₇	C₅×D₁₈₅	1	1	yes	characteristic, direct product factor, Sylow
29	C₂×C₅	—	185	1	no	—
30	D₅	—	37	1	no	—
31	C₅	—	2	2	no	—
32	C₅	C₅×C₁₇×D₃₇	1	1	yes	characteristic, complemented
33	C₅	C₁₇×D₁₈₅	1	1	yes	characteristic, direct product factor
34	C₂	—	185	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅×C₁₇	D₁₈₅
commutator, cosocle, hypocenter	C₅×C₃₇	C₂×C₅×C₁₇
Frattini	C₁	G
Fitting, socle	C₅²×C₁₇×C₃₇	C₂
LCS	G ▷ C₅×C₃₇
UCS	C₁ ◁ C₅×C₁₇

Complements

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

N	H ≅ G/N	type
1. C₅²×C₁₇×C₃₇	C₂	semidirect
2. C₁₇×D₁₈₅	C₅	direct (N × H)
5. C₅×C₁₇×C₃₇	D₅	semidirect
6. C₅×C₁₇×C₃₇	C₂×C₅	semidirect
7. C₅×D₁₈₅	C₁₇	direct (N × H)
9. C₅²×C₃₇	C₂×C₁₇	semidirect
11. C₁₇×C₃₇	C₅×D₅	semidirect
12. C₅²×C₁₇	D₃₇	semidirect
13. D₁₈₅	C₅×C₁₇	direct (N × H)
16. C₅×C₃₇	D₅×C₁₇	semidirect
17. C₅×C₃₇	C₂×C₅×C₁₇	semidirect
21. C₅×C₁₇	C₅×D₃₇	semidirect
22. C₅×C₁₇	D₁₈₅	direct (N × H)
25. C₃₇	C₅×D₅×C₁₇	semidirect
27. C₅²	C₁₇×D₃₇	semidirect
28. C₁₇	C₅×D₁₈₅	direct (N × H)
32. C₅	C₅×C₁₇×D₃₇	semidirect
33. C₅	C₁₇×D₁₈₅	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₅²×C₁₇×C₃₇	2
C₁₇×D₁₈₅	5
C₅×C₁₇×D₃₇	5
C₅×D₁₈₅	17
C₅×D₅×C₁₇	37

Subgroups — C5×C17×D185 #44537795

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₁₇×D₁₈₅ #44537795