Subgroups — C₅×D₃₆₈₉ #49146261

Order 36890.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₇×C₁₇×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₃₆₈₉	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₅×D₅₂₇	—	7	1	no	maximal, Hall
4	C₇×C₁₇×C₃₁	C₂×C₅	1	1	yes	characteristic, complemented, Hall
5	C₅×C₁₇×C₃₁	D₇	1	1	yes	characteristic, complemented, Hall
6	C₅×D₂₁₇	—	17	1	no	maximal, Hall
7	C₅×D₁₁₉	—	31	1	no	maximal, Hall
8	C₅×C₇×C₃₁	D₁₇	1	1	yes	characteristic, complemented, Hall
9	D₅₂₇	—	7	1	no	Hall
10	C₅×C₇×C₁₇	D₃₁	1	1	yes	characteristic, complemented, Hall
11	C₁₇×C₃₁	C₅×D₇	1	1	yes	characteristic, complemented, Hall
12	D₂₁₇	—	17	1	no	Hall
13	C₅×D₃₁	—	119	1	no	Hall
14	D₁₁₉	—	31	1	no	Hall
15	C₇×C₃₁	C₅×D₁₇	1	1	yes	characteristic, complemented, Hall
16	C₅×D₁₇	—	217	1	no	Hall
17	C₅×C₃₁	D₁₁₉	1	1	yes	characteristic, complemented, Hall
18	C₇×C₁₇	C₅×D₃₁	1	1	yes	characteristic, complemented, Hall
19	C₅×C₁₇	D₂₁₇	1	1	yes	characteristic, complemented, Hall
20	C₅×D₇	—	527	1	no	Hall
21	D₃₁	—	119	1	no	Hall
22	C₅×C₇	D₅₂₇	1	1	yes	characteristic, complemented, Hall
23	D₁₇	—	217	1	no	Hall
24	C₃₁	C₅×D₁₁₉	1	1	yes	characteristic, complemented, Sylow
25	C₁₇	C₅×D₂₁₇	1	1	yes	characteristic, complemented, Sylow
26	D₇	—	527	1	no	Hall
27	C₂×C₅	—	3689	1	no	Hall
28	C₇	C₅×D₅₂₇	1	1	yes	characteristic, complemented, Sylow
29	C₅	D₃₆₈₉	1	1	yes	characteristic, direct product factor, Sylow
30	C₂	—	3689	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅	D₃₆₈₉
commutator, cosocle, hypocenter	C₇×C₁₇×C₃₁	C₂×C₅
Frattini	C₁	G
Fitting, socle	C₅×C₇×C₁₇×C₃₁	C₂
LCS	G ▷ C₇×C₁₇×C₃₁
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
1. C₅×C₇×C₁₇×C₃₁	C₂	semidirect
2. D₃₆₈₉	C₅	direct (N × H)
4. C₇×C₁₇×C₃₁	C₂×C₅	semidirect
5. C₅×C₁₇×C₃₁	D₇	semidirect
8. C₅×C₇×C₃₁	D₁₇	semidirect
10. C₅×C₇×C₁₇	D₃₁	semidirect
11. C₁₇×C₃₁	C₅×D₇	semidirect
15. C₇×C₃₁	C₅×D₁₇	semidirect
17. C₅×C₃₁	D₁₁₉	semidirect
18. C₇×C₁₇	C₅×D₃₁	semidirect
19. C₅×C₁₇	D₂₁₇	semidirect
22. C₅×C₇	D₅₂₇	semidirect
24. C₃₁	C₅×D₁₁₉	semidirect
25. C₁₇	C₅×D₂₁₇	semidirect
28. C₇	C₅×D₅₂₇	semidirect
29. C₅	D₃₆₈₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×C₇×C₁₇×C₃₁	2
D₃₆₈₉	5
C₅×D₅₂₇	7
C₅×D₂₁₇	17
C₅×D₁₁₉	31

Subgroups — C5×D3689 #49146261

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₃₆₈₉ #49146261