Subgroups — C₅×C₁₉×D₁₈₇ #48001043

Order 35530.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₁×C₁₇×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₉×D₁₈₇	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₁₁×C₁₇×C₁₉	C₂×C₅	1	1	yes	characteristic, complemented, Hall
4	C₅×C₁₉×D₁₇	—	11	1	no	maximal, Hall
5	C₅×C₁₉×D₁₁	—	17	1	no	maximal, Hall
6	C₅×D₁₈₇	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₅×C₁₇×C₁₉	D₁₁	1	1	yes	characteristic, complemented, Hall
8	C₅×C₁₁×C₁₉	D₁₇	1	1	yes	characteristic, complemented, Hall
9	C₅×C₁₁×C₁₇	C₂×C₁₉	1	1	yes	characteristic, complemented, Hall
10	C₁₉×D₁₇	—	11	1	no	Hall
11	C₁₉×D₁₁	—	17	1	no	Hall
12	D₁₈₇	C₅×C₁₉	1	1	yes	characteristic, direct product factor, Hall
13	C₁₇×C₁₉	C₅×D₁₁	1	1	yes	characteristic, complemented, Hall
14	C₁₁×C₁₉	C₅×D₁₇	1	1	yes	characteristic, complemented, Hall
15	C₂×C₅×C₁₉	—	187	1	no	Hall
16	C₁₁×C₁₇	C₂×C₅×C₁₉	1	1	yes	characteristic, complemented, Hall
17	C₅×D₁₇	—	11	1	no	Hall
18	C₅×D₁₁	—	17	1	no	Hall
19	C₅×C₁₉	D₁₈₇	1	1	yes	characteristic, direct product factor, Hall
20	C₅×C₁₇	C₁₉×D₁₁	1	1	yes	characteristic, complemented, Hall
21	C₅×C₁₁	C₁₉×D₁₇	1	1	yes	characteristic, complemented, Hall
22	C₂×C₁₉	—	187	1	no	Hall
23	D₁₇	—	11	1	no	Hall
24	D₁₁	—	17	1	no	Hall
25	C₁₉	C₅×D₁₈₇	1	1	yes	characteristic, direct product factor, Sylow
26	C₁₇	C₅×C₁₉×D₁₁	1	1	yes	characteristic, complemented, Sylow
27	C₁₁	C₅×C₁₉×D₁₇	1	1	yes	characteristic, complemented, Sylow
28	C₂×C₅	—	187	1	no	Hall
29	C₅	C₁₉×D₁₈₇	1	1	yes	characteristic, direct product factor, Sylow
30	C₂	—	187	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅×C₁₉	D₁₈₇
commutator, cosocle, hypocenter	C₁₁×C₁₇	C₂×C₅×C₁₉
Frattini	C₁	G
Fitting, socle	C₅×C₁₁×C₁₇×C₁₉	C₂
LCS	G ▷ C₁₁×C₁₇
UCS	C₁ ◁ C₅×C₁₉

Complements

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

N	H ≅ G/N	type
1. C₅×C₁₁×C₁₇×C₁₉	C₂	semidirect
2. C₁₉×D₁₈₇	C₅	direct (N × H)
3. C₁₁×C₁₇×C₁₉	C₂×C₅	semidirect
6. C₅×D₁₈₇	C₁₉	direct (N × H)
7. C₅×C₁₇×C₁₉	D₁₁	semidirect
8. C₅×C₁₁×C₁₉	D₁₇	semidirect
9. C₅×C₁₁×C₁₇	C₂×C₁₉	semidirect
12. D₁₈₇	C₅×C₁₉	direct (N × H)
13. C₁₇×C₁₉	C₅×D₁₁	semidirect
14. C₁₁×C₁₉	C₅×D₁₇	semidirect
16. C₁₁×C₁₇	C₂×C₅×C₁₉	semidirect
19. C₅×C₁₉	D₁₈₇	direct (N × H)
20. C₅×C₁₇	C₁₉×D₁₁	semidirect
21. C₅×C₁₁	C₁₉×D₁₇	semidirect
25. C₁₉	C₅×D₁₈₇	direct (N × H)
26. C₁₇	C₅×C₁₉×D₁₁	semidirect
27. C₁₁	C₅×C₁₉×D₁₇	semidirect
29. C₅	C₁₉×D₁₈₇	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×C₁₁×C₁₇×C₁₉	2
C₁₉×D₁₈₇	5
C₅×C₁₉×D₁₇	11
C₅×C₁₉×D₁₁	17
C₅×D₁₈₇	19

Subgroups — C5×C19×D187 #48001043

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₁₉×D₁₈₇ #48001043