Subgroups — C₁₇×C₁₉×D₅₅ #48001049

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	C₁₇×C₁₉×D₁₁	—	5	1	no	maximal, Hall
3	C₁₁×C₁₇×C₁₉	D₅	1	1	yes	characteristic, complemented, Hall
4	D₅×C₁₇×C₁₉	—	11	1	no	maximal, Hall
5	C₁₉×D₅₅	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₁₇×D₅₅	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	C₂×C₁₇	1	1	yes	characteristic, complemented, Hall
9	C₅×C₁₁×C₁₇	C₂×C₁₉	1	1	yes	characteristic, complemented, Hall
10	C₂×C₁₇×C₁₉	—	55	1	no	Hall
11	C₁₉×D₁₁	—	5	1	no	Hall
12	C₁₇×D₁₁	—	5	1	no	Hall
13	C₁₇×C₁₉	D₅₅	1	1	yes	characteristic, direct product factor, Hall
14	C₁₁×C₁₉	D₅×C₁₇	1	1	yes	characteristic, complemented, Hall
15	D₅×C₁₉	—	11	1	no	Hall
16	C₁₁×C₁₇	D₅×C₁₉	1	1	yes	characteristic, complemented, Hall
17	D₅×C₁₇	—	11	1	no	Hall
18	D₅₅	C₁₇×C₁₉	1	1	yes	characteristic, direct product factor, Hall
19	C₅×C₁₉	C₁₇×D₁₁	1	1	yes	characteristic, complemented, Hall
20	C₅×C₁₇	C₁₉×D₁₁	1	1	yes	characteristic, complemented, Hall
21	C₅×C₁₁	C₂×C₁₇×C₁₉	1	1	yes	characteristic, complemented, Hall
22	C₂×C₁₉	—	55	1	no	Hall
23	C₂×C₁₇	—	55	1	no	Hall
24	D₁₁	—	5	1	no	Hall
25	C₁₉	C₁₇×D₅₅	1	1	yes	characteristic, direct product factor, Sylow
26	C₁₇	C₁₉×D₅₅	1	1	yes	characteristic, direct product factor, Sylow
27	C₁₁	D₅×C₁₇×C₁₉	1	1	yes	characteristic, complemented, Sylow
28	D₅	—	11	1	no	Hall
29	C₅	C₁₇×C₁₉×D₁₁	1	1	yes	characteristic, complemented, Sylow
30	C₂	—	55	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₇×C₁₉	D₅₅
commutator, cosocle, hypocenter	C₅×C₁₁	C₂×C₁₇×C₁₉
Frattini	C₁	G
Fitting, socle	C₅×C₁₁×C₁₇×C₁₉	C₂
LCS	G ▷ C₅×C₁₁
UCS	C₁ ◁ C₁₇×C₁₉

Complements

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

N	H ≅ G/N	type
1. C₅×C₁₁×C₁₇×C₁₉	C₂	semidirect
3. C₁₁×C₁₇×C₁₉	D₅	semidirect
5. C₁₉×D₅₅	C₁₇	direct (N × H)
6. C₁₇×D₅₅	C₁₉	direct (N × H)
7. C₅×C₁₇×C₁₉	D₁₁	semidirect
8. C₅×C₁₁×C₁₉	C₂×C₁₇	semidirect
9. C₅×C₁₁×C₁₇	C₂×C₁₉	semidirect
13. C₁₇×C₁₉	D₅₅	direct (N × H)
14. C₁₁×C₁₉	D₅×C₁₇	semidirect
16. C₁₁×C₁₇	D₅×C₁₉	semidirect
18. D₅₅	C₁₇×C₁₉	direct (N × H)
19. C₅×C₁₉	C₁₇×D₁₁	semidirect
20. C₅×C₁₇	C₁₉×D₁₁	semidirect
21. C₅×C₁₁	C₂×C₁₇×C₁₉	semidirect
25. C₁₉	C₁₇×D₅₅	direct (N × H)
26. C₁₇	C₁₉×D₅₅	direct (N × H)
27. C₁₁	D₅×C₁₇×C₁₉	semidirect
29. C₅	C₁₇×C₁₉×D₁₁	semidirect

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
C₁₇×C₁₉×D₁₁	5
D₅×C₁₇×C₁₉	11
C₁₉×D₅₅	17
C₁₇×D₅₅	19

Subgroups — C17×C19×D55 #48001049

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×C₁₉×D₅₅ #48001049