Subgroups — C₁₇×D₁₉×C₁₁⋊C₅ #48001053

Order 35530.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×C₁₉×C₁₁⋊C₅	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₁×C₁₇×D₁₉	C₅	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₁×C₁₇×C₁₉	C₂×C₅	1	1	yes	characteristic, complemented, Hall
4	C₅×C₁₇×D₁₉	—	11	1	no	maximal, Hall
5	D₁₉×C₁₁⋊C₅	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂×C₁₇×C₁₁⋊C₅	—	19	1	no	maximal, Hall
7	C₅×C₁₇×C₁₉	—	11	1	no	Hall
8	C₁₉×C₁₁⋊C₅	C₂×C₁₇	1	1	yes	characteristic, complemented, Hall
9	C₁₇×C₁₁⋊C₅	D₁₉	1	1	yes	characteristic, direct product factor, Hall
10	C₁₇×D₁₉	C₁₁⋊C₅	1	1	yes	characteristic, direct product factor, Hall
11	C₁₁×D₁₉	C₅×C₁₇	1	1	yes	characteristic, complemented, Hall
12	C₂×C₁₁×C₁₇	—	19	1	no	Hall
13	C₁₇×C₁₉	C₂×C₁₁⋊C₅	1	1	yes	characteristic, complemented, Hall
14	C₁₁×C₁₉	C₂×C₅×C₁₇	1	1	yes	characteristic, complemented, Hall
15	C₅×D₁₉	—	11	1	no	Hall
16	C₁₁×C₁₇	C₅×D₁₉	1	1	yes	characteristic, complemented, Hall
17	C₂×C₅×C₁₇	—	209	1	no	Hall
18	C₂×C₁₁⋊C₅	—	19	1	no	Hall
19	C₅×C₁₉	—	11	1	no	Hall
20	C₅×C₁₇	—	11	1	no	Hall
21	C₁₁⋊C₅	C₁₇×D₁₉	1	1	yes	characteristic, direct product factor, Hall
22	D₁₉	C₁₇×C₁₁⋊C₅	1	1	yes	characteristic, direct product factor, Hall
23	C₂×C₁₇	—	19	1	no	Hall
24	C₂×C₁₁	—	19	1	no	Hall
25	C₁₉	C₂×C₁₇×C₁₁⋊C₅	1	1	yes	characteristic, complemented, Sylow
26	C₁₇	D₁₉×C₁₁⋊C₅	1	1	yes	characteristic, direct product factor, Sylow
27	C₁₁	C₅×C₁₇×D₁₉	1	1	yes	characteristic, complemented, Sylow
28	C₂×C₅	—	209	1	no	Hall
29	C₅	—	11	1	no	Sylow
30	C₂	—	19	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₇	D₁₉×C₁₁⋊C₅
commutator, cosocle, hypocenter	C₁₁×C₁₉	C₂×C₅×C₁₇
Frattini	C₁	G
Fitting, socle	C₁₁×C₁₇×C₁₉	C₂×C₅
LCS	G ▷ C₁₁×C₁₉
UCS	C₁ ◁ C₁₇

Complements

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

N	H ≅ G/N	type
1. C₁₇×C₁₉×C₁₁⋊C₅	C₂	semidirect
2. C₁₁×C₁₇×D₁₉	C₅	semidirect
3. C₁₁×C₁₇×C₁₉	C₂×C₅	semidirect
5. D₁₉×C₁₁⋊C₅	C₁₇	direct (N × H)
8. C₁₉×C₁₁⋊C₅	C₂×C₁₇	semidirect
9. C₁₇×C₁₁⋊C₅	D₁₉	direct (N × H)
10. C₁₇×D₁₉	C₁₁⋊C₅	direct (N × H)
11. C₁₁×D₁₉	C₅×C₁₇	semidirect
13. C₁₇×C₁₉	C₂×C₁₁⋊C₅	semidirect
14. C₁₁×C₁₉	C₂×C₅×C₁₇	semidirect
16. C₁₁×C₁₇	C₅×D₁₉	semidirect
21. C₁₁⋊C₅	C₁₇×D₁₉	direct (N × H)
22. D₁₉	C₁₇×C₁₁⋊C₅	direct (N × H)
25. C₁₉	C₂×C₁₇×C₁₁⋊C₅	semidirect
26. C₁₇	D₁₉×C₁₁⋊C₅	direct (N × H)
27. C₁₁	C₅×C₁₇×D₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₁₇×C₁₉×C₁₁⋊C₅	2
C₁₁×C₁₇×D₁₉	5
C₅×C₁₇×D₁₉	11
D₁₉×C₁₁⋊C₅	17
C₂×C₁₇×C₁₁⋊C₅	19

Subgroups — C17×D19×C11⋊C5 #48001053

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×D₁₉×C₁₁⋊C₅ #48001053