Subgroups — C₅×C₁₇×D₂₀₉ #48001042

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×D₂₀₉	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₁₁×C₁₇×C₁₉	C₂×C₅	1	1	yes	characteristic, complemented, Hall
4	C₅×C₁₇×D₁₉	—	11	1	no	maximal, Hall
5	C₅×D₂₀₉	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₅×C₁₇×D₁₁	—	19	1	no	maximal, 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	D₁₉	1	1	yes	characteristic, complemented, Hall
10	C₁₇×D₁₉	—	11	1	no	Hall
11	D₂₀₉	C₅×C₁₇	1	1	yes	characteristic, direct product factor, Hall
12	C₁₇×D₁₁	—	19	1	no	Hall
13	C₁₇×C₁₉	C₅×D₁₁	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	C₅×D₁₁	—	19	1	no	Hall
19	C₅×C₁₉	C₁₇×D₁₁	1	1	yes	characteristic, complemented, Hall
20	C₅×C₁₇	D₂₀₉	1	1	yes	characteristic, direct product factor, Hall
21	C₅×C₁₁	C₁₇×D₁₉	1	1	yes	characteristic, complemented, Hall
22	D₁₉	—	11	1	no	Hall
23	C₂×C₁₇	—	209	1	no	Hall
24	D₁₁	—	19	1	no	Hall
25	C₁₉	C₅×C₁₇×D₁₁	1	1	yes	characteristic, complemented, Sylow
26	C₁₇	C₅×D₂₀₉	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	C₁₇×D₂₀₉	1	1	yes	characteristic, direct product factor, Sylow
30	C₂	—	209	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅×C₁₇	D₂₀₉
commutator, cosocle, hypocenter	C₁₁×C₁₉	C₂×C₅×C₁₇
Frattini	C₁	G
Fitting, socle	C₅×C₁₁×C₁₇×C₁₉	C₂
LCS	G ▷ C₁₁×C₁₉
UCS	C₁ ◁ C₅×C₁₇

Complements

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

N	H ≅ G/N	type
1. C₅×C₁₁×C₁₇×C₁₉	C₂	semidirect
2. C₁₇×D₂₀₉	C₅	direct (N × H)
3. C₁₁×C₁₇×C₁₉	C₂×C₅	semidirect
5. C₅×D₂₀₉	C₁₇	direct (N × H)
7. C₅×C₁₇×C₁₉	D₁₁	semidirect
8. C₅×C₁₁×C₁₉	C₂×C₁₇	semidirect
9. C₅×C₁₁×C₁₇	D₁₉	semidirect
11. D₂₀₉	C₅×C₁₇	direct (N × H)
13. C₁₇×C₁₉	C₅×D₁₁	semidirect
14. C₁₁×C₁₉	C₂×C₅×C₁₇	semidirect
16. C₁₁×C₁₇	C₅×D₁₉	semidirect
19. C₅×C₁₉	C₁₇×D₁₁	semidirect
20. C₅×C₁₇	D₂₀₉	direct (N × H)
21. C₅×C₁₁	C₁₇×D₁₉	semidirect
25. C₁₉	C₅×C₁₇×D₁₁	semidirect
26. C₁₇	C₅×D₂₀₉	direct (N × H)
27. C₁₁	C₅×C₁₇×D₁₉	semidirect
29. C₅	C₁₇×D₂₀₉	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
C₁₇×D₂₀₉	5
C₅×C₁₇×D₁₉	11
C₅×D₂₀₉	17
C₅×C₁₇×D₁₁	19

Subgroups — C5×C17×D209 #48001042

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₁₇×D₂₀₉ #48001042