Subgroups — C₅×C₉×D₂₀₉ #34037814

Order 18810.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₉×C₁₁×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₅×D₂₀₉	C₃	1	1	yes	maximal, characteristic
3	C₉×D₂₀₉	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₅×C₁₁×C₁₉	C₂×C₃	1	1	yes	characteristic
5	C₅×D₂₀₉	C₉	1	1	yes	characteristic, direct product factor, Hall
6	C₉×C₁₁×C₁₉	C₂×C₅	1	1	yes	characteristic, complemented, Hall
7	C₅×C₉×D₁₉	—	11	1	no	maximal, Hall
8	C₃×D₂₀₉	C₃×C₅	1	1	yes	characteristic
9	C₅×C₁₁×C₁₉	C₂×C₉	1	1	yes	characteristic, complemented, Hall
10	C₅×C₉×D₁₁	—	19	1	no	maximal, Hall
11	C₅×C₉×C₁₉	D₁₁	1	1	yes	characteristic, complemented, Hall
12	C₃×C₁₁×C₁₉	C₂×C₃×C₅	1	1	yes	characteristic
13	C₃×C₅×D₁₉	—	11	1	no	—
14	C₅×C₉×C₁₁	D₁₉	1	1	yes	characteristic, complemented, Hall
15	D₂₀₉	C₅×C₉	1	1	yes	characteristic, direct product factor, Hall
16	C₉×D₁₉	—	11	1	no	Hall
17	C₃×C₅×D₁₁	—	19	1	no	—
18	C₃×C₅×C₁₉	C₃×D₁₁	1	1	yes	characteristic
19	C₁₁×C₁₉	C₂×C₅×C₉	1	1	yes	characteristic, complemented, Hall
20	C₉×D₁₁	—	19	1	no	Hall
21	C₅×D₁₉	—	11	1	no	Hall
22	C₉×C₁₉	C₅×D₁₁	1	1	yes	characteristic, complemented, Hall
23	C₃×C₅×C₁₁	C₃×D₁₉	1	1	yes	characteristic
24	C₃×D₁₉	—	11	1	no	—
25	C₅×D₁₁	—	19	1	no	Hall
26	C₉×C₁₁	C₅×D₁₉	1	1	yes	characteristic, complemented, Hall
27	C₅×C₁₉	C₉×D₁₁	1	1	yes	characteristic, complemented, Hall
28	C₂×C₅×C₉	—	209	1	no	Hall
29	C₃×D₁₁	—	19	1	no	—
30	C₃×C₁₉	C₃×C₅×D₁₁	1	1	yes	characteristic
31	C₅×C₁₁	C₉×D₁₉	1	1	yes	characteristic, complemented, Hall
32	C₅×C₉	D₂₀₉	1	1	yes	characteristic, direct product factor, Hall
33	D₁₉	—	11	1	no	Hall
34	C₃×C₁₁	C₃×C₅×D₁₉	1	1	yes	characteristic
35	C₂×C₃×C₅	—	209	1	no	—
36	D₁₁	—	19	1	no	Hall
37	C₁₉	C₅×C₉×D₁₁	1	1	yes	characteristic, complemented, Sylow
38	C₂×C₉	—	209	1	no	Hall
39	C₃×C₅	C₃×D₂₀₉	1	1	yes	characteristic
40	C₁₁	C₅×C₉×D₁₉	1	1	yes	characteristic, complemented, Sylow
41	C₂×C₅	—	209	1	no	Hall
42	C₉	C₅×D₂₀₉	1	1	yes	characteristic, direct product factor, Sylow
43	C₂×C₃	—	209	1	no	—
44	C₅	C₉×D₂₀₉	1	1	yes	characteristic, direct product factor, Sylow
45	C₃	C₃×C₅×D₂₀₉	1	1	yes	characteristic
46	C₂	—	209	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅×C₉	D₂₀₉
commutator, hypocenter	C₁₁×C₁₉	C₂×C₅×C₉
Frattini	C₃	C₃×C₅×D₂₀₉
Fitting	C₅×C₉×C₁₁×C₁₉	C₂
socle	C₃×C₅×C₁₁×C₁₉	C₂×C₃
prime radical	C₃×C₅×D₂₀₉	C₃
cosocle	C₃×C₁₁×C₁₉	C₂×C₃×C₅
LCS	G ▷ C₁₁×C₁₉
UCS	C₁ ◁ C₅×C₉

Complements

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

N	H ≅ G/N	type
1. C₅×C₉×C₁₁×C₁₉	C₂	semidirect
3. C₉×D₂₀₉	C₅	direct (N × H)
5. C₅×D₂₀₉	C₉	direct (N × H)
6. C₉×C₁₁×C₁₉	C₂×C₅	semidirect
9. C₅×C₁₁×C₁₉	C₂×C₉	semidirect
11. C₅×C₉×C₁₉	D₁₁	semidirect
14. C₅×C₉×C₁₁	D₁₉	semidirect
15. D₂₀₉	C₅×C₉	direct (N × H)
19. C₁₁×C₁₉	C₂×C₅×C₉	semidirect
22. C₉×C₁₉	C₅×D₁₁	semidirect
26. C₉×C₁₁	C₅×D₁₉	semidirect
27. C₅×C₁₉	C₉×D₁₁	semidirect
31. C₅×C₁₁	C₉×D₁₉	semidirect
32. C₅×C₉	D₂₀₉	direct (N × H)
37. C₁₉	C₅×C₉×D₁₁	semidirect
40. C₁₁	C₅×C₉×D₁₉	semidirect
42. C₉	C₅×D₂₀₉	direct (N × H)
44. C₅	C₉×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×C₉×C₁₁×C₁₉	2
C₃×C₅×D₂₀₉	3
C₉×D₂₀₉	5
C₅×C₉×D₁₉	11
C₅×C₉×D₁₁	19

Subgroups — C5×C9×D209 #34037814

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₉×D₂₀₉ #34037814