Subgroups — C₁₁×C₁₉×C₃⋊(C₅⋊D₅) #44535540

Order 31350.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅²×C₁₁×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₁×C₁₉×C₅⋊D₅	—	3	1	no	maximal, Hall
3	C₁₁×C₁₉×D₁₅	—	5	6	no	maximal
4	C₅²×C₁₁×C₁₉	D₃	1	1	yes	characteristic, complemented, Hall
5	C₃×C₅×C₁₁×C₁₉	D₅	1	6	yes	complemented
6	C₁₉×C₃⋊(C₅⋊D₅)	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
7	D₅×C₁₁×C₁₉	—	15	6	no	—
8	C₁₁×C₃⋊(C₅⋊D₅)	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₃×C₅²×C₁₉	C₂×C₁₁	1	1	yes	characteristic, complemented, Hall
10	D₃×C₁₁×C₁₉	—	25	1	no	Hall
11	C₅×C₁₁×C₁₉	D₁₅	1	6	yes	complemented
12	C₁₉×C₅⋊D₅	—	3	1	no	Hall
13	C₃×C₅²×C₁₁	C₂×C₁₉	1	1	yes	characteristic, complemented, Hall
14	C₃×C₁₁×C₁₉	C₅⋊D₅	1	1	yes	characteristic, complemented, Hall
15	C₁₉×D₁₅	—	5	6	no	—
16	C₁₁×C₅⋊D₅	—	3	1	no	Hall
17	C₅²×C₁₉	D₃×C₁₁	1	1	yes	characteristic, complemented, Hall
18	C₂×C₁₁×C₁₉	—	75	1	no	Hall
19	C₁₁×D₁₅	—	5	6	no	—
20	C₃×C₅×C₁₉	D₅×C₁₁	1	6	yes	complemented
21	C₅²×C₁₁	D₃×C₁₉	1	1	yes	characteristic, complemented, Hall
22	C₁₁×C₁₉	C₃⋊(C₅⋊D₅)	1	1	yes	characteristic, direct product factor, Hall
23	D₅×C₁₉	—	15	6	no	—
24	C₃×C₅×C₁₁	D₅×C₁₉	1	6	yes	complemented
25	C₃⋊(C₅⋊D₅)	C₁₁×C₁₉	1	1	yes	characteristic, direct product factor, Hall
26	D₃×C₁₉	—	25	1	no	Hall
27	D₅×C₁₁	—	15	6	no	—
28	C₅×C₁₉	C₁₁×D₁₅	1	6	yes	complemented
29	C₃×C₅²	C₂×C₁₁×C₁₉	1	1	yes	characteristic, complemented, Hall
30	D₃×C₁₁	—	25	1	no	Hall
31	C₃×C₁₉	C₁₁×C₅⋊D₅	1	1	yes	characteristic, complemented, Hall
32	C₅×C₁₁	C₁₉×D₁₅	1	6	yes	complemented
33	C₅⋊D₅	—	3	1	no	Hall
34	C₂×C₁₉	—	75	1	no	Hall
35	C₃×C₁₁	C₁₉×C₅⋊D₅	1	1	yes	characteristic, complemented, Hall
36	D₁₅	—	5	6	no	—
37	C₅²	D₃×C₁₁×C₁₉	1	1	yes	characteristic, complemented, Sylow
38	C₂×C₁₁	—	75	1	no	Hall
39	C₁₉	C₁₁×C₃⋊(C₅⋊D₅)	1	1	yes	characteristic, direct product factor, Sylow
40	C₃×C₅	D₅×C₁₁×C₁₉	1	6	yes	complemented
41	C₁₁	C₁₉×C₃⋊(C₅⋊D₅)	1	1	yes	characteristic, direct product factor, Sylow
42	D₅	—	15	6	no	—
43	D₃	—	25	1	no	Hall
44	C₅	C₁₁×C₁₉×D₁₅	1	6	yes	complemented
45	C₃	C₁₁×C₁₉×C₅⋊D₅	1	1	yes	characteristic, complemented, Sylow
46	C₂	—	75	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₁×C₁₉	C₃⋊(C₅⋊D₅)
commutator, cosocle, hypocenter	C₃×C₅²	C₂×C₁₁×C₁₉
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₁₁×C₁₉	C₂
LCS	G ▷ C₃×C₅²
UCS	C₁ ◁ C₁₁×C₁₉

Complements

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

N	H ≅ G/N	type
1. C₃×C₅²×C₁₁×C₁₉	C₂	semidirect
4. C₅²×C₁₁×C₁₉	D₃	semidirect
5. C₃×C₅×C₁₁×C₁₉	D₅	semidirect
6. C₁₉×C₃⋊(C₅⋊D₅)	C₁₁	direct (N × H)
8. C₁₁×C₃⋊(C₅⋊D₅)	C₁₉	direct (N × H)
9. C₃×C₅²×C₁₉	C₂×C₁₁	semidirect
11. C₅×C₁₁×C₁₉	D₁₅	semidirect
13. C₃×C₅²×C₁₁	C₂×C₁₉	semidirect
14. C₃×C₁₁×C₁₉	C₅⋊D₅	semidirect
17. C₅²×C₁₉	D₃×C₁₁	semidirect
20. C₃×C₅×C₁₉	D₅×C₁₁	semidirect
21. C₅²×C₁₁	D₃×C₁₉	semidirect
22. C₁₁×C₁₉	C₃⋊(C₅⋊D₅)	direct (N × H)
24. C₃×C₅×C₁₁	D₅×C₁₉	semidirect
25. C₃⋊(C₅⋊D₅)	C₁₁×C₁₉	direct (N × H)
28. C₅×C₁₉	C₁₁×D₁₅	semidirect
29. C₃×C₅²	C₂×C₁₁×C₁₉	semidirect
31. C₃×C₁₉	C₁₁×C₅⋊D₅	semidirect
32. C₅×C₁₁	C₁₉×D₁₅	semidirect
35. C₃×C₁₁	C₁₉×C₅⋊D₅	semidirect
37. C₅²	D₃×C₁₁×C₁₉	semidirect
39. C₁₉	C₁₁×C₃⋊(C₅⋊D₅)	direct (N × H)
40. C₃×C₅	D₅×C₁₁×C₁₉	semidirect
41. C₁₁	C₁₉×C₃⋊(C₅⋊D₅)	direct (N × H)
44. C₅	C₁₁×C₁₉×D₁₅	semidirect
45. C₃	C₁₁×C₁₉×C₅⋊D₅	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅²×C₁₁×C₁₉	2
C₁₁×C₁₉×C₅⋊D₅	3
C₁₁×C₁₉×D₁₅	5
C₁₉×C₃⋊(C₅⋊D₅)	11
C₁₁×C₃⋊(C₅⋊D₅)	19

Subgroups — C11×C19×C3⋊(C5⋊D5) #44535540

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×C₁₉×C₃⋊(C₅⋊D₅) #44535540