Subgroups — C₁₁×C₅⋊(C₅⋊(D₁₉⋊C₃)) #44535513

Order 31350.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²×C₁₁×C₁₉⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₁×C₅⋊D₉₅	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₁×C₅⋊(D₁₉⋊C₃)	—	5	6	no	maximal
4	C₅²×C₁₁×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	C₅×C₁₁×C₁₉⋊C₃	D₅	1	6	yes	complemented
6	C₅⋊(C₅⋊(D₁₉⋊C₃))	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₁₁×D₉₅	—	5	6	no	—
8	C₃×C₁₁×C₅⋊D₅	—	19	1	no	maximal, Hall
9	C₅²×C₁₉⋊C₃	C₂×C₁₁	1	1	yes	characteristic, complemented, Hall
10	C₁₁×D₁₉⋊C₃	—	25	1	no	Hall
11	C₅×C₁₁×C₁₉	C₃×D₅	1	6	yes	complemented
12	C₅⋊D₉₅	C₃×C₁₁	1	1	yes	characteristic, complemented, Hall
13	C₃×C₅²×C₁₁	—	19	1	no	Hall
14	C₁₁×C₁₉⋊C₃	C₅⋊D₅	1	1	yes	characteristic, complemented, Hall
15	C₅⋊(D₁₉⋊C₃)	—	5	6	no	—
16	C₁₁×C₅⋊D₅	—	19	1	no	Hall
17	C₅²×C₁₉	C₂×C₃×C₁₁	1	1	yes	characteristic, complemented, Hall
18	C₁₁×D₁₉	—	25	1	no	Hall
19	C₃×D₅×C₁₁	—	95	6	no	—
20	C₅×C₁₉⋊C₃	D₅×C₁₁	1	6	yes	complemented
21	C₅²×C₁₁	D₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
22	C₁₁×C₁₉	C₃×C₅⋊D₅	1	1	yes	characteristic, complemented, Hall
23	D₉₅	—	5	6	no	—
24	C₃×C₅×C₁₁	—	19	6	no	—
25	C₃×C₅⋊D₅	—	19	1	no	Hall
26	D₁₉⋊C₃	—	25	1	no	Hall
27	D₅×C₁₁	—	95	6	no	—
28	C₅×C₁₉	C₃×D₅×C₁₁	1	6	yes	complemented
29	C₃×C₅²	—	19	1	no	Hall
30	C₂×C₃×C₁₁	—	475	1	no	Hall
31	C₁₉⋊C₃	C₁₁×C₅⋊D₅	1	1	yes	characteristic, complemented, Hall
32	C₅×C₁₁	C₅⋊(D₁₉⋊C₃)	1	6	yes	complemented
33	C₅⋊D₅	—	19	1	no	Hall
34	D₁₉	—	25	1	no	Hall
35	C₃×C₁₁	—	19	1	no	Hall
36	C₃×D₅	—	95	6	no	—
37	C₅²	C₁₁×D₁₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
38	C₂×C₁₁	—	475	1	no	Hall
39	C₁₉	C₃×C₁₁×C₅⋊D₅	1	1	yes	characteristic, complemented, Sylow
40	C₃×C₅	—	19	6	no	—
41	C₁₁	C₅⋊(C₅⋊(D₁₉⋊C₃))	1	1	yes	characteristic, direct product factor, Sylow
42	D₅	—	95	6	no	—
43	C₂×C₃	—	475	1	no	Hall
44	C₅	C₁₁×C₅⋊(D₁₉⋊C₃)	1	6	yes	complemented
45	C₃	—	19	1	no	Sylow
46	C₂	—	475	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₁	C₅⋊(C₅⋊(D₁₉⋊C₃))
commutator, cosocle, hypocenter	C₅²×C₁₉	C₂×C₃×C₁₁
Frattini	C₁	G
Fitting, socle	C₅²×C₁₁×C₁₉	C₂×C₃
LCS	G ▷ C₅²×C₁₉
UCS	C₁ ◁ C₁₁

Complements

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

N	H ≅ G/N	type
1. C₅²×C₁₁×C₁₉⋊C₃	C₂	semidirect
2. C₁₁×C₅⋊D₉₅	C₃	semidirect
4. C₅²×C₁₁×C₁₉	C₂×C₃	semidirect
5. C₅×C₁₁×C₁₉⋊C₃	D₅	semidirect
6. C₅⋊(C₅⋊(D₁₉⋊C₃))	C₁₁	direct (N × H)
9. C₅²×C₁₉⋊C₃	C₂×C₁₁	semidirect
11. C₅×C₁₁×C₁₉	C₃×D₅	semidirect
12. C₅⋊D₉₅	C₃×C₁₁	semidirect
14. C₁₁×C₁₉⋊C₃	C₅⋊D₅	semidirect
17. C₅²×C₁₉	C₂×C₃×C₁₁	semidirect
20. C₅×C₁₉⋊C₃	D₅×C₁₁	semidirect
21. C₅²×C₁₁	D₁₉⋊C₃	semidirect
22. C₁₁×C₁₉	C₃×C₅⋊D₅	semidirect
28. C₅×C₁₉	C₃×D₅×C₁₁	semidirect
31. C₁₉⋊C₃	C₁₁×C₅⋊D₅	semidirect
32. C₅×C₁₁	C₅⋊(D₁₉⋊C₃)	semidirect
37. C₅²	C₁₁×D₁₉⋊C₃	semidirect
39. C₁₉	C₃×C₁₁×C₅⋊D₅	semidirect
41. C₁₁	C₅⋊(C₅⋊(D₁₉⋊C₃))	direct (N × H)
44. C₅	C₁₁×C₅⋊(D₁₉⋊C₃)	semidirect

Maximal subgroups

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

subgroup	index
C₅²×C₁₁×C₁₉⋊C₃	2
C₁₁×C₅⋊D₉₅	3
C₁₁×C₅⋊(D₁₉⋊C₃)	5
C₅⋊(C₅⋊(D₁₉⋊C₃))	11
C₃×C₁₁×C₅⋊D₅	19

Subgroups — C11×C5⋊(C5⋊(D19⋊C3)) #44535513

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×C₅⋊(C₅⋊(D₁₉⋊C₃)) #44535513