Subgroups — C₅²×D₁₁×C₁₉⋊C₃ #44535508

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	C₅²×C₁₉×D₁₁	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₅×D₁₁×C₁₉⋊C₃	C₅	1	6	yes	maximal, direct product factor
4	C₅²×C₁₁×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	C₅×C₁₁×C₁₉⋊C₃	C₂×C₅	1	6	yes	complemented
6	C₂×C₅²×C₁₉⋊C₃	—	11	1	no	maximal, Hall
7	C₅×C₁₉×D₁₁	C₃×C₅	1	6	yes	complemented
8	C₃×C₅²×D₁₁	—	19	1	no	maximal, Hall
9	C₅²×C₁₉⋊C₃	D₁₁	1	1	yes	characteristic, direct product factor, Hall
10	D₁₁×C₁₉⋊C₃	C₅²	1	1	yes	characteristic, direct product factor, Hall
11	C₅×C₁₁×C₁₉	C₂×C₃×C₅	1	6	yes	complemented
12	C₂×C₅²×C₁₉	—	11	1	no	Hall
13	C₃×C₅²×C₁₁	—	19	1	no	Hall
14	C₁₁×C₁₉⋊C₃	C₂×C₅²	1	1	yes	characteristic, complemented, Hall
15	C₂×C₅×C₁₉⋊C₃	—	11	6	no	—
16	C₅²×D₁₁	C₁₉⋊C₃	1	1	yes	characteristic, direct product factor, Hall
17	C₅²×C₁₉	C₃×D₁₁	1	1	yes	characteristic, complemented, Hall
18	C₁₉×D₁₁	C₃×C₅²	1	1	yes	characteristic, complemented, Hall
19	C₃×C₅×D₁₁	—	19	6	no	—
20	C₅×C₁₉⋊C₃	C₅×D₁₁	1	6	yes	direct product factor
21	C₅²×C₁₁	C₂×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
22	C₁₁×C₁₉	C₂×C₃×C₅²	1	1	yes	characteristic, complemented, Hall
23	C₂×C₅×C₁₉	—	11	6	no	—
24	C₃×C₅×C₁₁	—	19	6	no	—
25	C₂×C₃×C₅²	—	209	1	no	Hall
26	C₂×C₁₉⋊C₃	—	11	1	no	Hall
27	C₅×D₁₁	C₅×C₁₉⋊C₃	1	6	yes	direct product factor
28	C₅×C₁₉	C₃×C₅×D₁₁	1	6	yes	complemented
29	C₃×C₅²	—	19	1	no	Hall
30	C₃×D₁₁	—	19	1	no	Hall
31	C₁₉⋊C₃	C₅²×D₁₁	1	1	yes	characteristic, direct product factor, Hall
32	C₅×C₁₁	C₂×C₅×C₁₉⋊C₃	1	6	yes	complemented
33	C₂×C₅²	—	11	1	no	Hall
34	C₂×C₁₉	—	11	1	no	Hall
35	C₃×C₁₁	—	19	1	no	Hall
36	C₂×C₃×C₅	—	209	6	no	—
37	C₅²	D₁₁×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
38	D₁₁	C₅²×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor, Hall
39	C₁₉	C₃×C₅²×D₁₁	1	1	yes	characteristic, complemented, Sylow
40	C₃×C₅	—	19	6	no	—
41	C₁₁	C₂×C₅²×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
42	C₂×C₅	—	11	6	no	—
43	C₂×C₃	—	209	1	no	Hall
44	C₅	C₅×D₁₁×C₁₉⋊C₃	1	6	yes	direct product factor
45	C₃	—	19	1	no	Sylow
46	C₂	—	11	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅²	D₁₁×C₁₉⋊C₃
commutator, cosocle, hypocenter	C₁₁×C₁₉	C₂×C₃×C₅²
Frattini	C₁	G
Fitting, socle	C₅²×C₁₁×C₁₉	C₂×C₃
LCS	G ▷ C₁₁×C₁₉
UCS	C₁ ◁ C₅²

Complements

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

N	H ≅ G/N	type
1. C₅²×C₁₁×C₁₉⋊C₃	C₂	semidirect
2. C₅²×C₁₉×D₁₁	C₃	semidirect
3. C₅×D₁₁×C₁₉⋊C₃	C₅	direct (N × H)
4. C₅²×C₁₁×C₁₉	C₂×C₃	semidirect
5. C₅×C₁₁×C₁₉⋊C₃	C₂×C₅	semidirect
7. C₅×C₁₉×D₁₁	C₃×C₅	semidirect
9. C₅²×C₁₉⋊C₃	D₁₁	direct (N × H)
10. D₁₁×C₁₉⋊C₃	C₅²	direct (N × H)
11. C₅×C₁₁×C₁₉	C₂×C₃×C₅	semidirect
14. C₁₁×C₁₉⋊C₃	C₂×C₅²	semidirect
16. C₅²×D₁₁	C₁₉⋊C₃	direct (N × H)
17. C₅²×C₁₉	C₃×D₁₁	semidirect
18. C₁₉×D₁₁	C₃×C₅²	semidirect
20. C₅×C₁₉⋊C₃	C₅×D₁₁	direct (N × H)
21. C₅²×C₁₁	C₂×C₁₉⋊C₃	semidirect
22. C₁₁×C₁₉	C₂×C₃×C₅²	semidirect
27. C₅×D₁₁	C₅×C₁₉⋊C₃	direct (N × H)
28. C₅×C₁₉	C₃×C₅×D₁₁	semidirect
31. C₁₉⋊C₃	C₅²×D₁₁	direct (N × H)
32. C₅×C₁₁	C₂×C₅×C₁₉⋊C₃	semidirect
37. C₅²	D₁₁×C₁₉⋊C₃	direct (N × H)
38. D₁₁	C₅²×C₁₉⋊C₃	direct (N × H)
39. C₁₉	C₃×C₅²×D₁₁	semidirect
41. C₁₁	C₂×C₅²×C₁₉⋊C₃	semidirect
44. C₅	C₅×D₁₁×C₁₉⋊C₃	direct (N × H)

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
C₅²×C₁₉×D₁₁	3
C₅×D₁₁×C₁₉⋊C₃	5
C₂×C₅²×C₁₉⋊C₃	11
C₃×C₅²×D₁₁	19

Subgroups — C52×D11×C19⋊C3 #44535508

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅²×D₁₁×C₁₉⋊C₃ #44535508