Subgroups — C₃×C₅²×C₁₁×D₁₉ #44535521

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	C₅²×C₁₁×D₁₉	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₅×C₁₁×D₁₉	C₅	1	6	yes	maximal, direct product factor
4	C₅²×C₁₁×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	C₃×C₅×C₁₁×C₁₉	C₂×C₅	1	6	yes	complemented
6	C₃×C₅²×D₁₉	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₅×C₁₁×D₁₉	C₃×C₅	1	6	yes	direct product factor
8	C₂×C₃×C₅²×C₁₁	—	19	1	no	maximal, Hall
9	C₃×C₅²×C₁₉	C₂×C₁₁	1	1	yes	characteristic, complemented, Hall
10	C₃×C₁₁×D₁₉	C₅²	1	1	yes	characteristic, direct product factor, Hall
11	C₅×C₁₁×C₁₉	C₂×C₃×C₅	1	6	yes	complemented
12	C₅²×D₁₉	C₃×C₁₁	1	1	yes	characteristic, direct product factor, Hall
13	C₃×C₅²×C₁₁	D₁₉	1	1	yes	characteristic, direct product factor, Hall
14	C₃×C₁₁×C₁₉	C₂×C₅²	1	1	yes	characteristic, complemented, Hall
15	C₃×C₅×D₁₉	C₅×C₁₁	1	6	yes	direct product factor
16	C₂×C₅²×C₁₁	—	19	1	no	Hall
17	C₅²×C₁₉	C₂×C₃×C₁₁	1	1	yes	characteristic, complemented, Hall
18	C₁₁×D₁₉	C₃×C₅²	1	1	yes	characteristic, direct product factor, Hall
19	C₂×C₃×C₅×C₁₁	—	19	6	no	—
20	C₃×C₅×C₁₉	C₂×C₅×C₁₁	1	6	yes	complemented
21	C₅²×C₁₁	C₃×D₁₉	1	1	yes	characteristic, direct product factor, Hall
22	C₁₁×C₁₉	C₂×C₃×C₅²	1	1	yes	characteristic, complemented, Hall
23	C₅×D₁₉	C₃×C₅×C₁₁	1	6	yes	direct product factor
24	C₃×C₅×C₁₁	C₅×D₁₉	1	6	yes	direct product factor
25	C₂×C₃×C₅²	—	19	1	no	Hall
26	C₃×D₁₉	C₅²×C₁₁	1	1	yes	characteristic, direct product factor, Hall
27	C₂×C₅×C₁₁	—	19	6	no	—
28	C₅×C₁₉	C₂×C₃×C₅×C₁₁	1	6	yes	complemented
29	C₃×C₅²	C₁₁×D₁₉	1	1	yes	characteristic, direct product factor, Hall
30	C₂×C₃×C₁₁	—	19	1	no	Hall
31	C₃×C₁₉	C₂×C₅²×C₁₁	1	1	yes	characteristic, complemented, Hall
32	C₅×C₁₁	C₃×C₅×D₁₉	1	6	yes	direct product factor
33	C₂×C₅²	—	19	1	no	Hall
34	D₁₉	C₃×C₅²×C₁₁	1	1	yes	characteristic, direct product factor, Hall
35	C₃×C₁₁	C₅²×D₁₉	1	1	yes	characteristic, direct product factor, Hall
36	C₂×C₃×C₅	—	19	6	no	—
37	C₅²	C₃×C₁₁×D₁₉	1	1	yes	characteristic, direct product factor, Sylow
38	C₂×C₁₁	—	19	1	no	Hall
39	C₁₉	C₂×C₃×C₅²×C₁₁	1	1	yes	characteristic, complemented, Sylow
40	C₃×C₅	C₅×C₁₁×D₁₉	1	6	yes	direct product factor
41	C₁₁	C₃×C₅²×D₁₉	1	1	yes	characteristic, direct product factor, Sylow
42	C₂×C₅	—	19	6	no	—
43	C₂×C₃	—	19	1	no	Hall
44	C₅	C₃×C₅×C₁₁×D₁₉	1	6	yes	direct product factor
45	C₃	C₅²×C₁₁×D₁₉	1	1	yes	characteristic, direct product factor, Sylow
46	C₂	—	19	1	no	Sylow

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

Complements

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

N	H ≅ G/N	type
1. C₃×C₅²×C₁₁×C₁₉	C₂	semidirect
2. C₅²×C₁₁×D₁₉	C₃	direct (N × H)
3. C₃×C₅×C₁₁×D₁₉	C₅	direct (N × H)
4. C₅²×C₁₁×C₁₉	C₂×C₃	semidirect
5. C₃×C₅×C₁₁×C₁₉	C₂×C₅	semidirect
6. C₃×C₅²×D₁₉	C₁₁	direct (N × H)
7. C₅×C₁₁×D₁₉	C₃×C₅	direct (N × H)
9. C₃×C₅²×C₁₉	C₂×C₁₁	semidirect
10. C₃×C₁₁×D₁₉	C₅²	direct (N × H)
11. C₅×C₁₁×C₁₉	C₂×C₃×C₅	semidirect
12. C₅²×D₁₉	C₃×C₁₁	direct (N × H)
13. C₃×C₅²×C₁₁	D₁₉	direct (N × H)
14. C₃×C₁₁×C₁₉	C₂×C₅²	semidirect
15. C₃×C₅×D₁₉	C₅×C₁₁	direct (N × H)
17. C₅²×C₁₉	C₂×C₃×C₁₁	semidirect
18. C₁₁×D₁₉	C₃×C₅²	direct (N × H)
20. C₃×C₅×C₁₉	C₂×C₅×C₁₁	semidirect
21. C₅²×C₁₁	C₃×D₁₉	direct (N × H)
22. C₁₁×C₁₉	C₂×C₃×C₅²	semidirect
23. C₅×D₁₉	C₃×C₅×C₁₁	direct (N × H)
24. C₃×C₅×C₁₁	C₅×D₁₉	direct (N × H)
26. C₃×D₁₉	C₅²×C₁₁	direct (N × H)
28. C₅×C₁₉	C₂×C₃×C₅×C₁₁	semidirect
29. C₃×C₅²	C₁₁×D₁₉	direct (N × H)
31. C₃×C₁₉	C₂×C₅²×C₁₁	semidirect
32. C₅×C₁₁	C₃×C₅×D₁₉	direct (N × H)
34. D₁₉	C₃×C₅²×C₁₁	direct (N × H)
35. C₃×C₁₁	C₅²×D₁₉	direct (N × H)
37. C₅²	C₃×C₁₁×D₁₉	direct (N × H)
39. C₁₉	C₂×C₃×C₅²×C₁₁	semidirect
40. C₃×C₅	C₅×C₁₁×D₁₉	direct (N × H)
41. C₁₁	C₃×C₅²×D₁₉	direct (N × H)
44. C₅	C₃×C₅×C₁₁×D₁₉	direct (N × H)
45. C₃	C₅²×C₁₁×D₁₉	direct (N × H)

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
C₅²×C₁₁×D₁₉	3
C₃×C₅×C₁₁×D₁₉	5
C₃×C₅²×D₁₉	11
C₂×C₃×C₅²×C₁₁	19

Subgroups — C3×C52×C11×D19 #44535521

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅²×C₁₁×D₁₉ #44535521