Subgroups — C₅×D₃×C₁₉×C₁₁⋊C₅ #44535482

Order 31350.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₁₉×C₁₁⋊C₅	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₂×C₅×C₁₉×C₁₁⋊C₅	—	3	1	no	maximal, Hall
3	D₃×C₁₉×C₁₁⋊C₅	C₅	1	5	yes	maximal, direct product factor
4	C₅×D₃×C₁₁×C₁₉	C₅	1	1	yes	maximal, characteristic, complemented
5	C₅×C₁₉×C₁₁⋊C₅	D₃	1	1	yes	characteristic, direct product factor, Hall
6	C₃×C₁₉×C₁₁⋊C₅	C₂×C₅	1	5	yes	complemented
7	C₃×C₅×C₁₁×C₁₉	C₂×C₅	1	1	yes	characteristic, complemented
8	C₅²×D₃×C₁₉	—	11	1	no	maximal, Hall
9	C₂×C₁₉×C₁₁⋊C₅	—	3	5	no	—
10	C₂×C₅×C₁₁×C₁₉	—	3	1	no	—
11	C₅×D₃×C₁₁⋊C₅	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₃×C₅²×C₁₉	—	11	1	no	Hall
13	D₃×C₁₁×C₁₉	C₅²	1	1	yes	characteristic, complemented, Hall
14	C₅×C₁₁×C₁₉	C₅×D₃	1	1	yes	characteristic, complemented
15	C₁₉×C₁₁⋊C₅	C₅×D₃	1	5	yes	direct product factor
16	C₂×C₅²×C₁₉	—	33	1	no	Hall
17	C₃×C₅×C₁₁⋊C₅	C₂×C₁₉	1	1	yes	characteristic, complemented, Hall
18	C₃×C₁₁×C₁₉	C₂×C₅²	1	1	yes	characteristic, complemented, Hall
19	C₅×D₃×C₁₉	—	11	5	no	—
20	C₅×D₃×C₁₉	C₁₁⋊C₅	1	1	yes	characteristic, direct product factor
21	C₂×C₅×C₁₁⋊C₅	—	3	1	no	Hall
22	C₅²×C₁₉	—	11	1	no	Hall
23	C₂×C₁₁×C₁₉	—	3	1	no	Hall
24	C₅×D₃×C₁₁	C₅×C₁₉	1	1	yes	characteristic, complemented
25	D₃×C₁₁⋊C₅	C₅×C₁₉	1	5	yes	direct product factor
26	C₃×C₅×C₁₉	—	11	5	no	—
27	C₃×C₅×C₁₉	C₂×C₁₁⋊C₅	1	1	yes	characteristic, complemented
28	C₅×C₁₁⋊C₅	D₃×C₁₉	1	1	yes	characteristic, direct product factor, Hall
29	C₁₁×C₁₉	C₅²×D₃	1	1	yes	characteristic, complemented, Hall
30	C₂×C₅×C₁₉	—	3	1	no	—
31	C₂×C₅×C₁₉	—	33	5	no	—
32	C₃×C₅×C₁₁	C₂×C₅×C₁₉	1	1	yes	characteristic, complemented
33	C₃×C₁₁⋊C₅	C₂×C₅×C₁₉	1	5	yes	complemented
34	C₅²×D₃	—	11	1	no	Hall
35	D₃×C₁₉	C₅×C₁₁⋊C₅	1	1	yes	characteristic, direct product factor, Hall
36	C₂×C₅×C₁₁	—	3	1	no	—
37	C₂×C₁₁⋊C₅	—	3	5	no	—
38	C₅×C₁₉	—	11	5	no	—
39	C₅×C₁₉	D₃×C₁₁⋊C₅	1	1	yes	characteristic, direct product factor
40	C₃×C₅²	—	11	1	no	Hall
41	D₃×C₁₁	C₅²×C₁₉	1	1	yes	characteristic, complemented, Hall
42	C₃×C₁₉	C₂×C₅×C₁₁⋊C₅	1	1	yes	characteristic, complemented, Hall
43	C₅×C₁₁	C₅×D₃×C₁₉	1	1	yes	characteristic, complemented
44	C₁₁⋊C₅	C₅×D₃×C₁₉	1	5	yes	direct product factor
45	C₂×C₅²	—	33	1	no	Hall
46	C₂×C₁₉	—	3	1	no	Hall
47	C₃×C₁₁	C₂×C₅²×C₁₉	1	1	yes	characteristic, complemented, Hall
48	C₅×D₃	—	11	5	no	—
49	C₅×D₃	C₁₉×C₁₁⋊C₅	1	1	yes	characteristic, direct product factor
50	C₅²	—	11	1	no	Sylow
51	C₂×C₁₁	—	3	1	no	Hall
52	C₁₉	C₅×D₃×C₁₁⋊C₅	1	1	yes	characteristic, direct product factor, Sylow
53	C₃×C₅	—	11	5	no	—
54	C₃×C₅	C₂×C₁₉×C₁₁⋊C₅	1	1	yes	characteristic, complemented
55	C₁₁	C₅²×D₃×C₁₉	1	1	yes	characteristic, complemented, Sylow
56	C₂×C₅	—	3	1	no	—
57	C₂×C₅	—	33	5	no	—
58	D₃	C₅×C₁₉×C₁₁⋊C₅	1	1	yes	characteristic, direct product factor, Hall
59	C₅	—	11	5	no	—
60	C₅	D₃×C₁₉×C₁₁⋊C₅	1	1	yes	characteristic, direct product factor
61	C₃	C₂×C₅×C₁₉×C₁₁⋊C₅	1	1	yes	characteristic, complemented, Sylow
62	C₂	—	3	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅×C₁₉	D₃×C₁₁⋊C₅
commutator, cosocle, hypocenter	C₃×C₁₁	C₂×C₅²×C₁₉
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₁₁×C₁₉	C₂×C₅
LCS	G ▷ C₃×C₁₁
UCS	C₁ ◁ C₅×C₁₉

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×C₁₉×C₁₁⋊C₅	C₂	semidirect
3. D₃×C₁₉×C₁₁⋊C₅	C₅	direct (N × H)
4. C₅×D₃×C₁₁×C₁₉	C₅	semidirect
5. C₅×C₁₉×C₁₁⋊C₅	D₃	direct (N × H)
6. C₃×C₁₉×C₁₁⋊C₅	C₂×C₅	semidirect
7. C₃×C₅×C₁₁×C₁₉	C₂×C₅	semidirect
11. C₅×D₃×C₁₁⋊C₅	C₁₉	direct (N × H)
13. D₃×C₁₁×C₁₉	C₅²	semidirect
14. C₅×C₁₁×C₁₉	C₅×D₃	semidirect
15. C₁₉×C₁₁⋊C₅	C₅×D₃	direct (N × H)
17. C₃×C₅×C₁₁⋊C₅	C₂×C₁₉	semidirect
18. C₃×C₁₁×C₁₉	C₂×C₅²	semidirect
20. C₅×D₃×C₁₉	C₁₁⋊C₅	direct (N × H)
24. C₅×D₃×C₁₁	C₅×C₁₉	semidirect
25. D₃×C₁₁⋊C₅	C₅×C₁₉	direct (N × H)
27. C₃×C₅×C₁₉	C₂×C₁₁⋊C₅	semidirect
28. C₅×C₁₁⋊C₅	D₃×C₁₉	direct (N × H)
29. C₁₁×C₁₉	C₅²×D₃	semidirect
32. C₃×C₅×C₁₁	C₂×C₅×C₁₉	semidirect
33. C₃×C₁₁⋊C₅	C₂×C₅×C₁₉	semidirect
35. D₃×C₁₉	C₅×C₁₁⋊C₅	direct (N × H)
39. C₅×C₁₉	D₃×C₁₁⋊C₅	direct (N × H)
41. D₃×C₁₁	C₅²×C₁₉	semidirect
42. C₃×C₁₉	C₂×C₅×C₁₁⋊C₅	semidirect
43. C₅×C₁₁	C₅×D₃×C₁₉	semidirect
44. C₁₁⋊C₅	C₅×D₃×C₁₉	direct (N × H)
47. C₃×C₁₁	C₂×C₅²×C₁₉	semidirect
49. C₅×D₃	C₁₉×C₁₁⋊C₅	direct (N × H)
52. C₁₉	C₅×D₃×C₁₁⋊C₅	direct (N × H)
54. C₃×C₅	C₂×C₁₉×C₁₁⋊C₅	semidirect
55. C₁₁	C₅²×D₃×C₁₉	semidirect
58. D₃	C₅×C₁₉×C₁₁⋊C₅	direct (N × H)
60. C₅	D₃×C₁₉×C₁₁⋊C₅	direct (N × H)
61. C₃	C₂×C₅×C₁₉×C₁₁⋊C₅	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅×C₁₉×C₁₁⋊C₅	2
C₂×C₅×C₁₉×C₁₁⋊C₅	3
D₃×C₁₉×C₁₁⋊C₅	5
C₅×D₃×C₁₁×C₁₉	5
C₅²×D₃×C₁₉	11
C₅×D₃×C₁₁⋊C₅	19

Subgroups — C5×D3×C19×C11⋊C5 #44535482

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₃×C₁₉×C₁₁⋊C₅ #44535482