Subgroups — C₃×C₅×C₁₁×D₁₉⋊C₃ #34037876

Order 18810.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₁₁×C₁₉⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×C₁₁×D₁₉⋊C₃	C₃	1	3	yes	maximal, direct product factor
3	C₃×C₅×C₁₁×D₁₉	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃×C₁₁×D₁₉⋊C₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₅×C₁₁×C₁₉⋊C₃	C₂×C₃	1	3	yes	complemented
6	C₃×C₅×C₁₁×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented
7	C₅×C₁₁×D₁₉	C₃²	1	1	yes	characteristic, complemented, Hall
8	C₃×C₁₁×C₁₉⋊C₃	C₂×C₅	1	1	yes	characteristic, complemented, Hall
9	C₃×C₅×D₁₉⋊C₃	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₃×C₁₁×D₁₉	C₃×C₅	1	1	yes	characteristic, complemented
11	C₁₁×D₁₉⋊C₃	C₃×C₅	1	3	yes	direct product factor
12	C₅×C₁₁×C₁₉	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
13	C₂×C₃²×C₅×C₁₁	—	19	1	no	maximal, Hall
14	C₃×C₅×C₁₉⋊C₃	C₂×C₁₁	1	1	yes	characteristic, complemented, Hall
15	C₃×C₁₁×C₁₉	C₂×C₃×C₅	1	1	yes	characteristic, complemented
16	C₁₁×C₁₉⋊C₃	C₂×C₃×C₅	1	3	yes	complemented
17	C₃×C₅×D₁₉	C₃×C₁₁	1	1	yes	characteristic, complemented
18	C₅×D₁₉⋊C₃	C₃×C₁₁	1	3	yes	direct product factor
19	C₃²×C₅×C₁₁	—	19	1	no	Hall
20	C₁₁×D₁₉	C₃²×C₅	1	1	yes	characteristic, complemented, Hall
21	C₃×D₁₉⋊C₃	C₅×C₁₁	1	1	yes	characteristic, direct product factor, Hall
22	C₂×C₃×C₅×C₁₁	—	19	3	no	—
23	C₂×C₃×C₅×C₁₁	—	19	1	no	—
24	C₃×C₅×C₁₉	C₂×C₃×C₁₁	1	1	yes	characteristic, complemented
25	C₅×C₁₉⋊C₃	C₂×C₃×C₁₁	1	3	yes	complemented
26	C₁₁×C₁₉	C₂×C₃²×C₅	1	1	yes	characteristic, complemented, Hall
27	C₂×C₃²×C₁₁	—	19	1	no	Hall
28	C₅×D₁₉	C₃²×C₁₁	1	1	yes	characteristic, complemented, Hall
29	C₃×C₁₉⋊C₃	C₂×C₅×C₁₁	1	1	yes	characteristic, complemented, Hall
30	C₃×C₅×C₁₁	—	19	3	no	—
31	C₃×C₅×C₁₁	D₁₉⋊C₃	1	1	yes	characteristic, direct product factor
32	C₃×D₁₉	C₃×C₅×C₁₁	1	1	yes	characteristic, complemented
33	D₁₉⋊C₃	C₃×C₅×C₁₁	1	3	yes	direct product factor
34	C₂×C₅×C₁₁	—	19	1	no	Hall
35	C₃²×C₁₁	—	19	1	no	Hall
36	C₅×C₁₉	C₂×C₃²×C₁₁	1	1	yes	characteristic, complemented, Hall
37	C₂×C₃²×C₅	—	19	1	no	Hall
38	C₂×C₃×C₁₁	—	19	3	no	—
39	C₂×C₃×C₁₁	—	19	1	no	—
40	C₃×C₁₉	C₂×C₃×C₅×C₁₁	1	1	yes	characteristic, complemented
41	C₁₉⋊C₃	C₂×C₃×C₅×C₁₁	1	3	yes	complemented
42	C₅×C₁₁	C₃×D₁₉⋊C₃	1	1	yes	characteristic, direct product factor, Hall
43	C₃²×C₅	—	19	1	no	Hall
44	D₁₉	C₃²×C₅×C₁₁	1	1	yes	characteristic, complemented, Hall
45	C₃×C₁₁	—	19	3	no	—
46	C₃×C₁₁	C₅×D₁₉⋊C₃	1	1	yes	characteristic, direct product factor
47	C₂×C₃×C₅	—	19	3	no	—
48	C₂×C₃×C₅	—	19	1	no	—
49	C₂×C₁₁	—	19	1	no	Hall
50	C₁₉	C₂×C₃²×C₅×C₁₁	1	1	yes	characteristic, complemented, Sylow
51	C₂×C₃²	—	19	1	no	Hall
52	C₃×C₅	—	19	3	no	—
53	C₃×C₅	C₁₁×D₁₉⋊C₃	1	1	yes	characteristic, direct product factor
54	C₁₁	C₃×C₅×D₁₉⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
55	C₂×C₅	—	19	1	no	Hall
56	C₃²	—	19	1	no	Sylow
57	C₂×C₃	—	19	3	no	—
58	C₂×C₃	—	19	1	no	—
59	C₅	C₃×C₁₁×D₁₉⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
60	C₃	—	19	3	no	—
61	C₃	C₅×C₁₁×D₁₉⋊C₃	1	1	yes	characteristic, direct product factor
62	C₂	—	19	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₅×C₁₁	D₁₉⋊C₃
commutator, cosocle, hypocenter	C₁₉	C₂×C₃²×C₅×C₁₁
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₁₁×C₁₉	C₂×C₃
LCS	G ▷ C₁₉
UCS	C₁ ◁ C₃×C₅×C₁₁

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×C₁₁×C₁₉⋊C₃	C₂	semidirect
2. C₅×C₁₁×D₁₉⋊C₃	C₃	direct (N × H)
3. C₃×C₅×C₁₁×D₁₉	C₃	semidirect
4. C₃×C₁₁×D₁₉⋊C₃	C₅	direct (N × H)
5. C₅×C₁₁×C₁₉⋊C₃	C₂×C₃	semidirect
6. C₃×C₅×C₁₁×C₁₉	C₂×C₃	semidirect
7. C₅×C₁₁×D₁₉	C₃²	semidirect
8. C₃×C₁₁×C₁₉⋊C₃	C₂×C₅	semidirect
9. C₃×C₅×D₁₉⋊C₃	C₁₁	direct (N × H)
10. C₃×C₁₁×D₁₉	C₃×C₅	semidirect
11. C₁₁×D₁₉⋊C₃	C₃×C₅	direct (N × H)
12. C₅×C₁₁×C₁₉	C₂×C₃²	semidirect
14. C₃×C₅×C₁₉⋊C₃	C₂×C₁₁	semidirect
15. C₃×C₁₁×C₁₉	C₂×C₃×C₅	semidirect
16. C₁₁×C₁₉⋊C₃	C₂×C₃×C₅	semidirect
17. C₃×C₅×D₁₉	C₃×C₁₁	semidirect
18. C₅×D₁₉⋊C₃	C₃×C₁₁	direct (N × H)
20. C₁₁×D₁₉	C₃²×C₅	semidirect
21. C₃×D₁₉⋊C₃	C₅×C₁₁	direct (N × H)
24. C₃×C₅×C₁₉	C₂×C₃×C₁₁	semidirect
25. C₅×C₁₉⋊C₃	C₂×C₃×C₁₁	semidirect
26. C₁₁×C₁₉	C₂×C₃²×C₅	semidirect
28. C₅×D₁₉	C₃²×C₁₁	semidirect
29. C₃×C₁₉⋊C₃	C₂×C₅×C₁₁	semidirect
31. C₃×C₅×C₁₁	D₁₉⋊C₃	direct (N × H)
32. C₃×D₁₉	C₃×C₅×C₁₁	semidirect
33. D₁₉⋊C₃	C₃×C₅×C₁₁	direct (N × H)
36. C₅×C₁₉	C₂×C₃²×C₁₁	semidirect
40. C₃×C₁₉	C₂×C₃×C₅×C₁₁	semidirect
41. C₁₉⋊C₃	C₂×C₃×C₅×C₁₁	semidirect
42. C₅×C₁₁	C₃×D₁₉⋊C₃	direct (N × H)
44. D₁₉	C₃²×C₅×C₁₁	semidirect
46. C₃×C₁₁	C₅×D₁₉⋊C₃	direct (N × H)
50. C₁₉	C₂×C₃²×C₅×C₁₁	semidirect
53. C₃×C₅	C₁₁×D₁₉⋊C₃	direct (N × H)
54. C₁₁	C₃×C₅×D₁₉⋊C₃	direct (N × H)
59. C₅	C₃×C₁₁×D₁₉⋊C₃	direct (N × H)
61. C₃	C₅×C₁₁×D₁₉⋊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
C₃×C₅×C₁₁×C₁₉⋊C₃	2
C₅×C₁₁×D₁₉⋊C₃	3
C₃×C₅×C₁₁×D₁₉	3
C₃×C₁₁×D₁₉⋊C₃	5
C₃×C₅×D₁₉⋊C₃	11
C₂×C₃²×C₅×C₁₁	19

Subgroups — C3×C5×C11×D19⋊C3 #34037876

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×C₁₁×D₁₉⋊C₃ #34037876