Subgroups — C₂×C₃×D₃×C₁₁×C₁₃ #19104250

Order 5148.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₃×C₁₁×C₁₃	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃²×C₁₁×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₃×C₁₁×C₁₃	—	3	1	no	maximal
4	C₂×D₃×C₁₁×C₁₃	C₃	1	1	yes	maximal, characteristic, direct product factor
5	C₃²×C₁₁×C₁₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×C₃×C₁₁×C₁₃	—	2	1	no	—
7	C₂×C₃×C₁₁×C₁₃	—	3	2	no	—
8	C₂×C₃×C₁₁×C₁₃	D₃	1	1	yes	characteristic, direct product factor
9	C₂×C₃×C₁₁×C₁₃	C₂×C₃	1	1	yes	characteristic, complemented
10	D₃×C₁₁×C₁₃	C₂×C₃	1	2	yes	direct product factor
11	C₂²×C₁₁×C₁₃	—	3	1	no	Hall
12	C₂×C₃×D₃×C₁₃	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₃×C₁₁×C₁₃	—	2	1	no	—
14	C₃×C₁₁×C₁₃	C₂×D₃	1	1	yes	characteristic, direct product factor
15	C₃×C₁₁×C₁₃	C₂²×C₃	1	1	yes	characteristic, complemented
16	C₂×C₃×D₃×C₁₁	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂×C₁₁×C₁₃	—	3	2	no	—
18	C₂×C₁₁×C₁₃	C₃×D₃	1	1	yes	characteristic, direct product factor
19	C₂×C₃²×C₁₃	C₂×C₁₁	1	1	yes	characteristic, complemented
20	C₃×D₃×C₁₃	C₂×C₁₁	1	2	yes	direct product factor
21	C₂×C₃²×C₁₁	C₂×C₁₃	1	1	yes	characteristic, complemented
22	C₃×D₃×C₁₁	C₂×C₁₃	1	2	yes	direct product factor
23	C₂²×C₃×C₁₃	—	3	1	no	—
24	C₂×D₃×C₁₃	C₃×C₁₁	1	1	yes	characteristic, direct product factor
25	C₁₁×C₁₃	C₂×C₃×D₃	1	1	yes	characteristic, direct product factor, Hall
26	C₂²×C₃×C₁₁	—	3	1	no	—
27	C₂×D₃×C₁₁	C₃×C₁₃	1	1	yes	characteristic, direct product factor
28	C₃²×C₁₃	C₂²×C₁₁	1	1	yes	characteristic, complemented, Hall
29	C₃²×C₁₁	C₂²×C₁₃	1	1	yes	characteristic, complemented, Hall
30	C₂×C₃×C₁₃	—	2	1	no	—
31	C₂×C₃×C₁₃	—	3	2	no	—
32	C₂×C₃×C₁₃	D₃×C₁₁	1	1	yes	characteristic, direct product factor
33	C₂×C₃×C₁₃	C₂×C₃×C₁₁	1	1	yes	characteristic, complemented
34	D₃×C₁₃	C₂×C₃×C₁₁	1	2	yes	direct product factor
35	C₂×C₃×C₁₁	—	2	1	no	—
36	C₂×C₃×C₁₁	—	3	2	no	—
37	C₂×C₃×C₁₁	D₃×C₁₃	1	1	yes	characteristic, direct product factor
38	C₂×C₃×C₁₁	C₂×C₃×C₁₃	1	1	yes	characteristic, complemented
39	D₃×C₁₁	C₂×C₃×C₁₃	1	2	yes	direct product factor
40	C₂²×C₁₃	—	3	1	no	Hall
41	C₂²×C₁₁	—	3	1	no	Hall
42	C₃×C₁₃	—	2	1	no	—
43	C₃×C₁₃	C₂×D₃×C₁₁	1	1	yes	characteristic, direct product factor
44	C₃×C₁₃	C₂²×C₃×C₁₁	1	1	yes	characteristic, complemented
45	C₂×C₃×D₃	C₁₁×C₁₃	1	1	yes	characteristic, direct product factor, Hall
46	C₃×C₁₁	—	2	1	no	—
47	C₃×C₁₁	C₂×D₃×C₁₃	1	1	yes	characteristic, direct product factor
48	C₃×C₁₁	C₂²×C₃×C₁₃	1	1	yes	characteristic, complemented
49	C₂×C₁₃	—	3	2	no	—
50	C₂×C₁₃	C₃×D₃×C₁₁	1	1	yes	characteristic, direct product factor
51	C₂×C₁₁	—	3	2	no	—
52	C₂×C₁₁	C₃×D₃×C₁₃	1	1	yes	characteristic, direct product factor
53	C₂×C₃²	C₂×C₁₁×C₁₃	1	1	yes	characteristic, complemented
54	C₃×D₃	C₂×C₁₁×C₁₃	1	2	yes	direct product factor
55	C₁₃	C₂×C₃×D₃×C₁₁	1	1	yes	characteristic, direct product factor, Sylow
56	C₂²×C₃	—	3	1	no	—
57	C₂×D₃	C₃×C₁₁×C₁₃	1	1	yes	characteristic, direct product factor
58	C₁₁	C₂×C₃×D₃×C₁₃	1	1	yes	characteristic, direct product factor, Sylow
59	C₃²	C₂²×C₁₁×C₁₃	1	1	yes	characteristic, complemented, Sylow
60	C₂×C₃	—	2	1	no	—
61	C₂×C₃	—	3	2	no	—
62	C₂×C₃	D₃×C₁₁×C₁₃	1	1	yes	characteristic, direct product factor
63	C₂×C₃	C₂×C₃×C₁₁×C₁₃	1	1	yes	characteristic, complemented
64	D₃	C₂×C₃×C₁₁×C₁₃	1	2	yes	direct product factor
65	C₂²	—	3	1	no	Sylow
66	C₃	—	2	1	no	—
67	C₃	C₂×D₃×C₁₁×C₁₃	1	1	yes	characteristic, direct product factor
68	C₃	C₂²×C₃×C₁₁×C₁₃	1	1	yes	characteristic, complemented
69	C₂	—	3	2	no	—
70	C₂	C₃×D₃×C₁₁×C₁₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃×C₁₁×C₁₃	D₃
commutator, hypocenter	C₃	C₂²×C₃×C₁₁×C₁₃
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₁₁×C₁₃	C₂
LCS	G ▷ C₃
UCS	C₁ ◁ C₂×C₃×C₁₁×C₁₃

Complements

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

N	H ≅ G/N	type
1. C₃×D₃×C₁₁×C₁₃	C₂	direct (N × H)
2. C₂×C₃²×C₁₁×C₁₃	C₂	semidirect
4. C₂×D₃×C₁₁×C₁₃	C₃	direct (N × H)
5. C₃²×C₁₁×C₁₃	C₂²	semidirect
8. C₂×C₃×C₁₁×C₁₃	D₃	direct (N × H)
9. C₂×C₃×C₁₁×C₁₃	C₂×C₃	semidirect
10. D₃×C₁₁×C₁₃	C₂×C₃	direct (N × H)
12. C₂×C₃×D₃×C₁₃	C₁₁	direct (N × H)
14. C₃×C₁₁×C₁₃	C₂×D₃	direct (N × H)
15. C₃×C₁₁×C₁₃	C₂²×C₃	semidirect
16. C₂×C₃×D₃×C₁₁	C₁₃	direct (N × H)
18. C₂×C₁₁×C₁₃	C₃×D₃	direct (N × H)
19. C₂×C₃²×C₁₃	C₂×C₁₁	semidirect
20. C₃×D₃×C₁₃	C₂×C₁₁	direct (N × H)
21. C₂×C₃²×C₁₁	C₂×C₁₃	semidirect
22. C₃×D₃×C₁₁	C₂×C₁₃	direct (N × H)
24. C₂×D₃×C₁₃	C₃×C₁₁	direct (N × H)
25. C₁₁×C₁₃	C₂×C₃×D₃	direct (N × H)
27. C₂×D₃×C₁₁	C₃×C₁₃	direct (N × H)
28. C₃²×C₁₃	C₂²×C₁₁	semidirect
29. C₃²×C₁₁	C₂²×C₁₃	semidirect
32. C₂×C₃×C₁₃	D₃×C₁₁	direct (N × H)
33. C₂×C₃×C₁₃	C₂×C₃×C₁₁	semidirect
34. D₃×C₁₃	C₂×C₃×C₁₁	direct (N × H)
37. C₂×C₃×C₁₁	D₃×C₁₃	direct (N × H)
38. C₂×C₃×C₁₁	C₂×C₃×C₁₃	semidirect
39. D₃×C₁₁	C₂×C₃×C₁₃	direct (N × H)
43. C₃×C₁₃	C₂×D₃×C₁₁	direct (N × H)
44. C₃×C₁₃	C₂²×C₃×C₁₁	semidirect
45. C₂×C₃×D₃	C₁₁×C₁₃	direct (N × H)
47. C₃×C₁₁	C₂×D₃×C₁₃	direct (N × H)
48. C₃×C₁₁	C₂²×C₃×C₁₃	semidirect
50. C₂×C₁₃	C₃×D₃×C₁₁	direct (N × H)
52. C₂×C₁₁	C₃×D₃×C₁₃	direct (N × H)
53. C₂×C₃²	C₂×C₁₁×C₁₃	semidirect
54. C₃×D₃	C₂×C₁₁×C₁₃	direct (N × H)
55. C₁₃	C₂×C₃×D₃×C₁₁	direct (N × H)
57. C₂×D₃	C₃×C₁₁×C₁₃	direct (N × H)
58. C₁₁	C₂×C₃×D₃×C₁₃	direct (N × H)
59. C₃²	C₂²×C₁₁×C₁₃	semidirect
62. C₂×C₃	D₃×C₁₁×C₁₃	direct (N × H)
63. C₂×C₃	C₂×C₃×C₁₁×C₁₃	semidirect
64. D₃	C₂×C₃×C₁₁×C₁₃	direct (N × H)
67. C₃	C₂×D₃×C₁₁×C₁₃	direct (N × H)
68. C₃	C₂²×C₃×C₁₁×C₁₃	semidirect
70. C₂	C₃×D₃×C₁₁×C₁₃	direct (N × H)

Subgroups — C2×C3×D3×C11×C13 #19104250

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₃×D₃×C₁₁×C₁₃ #19104250