Subgroups — C₂×C₃×C₅×C₁₁×D₁₁ #20300131

Order 7260.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₁₁×D₁₁	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₅×C₁₁²	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×C₁₁×D₁₁	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₅×C₁₁²	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃×C₁₁×D₁₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂×C₅×C₁₁²	C₂×C₃	1	1	yes	characteristic, complemented
7	C₅×C₁₁×D₁₁	C₂×C₃	1	2	yes	direct product factor
8	C₂×C₃×C₁₁²	C₂×C₅	1	1	yes	characteristic, complemented
9	C₃×C₁₁×D₁₁	C₂×C₅	1	2	yes	direct product factor
10	C₂²×C₃×C₅×C₁₁	—	11	1	no	maximal
11	C₂×C₃×C₅×D₁₁	C₁₁	1	1	yes	maximal, characteristic, direct product factor
12	C₅×C₁₁²	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
13	C₂×C₁₁×D₁₁	C₃×C₅	1	1	yes	characteristic, direct product factor, Hall
14	C₃×C₁₁²	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
15	C₂×C₃×C₅×C₁₁	—	2	5	no	—
16	C₂×C₃×C₅×C₁₁	—	11	2	no	—
17	C₂×C₃×C₅×C₁₁	D₁₁	1	1	yes	characteristic, direct product factor
18	C₂×C₃×C₅×C₁₁	C₂×C₁₁	1	1	yes	characteristic, complemented
19	C₃×C₅×D₁₁	C₂×C₁₁	1	2	yes	direct product factor
20	C₂×C₁₁²	C₂×C₃×C₅	1	1	yes	characteristic, complemented
21	C₁₁×D₁₁	C₂×C₃×C₅	1	2	yes	direct product factor
22	C₂²×C₅×C₁₁	—	11	1	no	—
23	C₂×C₅×D₁₁	C₃×C₁₁	1	1	yes	characteristic, direct product factor
24	C₃×C₅×C₁₁	—	2	5	no	—
25	C₃×C₅×C₁₁	C₂×D₁₁	1	1	yes	characteristic, direct product factor
26	C₃×C₅×C₁₁	C₂²×C₁₁	1	1	yes	characteristic, complemented
27	C₂²×C₃×C₁₁	—	11	1	no	—
28	C₂×C₃×D₁₁	C₅×C₁₁	1	1	yes	characteristic, direct product factor
29	C₁₁²	C₂²×C₃×C₅	1	1	yes	characteristic, complemented, Sylow
30	C₂×C₅×C₁₁	—	2	5	no	—
31	C₂×C₅×C₁₁	—	11	2	no	—
32	C₂×C₅×C₁₁	C₃×D₁₁	1	1	yes	characteristic, direct product factor
33	C₂×C₅×C₁₁	C₂×C₃×C₁₁	1	1	yes	characteristic, complemented
34	C₅×D₁₁	C₂×C₃×C₁₁	1	2	yes	direct product factor
35	C₂×C₃×C₁₁	—	2	5	no	—
36	C₂×C₃×C₁₁	—	11	2	no	—
37	C₂×C₃×C₁₁	C₅×D₁₁	1	1	yes	characteristic, direct product factor
38	C₂×C₃×C₁₁	C₂×C₅×C₁₁	1	1	yes	characteristic, complemented
39	C₃×D₁₁	C₂×C₅×C₁₁	1	2	yes	direct product factor
40	C₂²×C₃×C₅	—	11	1	no	Hall
41	C₅×C₁₁	—	2	5	no	—
42	C₅×C₁₁	C₂×C₃×D₁₁	1	1	yes	characteristic, direct product factor
43	C₅×C₁₁	C₂²×C₃×C₁₁	1	1	yes	characteristic, complemented
44	C₂²×C₁₁	—	11	1	no	—
45	C₂×D₁₁	C₃×C₅×C₁₁	1	1	yes	characteristic, direct product factor
46	C₃×C₁₁	—	2	5	no	—
47	C₃×C₁₁	C₂×C₅×D₁₁	1	1	yes	characteristic, direct product factor
48	C₃×C₁₁	C₂²×C₅×C₁₁	1	1	yes	characteristic, complemented
49	C₂×C₃×C₅	—	11	2	no	—
50	C₂×C₃×C₅	C₁₁×D₁₁	1	1	yes	characteristic, direct product factor
51	C₂×C₁₁	—	2	5	no	—
52	C₂×C₁₁	—	11	2	no	—
53	C₂×C₁₁	C₃×C₅×D₁₁	1	1	yes	characteristic, direct product factor
54	C₂×C₁₁	C₂×C₃×C₅×C₁₁	1	1	yes	characteristic, complemented
55	D₁₁	C₂×C₃×C₅×C₁₁	1	2	yes	direct product factor
56	C₂²×C₅	—	11	1	no	Hall
57	C₃×C₅	C₂×C₁₁×D₁₁	1	1	yes	characteristic, direct product factor, Hall
58	C₂²×C₃	—	11	1	no	Hall
59	C₁₁	—	2	5	no	—
60	C₁₁	C₂×C₃×C₅×D₁₁	1	1	yes	characteristic, direct product factor
61	C₁₁	C₂²×C₃×C₅×C₁₁	1	1	yes	characteristic, complemented
62	C₂×C₅	—	11	2	no	—
63	C₂×C₅	C₃×C₁₁×D₁₁	1	1	yes	characteristic, direct product factor
64	C₂×C₃	—	11	2	no	—
65	C₂×C₃	C₅×C₁₁×D₁₁	1	1	yes	characteristic, direct product factor
66	C₅	C₂×C₃×C₁₁×D₁₁	1	1	yes	characteristic, direct product factor, Sylow
67	C₂²	—	11	1	no	Sylow
68	C₃	C₂×C₅×C₁₁×D₁₁	1	1	yes	characteristic, direct product factor, Sylow
69	C₂	—	11	2	no	—
70	C₂	C₃×C₅×C₁₁×D₁₁	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃×C₅×C₁₁	D₁₁
commutator, hypocenter	C₁₁	C₂²×C₃×C₅×C₁₁
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₅×C₁₁²	C₂
LCS	G ▷ C₁₁
UCS	C₁ ◁ C₂×C₃×C₅×C₁₁

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×C₁₁×D₁₁	C₂	direct (N × H)
2. C₂×C₃×C₅×C₁₁²	C₂	semidirect
3. C₂×C₅×C₁₁×D₁₁	C₃	direct (N × H)
4. C₃×C₅×C₁₁²	C₂²	semidirect
5. C₂×C₃×C₁₁×D₁₁	C₅	direct (N × H)
6. C₂×C₅×C₁₁²	C₂×C₃	semidirect
7. C₅×C₁₁×D₁₁	C₂×C₃	direct (N × H)
8. C₂×C₃×C₁₁²	C₂×C₅	semidirect
9. C₃×C₁₁×D₁₁	C₂×C₅	direct (N × H)
11. C₂×C₃×C₅×D₁₁	C₁₁	direct (N × H)
12. C₅×C₁₁²	C₂²×C₃	semidirect
13. C₂×C₁₁×D₁₁	C₃×C₅	direct (N × H)
14. C₃×C₁₁²	C₂²×C₅	semidirect
17. C₂×C₃×C₅×C₁₁	D₁₁	direct (N × H)
18. C₂×C₃×C₅×C₁₁	C₂×C₁₁	semidirect
19. C₃×C₅×D₁₁	C₂×C₁₁	direct (N × H)
20. C₂×C₁₁²	C₂×C₃×C₅	semidirect
21. C₁₁×D₁₁	C₂×C₃×C₅	direct (N × H)
23. C₂×C₅×D₁₁	C₃×C₁₁	direct (N × H)
25. C₃×C₅×C₁₁	C₂×D₁₁	direct (N × H)
26. C₃×C₅×C₁₁	C₂²×C₁₁	semidirect
28. C₂×C₃×D₁₁	C₅×C₁₁	direct (N × H)
29. C₁₁²	C₂²×C₃×C₅	semidirect
32. C₂×C₅×C₁₁	C₃×D₁₁	direct (N × H)
33. C₂×C₅×C₁₁	C₂×C₃×C₁₁	semidirect
34. C₅×D₁₁	C₂×C₃×C₁₁	direct (N × H)
37. C₂×C₃×C₁₁	C₅×D₁₁	direct (N × H)
38. C₂×C₃×C₁₁	C₂×C₅×C₁₁	semidirect
39. C₃×D₁₁	C₂×C₅×C₁₁	direct (N × H)
42. C₅×C₁₁	C₂×C₃×D₁₁	direct (N × H)
43. C₅×C₁₁	C₂²×C₃×C₁₁	semidirect
45. C₂×D₁₁	C₃×C₅×C₁₁	direct (N × H)
47. C₃×C₁₁	C₂×C₅×D₁₁	direct (N × H)
48. C₃×C₁₁	C₂²×C₅×C₁₁	semidirect
50. C₂×C₃×C₅	C₁₁×D₁₁	direct (N × H)
53. C₂×C₁₁	C₃×C₅×D₁₁	direct (N × H)
54. C₂×C₁₁	C₂×C₃×C₅×C₁₁	semidirect
55. D₁₁	C₂×C₃×C₅×C₁₁	direct (N × H)
57. C₃×C₅	C₂×C₁₁×D₁₁	direct (N × H)
60. C₁₁	C₂×C₃×C₅×D₁₁	direct (N × H)
61. C₁₁	C₂²×C₃×C₅×C₁₁	semidirect
63. C₂×C₅	C₃×C₁₁×D₁₁	direct (N × H)
65. C₂×C₃	C₅×C₁₁×D₁₁	direct (N × H)
66. C₅	C₂×C₃×C₁₁×D₁₁	direct (N × H)
68. C₃	C₂×C₅×C₁₁×D₁₁	direct (N × H)
70. C₂	C₃×C₅×C₁₁×D₁₁	direct (N × H)

Subgroups — C2×C3×C5×C11×D11 #20300131

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₃×C₅×C₁₁×D₁₁ #20300131