Subgroups — C₂×C₃×C₁₁×C₁₃×D₁₁ #34038484

Order 18876.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₁×C₁₃×D₁₁	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₁₁²×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₁×C₁₃×D₁₁	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₁₁²×C₁₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₁₁×C₁₃×D₁₁	C₂×C₃	1	2	yes	direct product factor
6	C₂×C₁₁²×C₁₃	C₂×C₃	1	1	yes	characteristic, complemented
7	C₂²×C₃×C₁₁×C₁₃	—	11	1	no	maximal
8	C₂×C₃×C₁₃×D₁₁	C₁₁	1	1	yes	maximal, characteristic, direct product factor
9	C₁₁²×C₁₃	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
10	C₂×C₃×C₁₁×D₁₁	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂×C₃×C₁₁×C₁₃	—	2	5	no	—
12	C₂×C₃×C₁₁×C₁₃	—	11	2	no	—
13	C₂×C₃×C₁₁×C₁₃	D₁₁	1	1	yes	characteristic, direct product factor
14	C₂×C₃×C₁₁×C₁₃	C₂×C₁₁	1	1	yes	characteristic, complemented
15	C₃×C₁₃×D₁₁	C₂×C₁₁	1	2	yes	direct product factor
16	C₂×C₃×C₁₁²	C₂×C₁₃	1	1	yes	characteristic, complemented
17	C₃×C₁₁×D₁₁	C₂×C₁₃	1	2	yes	direct product factor
18	C₂²×C₁₁×C₁₃	—	11	1	no	—
19	C₂×C₁₃×D₁₁	C₃×C₁₁	1	1	yes	characteristic, direct product factor
20	C₂×C₁₁×D₁₁	C₃×C₁₃	1	1	yes	characteristic, direct product factor, Hall
21	C₃×C₁₁×C₁₃	—	2	5	no	—
22	C₃×C₁₁×C₁₃	C₂×D₁₁	1	1	yes	characteristic, direct product factor
23	C₃×C₁₁×C₁₃	C₂²×C₁₁	1	1	yes	characteristic, complemented
24	C₃×C₁₁²	C₂²×C₁₃	1	1	yes	characteristic, complemented, Hall
25	C₂×C₁₁×C₁₃	—	2	5	no	—
26	C₂×C₁₁×C₁₃	—	11	2	no	—
27	C₂×C₁₁×C₁₃	C₃×D₁₁	1	1	yes	characteristic, direct product factor
28	C₂×C₁₁×C₁₃	C₂×C₃×C₁₁	1	1	yes	characteristic, complemented
29	C₁₃×D₁₁	C₂×C₃×C₁₁	1	2	yes	direct product factor
30	C₂×C₁₁²	C₂×C₃×C₁₃	1	1	yes	characteristic, complemented
31	C₁₁×D₁₁	C₂×C₃×C₁₃	1	2	yes	direct product factor
32	C₂²×C₃×C₁₃	—	11	1	no	Hall
33	C₁₁×C₁₃	—	2	5	no	—
34	C₁₁×C₁₃	C₂×C₃×D₁₁	1	1	yes	characteristic, direct product factor
35	C₁₁×C₁₃	C₂²×C₃×C₁₁	1	1	yes	characteristic, complemented
36	C₂²×C₃×C₁₁	—	11	1	no	—
37	C₂×C₃×D₁₁	C₁₁×C₁₃	1	1	yes	characteristic, direct product factor
38	C₁₁²	C₂²×C₃×C₁₃	1	1	yes	characteristic, complemented, Sylow
39	C₂×C₃×C₁₃	—	11	2	no	—
40	C₂×C₃×C₁₃	C₁₁×D₁₁	1	1	yes	characteristic, direct product factor
41	C₂×C₃×C₁₁	—	2	5	no	—
42	C₂×C₃×C₁₁	—	11	2	no	—
43	C₂×C₃×C₁₁	C₁₃×D₁₁	1	1	yes	characteristic, direct product factor
44	C₂×C₃×C₁₁	C₂×C₁₁×C₁₃	1	1	yes	characteristic, complemented
45	C₃×D₁₁	C₂×C₁₁×C₁₃	1	2	yes	direct product factor
46	C₂²×C₁₃	—	11	1	no	Hall
47	C₂²×C₁₁	—	11	1	no	—
48	C₂×D₁₁	C₃×C₁₁×C₁₃	1	1	yes	characteristic, direct product factor
49	C₃×C₁₃	C₂×C₁₁×D₁₁	1	1	yes	characteristic, direct product factor, Hall
50	C₃×C₁₁	—	2	5	no	—
51	C₃×C₁₁	C₂×C₁₃×D₁₁	1	1	yes	characteristic, direct product factor
52	C₃×C₁₁	C₂²×C₁₁×C₁₃	1	1	yes	characteristic, complemented
53	C₂×C₁₃	—	11	2	no	—
54	C₂×C₁₃	C₃×C₁₁×D₁₁	1	1	yes	characteristic, direct product factor
55	C₂×C₁₁	—	2	5	no	—
56	C₂×C₁₁	—	11	2	no	—
57	C₂×C₁₁	C₃×C₁₃×D₁₁	1	1	yes	characteristic, direct product factor
58	C₂×C₁₁	C₂×C₃×C₁₁×C₁₃	1	1	yes	characteristic, complemented
59	D₁₁	C₂×C₃×C₁₁×C₁₃	1	2	yes	direct product factor
60	C₁₃	C₂×C₃×C₁₁×D₁₁	1	1	yes	characteristic, direct product factor, Sylow
61	C₂²×C₃	—	11	1	no	Hall
62	C₁₁	—	2	5	no	—
63	C₁₁	C₂×C₃×C₁₃×D₁₁	1	1	yes	characteristic, direct product factor
64	C₁₁	C₂²×C₃×C₁₁×C₁₃	1	1	yes	characteristic, complemented
65	C₂×C₃	—	11	2	no	—
66	C₂×C₃	C₁₁×C₁₃×D₁₁	1	1	yes	characteristic, direct product factor
67	C₂²	—	11	1	no	Sylow
68	C₃	C₂×C₁₁×C₁₃×D₁₁	1	1	yes	characteristic, direct product factor, Sylow
69	C₂	—	11	2	no	—
70	C₂	C₃×C₁₁×C₁₃×D₁₁	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃×C₁₁×C₁₃	D₁₁
commutator, cosocle, hypocenter	C₁₁	C₂²×C₃×C₁₁×C₁₃
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₁₁²×C₁₃	C₂
LCS	G ▷ C₁₁
UCS	C₁ ◁ C₂×C₃×C₁₁×C₁₃

Complements

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

N	H ≅ G/N	type
1. C₃×C₁₁×C₁₃×D₁₁	C₂	direct (N × H)
2. C₂×C₃×C₁₁²×C₁₃	C₂	semidirect
3. C₂×C₁₁×C₁₃×D₁₁	C₃	direct (N × H)
4. C₃×C₁₁²×C₁₃	C₂²	semidirect
5. C₁₁×C₁₃×D₁₁	C₂×C₃	direct (N × H)
6. C₂×C₁₁²×C₁₃	C₂×C₃	semidirect
8. C₂×C₃×C₁₃×D₁₁	C₁₁	direct (N × H)
9. C₁₁²×C₁₃	C₂²×C₃	semidirect
10. C₂×C₃×C₁₁×D₁₁	C₁₃	direct (N × H)
13. C₂×C₃×C₁₁×C₁₃	D₁₁	direct (N × H)
14. C₂×C₃×C₁₁×C₁₃	C₂×C₁₁	semidirect
15. C₃×C₁₃×D₁₁	C₂×C₁₁	direct (N × H)
16. C₂×C₃×C₁₁²	C₂×C₁₃	semidirect
17. C₃×C₁₁×D₁₁	C₂×C₁₃	direct (N × H)
19. C₂×C₁₃×D₁₁	C₃×C₁₁	direct (N × H)
20. C₂×C₁₁×D₁₁	C₃×C₁₃	direct (N × H)
22. C₃×C₁₁×C₁₃	C₂×D₁₁	direct (N × H)
23. C₃×C₁₁×C₁₃	C₂²×C₁₁	semidirect
24. C₃×C₁₁²	C₂²×C₁₃	semidirect
27. C₂×C₁₁×C₁₃	C₃×D₁₁	direct (N × H)
28. C₂×C₁₁×C₁₃	C₂×C₃×C₁₁	semidirect
29. C₁₃×D₁₁	C₂×C₃×C₁₁	direct (N × H)
30. C₂×C₁₁²	C₂×C₃×C₁₃	semidirect
31. C₁₁×D₁₁	C₂×C₃×C₁₃	direct (N × H)
34. C₁₁×C₁₃	C₂×C₃×D₁₁	direct (N × H)
35. C₁₁×C₁₃	C₂²×C₃×C₁₁	semidirect
37. C₂×C₃×D₁₁	C₁₁×C₁₃	direct (N × H)
38. C₁₁²	C₂²×C₃×C₁₃	semidirect
40. C₂×C₃×C₁₃	C₁₁×D₁₁	direct (N × H)
43. C₂×C₃×C₁₁	C₁₃×D₁₁	direct (N × H)
44. C₂×C₃×C₁₁	C₂×C₁₁×C₁₃	semidirect
45. C₃×D₁₁	C₂×C₁₁×C₁₃	direct (N × H)
48. C₂×D₁₁	C₃×C₁₁×C₁₃	direct (N × H)
49. C₃×C₁₃	C₂×C₁₁×D₁₁	direct (N × H)
51. C₃×C₁₁	C₂×C₁₃×D₁₁	direct (N × H)
52. C₃×C₁₁	C₂²×C₁₁×C₁₃	semidirect
54. C₂×C₁₃	C₃×C₁₁×D₁₁	direct (N × H)
57. C₂×C₁₁	C₃×C₁₃×D₁₁	direct (N × H)
58. C₂×C₁₁	C₂×C₃×C₁₁×C₁₃	semidirect
59. D₁₁	C₂×C₃×C₁₁×C₁₃	direct (N × H)
60. C₁₃	C₂×C₃×C₁₁×D₁₁	direct (N × H)
63. C₁₁	C₂×C₃×C₁₃×D₁₁	direct (N × H)
64. C₁₁	C₂²×C₃×C₁₁×C₁₃	semidirect
66. C₂×C₃	C₁₁×C₁₃×D₁₁	direct (N × H)
68. C₃	C₂×C₁₁×C₁₃×D₁₁	direct (N × H)
70. C₂	C₃×C₁₁×C₁₃×D₁₁	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×C₁₁×C₁₃×D₁₁	2
C₂×C₃×C₁₁²×C₁₃	2
C₂×C₁₁×C₁₃×D₁₁	3
C₂²×C₃×C₁₁×C₁₃	11
C₂×C₃×C₁₃×D₁₁	11
C₂×C₃×C₁₁×D₁₁	13

Subgroups — C2×C3×C11×C13×D11 #34038484

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₁₁×C₁₃×D₁₁ #34038484