Subgroups — C₂×C₃×C₇×C₁₃×D₁₁ #26046597

Order 12012.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×C₁₃×D₁₁	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₇×C₁₁×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₇×C₁₃×D₁₁	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₇×C₁₁×C₁₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₇×C₁₃×D₁₁	C₂×C₃	1	2	yes	direct product factor
6	C₂×C₇×C₁₁×C₁₃	C₂×C₃	1	1	yes	characteristic, complemented
7	C₂×C₃×C₁₃×D₁₁	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂²×C₃×C₇×C₁₃	—	11	1	no	maximal, Hall
9	C₇×C₁₁×C₁₃	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
10	C₂×C₃×C₇×D₁₁	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂×C₃×C₁₁×C₁₃	C₂×C₇	1	1	yes	characteristic, complemented
12	C₃×C₁₃×D₁₁	C₂×C₇	1	2	yes	direct product factor
13	C₂×C₁₃×D₁₁	C₃×C₇	1	1	yes	characteristic, direct product factor, Hall
14	C₂×C₃×C₇×C₁₃	—	11	2	no	—
15	C₂×C₃×C₇×C₁₃	D₁₁	1	1	yes	characteristic, direct product factor
16	C₂×C₃×C₇×C₁₁	C₂×C₁₃	1	1	yes	characteristic, complemented
17	C₃×C₇×D₁₁	C₂×C₁₃	1	2	yes	direct product factor
18	C₃×C₁₁×C₁₃	C₂²×C₇	1	1	yes	characteristic, complemented, Hall
19	C₂²×C₇×C₁₃	—	11	1	no	Hall
20	C₂×C₇×D₁₁	C₃×C₁₃	1	1	yes	characteristic, direct product factor, Hall
21	C₂×C₁₁×C₁₃	C₂×C₃×C₇	1	1	yes	characteristic, complemented
22	C₁₃×D₁₁	C₂×C₃×C₇	1	2	yes	direct product factor
23	C₃×C₇×C₁₃	C₂×D₁₁	1	1	yes	characteristic, direct product factor, Hall
24	C₃×C₇×C₁₁	C₂²×C₁₃	1	1	yes	characteristic, complemented, Hall
25	C₂×C₇×C₁₃	—	11	2	no	—
26	C₂×C₇×C₁₃	C₃×D₁₁	1	1	yes	characteristic, direct product factor
27	C₂²×C₃×C₁₃	—	11	1	no	Hall
28	C₂×C₇×C₁₁	C₂×C₃×C₁₃	1	1	yes	characteristic, complemented
29	C₇×D₁₁	C₂×C₃×C₁₃	1	2	yes	direct product factor
30	C₁₁×C₁₃	C₂²×C₃×C₇	1	1	yes	characteristic, complemented, Hall
31	C₂×C₃×D₁₁	C₇×C₁₃	1	1	yes	characteristic, direct product factor, Hall
32	C₇×C₁₃	C₂×C₃×D₁₁	1	1	yes	characteristic, direct product factor, Hall
33	C₂²×C₃×C₇	—	11	1	no	Hall
34	C₂×C₃×C₁₃	—	11	2	no	—
35	C₂×C₃×C₁₃	C₇×D₁₁	1	1	yes	characteristic, direct product factor
36	C₇×C₁₁	C₂²×C₃×C₁₃	1	1	yes	characteristic, complemented, Hall
37	C₂×C₃×C₁₁	C₂×C₇×C₁₃	1	1	yes	characteristic, complemented
38	C₃×D₁₁	C₂×C₇×C₁₃	1	2	yes	direct product factor
39	C₂²×C₁₃	—	11	1	no	Hall
40	C₂×D₁₁	C₃×C₇×C₁₃	1	1	yes	characteristic, direct product factor, Hall
41	C₂×C₃×C₇	—	11	2	no	—
42	C₂×C₃×C₇	C₁₃×D₁₁	1	1	yes	characteristic, direct product factor
43	C₃×C₁₃	C₂×C₇×D₁₁	1	1	yes	characteristic, direct product factor, Hall
44	C₃×C₁₁	C₂²×C₇×C₁₃	1	1	yes	characteristic, complemented, Hall
45	C₂²×C₇	—	11	1	no	Hall
46	C₂×C₁₃	—	11	2	no	—
47	C₂×C₁₃	C₃×C₇×D₁₁	1	1	yes	characteristic, direct product factor
48	C₂×C₁₁	C₂×C₃×C₇×C₁₃	1	1	yes	characteristic, complemented
49	D₁₁	C₂×C₃×C₇×C₁₃	1	2	yes	direct product factor
50	C₃×C₇	C₂×C₁₃×D₁₁	1	1	yes	characteristic, direct product factor, Hall
51	C₂×C₇	—	11	2	no	—
52	C₂×C₇	C₃×C₁₃×D₁₁	1	1	yes	characteristic, direct product factor
53	C₁₃	C₂×C₃×C₇×D₁₁	1	1	yes	characteristic, direct product factor, Sylow
54	C₂²×C₃	—	11	1	no	Hall
55	C₁₁	C₂²×C₃×C₇×C₁₃	1	1	yes	characteristic, complemented, Sylow
56	C₇	C₂×C₃×C₁₃×D₁₁	1	1	yes	characteristic, direct product factor, Sylow
57	C₂×C₃	—	11	2	no	—
58	C₂×C₃	C₇×C₁₃×D₁₁	1	1	yes	characteristic, direct product factor
59	C₂²	—	11	1	no	Sylow
60	C₃	C₂×C₇×C₁₃×D₁₁	1	1	yes	characteristic, direct product factor, Sylow
61	C₂	—	11	2	no	—
62	C₂	C₃×C₇×C₁₃×D₁₁	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃×C₇×C₁₃	D₁₁
commutator, cosocle, hypocenter	C₁₁	C₂²×C₃×C₇×C₁₃
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₇×C₁₁×C₁₃	C₂
LCS	G ▷ C₁₁
UCS	C₁ ◁ C₂×C₃×C₇×C₁₃

Complements

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

N	H ≅ G/N	type
1. C₃×C₇×C₁₃×D₁₁	C₂	direct (N × H)
2. C₂×C₃×C₇×C₁₁×C₁₃	C₂	semidirect
3. C₂×C₇×C₁₃×D₁₁	C₃	direct (N × H)
4. C₃×C₇×C₁₁×C₁₃	C₂²	semidirect
5. C₇×C₁₃×D₁₁	C₂×C₃	direct (N × H)
6. C₂×C₇×C₁₁×C₁₃	C₂×C₃	semidirect
7. C₂×C₃×C₁₃×D₁₁	C₇	direct (N × H)
9. C₇×C₁₁×C₁₃	C₂²×C₃	semidirect
10. C₂×C₃×C₇×D₁₁	C₁₃	direct (N × H)
11. C₂×C₃×C₁₁×C₁₃	C₂×C₇	semidirect
12. C₃×C₁₃×D₁₁	C₂×C₇	direct (N × H)
13. C₂×C₁₃×D₁₁	C₃×C₇	direct (N × H)
15. C₂×C₃×C₇×C₁₃	D₁₁	direct (N × H)
16. C₂×C₃×C₇×C₁₁	C₂×C₁₃	semidirect
17. C₃×C₇×D₁₁	C₂×C₁₃	direct (N × H)
18. C₃×C₁₁×C₁₃	C₂²×C₇	semidirect
20. C₂×C₇×D₁₁	C₃×C₁₃	direct (N × H)
21. C₂×C₁₁×C₁₃	C₂×C₃×C₇	semidirect
22. C₁₃×D₁₁	C₂×C₃×C₇	direct (N × H)
23. C₃×C₇×C₁₃	C₂×D₁₁	direct (N × H)
24. C₃×C₇×C₁₁	C₂²×C₁₃	semidirect
26. C₂×C₇×C₁₃	C₃×D₁₁	direct (N × H)
28. C₂×C₇×C₁₁	C₂×C₃×C₁₃	semidirect
29. C₇×D₁₁	C₂×C₃×C₁₃	direct (N × H)
30. C₁₁×C₁₃	C₂²×C₃×C₇	semidirect
31. C₂×C₃×D₁₁	C₇×C₁₃	direct (N × H)
32. C₇×C₁₃	C₂×C₃×D₁₁	direct (N × H)
35. C₂×C₃×C₁₃	C₇×D₁₁	direct (N × H)
36. C₇×C₁₁	C₂²×C₃×C₁₃	semidirect
37. C₂×C₃×C₁₁	C₂×C₇×C₁₃	semidirect
38. C₃×D₁₁	C₂×C₇×C₁₃	direct (N × H)
40. C₂×D₁₁	C₃×C₇×C₁₃	direct (N × H)
42. C₂×C₃×C₇	C₁₃×D₁₁	direct (N × H)
43. C₃×C₁₃	C₂×C₇×D₁₁	direct (N × H)
44. C₃×C₁₁	C₂²×C₇×C₁₃	semidirect
47. C₂×C₁₃	C₃×C₇×D₁₁	direct (N × H)
48. C₂×C₁₁	C₂×C₃×C₇×C₁₃	semidirect
49. D₁₁	C₂×C₃×C₇×C₁₃	direct (N × H)
50. C₃×C₇	C₂×C₁₃×D₁₁	direct (N × H)
52. C₂×C₇	C₃×C₁₃×D₁₁	direct (N × H)
53. C₁₃	C₂×C₃×C₇×D₁₁	direct (N × H)
55. C₁₁	C₂²×C₃×C₇×C₁₃	semidirect
56. C₇	C₂×C₃×C₁₃×D₁₁	direct (N × H)
58. C₂×C₃	C₇×C₁₃×D₁₁	direct (N × H)
60. C₃	C₂×C₇×C₁₃×D₁₁	direct (N × H)
62. C₂	C₃×C₇×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×C₇×C₁₃×D₁₁	2
C₂×C₃×C₇×C₁₁×C₁₃	2
C₂×C₇×C₁₃×D₁₁	3
C₂×C₃×C₁₃×D₁₁	7
C₂²×C₃×C₇×C₁₃	11
C₂×C₃×C₇×D₁₁	13

Subgroups — C2×C3×C7×C13×D11 #26046597

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₇×C₁₃×D₁₁ #26046597