Subgroups — C₂×C₃×C₅×C₁₁×D₁₃ #22575196

Order 8580.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₁₁×D₁₃	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₅×C₁₁×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×C₁₁×D₁₃	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₅×C₁₁×C₁₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃×C₁₁×D₁₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂×C₅×C₁₁×C₁₃	C₂×C₃	1	1	yes	characteristic, complemented
7	C₅×C₁₁×D₁₃	C₂×C₃	1	2	yes	direct product factor
8	C₂×C₃×C₁₁×C₁₃	C₂×C₅	1	1	yes	characteristic, complemented
9	C₃×C₁₁×D₁₃	C₂×C₅	1	2	yes	direct product factor
10	C₂×C₃×C₅×D₁₃	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₅×C₁₁×C₁₃	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
12	C₂²×C₃×C₅×C₁₁	—	13	1	no	maximal, Hall
13	C₂×C₁₁×D₁₃	C₃×C₅	1	1	yes	characteristic, direct product factor, Hall
14	C₃×C₁₁×C₁₃	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
15	C₂×C₃×C₅×C₁₃	C₂×C₁₁	1	1	yes	characteristic, complemented
16	C₃×C₅×D₁₃	C₂×C₁₁	1	2	yes	direct product factor
17	C₂×C₃×C₅×C₁₁	—	13	2	no	—
18	C₂×C₃×C₅×C₁₁	D₁₃	1	1	yes	characteristic, direct product factor
19	C₂×C₁₁×C₁₃	C₂×C₃×C₅	1	1	yes	characteristic, complemented
20	C₁₁×D₁₃	C₂×C₃×C₅	1	2	yes	direct product factor
21	C₂×C₅×D₁₃	C₃×C₁₁	1	1	yes	characteristic, direct product factor, Hall
22	C₂²×C₅×C₁₁	—	13	1	no	Hall
23	C₃×C₅×C₁₃	C₂²×C₁₁	1	1	yes	characteristic, complemented, Hall
24	C₃×C₅×C₁₁	C₂×D₁₃	1	1	yes	characteristic, direct product factor, Hall
25	C₂×C₃×D₁₃	C₅×C₁₁	1	1	yes	characteristic, direct product factor, Hall
26	C₁₁×C₁₃	C₂²×C₃×C₅	1	1	yes	characteristic, complemented, Hall
27	C₂²×C₃×C₁₁	—	13	1	no	Hall
28	C₂×C₅×C₁₃	C₂×C₃×C₁₁	1	1	yes	characteristic, complemented
29	C₅×D₁₃	C₂×C₃×C₁₁	1	2	yes	direct product factor
30	C₂×C₅×C₁₁	—	13	2	no	—
31	C₂×C₅×C₁₁	C₃×D₁₃	1	1	yes	characteristic, direct product factor
32	C₂×C₃×C₁₃	C₂×C₅×C₁₁	1	1	yes	characteristic, complemented
33	C₃×D₁₃	C₂×C₅×C₁₁	1	2	yes	direct product factor
34	C₂×C₃×C₁₁	—	13	2	no	—
35	C₂×C₃×C₁₁	C₅×D₁₃	1	1	yes	characteristic, direct product factor
36	C₅×C₁₃	C₂²×C₃×C₁₁	1	1	yes	characteristic, complemented, Hall
37	C₂²×C₃×C₅	—	13	1	no	Hall
38	C₅×C₁₁	C₂×C₃×D₁₃	1	1	yes	characteristic, direct product factor, Hall
39	C₂×D₁₃	C₃×C₅×C₁₁	1	1	yes	characteristic, direct product factor, Hall
40	C₂²×C₁₁	—	13	1	no	Hall
41	C₃×C₁₃	C₂²×C₅×C₁₁	1	1	yes	characteristic, complemented, Hall
42	C₃×C₁₁	C₂×C₅×D₁₃	1	1	yes	characteristic, direct product factor, Hall
43	C₂×C₃×C₅	—	13	2	no	—
44	C₂×C₃×C₅	C₁₁×D₁₃	1	1	yes	characteristic, direct product factor
45	C₂×C₁₃	C₂×C₃×C₅×C₁₁	1	1	yes	characteristic, complemented
46	D₁₃	C₂×C₃×C₅×C₁₁	1	2	yes	direct product factor
47	C₂×C₁₁	—	13	2	no	—
48	C₂×C₁₁	C₃×C₅×D₁₃	1	1	yes	characteristic, direct product factor
49	C₂²×C₅	—	13	1	no	Hall
50	C₃×C₅	C₂×C₁₁×D₁₃	1	1	yes	characteristic, direct product factor, Hall
51	C₁₃	C₂²×C₃×C₅×C₁₁	1	1	yes	characteristic, complemented, Sylow
52	C₂²×C₃	—	13	1	no	Hall
53	C₁₁	C₂×C₃×C₅×D₁₃	1	1	yes	characteristic, direct product factor, Sylow
54	C₂×C₅	—	13	2	no	—
55	C₂×C₅	C₃×C₁₁×D₁₃	1	1	yes	characteristic, direct product factor
56	C₂×C₃	—	13	2	no	—
57	C₂×C₃	C₅×C₁₁×D₁₃	1	1	yes	characteristic, direct product factor
58	C₅	C₂×C₃×C₁₁×D₁₃	1	1	yes	characteristic, direct product factor, Sylow
59	C₂²	—	13	1	no	Sylow
60	C₃	C₂×C₅×C₁₁×D₁₃	1	1	yes	characteristic, direct product factor, Sylow
61	C₂	—	13	2	no	—
62	C₂	C₃×C₅×C₁₁×D₁₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃×C₅×C₁₁	D₁₃
commutator, hypocenter	C₁₃	C₂²×C₃×C₅×C₁₁
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₅×C₁₁×C₁₃	C₂
LCS	G ▷ C₁₃
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×D₁₃	C₂	direct (N × H)
2. C₂×C₃×C₅×C₁₁×C₁₃	C₂	semidirect
3. C₂×C₅×C₁₁×D₁₃	C₃	direct (N × H)
4. C₃×C₅×C₁₁×C₁₃	C₂²	semidirect
5. C₂×C₃×C₁₁×D₁₃	C₅	direct (N × H)
6. C₂×C₅×C₁₁×C₁₃	C₂×C₃	semidirect
7. C₅×C₁₁×D₁₃	C₂×C₃	direct (N × H)
8. C₂×C₃×C₁₁×C₁₃	C₂×C₅	semidirect
9. C₃×C₁₁×D₁₃	C₂×C₅	direct (N × H)
10. C₂×C₃×C₅×D₁₃	C₁₁	direct (N × H)
11. C₅×C₁₁×C₁₃	C₂²×C₃	semidirect
13. C₂×C₁₁×D₁₃	C₃×C₅	direct (N × H)
14. C₃×C₁₁×C₁₃	C₂²×C₅	semidirect
15. C₂×C₃×C₅×C₁₃	C₂×C₁₁	semidirect
16. C₃×C₅×D₁₃	C₂×C₁₁	direct (N × H)
18. C₂×C₃×C₅×C₁₁	D₁₃	direct (N × H)
19. C₂×C₁₁×C₁₃	C₂×C₃×C₅	semidirect
20. C₁₁×D₁₃	C₂×C₃×C₅	direct (N × H)
21. C₂×C₅×D₁₃	C₃×C₁₁	direct (N × H)
23. C₃×C₅×C₁₃	C₂²×C₁₁	semidirect
24. C₃×C₅×C₁₁	C₂×D₁₃	direct (N × H)
25. C₂×C₃×D₁₃	C₅×C₁₁	direct (N × H)
26. C₁₁×C₁₃	C₂²×C₃×C₅	semidirect
28. C₂×C₅×C₁₃	C₂×C₃×C₁₁	semidirect
29. C₅×D₁₃	C₂×C₃×C₁₁	direct (N × H)
31. C₂×C₅×C₁₁	C₃×D₁₃	direct (N × H)
32. C₂×C₃×C₁₃	C₂×C₅×C₁₁	semidirect
33. C₃×D₁₃	C₂×C₅×C₁₁	direct (N × H)
35. C₂×C₃×C₁₁	C₅×D₁₃	direct (N × H)
36. C₅×C₁₃	C₂²×C₃×C₁₁	semidirect
38. C₅×C₁₁	C₂×C₃×D₁₃	direct (N × H)
39. C₂×D₁₃	C₃×C₅×C₁₁	direct (N × H)
41. C₃×C₁₃	C₂²×C₅×C₁₁	semidirect
42. C₃×C₁₁	C₂×C₅×D₁₃	direct (N × H)
44. C₂×C₃×C₅	C₁₁×D₁₃	direct (N × H)
45. C₂×C₁₃	C₂×C₃×C₅×C₁₁	semidirect
46. D₁₃	C₂×C₃×C₅×C₁₁	direct (N × H)
48. C₂×C₁₁	C₃×C₅×D₁₃	direct (N × H)
50. C₃×C₅	C₂×C₁₁×D₁₃	direct (N × H)
51. C₁₃	C₂²×C₃×C₅×C₁₁	semidirect
53. C₁₁	C₂×C₃×C₅×D₁₃	direct (N × H)
55. C₂×C₅	C₃×C₁₁×D₁₃	direct (N × H)
57. C₂×C₃	C₅×C₁₁×D₁₃	direct (N × H)
58. C₅	C₂×C₃×C₁₁×D₁₃	direct (N × H)
60. C₃	C₂×C₅×C₁₁×D₁₃	direct (N × H)
62. C₂	C₃×C₅×C₁₁×D₁₃	direct (N × H)

Subgroups — C2×C3×C5×C11×D13 #22575196

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₃×C₅×C₁₁×D₁₃ #22575196