Subgroups — C₂×C₃×D₅×C₁₁×C₁₃ #22575193

Order 8580.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₅×C₁₁×C₁₃	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₅×C₁₁×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₅×C₁₁×C₁₃	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₅×C₁₁×C₁₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂²×C₃×C₁₁×C₁₃	—	5	1	no	maximal, Hall
6	C₂×C₅×C₁₁×C₁₃	C₂×C₃	1	1	yes	characteristic, complemented
7	D₅×C₁₁×C₁₃	C₂×C₃	1	2	yes	direct product factor
8	C₂×C₃×C₁₁×C₁₃	—	5	2	no	—
9	C₂×C₃×C₁₁×C₁₃	D₅	1	1	yes	characteristic, direct product factor
10	C₂×C₃×D₅×C₁₃	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₅×C₁₁×C₁₃	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
12	C₂×C₃×D₅×C₁₁	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂²×C₁₁×C₁₃	—	5	1	no	Hall
14	C₃×C₁₁×C₁₃	C₂×D₅	1	1	yes	characteristic, direct product factor, Hall
15	C₂×C₃×C₅×C₁₃	C₂×C₁₁	1	1	yes	characteristic, complemented
16	C₃×D₅×C₁₃	C₂×C₁₁	1	2	yes	direct product factor
17	C₂×C₃×C₅×C₁₁	C₂×C₁₃	1	1	yes	characteristic, complemented
18	C₃×D₅×C₁₁	C₂×C₁₃	1	2	yes	direct product factor
19	C₂×C₁₁×C₁₃	—	5	2	no	—
20	C₂×C₁₁×C₁₃	C₃×D₅	1	1	yes	characteristic, direct product factor
21	C₂×D₅×C₁₃	C₃×C₁₁	1	1	yes	characteristic, direct product factor, Hall
22	C₂×D₅×C₁₁	C₃×C₁₃	1	1	yes	characteristic, direct product factor, Hall
23	C₃×C₅×C₁₃	C₂²×C₁₁	1	1	yes	characteristic, complemented, Hall
24	C₃×C₅×C₁₁	C₂²×C₁₃	1	1	yes	characteristic, complemented, Hall
25	C₂²×C₃×C₁₃	—	5	1	no	Hall
26	C₁₁×C₁₃	C₂×C₃×D₅	1	1	yes	characteristic, direct product factor, Hall
27	C₂²×C₃×C₁₁	—	5	1	no	Hall
28	C₂×C₅×C₁₃	C₂×C₃×C₁₁	1	1	yes	characteristic, complemented
29	D₅×C₁₃	C₂×C₃×C₁₁	1	2	yes	direct product factor
30	C₂×C₅×C₁₁	C₂×C₃×C₁₃	1	1	yes	characteristic, complemented
31	D₅×C₁₁	C₂×C₃×C₁₃	1	2	yes	direct product factor
32	C₂×C₃×C₁₃	—	5	2	no	—
33	C₂×C₃×C₁₃	D₅×C₁₁	1	1	yes	characteristic, direct product factor
34	C₂×C₃×C₁₁	—	5	2	no	—
35	C₂×C₃×C₁₁	D₅×C₁₃	1	1	yes	characteristic, direct product factor
36	C₅×C₁₃	C₂²×C₃×C₁₁	1	1	yes	characteristic, complemented, Hall
37	C₂×C₃×D₅	C₁₁×C₁₃	1	1	yes	characteristic, direct product factor, Hall
38	C₅×C₁₁	C₂²×C₃×C₁₃	1	1	yes	characteristic, complemented, Hall
39	C₂²×C₁₃	—	5	1	no	Hall
40	C₂²×C₁₁	—	5	1	no	Hall
41	C₃×C₁₃	C₂×D₅×C₁₁	1	1	yes	characteristic, direct product factor, Hall
42	C₃×C₁₁	C₂×D₅×C₁₃	1	1	yes	characteristic, direct product factor, Hall
43	C₂×C₃×C₅	C₂×C₁₁×C₁₃	1	1	yes	characteristic, complemented
44	C₃×D₅	C₂×C₁₁×C₁₃	1	2	yes	direct product factor
45	C₂×C₁₃	—	5	2	no	—
46	C₂×C₁₃	C₃×D₅×C₁₁	1	1	yes	characteristic, direct product factor
47	C₂×C₁₁	—	5	2	no	—
48	C₂×C₁₁	C₃×D₅×C₁₃	1	1	yes	characteristic, direct product factor
49	C₂×D₅	C₃×C₁₁×C₁₃	1	1	yes	characteristic, direct product factor, Hall
50	C₃×C₅	C₂²×C₁₁×C₁₃	1	1	yes	characteristic, complemented, Hall
51	C₁₃	C₂×C₃×D₅×C₁₁	1	1	yes	characteristic, direct product factor, Sylow
52	C₂²×C₃	—	5	1	no	Hall
53	C₁₁	C₂×C₃×D₅×C₁₃	1	1	yes	characteristic, direct product factor, Sylow
54	C₂×C₅	C₂×C₃×C₁₁×C₁₃	1	1	yes	characteristic, complemented
55	D₅	C₂×C₃×C₁₁×C₁₃	1	2	yes	direct product factor
56	C₂×C₃	—	5	2	no	—
57	C₂×C₃	D₅×C₁₁×C₁₃	1	1	yes	characteristic, direct product factor
58	C₅	C₂²×C₃×C₁₁×C₁₃	1	1	yes	characteristic, complemented, Sylow
59	C₂²	—	5	1	no	Sylow
60	C₃	C₂×D₅×C₁₁×C₁₃	1	1	yes	characteristic, direct product factor, Sylow
61	C₂	—	5	2	no	—
62	C₂	C₃×D₅×C₁₁×C₁₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃×C₁₁×C₁₃	D₅
commutator, hypocenter	C₅	C₂²×C₃×C₁₁×C₁₃
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₅×C₁₁×C₁₃	C₂
LCS	G ▷ C₅
UCS	C₁ ◁ C₂×C₃×C₁₁×C₁₃

Complements

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

N	H ≅ G/N	type
1. C₃×D₅×C₁₁×C₁₃	C₂	direct (N × H)
2. C₂×C₃×C₅×C₁₁×C₁₃	C₂	semidirect
3. C₂×D₅×C₁₁×C₁₃	C₃	direct (N × H)
4. C₃×C₅×C₁₁×C₁₃	C₂²	semidirect
6. C₂×C₅×C₁₁×C₁₃	C₂×C₃	semidirect
7. D₅×C₁₁×C₁₃	C₂×C₃	direct (N × H)
9. C₂×C₃×C₁₁×C₁₃	D₅	direct (N × H)
10. C₂×C₃×D₅×C₁₃	C₁₁	direct (N × H)
11. C₅×C₁₁×C₁₃	C₂²×C₃	semidirect
12. C₂×C₃×D₅×C₁₁	C₁₃	direct (N × H)
14. C₃×C₁₁×C₁₃	C₂×D₅	direct (N × H)
15. C₂×C₃×C₅×C₁₃	C₂×C₁₁	semidirect
16. C₃×D₅×C₁₃	C₂×C₁₁	direct (N × H)
17. C₂×C₃×C₅×C₁₁	C₂×C₁₃	semidirect
18. C₃×D₅×C₁₁	C₂×C₁₃	direct (N × H)
20. C₂×C₁₁×C₁₃	C₃×D₅	direct (N × H)
21. C₂×D₅×C₁₃	C₃×C₁₁	direct (N × H)
22. C₂×D₅×C₁₁	C₃×C₁₃	direct (N × H)
23. C₃×C₅×C₁₃	C₂²×C₁₁	semidirect
24. C₃×C₅×C₁₁	C₂²×C₁₃	semidirect
26. C₁₁×C₁₃	C₂×C₃×D₅	direct (N × H)
28. C₂×C₅×C₁₃	C₂×C₃×C₁₁	semidirect
29. D₅×C₁₃	C₂×C₃×C₁₁	direct (N × H)
30. C₂×C₅×C₁₁	C₂×C₃×C₁₃	semidirect
31. D₅×C₁₁	C₂×C₃×C₁₃	direct (N × H)
33. C₂×C₃×C₁₃	D₅×C₁₁	direct (N × H)
35. C₂×C₃×C₁₁	D₅×C₁₃	direct (N × H)
36. C₅×C₁₃	C₂²×C₃×C₁₁	semidirect
37. C₂×C₃×D₅	C₁₁×C₁₃	direct (N × H)
38. C₅×C₁₁	C₂²×C₃×C₁₃	semidirect
41. C₃×C₁₃	C₂×D₅×C₁₁	direct (N × H)
42. C₃×C₁₁	C₂×D₅×C₁₃	direct (N × H)
43. C₂×C₃×C₅	C₂×C₁₁×C₁₃	semidirect
44. C₃×D₅	C₂×C₁₁×C₁₃	direct (N × H)
46. C₂×C₁₃	C₃×D₅×C₁₁	direct (N × H)
48. C₂×C₁₁	C₃×D₅×C₁₃	direct (N × H)
49. C₂×D₅	C₃×C₁₁×C₁₃	direct (N × H)
50. C₃×C₅	C₂²×C₁₁×C₁₃	semidirect
51. C₁₃	C₂×C₃×D₅×C₁₁	direct (N × H)
53. C₁₁	C₂×C₃×D₅×C₁₃	direct (N × H)
54. C₂×C₅	C₂×C₃×C₁₁×C₁₃	semidirect
55. D₅	C₂×C₃×C₁₁×C₁₃	direct (N × H)
57. C₂×C₃	D₅×C₁₁×C₁₃	direct (N × H)
58. C₅	C₂²×C₃×C₁₁×C₁₃	semidirect
60. C₃	C₂×D₅×C₁₁×C₁₃	direct (N × H)
62. C₂	C₃×D₅×C₁₁×C₁₃	direct (N × H)

Subgroups — C2×C3×D5×C11×C13 #22575193

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₃×D₅×C₁₁×C₁₃ #22575193