Subgroups — C₂×C₃×D₅×C₁₁×C₃₁ #35205877

Order 20460.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₅×C₁₁×C₃₁	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×C₅×C₁₁×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₅×C₁₁×C₃₁	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₅×C₁₁×C₃₁	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂²×C₃×C₁₁×C₃₁	—	5	1	no	maximal, Hall
6	D₅×C₁₁×C₃₁	C₂×C₃	1	2	yes	direct product factor
7	C₂×C₅×C₁₁×C₃₁	C₂×C₃	1	1	yes	characteristic, complemented
8	C₂×C₃×C₁₁×C₃₁	—	5	2	no	—
9	C₂×C₃×C₁₁×C₃₁	D₅	1	1	yes	characteristic, direct product factor
10	C₂×C₃×D₅×C₃₁	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₅×C₁₁×C₃₁	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
12	C₂²×C₁₁×C₃₁	—	5	1	no	Hall
13	C₃×C₁₁×C₃₁	C₂×D₅	1	1	yes	characteristic, direct product factor, Hall
14	C₂×C₃×C₅×C₃₁	C₂×C₁₁	1	1	yes	characteristic, complemented
15	C₃×D₅×C₃₁	C₂×C₁₁	1	2	yes	direct product factor
16	C₂×C₁₁×C₃₁	—	5	2	no	—
17	C₂×C₁₁×C₃₁	C₃×D₅	1	1	yes	characteristic, direct product factor
18	C₂×C₃×D₅×C₁₁	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
19	C₂×D₅×C₃₁	C₃×C₁₁	1	1	yes	characteristic, direct product factor, Hall
20	C₃×C₅×C₃₁	C₂²×C₁₁	1	1	yes	characteristic, complemented, Hall
21	C₂²×C₃×C₃₁	—	5	1	no	Hall
22	C₁₁×C₃₁	C₂×C₃×D₅	1	1	yes	characteristic, direct product factor, Hall
23	C₂×C₃×C₅×C₁₁	C₂×C₃₁	1	1	yes	characteristic, complemented
24	C₃×D₅×C₁₁	C₂×C₃₁	1	2	yes	direct product factor
25	C₂×C₅×C₃₁	C₂×C₃×C₁₁	1	1	yes	characteristic, complemented
26	D₅×C₃₁	C₂×C₃×C₁₁	1	2	yes	direct product factor
27	C₂×D₅×C₁₁	C₃×C₃₁	1	1	yes	characteristic, direct product factor, Hall
28	C₂×C₃×C₃₁	—	5	2	no	—
29	C₂×C₃×C₃₁	D₅×C₁₁	1	1	yes	characteristic, direct product factor
30	C₃×C₅×C₁₁	C₂²×C₃₁	1	1	yes	characteristic, complemented, Hall
31	C₅×C₃₁	C₂²×C₃×C₁₁	1	1	yes	characteristic, complemented, Hall
32	C₂²×C₃×C₁₁	—	5	1	no	Hall
33	C₂²×C₃₁	—	5	1	no	Hall
34	C₂×C₅×C₁₁	C₂×C₃×C₃₁	1	1	yes	characteristic, complemented
35	D₅×C₁₁	C₂×C₃×C₃₁	1	2	yes	direct product factor
36	C₃×C₃₁	C₂×D₅×C₁₁	1	1	yes	characteristic, direct product factor, Hall
37	C₂×C₃×C₁₁	—	5	2	no	—
38	C₂×C₃×C₁₁	D₅×C₃₁	1	1	yes	characteristic, direct product factor
39	C₂×C₃₁	—	5	2	no	—
40	C₂×C₃₁	C₃×D₅×C₁₁	1	1	yes	characteristic, direct product factor
41	C₂×C₃×D₅	C₁₁×C₃₁	1	1	yes	characteristic, direct product factor, Hall
42	C₅×C₁₁	C₂²×C₃×C₃₁	1	1	yes	characteristic, complemented, Hall
43	C₂²×C₁₁	—	5	1	no	Hall
44	C₃×C₁₁	C₂×D₅×C₃₁	1	1	yes	characteristic, direct product factor, Hall
45	C₃₁	C₂×C₃×D₅×C₁₁	1	1	yes	characteristic, direct product factor, Sylow
46	C₂×C₃×C₅	C₂×C₁₁×C₃₁	1	1	yes	characteristic, complemented
47	C₃×D₅	C₂×C₁₁×C₃₁	1	2	yes	direct product factor
48	C₂×C₁₁	—	5	2	no	—
49	C₂×C₁₁	C₃×D₅×C₃₁	1	1	yes	characteristic, direct product factor
50	C₂×D₅	C₃×C₁₁×C₃₁	1	1	yes	characteristic, direct product factor, Hall
51	C₃×C₅	C₂²×C₁₁×C₃₁	1	1	yes	characteristic, complemented, Hall
52	C₂²×C₃	—	5	1	no	Hall
53	C₁₁	C₂×C₃×D₅×C₃₁	1	1	yes	characteristic, direct product factor, Sylow
54	C₂×C₅	C₂×C₃×C₁₁×C₃₁	1	1	yes	characteristic, complemented
55	D₅	C₂×C₃×C₁₁×C₃₁	1	2	yes	direct product factor
56	C₂×C₃	—	5	2	no	—
57	C₂×C₃	D₅×C₁₁×C₃₁	1	1	yes	characteristic, direct product factor
58	C₅	C₂²×C₃×C₁₁×C₃₁	1	1	yes	characteristic, complemented, Sylow
59	C₂²	—	5	1	no	Sylow
60	C₃	C₂×D₅×C₁₁×C₃₁	1	1	yes	characteristic, direct product factor, Sylow
61	C₂	—	5	2	no	—
62	C₂	C₃×D₅×C₁₁×C₃₁	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃×C₁₁×C₃₁	D₅
commutator, cosocle, hypocenter	C₅	C₂²×C₃×C₁₁×C₃₁
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₅×C₁₁×C₃₁	C₂
LCS	G ▷ C₅
UCS	C₁ ◁ C₂×C₃×C₁₁×C₃₁

Complements

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

N	H ≅ G/N	type
1. C₃×D₅×C₁₁×C₃₁	C₂	direct (N × H)
2. C₂×C₃×C₅×C₁₁×C₃₁	C₂	semidirect
3. C₂×D₅×C₁₁×C₃₁	C₃	direct (N × H)
4. C₃×C₅×C₁₁×C₃₁	C₂²	semidirect
6. D₅×C₁₁×C₃₁	C₂×C₃	direct (N × H)
7. C₂×C₅×C₁₁×C₃₁	C₂×C₃	semidirect
9. C₂×C₃×C₁₁×C₃₁	D₅	direct (N × H)
10. C₂×C₃×D₅×C₃₁	C₁₁	direct (N × H)
11. C₅×C₁₁×C₃₁	C₂²×C₃	semidirect
13. C₃×C₁₁×C₃₁	C₂×D₅	direct (N × H)
14. C₂×C₃×C₅×C₃₁	C₂×C₁₁	semidirect
15. C₃×D₅×C₃₁	C₂×C₁₁	direct (N × H)
17. C₂×C₁₁×C₃₁	C₃×D₅	direct (N × H)
18. C₂×C₃×D₅×C₁₁	C₃₁	direct (N × H)
19. C₂×D₅×C₃₁	C₃×C₁₁	direct (N × H)
20. C₃×C₅×C₃₁	C₂²×C₁₁	semidirect
22. C₁₁×C₃₁	C₂×C₃×D₅	direct (N × H)
23. C₂×C₃×C₅×C₁₁	C₂×C₃₁	semidirect
24. C₃×D₅×C₁₁	C₂×C₃₁	direct (N × H)
25. C₂×C₅×C₃₁	C₂×C₃×C₁₁	semidirect
26. D₅×C₃₁	C₂×C₃×C₁₁	direct (N × H)
27. C₂×D₅×C₁₁	C₃×C₃₁	direct (N × H)
29. C₂×C₃×C₃₁	D₅×C₁₁	direct (N × H)
30. C₃×C₅×C₁₁	C₂²×C₃₁	semidirect
31. C₅×C₃₁	C₂²×C₃×C₁₁	semidirect
34. C₂×C₅×C₁₁	C₂×C₃×C₃₁	semidirect
35. D₅×C₁₁	C₂×C₃×C₃₁	direct (N × H)
36. C₃×C₃₁	C₂×D₅×C₁₁	direct (N × H)
38. C₂×C₃×C₁₁	D₅×C₃₁	direct (N × H)
40. C₂×C₃₁	C₃×D₅×C₁₁	direct (N × H)
41. C₂×C₃×D₅	C₁₁×C₃₁	direct (N × H)
42. C₅×C₁₁	C₂²×C₃×C₃₁	semidirect
44. C₃×C₁₁	C₂×D₅×C₃₁	direct (N × H)
45. C₃₁	C₂×C₃×D₅×C₁₁	direct (N × H)
46. C₂×C₃×C₅	C₂×C₁₁×C₃₁	semidirect
47. C₃×D₅	C₂×C₁₁×C₃₁	direct (N × H)
49. C₂×C₁₁	C₃×D₅×C₃₁	direct (N × H)
50. C₂×D₅	C₃×C₁₁×C₃₁	direct (N × H)
51. C₃×C₅	C₂²×C₁₁×C₃₁	semidirect
53. C₁₁	C₂×C₃×D₅×C₃₁	direct (N × H)
54. C₂×C₅	C₂×C₃×C₁₁×C₃₁	semidirect
55. D₅	C₂×C₃×C₁₁×C₃₁	direct (N × H)
57. C₂×C₃	D₅×C₁₁×C₃₁	direct (N × H)
58. C₅	C₂²×C₃×C₁₁×C₃₁	semidirect
60. C₃	C₂×D₅×C₁₁×C₃₁	direct (N × H)
62. C₂	C₃×D₅×C₁₁×C₃₁	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×D₅×C₁₁×C₃₁	2
C₂×C₃×C₅×C₁₁×C₃₁	2
C₂×D₅×C₁₁×C₃₁	3
C₂²×C₃×C₁₁×C₃₁	5
C₂×C₃×D₅×C₃₁	11
C₂×C₃×D₅×C₁₁	31

Subgroups — C2×C3×D5×C11×C31 #35205877

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×D₅×C₁₁×C₃₁ #35205877