Subgroups — C₃×C₅×D₃×C₁₁×C₃₁ #44501874

Order 30690.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₅×C₁₁×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×D₃×C₁₁×C₃₁	C₃	1	1	yes	maximal, characteristic, direct product factor
3	C₂×C₃×C₅×C₁₁×C₃₁	—	3	1	no	maximal
4	C₃×D₃×C₁₁×C₃₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₅×C₁₁×C₃₁	—	2	1	no	—
6	C₃×C₅×C₁₁×C₃₁	D₃	1	1	yes	characteristic, direct product factor
7	C₃×C₅×C₁₁×C₃₁	C₂×C₃	1	1	yes	characteristic, complemented
8	C₂×C₅×C₁₁×C₃₁	—	3	1	no	Hall
9	C₃²×C₁₁×C₃₁	C₂×C₅	1	1	yes	characteristic, complemented, Hall
10	C₃×C₅×D₃×C₃₁	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
11	D₃×C₁₁×C₃₁	C₃×C₅	1	1	yes	characteristic, direct product factor
12	C₂×C₃×C₁₁×C₃₁	—	3	1	no	—
13	C₅×C₁₁×C₃₁	C₃×D₃	1	1	yes	characteristic, direct product factor, Hall
14	C₃²×C₅×C₃₁	C₂×C₁₁	1	1	yes	characteristic, complemented, Hall
15	C₃×C₁₁×C₃₁	—	2	1	no	—
16	C₃×C₁₁×C₃₁	C₅×D₃	1	1	yes	characteristic, direct product factor
17	C₃×C₁₁×C₃₁	C₂×C₃×C₅	1	1	yes	characteristic, complemented
18	C₃×C₅×D₃×C₁₁	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
19	C₂×C₃×C₅×C₃₁	—	3	1	no	—
20	C₅×D₃×C₃₁	C₃×C₁₁	1	1	yes	characteristic, direct product factor
21	C₂×C₁₁×C₃₁	—	3	1	no	Hall
22	C₃×D₃×C₃₁	C₅×C₁₁	1	1	yes	characteristic, direct product factor, Hall
23	C₃²×C₅×C₁₁	C₂×C₃₁	1	1	yes	characteristic, complemented, Hall
24	C₃×C₅×C₃₁	—	2	1	no	—
25	C₃×C₅×C₃₁	D₃×C₁₁	1	1	yes	characteristic, direct product factor
26	C₃×C₅×C₃₁	C₂×C₃×C₁₁	1	1	yes	characteristic, complemented
27	C₁₁×C₃₁	C₃×C₅×D₃	1	1	yes	characteristic, direct product factor, Hall
28	C₂×C₃×C₅×C₁₁	—	3	1	no	—
29	C₅×D₃×C₁₁	C₃×C₃₁	1	1	yes	characteristic, direct product factor
30	C₂×C₅×C₃₁	—	3	1	no	Hall
31	C₃²×C₃₁	C₂×C₅×C₁₁	1	1	yes	characteristic, complemented, Hall
32	C₃×D₃×C₁₁	C₅×C₃₁	1	1	yes	characteristic, direct product factor, Hall
33	C₂×C₃×C₃₁	—	3	1	no	—
34	D₃×C₃₁	C₃×C₅×C₁₁	1	1	yes	characteristic, direct product factor
35	C₃×C₅×C₁₁	—	2	1	no	—
36	C₃×C₅×C₁₁	D₃×C₃₁	1	1	yes	characteristic, direct product factor
37	C₃×C₅×C₁₁	C₂×C₃×C₃₁	1	1	yes	characteristic, complemented
38	C₅×C₃₁	C₃×D₃×C₁₁	1	1	yes	characteristic, direct product factor, Hall
39	C₂×C₅×C₁₁	—	3	1	no	Hall
40	C₃²×C₁₁	C₂×C₅×C₃₁	1	1	yes	characteristic, complemented, Hall
41	C₃×C₃₁	—	2	1	no	—
42	C₃×C₃₁	C₅×D₃×C₁₁	1	1	yes	characteristic, direct product factor
43	C₃×C₃₁	C₂×C₃×C₅×C₁₁	1	1	yes	characteristic, complemented
44	C₃×C₅×D₃	C₁₁×C₃₁	1	1	yes	characteristic, direct product factor, Hall
45	C₂×C₃×C₁₁	—	3	1	no	—
46	D₃×C₁₁	C₃×C₅×C₃₁	1	1	yes	characteristic, direct product factor
47	C₂×C₃₁	—	3	1	no	Hall
48	C₅×C₁₁	C₃×D₃×C₃₁	1	1	yes	characteristic, direct product factor, Hall
49	C₃²×C₅	C₂×C₁₁×C₃₁	1	1	yes	characteristic, complemented, Hall
50	C₃×C₁₁	—	2	1	no	—
51	C₃×C₁₁	C₅×D₃×C₃₁	1	1	yes	characteristic, direct product factor
52	C₃×C₁₁	C₂×C₃×C₅×C₃₁	1	1	yes	characteristic, complemented
53	C₃₁	C₃×C₅×D₃×C₁₁	1	1	yes	characteristic, direct product factor, Sylow
54	C₂×C₃×C₅	—	3	1	no	—
55	C₅×D₃	C₃×C₁₁×C₃₁	1	1	yes	characteristic, direct product factor
56	C₂×C₁₁	—	3	1	no	Hall
57	C₃×D₃	C₅×C₁₁×C₃₁	1	1	yes	characteristic, direct product factor, Hall
58	C₃×C₅	—	2	1	no	—
59	C₃×C₅	C₂×C₃×C₁₁×C₃₁	1	1	yes	characteristic, complemented
60	C₃×C₅	D₃×C₁₁×C₃₁	1	1	yes	characteristic, direct product factor
61	C₁₁	C₃×C₅×D₃×C₃₁	1	1	yes	characteristic, direct product factor, Sylow
62	C₂×C₅	—	3	1	no	Hall
63	C₃²	C₂×C₅×C₁₁×C₃₁	1	1	yes	characteristic, complemented, Sylow
64	C₂×C₃	—	3	1	no	—
65	D₃	C₃×C₅×C₁₁×C₃₁	1	1	yes	characteristic, direct product factor
66	C₅	C₃×D₃×C₁₁×C₃₁	1	1	yes	characteristic, direct product factor, Sylow
67	C₃	—	2	1	no	—
68	C₃	C₂×C₃×C₅×C₁₁×C₃₁	1	1	yes	characteristic, complemented
69	C₃	C₅×D₃×C₁₁×C₃₁	1	1	yes	characteristic, direct product factor
70	C₂	—	3	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₅×C₁₁×C₃₁	D₃
commutator, cosocle, hypocenter	C₃	C₂×C₃×C₅×C₁₁×C₃₁
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₁₁×C₃₁	C₂
LCS	G ▷ C₃
UCS	C₁ ◁ C₃×C₅×C₁₁×C₃₁

Complements

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

N	H ≅ G/N	type
1. C₃²×C₅×C₁₁×C₃₁	C₂	semidirect
2. C₅×D₃×C₁₁×C₃₁	C₃	direct (N × H)
4. C₃×D₃×C₁₁×C₃₁	C₅	direct (N × H)
6. C₃×C₅×C₁₁×C₃₁	D₃	direct (N × H)
7. C₃×C₅×C₁₁×C₃₁	C₂×C₃	semidirect
9. C₃²×C₁₁×C₃₁	C₂×C₅	semidirect
10. C₃×C₅×D₃×C₃₁	C₁₁	direct (N × H)
11. D₃×C₁₁×C₃₁	C₃×C₅	direct (N × H)
13. C₅×C₁₁×C₃₁	C₃×D₃	direct (N × H)
14. C₃²×C₅×C₃₁	C₂×C₁₁	semidirect
16. C₃×C₁₁×C₃₁	C₅×D₃	direct (N × H)
17. C₃×C₁₁×C₃₁	C₂×C₃×C₅	semidirect
18. C₃×C₅×D₃×C₁₁	C₃₁	direct (N × H)
20. C₅×D₃×C₃₁	C₃×C₁₁	direct (N × H)
22. C₃×D₃×C₃₁	C₅×C₁₁	direct (N × H)
23. C₃²×C₅×C₁₁	C₂×C₃₁	semidirect
25. C₃×C₅×C₃₁	D₃×C₁₁	direct (N × H)
26. C₃×C₅×C₃₁	C₂×C₃×C₁₁	semidirect
27. C₁₁×C₃₁	C₃×C₅×D₃	direct (N × H)
29. C₅×D₃×C₁₁	C₃×C₃₁	direct (N × H)
31. C₃²×C₃₁	C₂×C₅×C₁₁	semidirect
32. C₃×D₃×C₁₁	C₅×C₃₁	direct (N × H)
34. D₃×C₃₁	C₃×C₅×C₁₁	direct (N × H)
36. C₃×C₅×C₁₁	D₃×C₃₁	direct (N × H)
37. C₃×C₅×C₁₁	C₂×C₃×C₃₁	semidirect
38. C₅×C₃₁	C₃×D₃×C₁₁	direct (N × H)
40. C₃²×C₁₁	C₂×C₅×C₃₁	semidirect
42. C₃×C₃₁	C₅×D₃×C₁₁	direct (N × H)
43. C₃×C₃₁	C₂×C₃×C₅×C₁₁	semidirect
44. C₃×C₅×D₃	C₁₁×C₃₁	direct (N × H)
46. D₃×C₁₁	C₃×C₅×C₃₁	direct (N × H)
48. C₅×C₁₁	C₃×D₃×C₃₁	direct (N × H)
49. C₃²×C₅	C₂×C₁₁×C₃₁	semidirect
51. C₃×C₁₁	C₅×D₃×C₃₁	direct (N × H)
52. C₃×C₁₁	C₂×C₃×C₅×C₃₁	semidirect
53. C₃₁	C₃×C₅×D₃×C₁₁	direct (N × H)
55. C₅×D₃	C₃×C₁₁×C₃₁	direct (N × H)
57. C₃×D₃	C₅×C₁₁×C₃₁	direct (N × H)
59. C₃×C₅	C₂×C₃×C₁₁×C₃₁	semidirect
60. C₃×C₅	D₃×C₁₁×C₃₁	direct (N × H)
61. C₁₁	C₃×C₅×D₃×C₃₁	direct (N × H)
63. C₃²	C₂×C₅×C₁₁×C₃₁	semidirect
65. D₃	C₃×C₅×C₁₁×C₃₁	direct (N × H)
66. C₅	C₃×D₃×C₁₁×C₃₁	direct (N × H)
68. C₃	C₂×C₃×C₅×C₁₁×C₃₁	semidirect
69. C₃	C₅×D₃×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
C₃²×C₅×C₁₁×C₃₁	2
C₅×D₃×C₁₁×C₃₁	3
C₂×C₃×C₅×C₁₁×C₃₁	3
C₃×D₃×C₁₁×C₃₁	5
C₃×C₅×D₃×C₃₁	11
C₃×C₅×D₃×C₁₁	31

Subgroups — C3×C5×D3×C11×C31 #44501874

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×D₃×C₁₁×C₃₁ #44501874