Subgroups — C₂×C₃×C₅×C₁₁×C₃₁⋊C₃ #44501866

Order 30690.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, hypercenter	C₂×C₃×C₅×C₁₁	C₃₁⋊C₃
commutator, cosocle, hypocenter	C₃₁	C₂×C₃²×C₅×C₁₁
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₅×C₁₁×C₃₁	C₃
LCS	G ▷ C₃₁
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×C₃₁⋊C₃	C₂	direct (N × H)
2. C₂×C₅×C₁₁×C₃₁⋊C₃	C₃	direct (N × H)
3. C₂×C₃×C₅×C₁₁×C₃₁	C₃	semidirect
4. C₂×C₃×C₁₁×C₃₁⋊C₃	C₅	direct (N × H)
5. C₅×C₁₁×C₃₁⋊C₃	C₂×C₃	direct (N × H)
6. C₃×C₅×C₁₁×C₃₁	C₂×C₃	semidirect
7. C₂×C₅×C₁₁×C₃₁	C₃²	semidirect
8. C₃×C₁₁×C₃₁⋊C₃	C₂×C₅	direct (N × H)
9. C₂×C₃×C₅×C₃₁⋊C₃	C₁₁	direct (N × H)
10. C₂×C₁₁×C₃₁⋊C₃	C₃×C₅	direct (N × H)
11. C₂×C₃×C₁₁×C₃₁	C₃×C₅	semidirect
12. C₅×C₁₁×C₃₁	C₂×C₃²	semidirect
13. C₃×C₅×C₃₁⋊C₃	C₂×C₁₁	direct (N × H)
14. C₃×C₁₁×C₃₁	C₂×C₃×C₅	semidirect
15. C₁₁×C₃₁⋊C₃	C₂×C₃×C₅	direct (N × H)
17. C₂×C₃×C₅×C₃₁	C₃×C₁₁	semidirect
18. C₂×C₅×C₃₁⋊C₃	C₃×C₁₁	direct (N × H)
19. C₂×C₁₁×C₃₁	C₃²×C₅	semidirect
20. C₂×C₃×C₃₁⋊C₃	C₅×C₁₁	direct (N × H)
22. C₃×C₅×C₃₁	C₂×C₃×C₁₁	semidirect
23. C₅×C₃₁⋊C₃	C₂×C₃×C₁₁	direct (N × H)
24. C₁₁×C₃₁	C₂×C₃²×C₅	semidirect
26. C₂×C₃×C₅×C₁₁	C₃₁⋊C₃	direct (N × H)
27. C₂×C₅×C₃₁	C₃²×C₁₁	semidirect
28. C₃×C₃₁⋊C₃	C₂×C₅×C₁₁	direct (N × H)
30. C₂×C₃×C₃₁	C₃×C₅×C₁₁	semidirect
31. C₂×C₃₁⋊C₃	C₃×C₅×C₁₁	direct (N × H)
33. C₃×C₅×C₁₁	C₂×C₃₁⋊C₃	direct (N × H)
34. C₅×C₃₁	C₂×C₃²×C₁₁	semidirect
35. C₂×C₅×C₁₁	C₃×C₃₁⋊C₃	direct (N × H)
37. C₃×C₃₁	C₂×C₃×C₅×C₁₁	semidirect
38. C₃₁⋊C₃	C₂×C₃×C₅×C₁₁	direct (N × H)
41. C₂×C₃×C₁₁	C₅×C₃₁⋊C₃	direct (N × H)
42. C₂×C₃₁	C₃²×C₅×C₁₁	semidirect
43. C₅×C₁₁	C₂×C₃×C₃₁⋊C₃	direct (N × H)
46. C₃×C₁₁	C₂×C₅×C₃₁⋊C₃	direct (N × H)
47. C₃₁	C₂×C₃²×C₅×C₁₁	semidirect
49. C₂×C₃×C₅	C₁₁×C₃₁⋊C₃	direct (N × H)
50. C₂×C₁₁	C₃×C₅×C₃₁⋊C₃	direct (N × H)
53. C₃×C₅	C₂×C₁₁×C₃₁⋊C₃	direct (N × H)
54. C₁₁	C₂×C₃×C₅×C₃₁⋊C₃	direct (N × H)
55. C₂×C₅	C₃×C₁₁×C₃₁⋊C₃	direct (N × H)
58. C₂×C₃	C₅×C₁₁×C₃₁⋊C₃	direct (N × H)
59. C₅	C₂×C₃×C₁₁×C₃₁⋊C₃	direct (N × H)
61. C₃	C₂×C₅×C₁₁×C₃₁⋊C₃	direct (N × H)
62. C₂	C₃×C₅×C₁₁×C₃₁⋊C₃	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×C₅×C₁₁×C₃₁⋊C₃	2
C₂×C₅×C₁₁×C₃₁⋊C₃	3
C₂×C₃×C₅×C₁₁×C₃₁	3
C₂×C₃×C₁₁×C₃₁⋊C₃	5
C₂×C₃×C₅×C₃₁⋊C₃	11
C₂×C₃²×C₅×C₁₁	31

Subgroups — C2×C3×C5×C11×C31⋊C3 #44501866

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₅×C₁₁×C₃₁⋊C₃ #44501866