Subgroups — C₃²×C₇×C₁₁×C₅⋊D₅ #46831658

Order 34650.

384 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₅²×C₇×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₇×C₁₁×C₅⋊D₅	C₃	1	4	yes	maximal, direct product factor
3	C₃²×C₇×D₅×C₁₁	—	5	6	no	maximal
4	C₃×C₅²×C₇×C₁₁	C₂×C₃	1	4	yes	complemented
5	C₃²×C₁₁×C₅⋊D₅	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₇×C₁₁×C₅⋊D₅	C₃²	1	1	yes	characteristic, direct product factor, Hall
7	C₃²×C₅×C₇×C₁₁	D₅	1	6	yes	complemented
8	C₃²×C₇×C₅⋊D₅	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₃²×C₅²×C₁₁	C₂×C₇	1	1	yes	characteristic, complemented, Hall
10	C₃×C₇×D₅×C₁₁	—	5	24	no	—
11	C₅²×C₇×C₁₁	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
12	C₃×C₁₁×C₅⋊D₅	C₃×C₇	1	4	yes	direct product factor
13	C₃²×C₅²×C₇	C₂×C₁₁	1	1	yes	characteristic, complemented, Hall
14	C₂×C₃²×C₇×C₁₁	—	25	1	no	Hall
15	C₃×C₅×C₇×C₁₁	C₃×D₅	1	24	yes	complemented
16	C₃×C₇×C₅⋊D₅	C₃×C₁₁	1	4	yes	direct product factor
17	C₃²×D₅×C₁₁	—	5	6	no	—
18	C₃×C₅²×C₁₁	C₂×C₃×C₇	1	4	yes	complemented
19	C₇×D₅×C₁₁	—	5	6	no	—
20	C₃²×C₇×C₁₁	C₅⋊D₅	1	1	yes	characteristic, direct product factor, Hall
21	C₃²×C₇×D₅	—	5	6	no	—
22	C₁₁×C₅⋊D₅	C₃²×C₇	1	1	yes	characteristic, direct product factor, Hall
23	C₃×C₅²×C₇	C₂×C₃×C₁₁	1	4	yes	complemented
24	C₃²×C₅×C₁₁	C₇×D₅	1	6	yes	complemented
25	C₂×C₃×C₇×C₁₁	—	25	4	no	—
26	C₃²×C₅⋊D₅	C₇×C₁₁	1	1	yes	characteristic, direct product factor, Hall
27	C₅×C₇×C₁₁	C₃²×D₅	1	6	yes	complemented
28	C₇×C₅⋊D₅	C₃²×C₁₁	1	1	yes	characteristic, direct product factor, Hall
29	C₃×D₅×C₁₁	—	5	24	no	—
30	C₃²×C₅×C₇	D₅×C₁₁	1	6	yes	complemented
31	C₅²×C₁₁	C₂×C₃²×C₇	1	1	yes	characteristic, complemented, Hall
32	C₃×C₇×C₁₁	C₃×C₅⋊D₅	1	4	yes	direct product factor
33	C₃²×C₅²	C₂×C₇×C₁₁	1	1	yes	characteristic, complemented, Hall
34	C₃×C₇×D₅	—	5	24	no	—
35	C₂×C₃²×C₁₁	—	25	1	no	Hall
36	C₅²×C₇	C₂×C₃²×C₁₁	1	1	yes	characteristic, complemented, Hall
37	C₃×C₅×C₁₁	C₃×C₇×D₅	1	24	yes	complemented
38	C₂×C₇×C₁₁	—	25	1	no	Hall
39	C₃×C₅⋊D₅	C₃×C₇×C₁₁	1	4	yes	direct product factor
40	C₂×C₃²×C₇	—	25	1	no	Hall
41	D₅×C₁₁	—	5	6	no	—
42	C₃×C₅×C₇	C₃×D₅×C₁₁	1	24	yes	complemented
43	C₃²×C₁₁	C₇×C₅⋊D₅	1	1	yes	characteristic, direct product factor, Hall
44	C₃²×D₅	—	5	6	no	—
45	C₇×C₁₁	C₃²×C₅⋊D₅	1	1	yes	characteristic, direct product factor, Hall
46	C₃×C₅²	C₂×C₃×C₇×C₁₁	1	4	yes	complemented
47	C₇×D₅	—	5	6	no	—
48	C₂×C₃×C₁₁	—	25	4	no	—
49	C₃²×C₇	C₁₁×C₅⋊D₅	1	1	yes	characteristic, direct product factor, Hall
50	C₅×C₁₁	C₃²×C₇×D₅	1	6	yes	complemented
51	C₅⋊D₅	C₃²×C₇×C₁₁	1	1	yes	characteristic, direct product factor, Hall
52	C₃²×C₅	C₇×D₅×C₁₁	1	6	yes	complemented
53	C₂×C₃×C₇	—	25	4	no	—
54	C₅×C₇	C₃²×D₅×C₁₁	1	6	yes	complemented
55	C₃×C₁₁	C₃×C₇×C₅⋊D₅	1	4	yes	direct product factor
56	C₃×D₅	—	5	24	no	—
57	C₅²	C₂×C₃²×C₇×C₁₁	1	1	yes	characteristic, complemented, Sylow
58	C₂×C₁₁	—	25	1	no	Hall
59	C₃×C₇	C₃×C₁₁×C₅⋊D₅	1	4	yes	direct product factor
60	C₂×C₃²	—	25	1	no	Hall
61	C₃×C₅	C₃×C₇×D₅×C₁₁	1	24	yes	complemented
62	C₂×C₇	—	25	1	no	Hall
63	C₁₁	C₃²×C₇×C₅⋊D₅	1	1	yes	characteristic, direct product factor, Sylow
64	D₅	—	5	6	no	—
65	C₃²	C₇×C₁₁×C₅⋊D₅	1	1	yes	characteristic, direct product factor, Sylow
66	C₇	C₃²×C₁₁×C₅⋊D₅	1	1	yes	characteristic, direct product factor, Sylow
67	C₂×C₃	—	25	4	no	—
68	C₅	C₃²×C₇×D₅×C₁₁	1	6	yes	complemented
69	C₃	C₃×C₇×C₁₁×C₅⋊D₅	1	4	yes	direct product factor
70	C₂	—	25	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃²×C₇×C₁₁	C₅⋊D₅
commutator, cosocle, hypocenter	C₅²	C₂×C₃²×C₇×C₁₁
Frattini	C₁	G
Fitting, socle	C₃²×C₅²×C₇×C₁₁	C₂
LCS	G ▷ C₅²
UCS	C₁ ◁ C₃²×C₇×C₁₁

Complements

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

N	H ≅ G/N	type
1. C₃²×C₅²×C₇×C₁₁	C₂	semidirect
2. C₃×C₇×C₁₁×C₅⋊D₅	C₃	direct (N × H)
4. C₃×C₅²×C₇×C₁₁	C₂×C₃	semidirect
5. C₃²×C₁₁×C₅⋊D₅	C₇	direct (N × H)
6. C₇×C₁₁×C₅⋊D₅	C₃²	direct (N × H)
7. C₃²×C₅×C₇×C₁₁	D₅	semidirect
8. C₃²×C₇×C₅⋊D₅	C₁₁	direct (N × H)
9. C₃²×C₅²×C₁₁	C₂×C₇	semidirect
11. C₅²×C₇×C₁₁	C₂×C₃²	semidirect
12. C₃×C₁₁×C₅⋊D₅	C₃×C₇	direct (N × H)
13. C₃²×C₅²×C₇	C₂×C₁₁	semidirect
15. C₃×C₅×C₇×C₁₁	C₃×D₅	semidirect
16. C₃×C₇×C₅⋊D₅	C₃×C₁₁	direct (N × H)
18. C₃×C₅²×C₁₁	C₂×C₃×C₇	semidirect
20. C₃²×C₇×C₁₁	C₅⋊D₅	direct (N × H)
22. C₁₁×C₅⋊D₅	C₃²×C₇	direct (N × H)
23. C₃×C₅²×C₇	C₂×C₃×C₁₁	semidirect
24. C₃²×C₅×C₁₁	C₇×D₅	semidirect
26. C₃²×C₅⋊D₅	C₇×C₁₁	direct (N × H)
27. C₅×C₇×C₁₁	C₃²×D₅	semidirect
28. C₇×C₅⋊D₅	C₃²×C₁₁	direct (N × H)
30. C₃²×C₅×C₇	D₅×C₁₁	semidirect
31. C₅²×C₁₁	C₂×C₃²×C₇	semidirect
32. C₃×C₇×C₁₁	C₃×C₅⋊D₅	direct (N × H)
33. C₃²×C₅²	C₂×C₇×C₁₁	semidirect
36. C₅²×C₇	C₂×C₃²×C₁₁	semidirect
37. C₃×C₅×C₁₁	C₃×C₇×D₅	semidirect
39. C₃×C₅⋊D₅	C₃×C₇×C₁₁	direct (N × H)
42. C₃×C₅×C₇	C₃×D₅×C₁₁	semidirect
43. C₃²×C₁₁	C₇×C₅⋊D₅	direct (N × H)
45. C₇×C₁₁	C₃²×C₅⋊D₅	direct (N × H)
46. C₃×C₅²	C₂×C₃×C₇×C₁₁	semidirect
49. C₃²×C₇	C₁₁×C₅⋊D₅	direct (N × H)
50. C₅×C₁₁	C₃²×C₇×D₅	semidirect
51. C₅⋊D₅	C₃²×C₇×C₁₁	direct (N × H)
52. C₃²×C₅	C₇×D₅×C₁₁	semidirect
54. C₅×C₇	C₃²×D₅×C₁₁	semidirect
55. C₃×C₁₁	C₃×C₇×C₅⋊D₅	direct (N × H)
57. C₅²	C₂×C₃²×C₇×C₁₁	semidirect
59. C₃×C₇	C₃×C₁₁×C₅⋊D₅	direct (N × H)
61. C₃×C₅	C₃×C₇×D₅×C₁₁	semidirect
63. C₁₁	C₃²×C₇×C₅⋊D₅	direct (N × H)
65. C₃²	C₇×C₁₁×C₅⋊D₅	direct (N × H)
66. C₇	C₃²×C₁₁×C₅⋊D₅	direct (N × H)
68. C₅	C₃²×C₇×D₅×C₁₁	semidirect
69. C₃	C₃×C₇×C₁₁×C₅⋊D₅	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×C₅²×C₇×C₁₁	2
C₃×C₇×C₁₁×C₅⋊D₅	3
C₃²×C₇×D₅×C₁₁	5
C₃²×C₁₁×C₅⋊D₅	7
C₃²×C₇×C₅⋊D₅	11

Subgroups — C32×C7×C11×C5⋊D5 #46831658

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×C₇×C₁₁×C₅⋊D₅ #46831658