Subgroups — C₃×C₁₁×D₄₆₅ #44501879

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	C₁₁×D₄₆₅	C₃	1	1	yes	maximal, characteristic, direct product factor
3	C₃×C₁₁×D₁₅₅	—	3	1	no	maximal
4	C₃×C₁₁×D₉₃	—	5	1	no	maximal, Hall
5	C₃×C₅×C₁₁×C₃₁	—	2	1	no	—
6	C₃×C₅×C₁₁×C₃₁	D₃	1	1	yes	characteristic, complemented
7	C₃×C₅×C₁₁×C₃₁	C₂×C₃	1	1	yes	characteristic, complemented
8	C₁₁×D₁₅₅	—	3	1	no	Hall
9	C₃²×C₁₁×C₃₁	D₅	1	1	yes	characteristic, complemented, Hall
10	C₃×D₄₆₅	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₁₁×D₉₃	—	5	1	no	—
12	C₃×C₁₁×D₃₁	—	15	1	no	—
13	C₅×C₁₁×C₃₁	C₃×D₃	1	1	yes	characteristic, complemented, Hall
14	C₃²×C₅×C₃₁	C₂×C₁₁	1	1	yes	characteristic, complemented, Hall
15	C₃×C₁₁×C₃₁	—	2	1	no	—
16	C₃×C₁₁×C₃₁	C₃×D₅	1	1	yes	characteristic, complemented
17	C₃×C₁₁×C₃₁	D₁₅	1	1	yes	characteristic, complemented
18	C₃×C₁₁×D₁₅	—	31	1	no	maximal, Hall
19	D₄₆₅	C₃×C₁₁	1	1	yes	characteristic, direct product factor
20	C₃×D₁₅₅	—	3	1	no	—
21	C₁₁×D₃₁	—	15	1	no	Hall
22	C₃×D₉₃	—	5	1	no	Hall
23	C₃²×C₅×C₁₁	D₃₁	1	1	yes	characteristic, complemented, Hall
24	C₃×C₅×C₃₁	—	2	1	no	—
25	C₃×C₅×C₃₁	D₃×C₁₁	1	1	yes	characteristic, complemented
26	C₃×C₅×C₃₁	C₂×C₃×C₁₁	1	1	yes	characteristic, complemented
27	C₁₁×C₃₁	C₃×D₁₅	1	1	yes	characteristic, complemented, Hall
28	C₁₁×D₁₅	—	31	1	no	—
29	C₃×D₅×C₁₁	—	93	1	no	—
30	D₁₅₅	—	3	1	no	Hall
31	C₃²×C₃₁	D₅×C₁₁	1	1	yes	characteristic, complemented, Hall
32	C₃×D₃×C₁₁	—	155	1	no	Hall
33	D₉₃	—	5	1	no	—
34	C₃×D₃₁	—	15	1	no	—
35	C₃×C₅×C₁₁	—	2	1	no	—
36	C₃×C₅×C₁₁	C₃×D₃₁	1	1	yes	characteristic, complemented
37	C₃×C₅×C₁₁	D₉₃	1	1	yes	characteristic, complemented
38	C₅×C₃₁	C₃×D₃×C₁₁	1	1	yes	characteristic, complemented, Hall
39	D₅×C₁₁	—	93	1	no	Hall
40	C₃²×C₁₁	D₁₅₅	1	1	yes	characteristic, complemented, Hall
41	C₃×C₃₁	—	2	1	no	—
42	C₃×C₃₁	C₃×D₅×C₁₁	1	1	yes	characteristic, complemented
43	C₃×C₃₁	C₁₁×D₁₅	1	1	yes	characteristic, complemented
44	C₃×D₁₅	—	31	1	no	Hall
45	C₂×C₃×C₁₁	—	465	1	no	—
46	D₃×C₁₁	—	155	1	no	—
47	D₃₁	—	15	1	no	Hall
48	C₅×C₁₁	C₃×D₉₃	1	1	yes	characteristic, complemented, Hall
49	C₃²×C₅	C₁₁×D₃₁	1	1	yes	characteristic, complemented, Hall
50	C₃×C₁₁	—	2	1	no	—
51	C₃×C₁₁	C₃×D₁₅₅	1	1	yes	characteristic, complemented
52	C₃×C₁₁	D₄₆₅	1	1	yes	characteristic, direct product factor
53	C₃₁	C₃×C₁₁×D₁₅	1	1	yes	characteristic, complemented, Sylow
54	D₁₅	—	31	1	no	—
55	C₃×D₅	—	93	1	no	—
56	C₂×C₁₁	—	465	1	no	Hall
57	C₃×D₃	—	155	1	no	Hall
58	C₃×C₅	—	2	1	no	—
59	C₃×C₅	C₃×C₁₁×D₃₁	1	1	yes	characteristic, complemented
60	C₃×C₅	C₁₁×D₉₃	1	1	yes	characteristic, complemented
61	C₁₁	C₃×D₄₆₅	1	1	yes	characteristic, direct product factor, Sylow
62	D₅	—	93	1	no	Hall
63	C₃²	C₁₁×D₁₅₅	1	1	yes	characteristic, complemented, Sylow
64	C₂×C₃	—	465	1	no	—
65	D₃	—	155	1	no	—
66	C₅	C₃×C₁₁×D₉₃	1	1	yes	characteristic, complemented, Sylow
67	C₃	—	2	1	no	—
68	C₃	C₃×C₁₁×D₁₅₅	1	1	yes	characteristic, complemented
69	C₃	C₁₁×D₄₆₅	1	1	yes	characteristic, direct product factor
70	C₂	—	465	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₁₁	D₄₆₅
commutator, cosocle, hypocenter	C₃×C₅×C₃₁	C₂×C₃×C₁₁
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₁₁×C₃₁	C₂
LCS	G ▷ C₃×C₅×C₃₁
UCS	C₁ ◁ C₃×C₁₁

Complements

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

N	H ≅ G/N	type
1. C₃²×C₅×C₁₁×C₃₁	C₂	semidirect
2. C₁₁×D₄₆₅	C₃	direct (N × H)
6. C₃×C₅×C₁₁×C₃₁	D₃	semidirect
7. C₃×C₅×C₁₁×C₃₁	C₂×C₃	semidirect
9. C₃²×C₁₁×C₃₁	D₅	semidirect
10. C₃×D₄₆₅	C₁₁	direct (N × H)
13. C₅×C₁₁×C₃₁	C₃×D₃	semidirect
14. C₃²×C₅×C₃₁	C₂×C₁₁	semidirect
16. C₃×C₁₁×C₃₁	C₃×D₅	semidirect
17. C₃×C₁₁×C₃₁	D₁₅	semidirect
19. D₄₆₅	C₃×C₁₁	direct (N × H)
23. C₃²×C₅×C₁₁	D₃₁	semidirect
25. C₃×C₅×C₃₁	D₃×C₁₁	semidirect
26. C₃×C₅×C₃₁	C₂×C₃×C₁₁	semidirect
27. C₁₁×C₃₁	C₃×D₁₅	semidirect
31. C₃²×C₃₁	D₅×C₁₁	semidirect
36. C₃×C₅×C₁₁	C₃×D₃₁	semidirect
37. C₃×C₅×C₁₁	D₉₃	semidirect
38. C₅×C₃₁	C₃×D₃×C₁₁	semidirect
40. C₃²×C₁₁	D₁₅₅	semidirect
42. C₃×C₃₁	C₃×D₅×C₁₁	semidirect
43. C₃×C₃₁	C₁₁×D₁₅	semidirect
48. C₅×C₁₁	C₃×D₉₃	semidirect
49. C₃²×C₅	C₁₁×D₃₁	semidirect
51. C₃×C₁₁	C₃×D₁₅₅	semidirect
52. C₃×C₁₁	D₄₆₅	direct (N × H)
53. C₃₁	C₃×C₁₁×D₁₅	semidirect
59. C₃×C₅	C₃×C₁₁×D₃₁	semidirect
60. C₃×C₅	C₁₁×D₉₃	semidirect
61. C₁₁	C₃×D₄₆₅	direct (N × H)
63. C₃²	C₁₁×D₁₅₅	semidirect
66. C₅	C₃×C₁₁×D₉₃	semidirect
68. C₃	C₃×C₁₁×D₁₅₅	semidirect
69. C₃	C₁₁×D₄₆₅	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
C₁₁×D₄₆₅	3
C₃×C₁₁×D₁₅₅	3
C₃×C₁₁×D₉₃	5
C₃×D₄₆₅	11
C₃×C₁₁×D₁₅	31

Subgroups — C3×C11×D465 #44501879

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₁₁×D₄₆₅ #44501879