Subgroups — C₅×C₁₁×C₃⋊Dic₅₁ #46777972

Order 33660.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×C₅×C₁₁×C₁₇	C₂	1	1	yes	maximal, characteristic
2	C₅×C₁₁×Dic₅₁	—	3	4	no	maximal
3	C₃²×C₅×C₁₁×C₁₇	C₄	1	1	yes	characteristic, complemented, Hall
4	C₁₁×C₃⋊Dic₅₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₃×C₅×C₁₁×C₁₇	D₃	1	4	yes	—
6	C₅×C₁₁×Dic₁₇	—	9	1	no	Hall
7	C₂×C₃²×C₁₁×C₁₇	C₂×C₅	1	1	yes	characteristic
8	C₅×C₃⋊Dic₅₁	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₃×C₅×C₁₁×C₁₇	Dic₃	1	4	yes	complemented
10	C₁₁×Dic₅₁	—	3	4	no	—
11	C₅×C₁₁×C₃⋊Dic₃	—	17	1	no	maximal, Hall
12	C₂×C₅×C₁₁×C₁₇	C₃⋊D₃	1	1	yes	characteristic
13	C₃²×C₁₁×C₁₇	C₄×C₅	1	1	yes	characteristic, complemented, Hall
14	C₂×C₃²×C₅×C₁₇	C₂×C₁₁	1	1	yes	characteristic
15	C₂×C₃×C₁₁×C₁₇	C₅×D₃	1	4	yes	—
16	C₅×Dic₅₁	—	3	4	no	—
17	C₂×C₃²×C₅×C₁₁	D₁₇	1	1	yes	characteristic
18	C₅×C₁₁×C₁₇	C₃⋊Dic₃	1	1	yes	characteristic, complemented, Hall
19	C₃²×C₅×C₁₇	C₄×C₁₁	1	1	yes	characteristic, complemented, Hall
20	C₁₁×Dic₁₇	—	9	1	no	Hall
21	C₅×C₁₁×Dic₃	—	51	4	no	—
22	C₃⋊Dic₅₁	C₅×C₁₁	1	1	yes	characteristic, direct product factor, Hall
23	C₃×C₁₁×C₁₇	C₅×Dic₃	1	4	yes	complemented
24	C₂×C₃×C₅×C₁₇	D₃×C₁₁	1	4	yes	—
25	C₃²×C₅×C₁₁	Dic₁₇	1	1	yes	characteristic, complemented, Hall
26	C₁₁×C₃⋊Dic₃	—	17	1	no	Hall
27	C₂×C₁₁×C₁₇	C₅×C₃⋊D₃	1	1	yes	characteristic
28	C₅×Dic₁₇	—	9	1	no	Hall
29	C₂×C₃×C₅×C₁₁	D₅₁	1	4	yes	—
30	C₂×C₃²×C₁₇	C₂×C₅×C₁₁	1	1	yes	characteristic
31	C₃×C₅×C₁₇	C₁₁×Dic₃	1	4	yes	complemented
32	C₄×C₅×C₁₁	—	153	1	no	Hall
33	Dic₅₁	—	3	4	no	—
34	C₂×C₃²×C₁₁	C₅×D₁₇	1	1	yes	characteristic
35	C₁₁×C₁₇	C₅×C₃⋊Dic₃	1	1	yes	characteristic, complemented, Hall
36	C₅×C₃⋊Dic₃	—	17	1	no	Hall
37	C₂×C₅×C₁₇	C₁₁×C₃⋊D₃	1	1	yes	characteristic
38	C₃×C₅×C₁₁	Dic₅₁	1	4	yes	complemented
39	C₃²×C₁₇	C₄×C₅×C₁₁	1	1	yes	characteristic, complemented, Hall
40	C₁₁×Dic₃	—	51	4	no	—
41	C₂×C₅×C₁₁	C₃⋊D₅₁	1	1	yes	characteristic
42	C₂×C₃×C₁₇	C₅×D₃×C₁₁	1	4	yes	—
43	C₃²×C₁₁	C₅×Dic₁₇	1	1	yes	characteristic, complemented, Hall
44	C₂×C₃²×C₅	C₁₁×D₁₇	1	1	yes	characteristic
45	C₅×C₁₇	C₁₁×C₃⋊Dic₃	1	1	yes	characteristic, complemented, Hall
46	Dic₁₇	—	9	1	no	Hall
47	C₂×C₃×C₁₁	C₅×D₅₁	1	4	yes	—
48	C₅×Dic₃	—	51	4	no	—
49	C₅×C₁₁	C₃⋊Dic₅₁	1	1	yes	characteristic, direct product factor, Hall
50	C₃×C₁₇	C₅×C₁₁×Dic₃	1	4	yes	complemented
51	C₃²×C₅	C₁₁×Dic₁₇	1	1	yes	characteristic, complemented, Hall
52	C₄×C₁₁	—	153	1	no	Hall
53	C₃⋊Dic₃	—	17	1	no	Hall
54	C₂×C₁₇	C₅×C₁₁×C₃⋊D₃	1	1	yes	characteristic
55	C₃×C₁₁	C₅×Dic₅₁	1	4	yes	complemented
56	C₂×C₃×C₅	C₁₁×D₅₁	1	4	yes	—
57	C₂×C₁₁	C₅×C₃⋊D₅₁	1	1	yes	characteristic
58	C₄×C₅	—	153	1	no	Hall
59	C₂×C₃²	C₅×C₁₁×D₁₇	1	1	yes	characteristic
60	C₁₇	C₅×C₁₁×C₃⋊Dic₃	1	1	yes	characteristic, complemented, Sylow
61	C₃×C₅	C₁₁×Dic₅₁	1	4	yes	complemented
62	Dic₃	—	51	4	no	—
63	C₁₁	C₅×C₃⋊Dic₅₁	1	1	yes	characteristic, direct product factor, Sylow
64	C₂×C₅	C₁₁×C₃⋊D₅₁	1	1	yes	characteristic
65	C₃²	C₅×C₁₁×Dic₁₇	1	1	yes	characteristic, complemented, Sylow
66	C₂×C₃	C₅×C₁₁×D₅₁	1	4	yes	—
67	C₅	C₁₁×C₃⋊Dic₅₁	1	1	yes	characteristic, direct product factor, Sylow
68	C₄	—	153	1	no	Sylow
69	C₃	C₅×C₁₁×Dic₅₁	1	4	yes	complemented
70	C₂	C₅×C₁₁×C₃⋊D₅₁	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₅×C₁₁	C₃⋊D₅₁
commutator, hypocenter	C₃²×C₁₇	C₄×C₅×C₁₁
Frattini	C₂	C₅×C₁₁×C₃⋊D₅₁
Fitting, socle, prime radical	C₂×C₃²×C₅×C₁₁×C₁₇	C₂
cosocle	C₂×C₃²×C₁₇	C₂×C₅×C₁₁
LCS	G ▷ C₃²×C₁₇
UCS	C₁ ◁ C₂×C₅×C₁₁

Complements

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

N	H ≅ G/N	type
3. C₃²×C₅×C₁₁×C₁₇	C₄	semidirect
4. C₁₁×C₃⋊Dic₅₁	C₅	direct (N × H)
8. C₅×C₃⋊Dic₅₁	C₁₁	direct (N × H)
9. C₃×C₅×C₁₁×C₁₇	Dic₃	semidirect
13. C₃²×C₁₁×C₁₇	C₄×C₅	semidirect
18. C₅×C₁₁×C₁₇	C₃⋊Dic₃	semidirect
19. C₃²×C₅×C₁₇	C₄×C₁₁	semidirect
22. C₃⋊Dic₅₁	C₅×C₁₁	direct (N × H)
23. C₃×C₁₁×C₁₇	C₅×Dic₃	semidirect
25. C₃²×C₅×C₁₁	Dic₁₇	semidirect
31. C₃×C₅×C₁₇	C₁₁×Dic₃	semidirect
35. C₁₁×C₁₇	C₅×C₃⋊Dic₃	semidirect
38. C₃×C₅×C₁₁	Dic₅₁	semidirect
39. C₃²×C₁₇	C₄×C₅×C₁₁	semidirect
43. C₃²×C₁₁	C₅×Dic₁₇	semidirect
45. C₅×C₁₇	C₁₁×C₃⋊Dic₃	semidirect
49. C₅×C₁₁	C₃⋊Dic₅₁	direct (N × H)
50. C₃×C₁₇	C₅×C₁₁×Dic₃	semidirect
51. C₃²×C₅	C₁₁×Dic₁₇	semidirect
55. C₃×C₁₁	C₅×Dic₅₁	semidirect
60. C₁₇	C₅×C₁₁×C₃⋊Dic₃	semidirect
61. C₃×C₅	C₁₁×Dic₅₁	semidirect
63. C₁₁	C₅×C₃⋊Dic₅₁	direct (N × H)
65. C₃²	C₅×C₁₁×Dic₁₇	semidirect
67. C₅	C₁₁×C₃⋊Dic₅₁	direct (N × H)
69. C₃	C₅×C₁₁×Dic₅₁	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₃²×C₅×C₁₁×C₁₇	2
C₅×C₁₁×Dic₅₁	3
C₁₁×C₃⋊Dic₅₁	5
C₅×C₃⋊Dic₅₁	11
C₅×C₁₁×C₃⋊Dic₃	17

Subgroups — C5×C11×C3⋊Dic51 #46777972

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₁₁×C₃⋊Dic₅₁ #46777972