Subgroups — C₂×C₁₁⋊C₅×C₃⋊D₅₁ #46778036

Order 33660.

240 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×C₁₇×C₁₁⋊C₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₁⋊C₅×C₃⋊D₅₁	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₁₁⋊C₅×D₅₁	—	3	4	no	maximal
4	C₃²×C₁₇×C₁₁⋊C₅	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₁₁×C₃⋊D₅₁	C₅	1	1	yes	maximal, characteristic, complemented, Hall
6	C₁₁⋊C₅×D₅₁	—	3	8	no	—
7	C₂×C₃×C₁₇×C₁₁⋊C₅	D₃	1	4	yes	complemented
8	C₂×D₁₇×C₁₁⋊C₅	—	9	1	no	Hall
9	C₁₁×C₃⋊D₅₁	C₂×C₅	1	2	yes	complemented
10	C₂×C₃²×C₁₁×C₁₇	C₂×C₅	1	1	yes	characteristic, complemented
11	C₂×C₅×C₃⋊D₅₁	—	11	1	no	maximal, Hall
12	C₃×C₁₇×C₁₁⋊C₅	C₂×D₃	1	4	yes	complemented
13	C₂×C₁₁×D₅₁	—	3	4	no	—
14	C₂×C₃⋊D₃×C₁₁⋊C₅	—	17	1	no	maximal, Hall
15	C₂×C₁₇×C₁₁⋊C₅	C₃⋊D₃	1	1	yes	characteristic, complemented
16	D₁₇×C₁₁⋊C₅	—	9	2	no	—
17	C₃²×C₁₁×C₁₇	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
18	C₂×C₃²×C₅×C₁₇	—	11	1	no	—
19	C₅×C₃⋊D₅₁	—	11	2	no	—
20	C₂×C₃×C₁₁×C₁₇	C₅×D₃	1	4	yes	complemented
21	C₁₁×D₅₁	—	3	8	no	—
22	C₂×C₅×D₅₁	—	33	4	no	—
23	C₂×C₃²×C₁₁⋊C₅	D₁₇	1	1	yes	characteristic, complemented
24	C₃⋊D₃×C₁₁⋊C₅	—	17	2	no	—
25	C₁₇×C₁₁⋊C₅	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
26	C₃²×C₅×C₁₇	—	11	1	no	Hall
27	C₂×C₁₁×D₁₇	—	9	1	no	Hall
28	C₂×D₃×C₁₁⋊C₅	—	51	4	no	—
29	C₂×C₃⋊D₅₁	C₁₁⋊C₅	1	1	yes	characteristic, direct product factor, Hall
30	C₃×C₁₁×C₁₇	C₂×C₅×D₃	1	4	yes	complemented
31	C₂×C₃×C₅×C₁₇	—	11	4	no	—
32	C₅×D₅₁	—	33	8	no	—
33	C₃²×C₁₁⋊C₅	C₂×D₁₇	1	1	yes	characteristic, complemented, Hall
34	C₂×C₁₁×C₃⋊D₃	—	17	1	no	Hall
35	C₂×C₁₁×C₁₇	C₅×C₃⋊D₃	1	1	yes	characteristic, complemented
36	C₁₁×D₁₇	—	9	2	no	—
37	C₂×C₅×D₁₇	—	99	1	no	Hall
38	C₂×C₃×C₁₁⋊C₅	D₅₁	1	4	yes	complemented
39	D₃×C₁₁⋊C₅	—	51	8	no	—
40	C₂×C₃²×C₁₇	C₂×C₁₁⋊C₅	1	1	yes	characteristic, complemented
41	C₃⋊D₅₁	C₂×C₁₁⋊C₅	1	2	yes	direct product factor
42	C₃×C₅×C₁₇	—	11	4	no	—
43	C₂²×C₁₁⋊C₅	—	153	1	no	Hall
44	C₂×D₅₁	—	3	4	no	—
45	C₂×C₃²×C₁₁	C₅×D₁₇	1	1	yes	characteristic, complemented
46	C₁₁×C₃⋊D₃	—	17	2	no	—
47	C₁₁×C₁₇	C₂×C₅×C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
48	C₂×C₅×C₃⋊D₃	—	187	1	no	Hall
49	C₂×C₅×C₁₇	—	11	1	no	—
50	C₅×D₁₇	—	99	2	no	—
51	C₃×C₁₁⋊C₅	C₂×D₅₁	1	4	yes	complemented
52	C₃²×C₁₇	C₂²×C₁₁⋊C₅	1	1	yes	characteristic, complemented, Hall
53	C₂×D₃×C₁₁	—	51	4	no	—
54	C₂×C₁₁⋊C₅	—	153	2	no	—
55	C₂×C₁₁⋊C₅	C₃⋊D₅₁	1	1	yes	characteristic, direct product factor
56	C₂×C₃×C₁₇	D₃×C₁₁⋊C₅	1	4	yes	complemented
57	D₅₁	—	3	8	no	—
58	C₃²×C₁₁	C₂×C₅×D₁₇	1	1	yes	characteristic, complemented, Hall
59	C₂×C₃²×C₅	—	11	1	no	—
60	C₅×C₃⋊D₃	—	187	2	no	—
61	C₅×C₁₇	—	11	1	no	Hall
62	C₂×D₁₇	—	9	1	no	Hall
63	C₂×C₃×C₁₁	C₅×D₅₁	1	4	yes	complemented
64	D₃×C₁₁	—	51	8	no	—
65	C₂×C₅×D₃	—	561	4	no	—
66	C₁₁⋊C₅	C₂×C₃⋊D₅₁	1	1	yes	characteristic, direct product factor, Hall
67	C₃×C₁₇	C₂×D₃×C₁₁⋊C₅	1	4	yes	complemented
68	C₃²×C₅	—	11	1	no	Hall
69	C₂²×C₁₁	—	153	1	no	Hall
70	C₂×C₃⋊D₃	—	17	1	no	Hall
71	C₂×C₁₇	C₃⋊D₃×C₁₁⋊C₅	1	1	yes	characteristic, complemented
72	D₁₇	—	9	2	no	—
73	C₃×C₁₁	C₂×C₅×D₅₁	1	4	yes	complemented
74	C₂×C₃×C₅	—	11	4	no	—
75	C₅×D₃	—	561	8	no	—
76	C₂×C₁₁	—	153	2	no	—
77	C₂×C₁₁	C₅×C₃⋊D₅₁	1	1	yes	characteristic, complemented
78	C₂²×C₅	—	1683	1	no	Hall
79	C₂×C₃²	D₁₇×C₁₁⋊C₅	1	1	yes	characteristic, complemented
80	C₃⋊D₃	—	17	2	no	—
81	C₁₇	C₂×C₃⋊D₃×C₁₁⋊C₅	1	1	yes	characteristic, complemented, Sylow
82	C₃×C₅	—	11	4	no	—
83	C₂×D₃	—	51	4	no	—
84	C₁₁	C₂×C₅×C₃⋊D₅₁	1	1	yes	characteristic, complemented, Sylow
85	C₂×C₅	—	11	1	no	—
86	C₂×C₅	—	1683	2	no	—
87	C₃²	C₂×D₁₇×C₁₁⋊C₅	1	1	yes	characteristic, complemented, Sylow
88	C₂×C₃	C₁₁⋊C₅×D₅₁	1	4	yes	complemented
89	D₃	—	51	8	no	—
90	C₅	—	11	1	no	Sylow
91	C₂²	—	153	1	no	Sylow
92	C₃	C₂×C₁₁⋊C₅×D₅₁	1	4	yes	complemented
93	C₂	—	153	2	no	—
94	C₂	C₁₁⋊C₅×C₃⋊D₅₁	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	C₁₁⋊C₅×C₃⋊D₅₁
commutator, cosocle, hypocenter	C₃²×C₁₁×C₁₇	C₂²×C₅
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₁₁×C₁₇	C₂×C₅
LCS	G ▷ C₃²×C₁₁×C₁₇
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₂×C₃²×C₁₇×C₁₁⋊C₅	C₂	semidirect
2. C₁₁⋊C₅×C₃⋊D₅₁	C₂	direct (N × H)
4. C₃²×C₁₇×C₁₁⋊C₅	C₂²	semidirect
5. C₂×C₁₁×C₃⋊D₅₁	C₅	semidirect
7. C₂×C₃×C₁₇×C₁₁⋊C₅	D₃	semidirect
9. C₁₁×C₃⋊D₅₁	C₂×C₅	semidirect
10. C₂×C₃²×C₁₁×C₁₇	C₂×C₅	semidirect
12. C₃×C₁₇×C₁₁⋊C₅	C₂×D₃	semidirect
15. C₂×C₁₇×C₁₁⋊C₅	C₃⋊D₃	semidirect
17. C₃²×C₁₁×C₁₇	C₂²×C₅	semidirect
20. C₂×C₃×C₁₁×C₁₇	C₅×D₃	semidirect
23. C₂×C₃²×C₁₁⋊C₅	D₁₇	semidirect
25. C₁₇×C₁₁⋊C₅	C₂×C₃⋊D₃	semidirect
29. C₂×C₃⋊D₅₁	C₁₁⋊C₅	direct (N × H)
30. C₃×C₁₁×C₁₇	C₂×C₅×D₃	semidirect
33. C₃²×C₁₁⋊C₅	C₂×D₁₇	semidirect
35. C₂×C₁₁×C₁₇	C₅×C₃⋊D₃	semidirect
38. C₂×C₃×C₁₁⋊C₅	D₅₁	semidirect
40. C₂×C₃²×C₁₇	C₂×C₁₁⋊C₅	semidirect
41. C₃⋊D₅₁	C₂×C₁₁⋊C₅	direct (N × H)
45. C₂×C₃²×C₁₁	C₅×D₁₇	semidirect
47. C₁₁×C₁₇	C₂×C₅×C₃⋊D₃	semidirect
51. C₃×C₁₁⋊C₅	C₂×D₅₁	semidirect
52. C₃²×C₁₇	C₂²×C₁₁⋊C₅	semidirect
55. C₂×C₁₁⋊C₅	C₃⋊D₅₁	direct (N × H)
56. C₂×C₃×C₁₇	D₃×C₁₁⋊C₅	semidirect
58. C₃²×C₁₁	C₂×C₅×D₁₇	semidirect
63. C₂×C₃×C₁₁	C₅×D₅₁	semidirect
66. C₁₁⋊C₅	C₂×C₃⋊D₅₁	direct (N × H)
67. C₃×C₁₇	C₂×D₃×C₁₁⋊C₅	semidirect
71. C₂×C₁₇	C₃⋊D₃×C₁₁⋊C₅	semidirect
73. C₃×C₁₁	C₂×C₅×D₅₁	semidirect
77. C₂×C₁₁	C₅×C₃⋊D₅₁	semidirect
79. C₂×C₃²	D₁₇×C₁₁⋊C₅	semidirect
81. C₁₇	C₂×C₃⋊D₃×C₁₁⋊C₅	semidirect
84. C₁₁	C₂×C₅×C₃⋊D₅₁	semidirect
87. C₃²	C₂×D₁₇×C₁₁⋊C₅	semidirect
88. C₂×C₃	C₁₁⋊C₅×D₅₁	semidirect
92. C₃	C₂×C₁₁⋊C₅×D₅₁	semidirect
94. C₂	C₁₁⋊C₅×C₃⋊D₅₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃²×C₁₇×C₁₁⋊C₅	2
C₁₁⋊C₅×C₃⋊D₅₁	2
C₂×C₁₁⋊C₅×D₅₁	3
C₂×C₁₁×C₃⋊D₅₁	5
C₂×C₅×C₃⋊D₅₁	11
C₂×C₃⋊D₃×C₁₁⋊C₅	17

Subgroups — C2×C11⋊C5×C3⋊D51 #46778036

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₁⋊C₅×C₃⋊D₅₁ #46778036