Subgroups — C₂×C₅×C₉×C₁₇×D₁₁ #46777951

Order 33660.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₉×C₁₇×D₁₁	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₅×C₉×C₁₁×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₅×C₁₇×D₁₁	C₃	1	1	yes	maximal, characteristic
4	C₅×C₉×C₁₁×C₁₇	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₉×C₁₇×D₁₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₃×C₅×C₁₇×D₁₁	C₂×C₃	1	2	yes	—
7	C₂×C₃×C₅×C₁₁×C₁₇	C₂×C₃	1	1	yes	characteristic
8	C₂×C₅×C₁₇×D₁₁	C₉	1	1	yes	characteristic, direct product factor, Hall
9	C₉×C₁₇×D₁₁	C₂×C₅	1	2	yes	direct product factor
10	C₂×C₉×C₁₁×C₁₇	C₂×C₅	1	1	yes	characteristic, complemented
11	C₂²×C₅×C₉×C₁₇	—	11	1	no	maximal, Hall
12	C₃×C₅×C₁₁×C₁₇	C₂²×C₃	1	1	yes	characteristic
13	C₂×C₃×C₁₇×D₁₁	C₃×C₅	1	1	yes	characteristic
14	C₂×C₅×C₉×D₁₁	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
15	C₂×C₅×C₁₁×C₁₇	C₂×C₉	1	1	yes	characteristic, complemented
16	C₅×C₁₇×D₁₁	C₂×C₉	1	2	yes	direct product factor
17	C₉×C₁₁×C₁₇	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
18	C₂×C₅×C₉×C₁₇	—	11	2	no	—
19	C₂×C₅×C₉×C₁₇	D₁₁	1	1	yes	characteristic, direct product factor
20	C₂×C₃×C₁₁×C₁₇	C₂×C₃×C₅	1	1	yes	characteristic
21	C₃×C₁₇×D₁₁	C₂×C₃×C₅	1	2	yes	—
22	C₂²×C₃×C₅×C₁₇	—	11	1	no	—
23	C₂×C₅×C₉×C₁₁	C₂×C₁₇	1	1	yes	characteristic, complemented
24	C₅×C₉×D₁₁	C₂×C₁₇	1	2	yes	direct product factor
25	C₅×C₁₁×C₁₇	C₂²×C₉	1	1	yes	characteristic, complemented, Hall
26	C₅×C₉×C₁₇	C₂×D₁₁	1	1	yes	characteristic, direct product factor, Hall
27	C₂×C₁₇×D₁₁	C₅×C₉	1	1	yes	characteristic, direct product factor, Hall
28	C₂×C₃×C₅×D₁₁	C₃×C₁₇	1	1	yes	characteristic
29	C₂²×C₉×C₁₇	—	11	1	no	Hall
30	C₃×C₁₁×C₁₇	C₂²×C₃×C₅	1	1	yes	characteristic
31	C₂×C₃×C₅×C₁₇	—	11	2	no	—
32	C₂×C₃×C₅×C₁₇	C₃×D₁₁	1	1	yes	characteristic
33	C₅×C₉×C₁₁	C₂²×C₁₇	1	1	yes	characteristic, complemented, Hall
34	C₂×C₉×D₁₁	C₅×C₁₇	1	1	yes	characteristic, direct product factor, Hall
35	C₂×C₁₁×C₁₇	C₂×C₅×C₉	1	1	yes	characteristic, complemented
36	C₁₇×D₁₁	C₂×C₅×C₉	1	2	yes	direct product factor
37	C₂²×C₅×C₁₇	—	11	1	no	Hall
38	C₂×C₃×C₅×C₁₁	C₂×C₃×C₁₇	1	1	yes	characteristic
39	C₃×C₅×D₁₁	C₂×C₃×C₁₇	1	2	yes	—
40	C₂×C₉×C₁₇	—	11	2	no	—
41	C₂×C₉×C₁₇	C₅×D₁₁	1	1	yes	characteristic, direct product factor
42	C₃×C₅×C₁₇	C₂×C₃×D₁₁	1	1	yes	characteristic
43	C₂×C₅×D₁₁	C₉×C₁₇	1	1	yes	characteristic, direct product factor, Hall
44	C₂²×C₃×C₁₇	—	11	1	no	—
45	C₂×C₉×C₁₁	C₂×C₅×C₁₇	1	1	yes	characteristic, complemented
46	C₉×D₁₁	C₂×C₅×C₁₇	1	2	yes	direct product factor
47	C₁₁×C₁₇	C₂²×C₅×C₉	1	1	yes	characteristic, complemented, Hall
48	C₂²×C₅×C₉	—	11	1	no	Hall
49	C₂×C₅×C₁₇	—	11	2	no	—
50	C₂×C₅×C₁₇	C₉×D₁₁	1	1	yes	characteristic, direct product factor
51	C₃×C₅×C₁₁	C₂²×C₃×C₁₇	1	1	yes	characteristic
52	C₉×C₁₇	C₂×C₅×D₁₁	1	1	yes	characteristic, direct product factor, Hall
53	C₂×C₃×D₁₁	C₃×C₅×C₁₇	1	1	yes	characteristic
54	C₂×C₅×C₁₁	C₂×C₉×C₁₇	1	1	yes	characteristic, complemented
55	C₅×D₁₁	C₂×C₉×C₁₇	1	2	yes	direct product factor
56	C₂×C₃×C₁₇	—	11	2	no	—
57	C₂×C₃×C₁₇	C₃×C₅×D₁₁	1	1	yes	characteristic
58	C₉×C₁₁	C₂²×C₅×C₁₇	1	1	yes	characteristic, complemented, Hall
59	C₂×C₅×C₉	—	11	2	no	—
60	C₂×C₅×C₉	C₁₇×D₁₁	1	1	yes	characteristic, direct product factor
61	C₅×C₁₇	C₂×C₉×D₁₁	1	1	yes	characteristic, direct product factor, Hall
62	C₂²×C₁₇	—	11	1	no	Hall
63	C₂×C₃×C₁₁	C₂×C₃×C₅×C₁₇	1	1	yes	characteristic
64	C₃×D₁₁	C₂×C₃×C₅×C₁₇	1	2	yes	—
65	C₂²×C₃×C₅	—	11	1	no	—
66	C₅×C₁₁	C₂²×C₉×C₁₇	1	1	yes	characteristic, complemented, Hall
67	C₃×C₁₇	C₂×C₃×C₅×D₁₁	1	1	yes	characteristic
68	C₅×C₉	C₂×C₁₇×D₁₁	1	1	yes	characteristic, direct product factor, Hall
69	C₂×D₁₁	C₅×C₉×C₁₇	1	1	yes	characteristic, direct product factor, Hall
70	C₂²×C₉	—	11	1	no	Hall
71	C₂×C₁₇	—	11	2	no	—
72	C₂×C₁₇	C₅×C₉×D₁₁	1	1	yes	characteristic, direct product factor
73	C₃×C₁₁	C₂²×C₃×C₅×C₁₇	1	1	yes	characteristic
74	C₂×C₃×C₅	—	11	2	no	—
75	C₂×C₃×C₅	C₃×C₁₇×D₁₁	1	1	yes	characteristic
76	C₂×C₁₁	C₂×C₅×C₉×C₁₇	1	1	yes	characteristic, complemented
77	D₁₁	C₂×C₅×C₉×C₁₇	1	2	yes	direct product factor
78	C₂²×C₅	—	11	1	no	Hall
79	C₂×C₉	—	11	2	no	—
80	C₂×C₉	C₅×C₁₇×D₁₁	1	1	yes	characteristic, direct product factor
81	C₁₇	C₂×C₅×C₉×D₁₁	1	1	yes	characteristic, direct product factor, Sylow
82	C₃×C₅	C₂×C₃×C₁₇×D₁₁	1	1	yes	characteristic
83	C₂²×C₃	—	11	1	no	—
84	C₁₁	C₂²×C₅×C₉×C₁₇	1	1	yes	characteristic, complemented, Sylow
85	C₂×C₅	—	11	2	no	—
86	C₂×C₅	C₉×C₁₇×D₁₁	1	1	yes	characteristic, direct product factor
87	C₉	C₂×C₅×C₁₇×D₁₁	1	1	yes	characteristic, direct product factor, Sylow
88	C₂×C₃	—	11	2	no	—
89	C₂×C₃	C₃×C₅×C₁₇×D₁₁	1	1	yes	characteristic
90	C₅	C₂×C₉×C₁₇×D₁₁	1	1	yes	characteristic, direct product factor, Sylow
91	C₂²	—	11	1	no	Sylow
92	C₃	C₂×C₃×C₅×C₁₇×D₁₁	1	1	yes	characteristic
93	C₂	—	11	2	no	—
94	C₂	C₅×C₉×C₁₇×D₁₁	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₅×C₉×C₁₇	D₁₁
commutator, hypocenter	C₁₁	C₂²×C₅×C₉×C₁₇
Frattini	C₃	C₂×C₃×C₅×C₁₇×D₁₁
Fitting	C₂×C₅×C₉×C₁₁×C₁₇	C₂
socle	C₂×C₃×C₅×C₁₁×C₁₇	C₂×C₃
prime radical	C₂×C₃×C₅×C₁₇×D₁₁	C₃
cosocle	C₃×C₁₁	C₂²×C₃×C₅×C₁₇
LCS	G ▷ C₁₁
UCS	C₁ ◁ C₂×C₅×C₉×C₁₇

Complements

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

N	H ≅ G/N	type
1. C₅×C₉×C₁₇×D₁₁	C₂	direct (N × H)
2. C₂×C₅×C₉×C₁₁×C₁₇	C₂	semidirect
4. C₅×C₉×C₁₁×C₁₇	C₂²	semidirect
5. C₂×C₉×C₁₇×D₁₁	C₅	direct (N × H)
8. C₂×C₅×C₁₇×D₁₁	C₉	direct (N × H)
9. C₉×C₁₇×D₁₁	C₂×C₅	direct (N × H)
10. C₂×C₉×C₁₁×C₁₇	C₂×C₅	semidirect
14. C₂×C₅×C₉×D₁₁	C₁₇	direct (N × H)
15. C₂×C₅×C₁₁×C₁₇	C₂×C₉	semidirect
16. C₅×C₁₇×D₁₁	C₂×C₉	direct (N × H)
17. C₉×C₁₁×C₁₇	C₂²×C₅	semidirect
19. C₂×C₅×C₉×C₁₇	D₁₁	direct (N × H)
23. C₂×C₅×C₉×C₁₁	C₂×C₁₇	semidirect
24. C₅×C₉×D₁₁	C₂×C₁₇	direct (N × H)
25. C₅×C₁₁×C₁₇	C₂²×C₉	semidirect
26. C₅×C₉×C₁₇	C₂×D₁₁	direct (N × H)
27. C₂×C₁₇×D₁₁	C₅×C₉	direct (N × H)
33. C₅×C₉×C₁₁	C₂²×C₁₇	semidirect
34. C₂×C₉×D₁₁	C₅×C₁₇	direct (N × H)
35. C₂×C₁₁×C₁₇	C₂×C₅×C₉	semidirect
36. C₁₇×D₁₁	C₂×C₅×C₉	direct (N × H)
41. C₂×C₉×C₁₇	C₅×D₁₁	direct (N × H)
43. C₂×C₅×D₁₁	C₉×C₁₇	direct (N × H)
45. C₂×C₉×C₁₁	C₂×C₅×C₁₇	semidirect
46. C₉×D₁₁	C₂×C₅×C₁₇	direct (N × H)
47. C₁₁×C₁₇	C₂²×C₅×C₉	semidirect
50. C₂×C₅×C₁₇	C₉×D₁₁	direct (N × H)
52. C₉×C₁₇	C₂×C₅×D₁₁	direct (N × H)
54. C₂×C₅×C₁₁	C₂×C₉×C₁₇	semidirect
55. C₅×D₁₁	C₂×C₉×C₁₇	direct (N × H)
58. C₉×C₁₁	C₂²×C₅×C₁₇	semidirect
60. C₂×C₅×C₉	C₁₇×D₁₁	direct (N × H)
61. C₅×C₁₇	C₂×C₉×D₁₁	direct (N × H)
66. C₅×C₁₁	C₂²×C₉×C₁₇	semidirect
68. C₅×C₉	C₂×C₁₇×D₁₁	direct (N × H)
69. C₂×D₁₁	C₅×C₉×C₁₇	direct (N × H)
72. C₂×C₁₇	C₅×C₉×D₁₁	direct (N × H)
76. C₂×C₁₁	C₂×C₅×C₉×C₁₇	semidirect
77. D₁₁	C₂×C₅×C₉×C₁₇	direct (N × H)
80. C₂×C₉	C₅×C₁₇×D₁₁	direct (N × H)
81. C₁₇	C₂×C₅×C₉×D₁₁	direct (N × H)
84. C₁₁	C₂²×C₅×C₉×C₁₇	semidirect
86. C₂×C₅	C₉×C₁₇×D₁₁	direct (N × H)
87. C₉	C₂×C₅×C₁₇×D₁₁	direct (N × H)
90. C₅	C₂×C₉×C₁₇×D₁₁	direct (N × H)
94. C₂	C₅×C₉×C₁₇×D₁₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×C₉×C₁₇×D₁₁	2
C₂×C₅×C₉×C₁₁×C₁₇	2
C₂×C₃×C₅×C₁₇×D₁₁	3
C₂×C₉×C₁₇×D₁₁	5
C₂²×C₅×C₉×C₁₇	11
C₂×C₅×C₉×D₁₁	17

Subgroups — C2×C5×C9×C17×D11 #46777951

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×C₉×C₁₇×D₁₁ #46777951