Subgroups — C₂×C₅×C₉×C₁₁×D₁₇ #46777952

Order 33660.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₉×C₁₁×D₁₇	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×C₁₁×D₁₇	C₃	1	1	yes	maximal, characteristic
4	C₅×C₉×C₁₁×C₁₇	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₉×C₁₁×D₁₇	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₃×C₅×C₁₁×D₁₇	C₂×C₃	1	2	yes	—
7	C₂×C₃×C₅×C₁₁×C₁₇	C₂×C₃	1	1	yes	characteristic
8	C₂×C₅×C₁₁×D₁₇	C₉	1	1	yes	characteristic, direct product factor, Hall
9	C₉×C₁₁×D₁₇	C₂×C₅	1	2	yes	direct product factor
10	C₂×C₉×C₁₁×C₁₇	C₂×C₅	1	1	yes	characteristic, complemented
11	C₂×C₅×C₉×D₁₇	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₃×C₅×C₁₁×C₁₇	C₂²×C₃	1	1	yes	characteristic
13	C₂×C₃×C₁₁×D₁₇	C₃×C₅	1	1	yes	characteristic
14	C₂²×C₅×C₉×C₁₁	—	17	1	no	maximal, Hall
15	C₂×C₅×C₁₁×C₁₇	C₂×C₉	1	1	yes	characteristic, complemented
16	C₅×C₁₁×D₁₇	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	C₂×C₁₁	1	1	yes	characteristic, complemented
19	C₅×C₉×D₁₇	C₂×C₁₁	1	2	yes	direct product factor
20	C₂×C₃×C₁₁×C₁₇	C₂×C₃×C₅	1	1	yes	characteristic
21	C₃×C₁₁×D₁₇	C₂×C₃×C₅	1	2	yes	—
22	C₂×C₃×C₅×D₁₇	C₃×C₁₁	1	1	yes	characteristic
23	C₂×C₅×C₉×C₁₁	—	17	2	no	—
24	C₂×C₅×C₉×C₁₁	D₁₇	1	1	yes	characteristic, direct product factor
25	C₅×C₁₁×C₁₇	C₂²×C₉	1	1	yes	characteristic, complemented, Hall
26	C₅×C₉×C₁₇	C₂²×C₁₁	1	1	yes	characteristic, complemented, Hall
27	C₂×C₁₁×D₁₇	C₅×C₉	1	1	yes	characteristic, direct product factor, Hall
28	C₂²×C₃×C₅×C₁₁	—	17	1	no	—
29	C₂×C₉×D₁₇	C₅×C₁₁	1	1	yes	characteristic, direct product factor, Hall
30	C₃×C₁₁×C₁₇	C₂²×C₃×C₅	1	1	yes	characteristic
31	C₂×C₃×C₅×C₁₇	C₂×C₃×C₁₁	1	1	yes	characteristic
32	C₃×C₅×D₁₇	C₂×C₃×C₁₁	1	2	yes	—
33	C₅×C₉×C₁₁	C₂×D₁₇	1	1	yes	characteristic, direct product factor, Hall
34	C₂²×C₉×C₁₁	—	17	1	no	Hall
35	C₂×C₁₁×C₁₇	C₂×C₅×C₉	1	1	yes	characteristic, complemented
36	C₁₁×D₁₇	C₂×C₅×C₉	1	2	yes	direct product factor
37	C₂×C₅×D₁₇	C₉×C₁₁	1	1	yes	characteristic, direct product factor, Hall
38	C₂×C₃×C₅×C₁₁	—	17	2	no	—
39	C₂×C₃×C₅×C₁₁	C₃×D₁₇	1	1	yes	characteristic
40	C₂×C₉×C₁₇	C₂×C₅×C₁₁	1	1	yes	characteristic, complemented
41	C₉×D₁₇	C₂×C₅×C₁₁	1	2	yes	direct product factor
42	C₃×C₅×C₁₇	C₂²×C₃×C₁₁	1	1	yes	characteristic
43	C₂²×C₅×C₁₁	—	17	1	no	Hall
44	C₂×C₃×D₁₇	C₃×C₅×C₁₁	1	1	yes	characteristic
45	C₂×C₉×C₁₁	—	17	2	no	—
46	C₂×C₉×C₁₁	C₅×D₁₇	1	1	yes	characteristic, direct product factor
47	C₁₁×C₁₇	C₂²×C₅×C₉	1	1	yes	characteristic, complemented, Hall
48	C₂²×C₅×C₉	—	17	1	no	Hall
49	C₂×C₅×C₁₇	C₂×C₉×C₁₁	1	1	yes	characteristic, complemented
50	C₅×D₁₇	C₂×C₉×C₁₁	1	2	yes	direct product factor
51	C₃×C₅×C₁₁	C₂×C₃×D₁₇	1	1	yes	characteristic
52	C₉×C₁₇	C₂²×C₅×C₁₁	1	1	yes	characteristic, complemented, Hall
53	C₂²×C₃×C₁₁	—	17	1	no	—
54	C₂×C₅×C₁₁	—	17	2	no	—
55	C₂×C₅×C₁₁	C₉×D₁₇	1	1	yes	characteristic, direct product factor
56	C₂×C₃×C₁₇	C₂×C₃×C₅×C₁₁	1	1	yes	characteristic
57	C₃×D₁₇	C₂×C₃×C₅×C₁₁	1	2	yes	—
58	C₉×C₁₁	C₂×C₅×D₁₇	1	1	yes	characteristic, direct product factor, Hall
59	C₂×C₅×C₉	—	17	2	no	—
60	C₂×C₅×C₉	C₁₁×D₁₇	1	1	yes	characteristic, direct product factor
61	C₅×C₁₇	C₂²×C₉×C₁₁	1	1	yes	characteristic, complemented, Hall
62	C₂×D₁₇	C₅×C₉×C₁₁	1	1	yes	characteristic, direct product factor, Hall
63	C₂×C₃×C₁₁	—	17	2	no	—
64	C₂×C₃×C₁₁	C₃×C₅×D₁₇	1	1	yes	characteristic
65	C₂²×C₃×C₅	—	17	1	no	—
66	C₅×C₁₁	C₂×C₉×D₁₇	1	1	yes	characteristic, direct product factor, Hall
67	C₃×C₁₇	C₂²×C₃×C₅×C₁₁	1	1	yes	characteristic
68	C₅×C₉	C₂×C₁₁×D₁₇	1	1	yes	characteristic, direct product factor, Hall
69	C₂²×C₁₁	—	17	1	no	Hall
70	C₂²×C₉	—	17	1	no	Hall
71	C₂×C₁₇	C₂×C₅×C₉×C₁₁	1	1	yes	characteristic, complemented
72	D₁₇	C₂×C₅×C₉×C₁₁	1	2	yes	direct product factor
73	C₃×C₁₁	C₂×C₃×C₅×D₁₇	1	1	yes	characteristic
74	C₂×C₃×C₅	—	17	2	no	—
75	C₂×C₃×C₅	C₃×C₁₁×D₁₇	1	1	yes	characteristic
76	C₂×C₁₁	—	17	2	no	—
77	C₂×C₁₁	C₅×C₉×D₁₇	1	1	yes	characteristic, direct product factor
78	C₂²×C₅	—	17	1	no	Hall
79	C₂×C₉	—	17	2	no	—
80	C₂×C₉	C₅×C₁₁×D₁₇	1	1	yes	characteristic, direct product factor
81	C₁₇	C₂²×C₅×C₉×C₁₁	1	1	yes	characteristic, complemented, Sylow
82	C₃×C₅	C₂×C₃×C₁₁×D₁₇	1	1	yes	characteristic
83	C₂²×C₃	—	17	1	no	—
84	C₁₁	C₂×C₅×C₉×D₁₇	1	1	yes	characteristic, direct product factor, Sylow
85	C₂×C₅	—	17	2	no	—
86	C₂×C₅	C₉×C₁₁×D₁₇	1	1	yes	characteristic, direct product factor
87	C₉	C₂×C₅×C₁₁×D₁₇	1	1	yes	characteristic, direct product factor, Sylow
88	C₂×C₃	—	17	2	no	—
89	C₂×C₃	C₃×C₅×C₁₁×D₁₇	1	1	yes	characteristic
90	C₅	C₂×C₉×C₁₁×D₁₇	1	1	yes	characteristic, direct product factor, Sylow
91	C₂²	—	17	1	no	Sylow
92	C₃	C₂×C₃×C₅×C₁₁×D₁₇	1	1	yes	characteristic
93	C₂	—	17	2	no	—
94	C₂	C₅×C₉×C₁₁×D₁₇	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₅×C₉×C₁₁	D₁₇
commutator, hypocenter	C₁₇	C₂²×C₅×C₉×C₁₁
Frattini	C₃	C₂×C₃×C₅×C₁₁×D₁₇
Fitting	C₂×C₅×C₉×C₁₁×C₁₇	C₂
socle	C₂×C₃×C₅×C₁₁×C₁₇	C₂×C₃
prime radical	C₂×C₃×C₅×C₁₁×D₁₇	C₃
cosocle	C₃×C₁₇	C₂²×C₃×C₅×C₁₁
LCS	G ▷ C₁₇
UCS	C₁ ◁ C₂×C₅×C₉×C₁₁

Complements

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

N	H ≅ G/N	type
1. C₅×C₉×C₁₁×D₁₇	C₂	direct (N × H)
2. C₂×C₅×C₉×C₁₁×C₁₇	C₂	semidirect
4. C₅×C₉×C₁₁×C₁₇	C₂²	semidirect
5. C₂×C₉×C₁₁×D₁₇	C₅	direct (N × H)
8. C₂×C₅×C₁₁×D₁₇	C₉	direct (N × H)
9. C₉×C₁₁×D₁₇	C₂×C₅	direct (N × H)
10. C₂×C₉×C₁₁×C₁₇	C₂×C₅	semidirect
11. C₂×C₅×C₉×D₁₇	C₁₁	direct (N × H)
15. C₂×C₅×C₁₁×C₁₇	C₂×C₉	semidirect
16. C₅×C₁₁×D₁₇	C₂×C₉	direct (N × H)
17. C₉×C₁₁×C₁₇	C₂²×C₅	semidirect
18. C₂×C₅×C₉×C₁₇	C₂×C₁₁	semidirect
19. C₅×C₉×D₁₇	C₂×C₁₁	direct (N × H)
24. C₂×C₅×C₉×C₁₁	D₁₇	direct (N × H)
25. C₅×C₁₁×C₁₇	C₂²×C₉	semidirect
26. C₅×C₉×C₁₇	C₂²×C₁₁	semidirect
27. C₂×C₁₁×D₁₇	C₅×C₉	direct (N × H)
29. C₂×C₉×D₁₇	C₅×C₁₁	direct (N × H)
33. C₅×C₉×C₁₁	C₂×D₁₇	direct (N × H)
35. C₂×C₁₁×C₁₇	C₂×C₅×C₉	semidirect
36. C₁₁×D₁₇	C₂×C₅×C₉	direct (N × H)
37. C₂×C₅×D₁₇	C₉×C₁₁	direct (N × H)
40. C₂×C₉×C₁₇	C₂×C₅×C₁₁	semidirect
41. C₉×D₁₇	C₂×C₅×C₁₁	direct (N × H)
46. C₂×C₉×C₁₁	C₅×D₁₇	direct (N × H)
47. C₁₁×C₁₇	C₂²×C₅×C₉	semidirect
49. C₂×C₅×C₁₇	C₂×C₉×C₁₁	semidirect
50. C₅×D₁₇	C₂×C₉×C₁₁	direct (N × H)
52. C₉×C₁₇	C₂²×C₅×C₁₁	semidirect
55. C₂×C₅×C₁₁	C₉×D₁₇	direct (N × H)
58. C₉×C₁₁	C₂×C₅×D₁₇	direct (N × H)
60. C₂×C₅×C₉	C₁₁×D₁₇	direct (N × H)
61. C₅×C₁₇	C₂²×C₉×C₁₁	semidirect
62. C₂×D₁₇	C₅×C₉×C₁₁	direct (N × H)
66. C₅×C₁₁	C₂×C₉×D₁₇	direct (N × H)
68. C₅×C₉	C₂×C₁₁×D₁₇	direct (N × H)
71. C₂×C₁₇	C₂×C₅×C₉×C₁₁	semidirect
72. D₁₇	C₂×C₅×C₉×C₁₁	direct (N × H)
77. C₂×C₁₁	C₅×C₉×D₁₇	direct (N × H)
80. C₂×C₉	C₅×C₁₁×D₁₇	direct (N × H)
81. C₁₇	C₂²×C₅×C₉×C₁₁	semidirect
84. C₁₁	C₂×C₅×C₉×D₁₇	direct (N × H)
86. C₂×C₅	C₉×C₁₁×D₁₇	direct (N × H)
87. C₉	C₂×C₅×C₁₁×D₁₇	direct (N × H)
90. C₅	C₂×C₉×C₁₁×D₁₇	direct (N × H)
94. C₂	C₅×C₉×C₁₁×D₁₇	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×C₁₁×D₁₇	2
C₂×C₅×C₉×C₁₁×C₁₇	2
C₂×C₃×C₅×C₁₁×D₁₇	3
C₂×C₉×C₁₁×D₁₇	5
C₂×C₅×C₉×D₁₇	11
C₂²×C₅×C₉×C₁₁	17

Subgroups — C2×C5×C9×C11×D17 #46777952

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×C₉×C₁₁×D₁₇ #46777952