Subgroups — C₃×C₅×C₁₁×A₄×C₁₇ #46778193

Order 33660.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₁×A₄×C₁₇	C₃	1	3	yes	maximal, direct product factor
2	C₂²×C₃×C₅×C₁₁×C₁₇	C₃	1	1	yes	maximal, characteristic, complemented
3	C₃²×C₅×C₁₁×C₁₇	—	4	1	no	maximal, Hall
4	C₃×C₁₁×A₄×C₁₇	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₃×C₅×C₁₁×C₁₇	—	3	1	no	—
6	C₂²×C₅×C₁₁×C₁₇	C₃²	1	1	yes	characteristic, complemented, Hall
7	C₃×C₅×A₄×C₁₇	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₃×C₅×C₁₁×C₁₇	—	4	3	no	—
9	C₃×C₅×C₁₁×C₁₇	A₄	1	1	yes	characteristic, direct product factor
10	C₁₁×A₄×C₁₇	C₃×C₅	1	3	yes	direct product factor
11	C₂²×C₃×C₁₁×C₁₇	C₃×C₅	1	1	yes	characteristic, complemented
12	C₃×C₅×C₁₁×A₄	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₅×C₁₁×C₁₇	—	3	1	no	—
14	C₃²×C₁₁×C₁₇	—	4	1	no	Hall
15	C₂×C₃×C₁₁×C₁₇	—	3	1	no	—
16	C₂²×C₃×C₅×C₁₇	C₃×C₁₁	1	1	yes	characteristic, complemented
17	C₅×A₄×C₁₇	C₃×C₁₁	1	3	yes	direct product factor
18	C₅×C₁₁×C₁₇	C₃×A₄	1	1	yes	characteristic, direct product factor, Hall
19	C₃²×C₅×C₁₇	—	4	1	no	Hall
20	C₂²×C₁₁×C₁₇	C₃²×C₅	1	1	yes	characteristic, complemented, Hall
21	C₂²×C₃×C₅×C₁₁	C₃×C₁₇	1	1	yes	characteristic, complemented
22	C₅×C₁₁×A₄	C₃×C₁₇	1	3	yes	direct product factor
23	C₃×A₄×C₁₇	C₅×C₁₁	1	1	yes	characteristic, direct product factor, Hall
24	C₃×C₁₁×C₁₇	—	4	3	no	—
25	C₃×C₁₁×C₁₇	C₅×A₄	1	1	yes	characteristic, direct product factor
26	C₂×C₃×C₅×C₁₇	—	3	1	no	—
27	C₃²×C₅×C₁₁	—	4	1	no	Hall
28	C₃×C₁₁×A₄	C₅×C₁₇	1	1	yes	characteristic, direct product factor, Hall
29	C₂×C₁₁×C₁₇	—	3	1	no	—
30	C₂²×C₅×C₁₇	C₃²×C₁₁	1	1	yes	characteristic, complemented, Hall
31	C₂×C₃×C₅×C₁₁	—	3	1	no	—
32	C₃×C₅×C₁₇	—	4	3	no	—
33	C₃×C₅×C₁₇	C₁₁×A₄	1	1	yes	characteristic, direct product factor
34	C₂²×C₅×C₁₁	C₃²×C₁₇	1	1	yes	characteristic, complemented, Hall
35	C₂²×C₃×C₁₇	C₃×C₅×C₁₁	1	1	yes	characteristic, complemented
36	A₄×C₁₇	C₃×C₅×C₁₁	1	3	yes	direct product factor
37	C₁₁×C₁₇	C₃×C₅×A₄	1	1	yes	characteristic, direct product factor, Hall
38	C₃×C₅×A₄	C₁₁×C₁₇	1	1	yes	characteristic, direct product factor, Hall
39	C₂×C₅×C₁₇	—	3	1	no	—
40	C₃×C₅×C₁₁	—	4	3	no	—
41	C₃×C₅×C₁₁	A₄×C₁₇	1	1	yes	characteristic, direct product factor
42	C₃²×C₁₇	—	4	1	no	Hall
43	C₂²×C₃×C₁₁	C₃×C₅×C₁₇	1	1	yes	characteristic, complemented
44	C₁₁×A₄	C₃×C₅×C₁₇	1	3	yes	direct product factor
45	C₂×C₅×C₁₁	—	3	1	no	—
46	C₂×C₃×C₁₇	—	3	1	no	—
47	C₃²×C₁₁	—	4	1	no	Hall
48	C₅×C₁₇	C₃×C₁₁×A₄	1	1	yes	characteristic, direct product factor, Hall
49	C₂²×C₁₇	C₃²×C₅×C₁₁	1	1	yes	characteristic, complemented, Hall
50	C₂×C₃×C₁₁	—	3	1	no	—
51	C₂²×C₃×C₅	C₃×C₁₁×C₁₇	1	1	yes	characteristic, complemented
52	C₅×A₄	C₃×C₁₁×C₁₇	1	3	yes	direct product factor
53	C₅×C₁₁	C₃×A₄×C₁₇	1	1	yes	characteristic, direct product factor, Hall
54	C₃×C₁₇	—	4	3	no	—
55	C₃×C₁₇	C₅×C₁₁×A₄	1	1	yes	characteristic, direct product factor
56	C₃²×C₅	—	4	1	no	Hall
57	C₂²×C₁₁	C₃²×C₅×C₁₇	1	1	yes	characteristic, complemented, Hall
58	C₃×A₄	C₅×C₁₁×C₁₇	1	1	yes	characteristic, direct product factor, Hall
59	C₂×C₁₇	—	3	1	no	—
60	C₃×C₁₁	—	4	3	no	—
61	C₃×C₁₁	C₅×A₄×C₁₇	1	1	yes	characteristic, direct product factor
62	C₂×C₃×C₅	—	3	1	no	—
63	C₂×C₁₁	—	3	1	no	—
64	C₂²×C₅	C₃²×C₁₁×C₁₇	1	1	yes	characteristic, complemented, Hall
65	C₁₇	C₃×C₅×C₁₁×A₄	1	1	yes	characteristic, direct product factor, Sylow
66	C₃×C₅	—	4	3	no	—
67	C₃×C₅	C₁₁×A₄×C₁₇	1	1	yes	characteristic, direct product factor
68	C₂²×C₃	C₃×C₅×C₁₁×C₁₇	1	1	yes	characteristic, complemented
69	A₄	C₃×C₅×C₁₁×C₁₇	1	3	yes	direct product factor
70	C₁₁	C₃×C₅×A₄×C₁₇	1	1	yes	characteristic, direct product factor, Sylow
71	C₂×C₅	—	3	1	no	—
72	C₃²	—	4	1	no	Sylow
73	C₂×C₃	—	3	1	no	—
74	C₅	C₃×C₁₁×A₄×C₁₇	1	1	yes	characteristic, direct product factor, Sylow
75	C₂²	C₃²×C₅×C₁₁×C₁₇	1	1	yes	characteristic, complemented, Sylow
76	C₃	—	4	3	no	—
77	C₃	C₅×C₁₁×A₄×C₁₇	1	1	yes	characteristic, direct product factor
78	C₂	—	3	1	no	—

	subgroup	G/H
center, hypercenter	C₃×C₅×C₁₁×C₁₇	A₄
commutator, cosocle, hypocenter	C₂²	C₃²×C₅×C₁₁×C₁₇
Frattini	C₁	G
Fitting, socle	C₂²×C₃×C₅×C₁₁×C₁₇	C₃
LCS	G ▷ C₂²
UCS	C₁ ◁ C₃×C₅×C₁₁×C₁₇

Complements

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

N	H ≅ G/N	type
1. C₅×C₁₁×A₄×C₁₇	C₃	direct (N × H)
2. C₂²×C₃×C₅×C₁₁×C₁₇	C₃	semidirect
4. C₃×C₁₁×A₄×C₁₇	C₅	direct (N × H)
6. C₂²×C₅×C₁₁×C₁₇	C₃²	semidirect
7. C₃×C₅×A₄×C₁₇	C₁₁	direct (N × H)
9. C₃×C₅×C₁₁×C₁₇	A₄	direct (N × H)
10. C₁₁×A₄×C₁₇	C₃×C₅	direct (N × H)
11. C₂²×C₃×C₁₁×C₁₇	C₃×C₅	semidirect
12. C₃×C₅×C₁₁×A₄	C₁₇	direct (N × H)
16. C₂²×C₃×C₅×C₁₇	C₃×C₁₁	semidirect
17. C₅×A₄×C₁₇	C₃×C₁₁	direct (N × H)
18. C₅×C₁₁×C₁₇	C₃×A₄	direct (N × H)
20. C₂²×C₁₁×C₁₇	C₃²×C₅	semidirect
21. C₂²×C₃×C₅×C₁₁	C₃×C₁₇	semidirect
22. C₅×C₁₁×A₄	C₃×C₁₇	direct (N × H)
23. C₃×A₄×C₁₇	C₅×C₁₁	direct (N × H)
25. C₃×C₁₁×C₁₇	C₅×A₄	direct (N × H)
28. C₃×C₁₁×A₄	C₅×C₁₇	direct (N × H)
30. C₂²×C₅×C₁₇	C₃²×C₁₁	semidirect
33. C₃×C₅×C₁₇	C₁₁×A₄	direct (N × H)
34. C₂²×C₅×C₁₁	C₃²×C₁₇	semidirect
35. C₂²×C₃×C₁₇	C₃×C₅×C₁₁	semidirect
36. A₄×C₁₇	C₃×C₅×C₁₁	direct (N × H)
37. C₁₁×C₁₇	C₃×C₅×A₄	direct (N × H)
38. C₃×C₅×A₄	C₁₁×C₁₇	direct (N × H)
41. C₃×C₅×C₁₁	A₄×C₁₇	direct (N × H)
43. C₂²×C₃×C₁₁	C₃×C₅×C₁₇	semidirect
44. C₁₁×A₄	C₃×C₅×C₁₇	direct (N × H)
48. C₅×C₁₇	C₃×C₁₁×A₄	direct (N × H)
49. C₂²×C₁₇	C₃²×C₅×C₁₁	semidirect
51. C₂²×C₃×C₅	C₃×C₁₁×C₁₇	semidirect
52. C₅×A₄	C₃×C₁₁×C₁₇	direct (N × H)
53. C₅×C₁₁	C₃×A₄×C₁₇	direct (N × H)
55. C₃×C₁₇	C₅×C₁₁×A₄	direct (N × H)
57. C₂²×C₁₁	C₃²×C₅×C₁₇	semidirect
58. C₃×A₄	C₅×C₁₁×C₁₇	direct (N × H)
61. C₃×C₁₁	C₅×A₄×C₁₇	direct (N × H)
64. C₂²×C₅	C₃²×C₁₁×C₁₇	semidirect
65. C₁₇	C₃×C₅×C₁₁×A₄	direct (N × H)
67. C₃×C₅	C₁₁×A₄×C₁₇	direct (N × H)
68. C₂²×C₃	C₃×C₅×C₁₁×C₁₇	semidirect
69. A₄	C₃×C₅×C₁₁×C₁₇	direct (N × H)
70. C₁₁	C₃×C₅×A₄×C₁₇	direct (N × H)
74. C₅	C₃×C₁₁×A₄×C₁₇	direct (N × H)
75. C₂²	C₃²×C₅×C₁₁×C₁₇	semidirect
77. C₃	C₅×C₁₁×A₄×C₁₇	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×C₁₁×A₄×C₁₇	3
C₂²×C₃×C₅×C₁₁×C₁₇	3
C₃²×C₅×C₁₁×C₁₇	4
C₃×C₁₁×A₄×C₁₇	5
C₃×C₅×A₄×C₁₇	11
C₃×C₅×C₁₁×A₄	17

Subgroups — C3×C5×C11×A4×C17 #46778193

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×C₁₁×A₄×C₁₇ #46778193