Subgroups — C₂×C₃²×C₁₇×D₅₅ #46778199

Order 33660.

240 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₁₇×D₅₅	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃²×C₅×C₁₁×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₁₇×D₅₅	C₃	1	4	yes	maximal, direct product factor
4	C₃²×C₅×C₁₁×C₁₇	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃²×C₁₇×D₁₁	—	5	1	no	maximal, Hall
6	C₃×C₁₇×D₅₅	C₂×C₃	1	8	yes	direct product factor
7	C₂×C₃×C₅×C₁₁×C₁₇	C₂×C₃	1	4	yes	complemented
8	C₂×C₁₇×D₅₅	C₃²	1	1	yes	characteristic, direct product factor, Hall
9	C₃²×C₁₇×D₁₁	—	5	2	no	—
10	C₂×C₃²×C₁₁×C₁₇	D₅	1	1	yes	characteristic, complemented
11	C₂×C₃²×D₅×C₁₇	—	11	1	no	maximal, Hall
12	C₃×C₅×C₁₁×C₁₇	C₂²×C₃	1	4	yes	complemented
13	C₂×C₃×C₁₇×D₁₁	—	5	4	no	—
14	C₂×C₃²×D₅₅	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
15	C₂×C₅×C₁₁×C₁₇	C₂×C₃²	1	1	yes	characteristic, complemented
16	C₁₇×D₅₅	C₂×C₃²	1	2	yes	direct product factor
17	C₃²×C₁₁×C₁₇	C₂×D₅	1	1	yes	characteristic, complemented, Hall
18	C₂×C₃²×C₅×C₁₇	D₁₁	1	1	yes	characteristic, complemented
19	C₃²×D₅×C₁₇	—	11	2	no	—
20	C₂×C₃×C₁₁×C₁₇	C₃×D₅	1	4	yes	complemented
21	C₃×C₁₇×D₁₁	—	5	8	no	—
22	C₂×C₃×D₅×C₁₇	—	11	4	no	—
23	C₂×C₃²×C₅×C₁₁	C₂×C₁₇	1	1	yes	characteristic, complemented
24	C₃²×D₅₅	C₂×C₁₇	1	2	yes	direct product factor
25	C₅×C₁₁×C₁₇	C₂²×C₃²	1	1	yes	characteristic, complemented, Hall
26	C₃²×C₅×C₁₇	C₂×D₁₁	1	1	yes	characteristic, complemented, Hall
27	C₂×C₁₇×D₁₁	—	5	1	no	Hall
28	C₂×C₃×D₅₅	C₃×C₁₇	1	4	yes	direct product factor
29	C₂²×C₃²×C₁₇	—	55	1	no	Hall
30	C₃×C₁₁×C₁₇	C₂×C₃×D₅	1	4	yes	complemented
31	C₂×C₃×C₅×C₁₇	C₃×D₁₁	1	4	yes	complemented
32	C₃×D₅×C₁₇	—	11	8	no	—
33	C₃²×C₅×C₁₁	C₂²×C₁₇	1	1	yes	characteristic, complemented, Hall
34	C₂×C₃²×D₁₁	—	5	1	no	Hall
35	C₂×C₁₁×C₁₇	C₃²×D₅	1	1	yes	characteristic, complemented
36	C₁₇×D₁₁	—	5	2	no	—
37	C₂×D₅×C₁₇	—	11	1	no	Hall
38	C₂×C₃×C₅×C₁₁	C₂×C₃×C₁₇	1	4	yes	complemented
39	C₃×D₅₅	C₂×C₃×C₁₇	1	8	yes	direct product factor
40	C₂×C₃²×C₁₇	—	55	2	no	—
41	C₂×C₃²×C₁₇	D₅₅	1	1	yes	characteristic, direct product factor
42	C₃×C₅×C₁₇	C₂×C₃×D₁₁	1	4	yes	complemented
43	C₂×D₅₅	C₃²×C₁₇	1	1	yes	characteristic, direct product factor, Hall
44	C₂²×C₃×C₁₇	—	55	4	no	—
45	C₂×C₃²×C₁₁	D₅×C₁₇	1	1	yes	characteristic, complemented
46	C₃²×D₁₁	—	5	2	no	—
47	C₁₁×C₁₇	C₂×C₃²×D₅	1	1	yes	characteristic, complemented, Hall
48	C₂×C₃²×D₅	—	11	1	no	Hall
49	C₂×C₅×C₁₇	C₃²×D₁₁	1	1	yes	characteristic, complemented
50	D₅×C₁₇	—	11	2	no	—
51	C₃×C₅×C₁₁	C₂²×C₃×C₁₇	1	4	yes	complemented
52	C₃²×C₁₇	C₂×D₅₅	1	1	yes	characteristic, direct product factor, Hall
53	C₂×C₃×D₁₁	—	5	4	no	—
54	C₂×C₅×C₁₁	C₂×C₃²×C₁₇	1	1	yes	characteristic, complemented
55	D₅₅	C₂×C₃²×C₁₇	1	2	yes	direct product factor
56	C₂×C₃×C₁₇	—	55	8	no	—
57	C₂×C₃×C₁₇	C₃×D₅₅	1	4	yes	direct product factor
58	C₃²×C₁₁	C₂×D₅×C₁₇	1	1	yes	characteristic, complemented, Hall
59	C₂×C₃²×C₅	C₁₇×D₁₁	1	1	yes	characteristic, complemented
60	C₃²×D₅	—	11	2	no	—
61	C₅×C₁₇	C₂×C₃²×D₁₁	1	1	yes	characteristic, complemented, Hall
62	C₂²×C₁₇	—	55	1	no	Hall
63	C₂×C₃×C₁₁	C₃×D₅×C₁₇	1	4	yes	complemented
64	C₃×D₁₁	—	5	8	no	—
65	C₂×C₃×D₅	—	11	4	no	—
66	C₅×C₁₁	C₂²×C₃²×C₁₇	1	1	yes	characteristic, complemented, Hall
67	C₃×C₁₇	C₂×C₃×D₅₅	1	4	yes	direct product factor
68	C₃²×C₅	C₂×C₁₇×D₁₁	1	1	yes	characteristic, complemented, Hall
69	C₂×D₁₁	—	5	1	no	Hall
70	C₂²×C₃²	—	55	1	no	Hall
71	C₂×C₁₇	—	55	2	no	—
72	C₂×C₁₇	C₃²×D₅₅	1	1	yes	characteristic, direct product factor
73	C₃×C₁₁	C₂×C₃×D₅×C₁₇	1	4	yes	complemented
74	C₂×C₃×C₅	C₃×C₁₇×D₁₁	1	4	yes	complemented
75	C₃×D₅	—	11	8	no	—
76	C₂×C₁₁	C₃²×D₅×C₁₇	1	1	yes	characteristic, complemented
77	D₁₁	—	5	2	no	—
78	C₂×D₅	—	11	1	no	Hall
79	C₂×C₃²	—	55	2	no	—
80	C₂×C₃²	C₁₇×D₅₅	1	1	yes	characteristic, direct product factor
81	C₁₇	C₂×C₃²×D₅₅	1	1	yes	characteristic, direct product factor, Sylow
82	C₃×C₅	C₂×C₃×C₁₇×D₁₁	1	4	yes	complemented
83	C₂²×C₃	—	55	4	no	—
84	C₁₁	C₂×C₃²×D₅×C₁₇	1	1	yes	characteristic, complemented, Sylow
85	C₂×C₅	C₃²×C₁₇×D₁₁	1	1	yes	characteristic, complemented
86	D₅	—	11	2	no	—
87	C₃²	C₂×C₁₇×D₅₅	1	1	yes	characteristic, direct product factor, Sylow
88	C₂×C₃	—	55	8	no	—
89	C₂×C₃	C₃×C₁₇×D₅₅	1	4	yes	direct product factor
90	C₅	C₂×C₃²×C₁₇×D₁₁	1	1	yes	characteristic, complemented, Sylow
91	C₂²	—	55	1	no	Sylow
92	C₃	C₂×C₃×C₁₇×D₅₅	1	4	yes	direct product factor
93	C₂	—	55	2	no	—
94	C₂	C₃²×C₁₇×D₅₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃²×C₁₇	D₅₅
commutator, cosocle, hypocenter	C₅×C₁₁	C₂²×C₃²×C₁₇
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₅×C₁₁×C₁₇	C₂
LCS	G ▷ C₅×C₁₁
UCS	C₁ ◁ C₂×C₃²×C₁₇

Complements

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

N	H ≅ G/N	type
1. C₃²×C₁₇×D₅₅	C₂	direct (N × H)
2. C₂×C₃²×C₅×C₁₁×C₁₇	C₂	semidirect
3. C₂×C₃×C₁₇×D₅₅	C₃	direct (N × H)
4. C₃²×C₅×C₁₁×C₁₇	C₂²	semidirect
6. C₃×C₁₇×D₅₅	C₂×C₃	direct (N × H)
7. C₂×C₃×C₅×C₁₁×C₁₇	C₂×C₃	semidirect
8. C₂×C₁₇×D₅₅	C₃²	direct (N × H)
10. C₂×C₃²×C₁₁×C₁₇	D₅	semidirect
12. C₃×C₅×C₁₁×C₁₇	C₂²×C₃	semidirect
14. C₂×C₃²×D₅₅	C₁₇	direct (N × H)
15. C₂×C₅×C₁₁×C₁₇	C₂×C₃²	semidirect
16. C₁₇×D₅₅	C₂×C₃²	direct (N × H)
17. C₃²×C₁₁×C₁₇	C₂×D₅	semidirect
18. C₂×C₃²×C₅×C₁₇	D₁₁	semidirect
20. C₂×C₃×C₁₁×C₁₇	C₃×D₅	semidirect
23. C₂×C₃²×C₅×C₁₁	C₂×C₁₇	semidirect
24. C₃²×D₅₅	C₂×C₁₇	direct (N × H)
25. C₅×C₁₁×C₁₇	C₂²×C₃²	semidirect
26. C₃²×C₅×C₁₇	C₂×D₁₁	semidirect
28. C₂×C₃×D₅₅	C₃×C₁₇	direct (N × H)
30. C₃×C₁₁×C₁₇	C₂×C₃×D₅	semidirect
31. C₂×C₃×C₅×C₁₇	C₃×D₁₁	semidirect
33. C₃²×C₅×C₁₁	C₂²×C₁₇	semidirect
35. C₂×C₁₁×C₁₇	C₃²×D₅	semidirect
38. C₂×C₃×C₅×C₁₁	C₂×C₃×C₁₇	semidirect
39. C₃×D₅₅	C₂×C₃×C₁₇	direct (N × H)
41. C₂×C₃²×C₁₇	D₅₅	direct (N × H)
42. C₃×C₅×C₁₇	C₂×C₃×D₁₁	semidirect
43. C₂×D₅₅	C₃²×C₁₇	direct (N × H)
45. C₂×C₃²×C₁₁	D₅×C₁₇	semidirect
47. C₁₁×C₁₇	C₂×C₃²×D₅	semidirect
49. C₂×C₅×C₁₇	C₃²×D₁₁	semidirect
51. C₃×C₅×C₁₁	C₂²×C₃×C₁₇	semidirect
52. C₃²×C₁₇	C₂×D₅₅	direct (N × H)
54. C₂×C₅×C₁₁	C₂×C₃²×C₁₇	semidirect
55. D₅₅	C₂×C₃²×C₁₇	direct (N × H)
57. C₂×C₃×C₁₇	C₃×D₅₅	direct (N × H)
58. C₃²×C₁₁	C₂×D₅×C₁₇	semidirect
59. C₂×C₃²×C₅	C₁₇×D₁₁	semidirect
61. C₅×C₁₇	C₂×C₃²×D₁₁	semidirect
63. C₂×C₃×C₁₁	C₃×D₅×C₁₇	semidirect
66. C₅×C₁₁	C₂²×C₃²×C₁₇	semidirect
67. C₃×C₁₇	C₂×C₃×D₅₅	direct (N × H)
68. C₃²×C₅	C₂×C₁₇×D₁₁	semidirect
72. C₂×C₁₇	C₃²×D₅₅	direct (N × H)
73. C₃×C₁₁	C₂×C₃×D₅×C₁₇	semidirect
74. C₂×C₃×C₅	C₃×C₁₇×D₁₁	semidirect
76. C₂×C₁₁	C₃²×D₅×C₁₇	semidirect
80. C₂×C₃²	C₁₇×D₅₅	direct (N × H)
81. C₁₇	C₂×C₃²×D₅₅	direct (N × H)
82. C₃×C₅	C₂×C₃×C₁₇×D₁₁	semidirect
84. C₁₁	C₂×C₃²×D₅×C₁₇	semidirect
85. C₂×C₅	C₃²×C₁₇×D₁₁	semidirect
87. C₃²	C₂×C₁₇×D₅₅	direct (N × H)
89. C₂×C₃	C₃×C₁₇×D₅₅	direct (N × H)
90. C₅	C₂×C₃²×C₁₇×D₁₁	semidirect
92. C₃	C₂×C₃×C₁₇×D₅₅	direct (N × H)
94. C₂	C₃²×C₁₇×D₅₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃²×C₁₇×D₅₅	2
C₂×C₃²×C₅×C₁₁×C₁₇	2
C₂×C₃×C₁₇×D₅₅	3
C₂×C₃²×C₁₇×D₁₁	5
C₂×C₃²×D₅×C₁₇	11
C₂×C₃²×D₅₅	17

Subgroups — C2×C32×C17×D55 #46778199

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃²×C₁₇×D₅₅ #46778199