Subgroups — C₂×C₃×C₁₇×D₅₁ #23780946

Order 10404.

184 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₇×D₅₁	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃²×C₁₇²	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₇×D₅₁	C₃	1	1	yes	maximal, characteristic, direct product factor
4	C₂×C₃×C₁₇×D₁₇	—	3	1	no	maximal
5	C₃²×C₁₇²	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×C₃×C₁₇²	—	2	1	no	—
7	C₂×C₃×C₁₇²	D₃	1	1	yes	characteristic, complemented
8	C₂×C₃×C₁₇²	C₂×C₃	1	1	yes	characteristic, complemented
9	C₃×C₁₇×D₁₇	—	3	2	no	—
10	C₁₇×D₅₁	C₂×C₃	1	2	yes	direct product factor
11	C₂×C₁₇×D₁₇	—	3	1	no	Hall
12	C₃×C₁₇²	—	2	1	no	—
13	C₃×C₁₇²	C₂×D₃	1	1	yes	characteristic, complemented
14	C₃×C₁₇²	C₂²×C₃	1	1	yes	characteristic, complemented
15	C₂×C₃×D₅₁	C₁₇	1	1	yes	maximal, characteristic, direct product factor
16	C₂×C₃×D₃×C₁₇	—	17	1	no	maximal
17	C₂×C₁₇²	C₃×D₃	1	1	yes	characteristic, complemented
18	C₁₇×D₁₇	—	3	2	no	—
19	C₂×C₃²×C₁₇	—	2	8	no	—
20	C₂×C₃²×C₁₇	D₁₇	1	1	yes	characteristic, complemented
21	C₂×C₃²×C₁₇	C₂×C₁₇	1	1	yes	characteristic, complemented
22	C₃×D₅₁	C₂×C₁₇	1	2	yes	direct product factor
23	C₃×D₃×C₁₇	—	17	2	no	—
24	C₁₇²	C₂×C₃×D₃	1	1	yes	characteristic, complemented, Sylow
25	C₂²×C₃×C₁₇	—	51	1	no	—
26	C₂×D₅₁	C₃×C₁₇	1	1	yes	characteristic, direct product factor
27	C₂×D₃×C₁₇	—	17	1	no	—
28	C₂×C₃×D₁₇	—	3	1	no	—
29	C₃²×C₁₇	—	2	8	no	—
30	C₃²×C₁₇	C₂×D₁₇	1	1	yes	characteristic, complemented
31	C₃²×C₁₇	C₂²×C₁₇	1	1	yes	characteristic, complemented
32	C₂×C₃×C₁₇	—	2	16	no	—
33	C₂×C₃×C₁₇	—	2	1	no	—
34	C₂×C₃×C₁₇	—	2	1	no	—
35	C₂×C₃×C₁₇	—	2	8	no	—
36	C₂×C₃×C₁₇	—	2	8	no	—
37	C₂×C₃×C₁₇	—	51	2	no	—
38	C₂×C₃×C₁₇	D₃×C₁₇	1	1	yes	characteristic, complemented
39	C₂×C₃×C₁₇	C₃×D₁₇	1	1	yes	characteristic, complemented
40	C₂×C₃×C₁₇	D₅₁	1	1	yes	characteristic, direct product factor
41	C₂×C₃×C₁₇	C₂×C₃×C₁₇	1	1	yes	characteristic, complemented
42	D₅₁	C₂×C₃×C₁₇	1	2	yes	direct product factor
43	C₃×D₁₇	—	3	2	no	—
44	D₃×C₁₇	—	17	2	no	—
45	C₂²×C₁₇	—	51	1	no	—
46	C₂×D₁₇	—	3	1	no	—
47	C₃×C₁₇	—	2	16	no	—
48	C₃×C₁₇	—	2	1	no	—
49	C₃×C₁₇	—	2	1	no	—
50	C₃×C₁₇	—	2	8	no	—
51	C₃×C₁₇	—	2	8	no	—
52	C₃×C₁₇	C₂×C₃×D₁₇	1	1	yes	characteristic, complemented
53	C₃×C₁₇	C₂×D₃×C₁₇	1	1	yes	characteristic, complemented
54	C₃×C₁₇	C₂×D₅₁	1	1	yes	characteristic, direct product factor
55	C₃×C₁₇	C₂²×C₃×C₁₇	1	1	yes	characteristic, complemented
56	C₂×C₃×D₃	—	17	1	no	Hall
57	C₂×C₁₇	—	2	8	no	—
58	C₂×C₁₇	—	51	2	no	—
59	C₂×C₁₇	C₃×D₃×C₁₇	1	1	yes	characteristic, complemented
60	C₂×C₁₇	C₃×D₅₁	1	1	yes	characteristic, direct product factor
61	D₁₇	—	3	2	no	—
62	C₂×C₃²	C₁₇×D₁₇	1	1	yes	characteristic, complemented
63	C₃×D₃	—	17	2	no	—
64	C₁₇	—	2	8	no	—
65	C₁₇	C₂×C₃×D₃×C₁₇	1	1	yes	characteristic, complemented
66	C₁₇	C₂×C₃×D₅₁	1	1	yes	characteristic, direct product factor
67	C₂²×C₃	—	51	1	no	—
68	C₂×D₃	—	17	1	no	—
69	C₃²	C₂×C₁₇×D₁₇	1	1	yes	characteristic, complemented, Sylow
70	C₂×C₃	—	2	1	no	—
71	C₂×C₃	—	51	2	no	—
72	C₂×C₃	C₁₇×D₅₁	1	1	yes	characteristic, direct product factor
73	C₂×C₃	C₃×C₁₇×D₁₇	1	1	yes	characteristic, complemented
74	D₃	—	17	2	no	—
75	C₂²	—	51	1	no	Sylow
76	C₃	—	2	1	no	—
77	C₃	C₂×C₃×C₁₇×D₁₇	1	1	yes	characteristic, complemented
78	C₃	C₂×C₁₇×D₅₁	1	1	yes	characteristic, direct product factor
79	C₂	—	51	2	no	—
80	C₂	C₃×C₁₇×D₅₁	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃×C₁₇	D₅₁
commutator, cosocle, hypocenter	C₃×C₁₇	C₂²×C₃×C₁₇
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₁₇²	C₂
LCS	G ▷ C₃×C₁₇
UCS	C₁ ◁ C₂×C₃×C₁₇

Complements

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

N	H ≅ G/N	type
1. C₃×C₁₇×D₅₁	C₂	direct (N × H)
2. C₂×C₃²×C₁₇²	C₂	semidirect
3. C₂×C₁₇×D₅₁	C₃	direct (N × H)
5. C₃²×C₁₇²	C₂²	semidirect
7. C₂×C₃×C₁₇²	D₃	semidirect
8. C₂×C₃×C₁₇²	C₂×C₃	semidirect
10. C₁₇×D₅₁	C₂×C₃	direct (N × H)
13. C₃×C₁₇²	C₂×D₃	semidirect
14. C₃×C₁₇²	C₂²×C₃	semidirect
15. C₂×C₃×D₅₁	C₁₇	direct (N × H)
17. C₂×C₁₇²	C₃×D₃	semidirect
20. C₂×C₃²×C₁₇	D₁₇	semidirect
21. C₂×C₃²×C₁₇	C₂×C₁₇	semidirect
22. C₃×D₅₁	C₂×C₁₇	direct (N × H)
24. C₁₇²	C₂×C₃×D₃	semidirect
26. C₂×D₅₁	C₃×C₁₇	direct (N × H)
30. C₃²×C₁₇	C₂×D₁₇	semidirect
31. C₃²×C₁₇	C₂²×C₁₇	semidirect
38. C₂×C₃×C₁₇	D₃×C₁₇	semidirect
39. C₂×C₃×C₁₇	C₃×D₁₇	semidirect
40. C₂×C₃×C₁₇	D₅₁	direct (N × H)
41. C₂×C₃×C₁₇	C₂×C₃×C₁₇	semidirect
42. D₅₁	C₂×C₃×C₁₇	direct (N × H)
52. C₃×C₁₇	C₂×C₃×D₁₇	semidirect
53. C₃×C₁₇	C₂×D₃×C₁₇	semidirect
54. C₃×C₁₇	C₂×D₅₁	direct (N × H)
55. C₃×C₁₇	C₂²×C₃×C₁₇	semidirect
59. C₂×C₁₇	C₃×D₃×C₁₇	semidirect
60. C₂×C₁₇	C₃×D₅₁	direct (N × H)
62. C₂×C₃²	C₁₇×D₁₇	semidirect
65. C₁₇	C₂×C₃×D₃×C₁₇	semidirect
66. C₁₇	C₂×C₃×D₅₁	direct (N × H)
69. C₃²	C₂×C₁₇×D₁₇	semidirect
72. C₂×C₃	C₁₇×D₅₁	direct (N × H)
73. C₂×C₃	C₃×C₁₇×D₁₇	semidirect
77. C₃	C₂×C₃×C₁₇×D₁₇	semidirect
78. C₃	C₂×C₁₇×D₅₁	direct (N × H)
80. C₂	C₃×C₁₇×D₅₁	direct (N × H)

Subgroups — C2×C3×C17×D51 #23780946

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₃×C₁₇×D₅₁ #23780946