Subgroups — D₅₁⋊D₅₁ #23780931

Order 10404.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×C₃⋊D₅₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₃⋊(C₁₇⋊D₁₇)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₁₇×D₅₁	C₂	1	1	yes	maximal, characteristic, complemented
4	D₅₁⋊D₁₇	—	3	1	no	maximal
5	D₁₇×D₅₁	—	3	1	no	maximal
6	C₃²×C₁₇²	C₂²	1	1	yes	characteristic, complemented, Hall
7	C₃×C₁₇×D₁₇	—	3	1	no	—
8	C₃×C₁₇⋊D₁₇	—	3	1	no	—
9	C₁₇×D₅₁	—	3	1	no	—
10	C₁₇×D₅₁	—	3	1	no	—
11	C₁₇×D₅₁	—	6	1	no	—
12	C₁₇×D₅₁	D₃	1	1	yes	characteristic, complemented
13	C₃⋊(C₁₇⋊D₁₇)	D₃	1	1	yes	characteristic, complemented
14	D₁₇²	—	9	1	no	Hall
15	C₃×C₁₇²	—	2	1	no	—
16	C₃×C₁₇²	C₂×D₃	1	1	yes	characteristic, complemented
17	C₃×C₁₇²	C₂×D₃	1	1	yes	characteristic, complemented
18	(C₃⋊D₃)⋊D₁₇	—	17	1	no	maximal
19	D₃×D₅₁	—	17	1	no	maximal
20	C₁₇⋊D₁₇	—	3	1	no	—
21	C₁₇×D₁₇	—	3	1	no	—
22	C₁₇×D₁₇	—	9	1	no	—
23	C₃⋊D₅₁	D₁₇	1	1	yes	characteristic, complemented
24	C₁₇×C₃⋊D₃	—	17	1	no	—
25	C₃×D₅₁	—	17	1	no	—
26	C₃×D₅₁	—	17	1	no	—
27	C₃×D₅₁	—	34	8	no	—
28	C₃×D₅₁	D₁₇	1	1	yes	characteristic, complemented
29	C₃×D₃×C₁₇	—	17	1	no	—
30	C₁₇²	D₃²	1	1	yes	characteristic, complemented, Sylow
31	C₂×D₅₁	—	51	1	no	—
32	D₃×D₁₇	—	51	1	no	—
33	D₃×D₁₇	—	51	1	no	—
34	D₃×D₁₇	—	51	1	no	—
35	C₃²×C₁₇	—	2	8	no	—
36	C₃²×C₁₇	C₂×D₁₇	1	1	yes	characteristic, complemented
37	C₃²×C₁₇	C₂×D₁₇	1	1	yes	characteristic, complemented
38	C₂×C₃×C₁₇	—	51	1	no	—
39	D₅₁	—	3	1	no	—
40	D₅₁	—	3	1	no	—
41	D₅₁	—	6	1	no	—
42	D₅₁	—	17	1	no	—
43	D₅₁	—	17	1	no	—
44	D₅₁	—	34	8	no	—
45	D₅₁	D₅₁	1	1	yes	characteristic, complemented
46	C₃×D₁₇	—	3	1	no	—
47	C₃×D₁₇	—	51	1	no	—
48	C₃×D₁₇	—	51	1	no	—
49	C₃×D₁₇	—	102	8	no	—
50	D₃×C₁₇	—	17	1	no	—
51	D₃×C₁₇	—	51	1	no	—
52	D₃×C₁₇	—	51	1	no	—
53	D₃×C₁₇	—	102	1	no	—
54	C₂×D₁₇	—	153	1	no	—
55	C₂×D₁₇	—	153	1	no	—
56	C₃×C₁₇	—	2	1	no	—
57	C₃×C₁₇	—	2	1	no	—
58	C₃×C₁₇	—	2	8	no	—
59	C₃×C₁₇	—	2	8	no	—
60	C₃×C₁₇	—	4	8	no	—
61	C₃×C₁₇	D₃×D₁₇	1	1	yes	characteristic, complemented
62	C₃×C₁₇	D₃×D₁₇	1	1	yes	characteristic, complemented
63	C₃×C₁₇	D₃×D₁₇	1	1	yes	characteristic, complemented
64	C₃×C₁₇	C₂×D₅₁	1	1	yes	characteristic, complemented
65	D₃²	—	289	1	no	Hall
66	C₂×C₁₇	—	51	1	no	—
67	C₂×C₁₇	—	153	1	no	—
68	D₁₇	—	3	1	no	—
69	D₁₇	—	9	1	no	—
70	D₁₇	—	51	1	no	—
71	D₁₇	—	51	1	no	—
72	D₁₇	—	102	8	no	—
73	C₃⋊D₃	—	17	1	no	—
74	C₃×D₃	—	17	1	no	—
75	C₃×D₃	—	289	1	no	—
76	C₁₇	—	2	8	no	—
77	C₁₇	D₃×D₅₁	1	1	yes	characteristic, complemented
78	C₁₇	(C₃⋊D₃)⋊D₁₇	1	1	yes	characteristic, complemented
79	C₂×D₃	—	867	1	no	—
80	C₂×D₃	—	867	1	no	—
81	C₃²	D₁₇²	1	1	yes	characteristic, complemented, Sylow
82	C₂×C₃	—	51	1	no	—
83	C₂×C₃	—	867	1	no	—
84	D₃	—	17	1	no	—
85	D₃	—	289	1	no	—
86	D₃	—	51	1	no	—
87	D₃	—	51	1	no	—
88	D₃	—	102	1	no	—
89	C₂²	—	2601	1	no	Sylow
90	C₃	—	2	1	no	—
91	C₃	D₁₇×D₅₁	1	1	yes	characteristic, complemented
92	C₃	D₅₁⋊D₁₇	1	1	yes	characteristic, complemented
93	C₂	—	51	1	no	—
94	C₂	—	867	1	no	—
95	C₂	—	153	1	no	—

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

Complements

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

N	H ≅ G/N	type
1. C₁₇×C₃⋊D₅₁	C₂	semidirect
2. C₃×C₃⋊(C₁₇⋊D₁₇)	C₂	semidirect
3. C₃×C₁₇×D₅₁	C₂	semidirect
6. C₃²×C₁₇²	C₂²	semidirect
12. C₁₇×D₅₁	D₃	semidirect
13. C₃⋊(C₁₇⋊D₁₇)	D₃	semidirect
16. C₃×C₁₇²	C₂×D₃	semidirect
17. C₃×C₁₇²	C₂×D₃	semidirect
23. C₃⋊D₅₁	D₁₇	semidirect
28. C₃×D₅₁	D₁₇	semidirect
30. C₁₇²	D₃²	semidirect
36. C₃²×C₁₇	C₂×D₁₇	semidirect
37. C₃²×C₁₇	C₂×D₁₇	semidirect
45. D₅₁	D₅₁	semidirect
61. C₃×C₁₇	D₃×D₁₇	semidirect
62. C₃×C₁₇	D₃×D₁₇	semidirect
63. C₃×C₁₇	D₃×D₁₇	semidirect
64. C₃×C₁₇	C₂×D₅₁	semidirect
77. C₁₇	D₃×D₅₁	semidirect
78. C₁₇	(C₃⋊D₃)⋊D₁₇	semidirect
81. C₃²	D₁₇²	semidirect
91. C₃	D₁₇×D₅₁	semidirect
92. C₃	D₅₁⋊D₁₇	semidirect

Subgroups — D51⋊D51 #23780931

Conjugacy classes of subgroups

Complements

Subgroups — D₅₁⋊D₅₁ #23780931