Subgroups — D₅₁² #23780930

Order 10404.

184 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⋊(C₃⋊(C₁₇⋊D₁₇))	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₁₇×D₅₁	C₂	1	2	yes	maximal, complemented
3	D₁₇×D₅₁	—	3	2	no	maximal
4	C₃²×C₁₇²	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₃×C₁₇×D₁₇	—	3	2	no	—
6	C₁₇×D₅₁	D₃	1	2	yes	complemented
7	C₃⋊(C₁₇⋊D₁₇)	—	3	2	no	—
8	C₃⋊(C₁₇⋊D₁₇)	—	6	1	no	—
9	D₁₇²	—	9	1	no	Hall
10	C₃×C₁₇²	—	2	1	no	—
11	C₃×C₁₇²	C₂×D₃	1	2	yes	complemented
12	D₃×D₅₁	—	17	2	no	maximal
13	C₁₇⋊D₁₇	—	9	1	no	—
14	C₁₇×D₁₇	—	3	2	no	—
15	C₃⋊D₅₁	—	17	2	no	—
16	C₃⋊D₅₁	—	34	8	no	—
17	C₃×D₅₁	D₁₇	1	2	yes	complemented
18	C₃×D₃×C₁₇	—	17	2	no	—
19	C₁₇²	D₃²	1	1	yes	characteristic, complemented, Sylow
20	C₂×D₅₁	—	51	2	no	—
21	D₃×D₁₇	—	51	2	no	—
22	C₃²×C₁₇	—	2	8	no	—
23	C₃²×C₁₇	C₂×D₁₇	1	2	yes	complemented
24	C₂×C₃×C₁₇	—	51	2	no	—
25	D₅₁	—	51	2	no	—
26	D₅₁	—	51	2	no	—
27	D₅₁	—	102	16	no	—
28	D₅₁	—	102	16	no	—
29	D₅₁	—	102	2	no	—
30	D₅₁	D₅₁	1	2	yes	direct product factor
31	C₃×D₁₇	—	3	2	no	—
32	D₃×C₁₇	—	17	2	no	—
33	C₂×D₁₇	—	153	2	no	—
34	C₃×C₁₇	—	2	16	no	—
35	C₃×C₁₇	—	2	2	no	—
36	C₃×C₁₇	—	2	16	no	—
37	C₃×C₁₇	D₃×D₁₇	1	2	yes	complemented
38	C₃×C₁₇	C₂×D₅₁	1	2	yes	complemented
39	D₃²	—	289	1	no	Hall
40	C₂×C₁₇	—	51	2	no	—
41	D₁₇	—	3	2	no	—
42	D₁₇	—	306	8	no	—
43	D₁₇	—	153	2	no	—
44	C₃⋊D₃	—	289	1	no	—
45	C₃×D₃	—	17	2	no	—
46	C₁₇	—	2	8	no	—
47	C₁₇	D₃×D₅₁	1	2	yes	complemented
48	C₂×D₃	—	867	2	no	—
49	C₃²	D₁₇²	1	1	yes	characteristic, complemented, Sylow
50	C₂×C₃	—	51	2	no	—
51	D₃	—	17	2	no	—
52	D₃	—	867	2	no	—
53	D₃	—	1734	1	no	—
54	C₂²	—	2601	1	no	Sylow
55	C₃	—	2	1	no	—
56	C₃	D₁₇×D₅₁	1	2	yes	complemented
57	C₂	—	2601	1	no	—
58	C₂	—	51	2	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. C₃⋊(C₃⋊(C₁₇⋊D₁₇))	C₂	semidirect
2. C₃×C₁₇×D₅₁	C₂	semidirect
4. C₃²×C₁₇²	C₂²	semidirect
6. C₁₇×D₅₁	D₃	semidirect
11. C₃×C₁₇²	C₂×D₃	semidirect
17. C₃×D₅₁	D₁₇	semidirect
19. C₁₇²	D₃²	semidirect
23. C₃²×C₁₇	C₂×D₁₇	semidirect
30. D₅₁	D₅₁	direct (N × H)
37. C₃×C₁₇	D₃×D₁₇	semidirect
38. C₃×C₁₇	C₂×D₅₁	semidirect
47. C₁₇	D₃×D₅₁	semidirect
49. C₃²	D₁₇²	semidirect
56. C₃	D₁₇×D₅₁	semidirect

Subgroups — D512 #23780930

Conjugacy classes of subgroups

Complements

Subgroups — D₅₁² #23780930