Subgroups — C₃×D₅₁⋊D₁₇ #23780916

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, complemented
2	C₃²×C₁₇⋊D₁₇	C₂	1	1	yes	maximal, characteristic, complemented
3	D₅₁⋊D₁₇	C₃	1	1	yes	maximal, characteristic, direct product factor
4	C₃×D₁₇²	—	3	1	no	maximal
5	C₃²×C₁₇²	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₃×C₁₇×D₁₇	—	3	2	no	—
7	C₃×C₁₇⋊D₁₇	—	2	1	no	—
8	C₃×C₁₇⋊D₁₇	D₃	1	1	yes	characteristic, complemented
9	C₃×C₁₇⋊D₁₇	C₂×C₃	1	1	yes	characteristic, complemented
10	C₁₇×D₅₁	C₂×C₃	1	2	yes	complemented
11	D₁₇²	—	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	C₃×D₃×D₁₇	—	17	2	no	maximal
16	C₁₇⋊D₁₇	C₃×D₃	1	1	yes	characteristic, complemented
17	C₁₇×D₁₇	—	3	2	no	—
18	C₃×D₅₁	D₁₇	1	2	yes	complemented
19	C₃×D₃×C₁₇	—	17	2	no	—
20	C₃²×D₁₇	—	17	2	no	—
21	C₃²×D₁₇	—	34	8	no	—
22	C₁₇²	C₂×C₃×D₃	1	1	yes	characteristic, complemented, Sylow
23	C₂×C₃×D₁₇	—	51	2	no	—
24	D₃×D₁₇	—	17	2	no	—
25	C₃²×C₁₇	—	2	8	no	—
26	C₃²×C₁₇	C₂×D₁₇	1	2	yes	complemented
27	C₂×C₃×C₁₇	—	51	2	no	—
28	D₅₁	C₃×D₁₇	1	2	yes	complemented
29	C₃×D₁₇	—	3	2	no	—
30	C₃×D₁₇	—	17	2	no	—
31	C₃×D₁₇	—	17	2	no	—
32	C₃×D₁₇	—	34	8	no	—
33	C₃×D₁₇	—	34	8	no	—
34	C₃×D₁₇	—	34	2	no	—
35	C₃×D₁₇	—	34	16	no	—
36	D₃×C₁₇	—	17	2	no	—
37	C₂×D₁₇	—	51	2	no	—
38	C₃×C₁₇	—	2	16	no	—
39	C₃×C₁₇	—	2	2	no	—
40	C₃×C₁₇	—	2	8	no	—
41	C₃×C₁₇	—	2	8	no	—
42	C₃×C₁₇	D₃×D₁₇	1	2	yes	complemented
43	C₃×C₁₇	C₂×C₃×D₁₇	1	2	yes	complemented
44	C₂×C₃×D₃	—	289	1	no	Hall
45	C₂×C₁₇	—	51	2	no	—
46	D₁₇	—	3	2	no	—
47	D₁₇	—	17	2	no	—
48	D₁₇	—	34	8	no	—
49	C₂×C₃²	—	289	1	no	—
50	C₃×D₃	—	17	2	no	—
51	C₁₇	—	2	8	no	—
52	C₁₇	C₃×D₃×D₁₇	1	2	yes	complemented
53	C₂²×C₃	—	867	1	no	—
54	C₂×D₃	—	289	1	no	—
55	C₃²	D₁₇²	1	1	yes	characteristic, complemented, Sylow
56	C₂×C₃	—	289	1	no	—
57	C₂×C₃	—	289	1	no	—
58	C₂×C₃	—	51	2	no	—
59	C₂×C₃	—	578	1	no	—
60	D₃	—	17	2	no	—
61	C₂²	—	867	1	no	Sylow
62	C₃	—	2	1	no	—
63	C₃	C₃×D₁₇²	1	1	yes	characteristic, complemented
64	C₃	D₅₁⋊D₁₇	1	1	yes	characteristic, direct product factor
65	C₂	—	289	1	no	—
66	C₂	—	51	2	no	—

	subgroup	G/H
center, hypercenter	C₃	D₅₁⋊D₁₇
commutator, cosocle, hypocenter	C₃×C₁₇²	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₃²×C₁₇²	C₂²
LCS	G ▷ C₃×C₁₇²
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₃×C₁₇×D₅₁	C₂	semidirect
2. C₃²×C₁₇⋊D₁₇	C₂	semidirect
3. D₅₁⋊D₁₇	C₃	direct (N × H)
5. C₃²×C₁₇²	C₂²	semidirect
8. C₃×C₁₇⋊D₁₇	D₃	semidirect
9. C₃×C₁₇⋊D₁₇	C₂×C₃	semidirect
10. C₁₇×D₅₁	C₂×C₃	semidirect
13. C₃×C₁₇²	C₂×D₃	semidirect
14. C₃×C₁₇²	C₂²×C₃	semidirect
16. C₁₇⋊D₁₇	C₃×D₃	semidirect
18. C₃×D₅₁	D₁₇	semidirect
22. C₁₇²	C₂×C₃×D₃	semidirect
26. C₃²×C₁₇	C₂×D₁₇	semidirect
28. D₅₁	C₃×D₁₇	semidirect
42. C₃×C₁₇	D₃×D₁₇	semidirect
43. C₃×C₁₇	C₂×C₃×D₁₇	semidirect
52. C₁₇	C₃×D₃×D₁₇	semidirect
55. C₃²	D₁₇²	semidirect
63. C₃	C₃×D₁₇²	semidirect
64. C₃	D₅₁⋊D₁₇	direct (N × H)

Subgroups — C3×D51⋊D17 #23780916

Conjugacy classes of subgroups

Complements

Subgroups — C₃×D₅₁⋊D₁₇ #23780916