Subgroups — C₃×C₁₇×C₃⋊#595 #23780909

Order 10404.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₁₇×D₁₇	C₂	1	1	yes	maximal, characteristic
2	C₁₇×C₃⋊#595	C₃	1	1	yes	maximal, characteristic, direct product factor
3	C₃×C₁₇×#595	—	3	1	no	maximal
4	C₃²×C₁₇²	C₄	1	1	yes	characteristic, complemented, Hall
5	C₃×C₁₇×D₁₇	—	2	1	no	—
6	C₃×C₁₇×D₁₇	D₃	1	1	yes	characteristic
7	C₃×C₁₇×D₁₇	C₂×C₃	1	1	yes	characteristic
8	C₁₇×#595	—	3	1	no	Hall
9	C₃×C₁₇²	—	2	1	no	—
10	C₃×C₁₇²	Dic₃	1	1	yes	characteristic, complemented
11	C₃×C₁₇²	C₃×C₄	1	1	yes	characteristic, complemented
12	C₃×C₃⋊#595	C₁₇	1	1	yes	maximal, characteristic, direct product factor
13	C₃×Dic₃×C₁₇	—	17	1	no	maximal
14	C₁₇×D₁₇	C₃×D₃	1	1	yes	characteristic
15	C₂×C₃²×C₁₇	—	17	1	no	—
16	C₃²×D₁₇	C₂×C₁₇	1	1	yes	characteristic
17	C₁₇²	C₃×Dic₃	1	1	yes	characteristic, complemented, Sylow
18	C₃⋊#595	C₃×C₁₇	1	1	yes	characteristic, direct product factor
19	C₃×#595	—	3	1	no	—
20	C₃×C₄×C₁₇	—	51	1	no	—
21	Dic₃×C₁₇	—	17	1	no	—
22	C₃²×C₁₇	—	4	4	no	—
23	C₃²×C₁₇	C₄×C₁₇	1	1	yes	characteristic, complemented
24	C₃²×C₁₇	#595	1	1	yes	characteristic, complemented
25	C₂×C₃×C₁₇	—	17	1	no	—
26	C₂×C₃×C₁₇	—	17	1	no	—
27	C₂×C₃×C₁₇	—	34	1	no	—
28	C₃×D₁₇	—	2	1	no	—
29	C₃×D₁₇	D₃×C₁₇	1	1	yes	characteristic
30	C₃×D₁₇	C₂×C₃×C₁₇	1	1	yes	characteristic
31	#595	—	3	1	no	—
32	C₄×C₁₇	—	51	1	no	—
33	C₃×C₁₇	—	2	1	no	—
34	C₃×C₁₇	—	2	1	no	—
35	C₃×C₁₇	—	4	8	no	—
36	C₃×C₁₇	—	4	4	no	—
37	C₃×C₁₇	—	4	4	no	—
38	C₃×C₁₇	Dic₃×C₁₇	1	1	yes	characteristic, complemented
39	C₃×C₁₇	C₃×C₄×C₁₇	1	1	yes	characteristic, complemented
40	C₃×C₁₇	C₃×#595	1	1	yes	characteristic, complemented
41	C₃×C₁₇	C₃⋊#595	1	1	yes	characteristic, direct product factor
42	C₃×Dic₃	—	17	1	no	Hall
43	C₂×C₁₇	—	17	1	no	—
44	D₁₇	C₃×D₃×C₁₇	1	1	yes	characteristic
45	C₂×C₃²	—	17	1	no	—
46	C₁₇	—	4	4	no	—
47	C₁₇	C₃×Dic₃×C₁₇	1	1	yes	characteristic, complemented
48	C₁₇	C₃×C₃⋊#595	1	1	yes	characteristic, direct product factor
49	C₃×C₄	—	51	1	no	—
50	Dic₃	—	17	1	no	—
51	C₃²	C₁₇×#595	1	1	yes	characteristic, complemented, Sylow
52	C₂×C₃	—	17	1	no	—
53	C₂×C₃	—	17	1	no	—
54	C₂×C₃	—	34	1	no	—
55	C₄	—	51	1	no	Sylow
56	C₃	—	2	1	no	—
57	C₃	C₃×C₁₇×#595	1	1	yes	characteristic, complemented
58	C₃	C₁₇×C₃⋊#595	1	1	yes	characteristic, direct product factor
59	C₂	—	17	1	no	—

	subgroup	G/H
center, hypercenter	C₃×C₁₇	C₃⋊#595
commutator, hypocenter	C₃×C₁₇	C₃×C₄×C₁₇
Frattini	C₁	G
Fitting, socle	C₃²×C₁₇²	C₄
prime radical	C₃²×C₁₇×D₁₇	C₂
cosocle	C₃×D₁₇	C₂×C₃×C₁₇
LCS	G ▷ C₃×C₁₇
UCS	C₁ ◁ C₃×C₁₇

Complements

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

N	H ≅ G/N	type
2. C₁₇×C₃⋊#595	C₃	direct (N × H)
4. C₃²×C₁₇²	C₄	semidirect
10. C₃×C₁₇²	Dic₃	semidirect
11. C₃×C₁₇²	C₃×C₄	semidirect
12. C₃×C₃⋊#595	C₁₇	direct (N × H)
17. C₁₇²	C₃×Dic₃	semidirect
18. C₃⋊#595	C₃×C₁₇	direct (N × H)
23. C₃²×C₁₇	C₄×C₁₇	semidirect
24. C₃²×C₁₇	#595	semidirect
38. C₃×C₁₇	Dic₃×C₁₇	semidirect
39. C₃×C₁₇	C₃×C₄×C₁₇	semidirect
40. C₃×C₁₇	C₃×#595	semidirect
41. C₃×C₁₇	C₃⋊#595	direct (N × H)
47. C₁₇	C₃×Dic₃×C₁₇	semidirect
48. C₁₇	C₃×C₃⋊#595	direct (N × H)
51. C₃²	C₁₇×#595	semidirect
57. C₃	C₃×C₁₇×#595	semidirect
58. C₃	C₁₇×C₃⋊#595	direct (N × H)

Subgroups — C3×C17×C3⋊#595 #23780909

Conjugacy classes of subgroups

Complements

Subgroups — C₃×C₁₇×C₃⋊#595 #23780909