Subgroups — C₃×C₁₃×#6891 #23745017

Order 9477.

2636 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⁵×C₁₃	C₃	1	1	yes	maximal, characteristic
2	C₃²×C₁₃×3₋¹⁺²	C₃	1	3	yes	maximal, complemented
3	C₁₃×#6891	C₃	1	27	yes	maximal, direct product factor
4	C₃×C₁₃×C₃²⋊C₉	C₃	1	9	yes	maximal, complemented
5	C₃⁴×C₁₃	—	3	9	no	—
6	C₃⁴×C₁₃	—	3	27	no	—
7	C₃⁴×C₁₃	C₃²	1	9	yes	—
8	C₃⁴×C₁₃	C₃²	1	1	yes	characteristic
9	C₃⁴×C₁₃	C₃²	1	3	yes	—
10	C₃×C₁₃×3₋¹⁺²	—	3	27	no	—
11	C₃×C₁₃×3₋¹⁺²	C₃²	1	27	yes	complemented
12	C₃²×C₉×C₁₃	C₃²	1	9	yes	complemented
13	C₁₃×C₃²⋊C₉	C₃²	1	81	yes	complemented
14	C₃×#6891	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
15	C₃³×C₁₃	—	3	243	no	—
16	C₃³×C₁₃	—	3	27	no	—
17	C₃³×C₁₃	—	3	9	no	—
18	C₃³×C₁₃	—	3	9	no	—
19	C₃³×C₁₃	—	3	18	no	—
20	C₃³×C₁₃	—	3	81	no	—
21	C₃³×C₁₃	H(3,𝔽₃)	1	9	yes	—
22	C₃³×C₁₃	3₋¹⁺²	1	27	yes	complemented
23	C₃³×C₁₃	C₃³	1	3	yes	—
24	C₃³×C₁₃	C₃³	1	9	yes	—
25	C₃³×C₁₃	C₃³	1	1	yes	characteristic
26	C₁₃×3₋¹⁺²	—	3	81	no	—
27	C₃×C₉×C₁₃	—	3	27	no	—
28	C₃×C₉×C₁₃	C₃³	1	27	yes	complemented
29	C₃⁵	C₃×C₁₃	1	1	yes	characteristic
30	C₃²×3₋¹⁺²	C₃×C₁₃	1	3	yes	complemented
31	#6891	C₃×C₁₃	1	27	yes	direct product factor
32	C₃×C₃²⋊C₉	C₃×C₁₃	1	9	yes	complemented
33	C₃²×C₁₃	—	3	243	no	—
34	C₃²×C₁₃	—	3	9	no	—
35	C₃²×C₁₃	—	3	9	no	—
36	C₃²×C₁₃	—	3	18	no	—
37	C₃²×C₁₃	—	3	27	no	—
38	C₃²×C₁₃	—	3	81	no	—
39	C₃²×C₁₃	C₃×H(3,𝔽₃)	1	9	yes	—
40	C₃²×C₁₃	C₃×H(3,𝔽₃)	1	3	yes	—
41	C₃²×C₁₃	C₃×3₋¹⁺²	1	9	yes	—
42	C₃²×C₁₃	C₃×3₋¹⁺²	1	27	yes	complemented
43	C₃²×C₁₃	C₃⁴	1	1	yes	characteristic
44	C₉×C₁₃	—	3	27	no	—
45	C₃⁴	—	3	9	no	—
46	C₃⁴	—	3	27	no	—
47	C₃⁴	C₃²×C₁₃	1	9	yes	—
48	C₃⁴	C₃²×C₁₃	1	1	yes	characteristic
49	C₃⁴	C₃²×C₁₃	1	3	yes	—
50	C₃×3₋¹⁺²	—	3	27	no	—
51	C₃×3₋¹⁺²	C₃²×C₁₃	1	27	yes	complemented
52	C₃²×C₉	C₃²×C₁₃	1	9	yes	complemented
53	C₃²⋊C₉	C₃²×C₁₃	1	81	yes	complemented
54	C₃×C₁₃	—	3	9	no	—
55	C₃×C₁₃	—	3	27	no	—
56	C₃×C₁₃	#6891	1	9	yes	direct product factor
57	C₃×C₁₃	C₃²×H(3,𝔽₃)	1	1	yes	characteristic
58	C₃×C₁₃	C₃²×3₋¹⁺²	1	3	yes	—
59	C₃³	—	3	243	no	—
60	C₃³	—	3	27	no	—
61	C₃³	—	3	9	no	—
62	C₃³	—	3	9	no	—
63	C₃³	—	3	18	no	—
64	C₃³	—	3	81	no	—
65	C₃³	C₁₃×H(3,𝔽₃)	1	9	yes	—
66	C₃³	C₁₃×3₋¹⁺²	1	27	yes	complemented
67	C₃³	C₃³×C₁₃	1	3	yes	—
68	C₃³	C₃³×C₁₃	1	9	yes	—
69	C₃³	C₃³×C₁₃	1	1	yes	characteristic
70	3₋¹⁺²	—	3	81	no	—
71	C₃×C₉	—	3	27	no	—
72	C₃×C₉	C₃³×C₁₃	1	27	yes	complemented
73	C₁₃	C₃×#6891	1	1	yes	characteristic, direct product factor, Sylow
74	C₃²	—	3	243	no	—
75	C₃²	—	3	27	no	—
76	C₃²	—	3	81	no	—
77	C₃²	—	3	9	no	—
78	C₃²	—	3	9	no	—
79	C₃²	—	3	18	no	—
80	C₃²	C₃×C₁₃×H(3,𝔽₃)	1	9	yes	—
81	C₃²	C₃×C₁₃×H(3,𝔽₃)	1	3	yes	—
82	C₃²	C₃×C₁₃×3₋¹⁺²	1	9	yes	—
83	C₃²	C₃×C₁₃×3₋¹⁺²	1	27	yes	complemented
84	C₃²	C₃⁴×C₁₃	1	1	yes	characteristic
85	C₉	—	3	27	no	—
86	C₃	—	3	9	no	—
87	C₃	—	3	27	no	—
88	C₃	C₁₃×#6891	1	9	yes	direct product factor
89	C₃	C₃²×C₁₃×H(3,𝔽₃)	1	1	yes	characteristic
90	C₃	C₃²×C₁₃×3₋¹⁺²	1	3	yes	—

	subgroup	G/H
center, socle	C₃³×C₁₃	C₃³
commutator, Frattini, cosocle	C₃²	C₃⁴×C₁₃
prime radical	C₃⁵×C₁₃	C₃
LCS	G ▷ C₃² ▷ C₁
UCS	C₁ ◁ C₃³×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃²×C₁₃×3₋¹⁺²	C₃	semidirect
3. C₁₃×#6891	C₃	direct (N × H)
4. C₃×C₁₃×C₃²⋊C₉	C₃	semidirect
11. C₃×C₁₃×3₋¹⁺²	C₃²	semidirect
12. C₃²×C₉×C₁₃	C₃²	semidirect
13. C₁₃×C₃²⋊C₉	C₃²	semidirect
14. C₃×#6891	C₁₃	direct (N × H)
22. C₃³×C₁₃	3₋¹⁺²	semidirect
28. C₃×C₉×C₁₃	C₃³	semidirect
30. C₃²×3₋¹⁺²	C₃×C₁₃	semidirect
31. #6891	C₃×C₁₃	direct (N × H)
32. C₃×C₃²⋊C₉	C₃×C₁₃	semidirect
42. C₃²×C₁₃	C₃×3₋¹⁺²	semidirect
51. C₃×3₋¹⁺²	C₃²×C₁₃	semidirect
52. C₃²×C₉	C₃²×C₁₃	semidirect
53. C₃²⋊C₉	C₃²×C₁₃	semidirect
56. C₃×C₁₃	#6891	direct (N × H)
66. C₃³	C₁₃×3₋¹⁺²	semidirect
72. C₃×C₉	C₃³×C₁₃	semidirect
73. C₁₃	C₃×#6891	direct (N × H)
83. C₃²	C₃×C₁₃×3₋¹⁺²	semidirect
88. C₃	C₁₃×#6891	direct (N × H)

Subgroups — C3×C13×#6891 #23745017

Conjugacy classes of subgroups

Complements

Subgroups — C₃×C₁₃×#6891 #23745017