Subgroups — C₁₃×#10624883 #23745034

Order 9477.

926 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₁₃×H(3,𝔽₃)	C₃	1	1	yes	maximal, characteristic
2	C₁₃×C₉⋊H(3,𝔽₃)	C₃	1	27	yes	maximal, complemented
3	C₁₃×#6891	C₃	1	9	yes	maximal, complemented
4	C₃×C₁₃×C₃²⋊C₉	C₃	1	3	yes	maximal, complemented
5	C₃⁴×C₁₃	C₃²	1	3	yes	—
6	C₃⁴×C₁₃	C₃²	1	1	yes	characteristic
7	C₃×C₁₃×3₋¹⁺²	C₃²	1	27	yes	complemented
8	C₃×C₁₃×H(3,𝔽₃)	—	3	9	no	—
9	C₃×C₁₃×H(3,𝔽₃)	C₃²	1	9	yes	—
10	C₃²×C₉×C₁₃	C₃²	1	9	yes	complemented
11	C₁₃×C₃²⋊C₉	C₃²	1	9	yes	—
12	C₁₃×C₃²⋊C₉	C₃²	1	18	yes	complemented
13	C₁₃×C₃²⋊C₉	C₃²	1	54	yes	complemented
14	#10624883	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
15	C₃³×C₁₃	—	3	9	no	—
16	C₃³×C₁₃	—	9	1	no	—
17	C₃³×C₁₃	—	9	3	no	—
18	C₃³×C₁₃	—	9	2	no	—
19	C₃³×C₁₃	—	9	6	no	—
20	C₃³×C₁₃	3₋¹⁺²	1	9	yes	complemented
21	C₃³×C₁₃	C₃³	1	9	yes	—
22	C₃³×C₁₃	C₃³	1	1	yes	characteristic
23	C₃³×C₁₃	C₃³	1	3	yes	—
24	C₁₃×3₋¹⁺²	—	9	27	no	—
25	C₁₃×H(3,𝔽₃)	—	3	27	no	—
26	C₃×C₉×C₁₃	—	9	9	no	—
27	C₃×C₉×C₁₃	C₃³	1	27	yes	—
28	C₃²×H(3,𝔽₃)	C₃×C₁₃	1	1	yes	characteristic
29	C₉⋊H(3,𝔽₃)	C₃×C₁₃	1	27	yes	complemented
30	#6891	C₃×C₁₃	1	9	yes	complemented
31	C₃×C₃²⋊C₉	C₃×C₁₃	1	3	yes	complemented
32	C₃²×C₁₃	—	3	3	no	—
33	C₃²×C₁₃	—	3	1	no	—
34	C₃²×C₁₃	—	3	2	no	—
35	C₃²×C₁₃	—	3	6	no	—
36	C₃²×C₁₃	—	3	9	no	—
37	C₃²×C₁₃	—	3	9	no	—
38	C₃²×C₁₃	—	3	18	no	—
39	C₃²×C₁₃	—	9	9	no	—
40	C₃²×C₁₃	—	9	27	no	—
41	C₃²×C₁₃	C₃×3₋¹⁺²	1	9	yes	—
42	C₃²×C₁₃	C₃×3₋¹⁺²	1	3	yes	—
43	C₃²×C₁₃	C₃⁴	1	1	yes	characteristic
44	C₉×C₁₃	—	3	27	no	—
45	C₃⁴	C₃²×C₁₃	1	3	yes	—
46	C₃⁴	C₃²×C₁₃	1	1	yes	characteristic
47	C₃×3₋¹⁺²	C₃²×C₁₃	1	27	yes	complemented
48	C₃×H(3,𝔽₃)	—	3	9	no	—
49	C₃×H(3,𝔽₃)	C₃²×C₁₃	1	9	yes	—
50	C₃²×C₉	C₃²×C₁₃	1	9	yes	complemented
51	C₃²⋊C₉	C₃²×C₁₃	1	9	yes	—
52	C₃²⋊C₉	C₃²×C₁₃	1	18	yes	complemented
53	C₃²⋊C₉	C₃²×C₁₃	1	54	yes	complemented
54	C₃×C₁₃	—	3	3	no	—
55	C₃×C₁₃	—	3	9	no	—
56	C₃×C₁₃	—	9	9	no	—
57	C₃×C₁₃	C₃²×3₋¹⁺²	1	1	yes	characteristic
58	C₃×C₁₃	H(5,𝔽₃)	1	1	yes	characteristic
59	C₃×C₁₃	3₋¹⁺⁴	1	2	yes	—
60	C₃³	—	3	9	no	—
61	C₃³	—	9	1	no	—
62	C₃³	—	9	3	no	—
63	C₃³	—	9	2	no	—
64	C₃³	—	9	6	no	—
65	C₃³	C₁₃×3₋¹⁺²	1	9	yes	complemented
66	C₃³	C₃³×C₁₃	1	9	yes	—
67	C₃³	C₃³×C₁₃	1	1	yes	characteristic
68	C₃³	C₃³×C₁₃	1	3	yes	—
69	3₋¹⁺²	—	9	27	no	—
70	H(3,𝔽₃)	—	3	27	no	—
71	C₃×C₉	—	9	9	no	—
72	C₃×C₉	C₃³×C₁₃	1	27	yes	—
73	C₁₃	#10624883	1	1	yes	characteristic, direct product factor, Sylow
74	C₃²	—	3	3	no	—
75	C₃²	—	3	1	no	—
76	C₃²	—	3	2	no	—
77	C₃²	—	3	6	no	—
78	C₃²	—	3	9	no	—
79	C₃²	—	3	9	no	—
80	C₃²	—	3	18	no	—
81	C₃²	—	9	9	no	—
82	C₃²	—	9	27	no	—
83	C₃²	C₃×C₁₃×3₋¹⁺²	1	9	yes	—
84	C₃²	C₃×C₁₃×3₋¹⁺²	1	3	yes	—
85	C₃²	C₃⁴×C₁₃	1	1	yes	characteristic
86	C₉	—	3	27	no	—
87	C₃	—	3	3	no	—
88	C₃	—	3	9	no	—
89	C₃	—	9	9	no	—
90	C₃	C₃²×C₁₃×3₋¹⁺²	1	1	yes	characteristic
91	C₃	C₁₃×H(5,𝔽₃)	1	1	yes	characteristic
92	C₃	C₁₃×3₋¹⁺⁴	1	2	yes	—

	subgroup	G/H
center, socle	C₃²×C₁₃	C₃⁴
commutator, Frattini, cosocle	C₃²	C₃⁴×C₁₃
prime radical	C₃²×C₁₃×H(3,𝔽₃)	C₃
LCS	G ▷ C₃² ▷ C₁
UCS	C₁ ◁ C₃²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×C₉⋊H(3,𝔽₃)	C₃	semidirect
3. C₁₃×#6891	C₃	semidirect
4. C₃×C₁₃×C₃²⋊C₉	C₃	semidirect
7. C₃×C₁₃×3₋¹⁺²	C₃²	semidirect
10. C₃²×C₉×C₁₃	C₃²	semidirect
12. C₁₃×C₃²⋊C₉	C₃²	semidirect
13. C₁₃×C₃²⋊C₉	C₃²	semidirect
14. #10624883	C₁₃	direct (N × H)
20. C₃³×C₁₃	3₋¹⁺²	semidirect
29. C₉⋊H(3,𝔽₃)	C₃×C₁₃	semidirect
30. #6891	C₃×C₁₃	semidirect
31. C₃×C₃²⋊C₉	C₃×C₁₃	semidirect
47. C₃×3₋¹⁺²	C₃²×C₁₃	semidirect
50. C₃²×C₉	C₃²×C₁₃	semidirect
52. C₃²⋊C₉	C₃²×C₁₃	semidirect
53. C₃²⋊C₉	C₃²×C₁₃	semidirect
65. C₃³	C₁₃×3₋¹⁺²	semidirect
73. C₁₃	#10624883	direct (N × H)

Subgroups — C13×#10624883 #23745034

Conjugacy classes of subgroups

Complements

Subgroups — C₁₃×#10624883 #23745034