Subgroups — C₁₃×#10624881 #23745032

Order 9477.

1124 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₁₃×3₋¹⁺²	C₃	1	3	yes	maximal, complemented
2	C₃²×C₁₃×H(3,𝔽₃)	C₃	1	1	yes	maximal, characteristic
3	C₁₃×#6893	C₃	1	27	yes	maximal, complemented
4	C₁₃×#6891	C₃	1	9	yes	maximal, complemented
5	C₃⁴×C₁₃	C₃²	1	3	yes	—
6	C₃⁴×C₁₃	C₃²	1	1	yes	characteristic
7	C₃×C₁₃×3₋¹⁺²	—	3	27	no	—
8	C₃×C₁₃×3₋¹⁺²	C₃²	1	9	yes	—
9	C₃×C₁₃×3₋¹⁺²	C₃²	1	18	yes	complemented
10	C₃×C₁₃×H(3,𝔽₃)	—	3	9	no	—
11	C₃×C₁₃×H(3,𝔽₃)	C₃²	1	9	yes	—
12	C₃²×C₉×C₁₃	C₃²	1	9	yes	complemented
13	C₁₃×C₃²⋊C₉	C₃²	1	81	yes	complemented
14	#10624881	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
15	C₃³×C₁₃	—	3	9	no	—
16	C₃³×C₁₃	—	9	3	no	—
17	C₃³×C₁₃	—	9	9	no	—
18	C₃³×C₁₃	H(3,𝔽₃)	1	9	yes	—
19	C₃³×C₁₃	C₃³	1	9	yes	—
20	C₃³×C₁₃	C₃³	1	3	yes	—
21	C₃³×C₁₃	C₃³	1	1	yes	characteristic
22	C₁₃×3₋¹⁺²	—	3	27	no	—
23	C₁₃×3₋¹⁺²	—	3	54	no	—
24	C₁₃×H(3,𝔽₃)	—	3	27	no	—
25	C₃×C₉×C₁₃	—	3	27	no	—
26	C₃×C₉×C₁₃	C₃³	1	27	yes	—
27	C₃²×3₋¹⁺²	C₃×C₁₃	1	3	yes	complemented
28	C₃²×H(3,𝔽₃)	C₃×C₁₃	1	1	yes	characteristic
29	#6893	C₃×C₁₃	1	27	yes	complemented
30	#6891	C₃×C₁₃	1	9	yes	complemented
31	C₃²×C₁₃	—	3	3	no	—
32	C₃²×C₁₃	—	3	9	no	—
33	C₃²×C₁₃	—	3	9	no	—
34	C₃²×C₁₃	—	3	27	no	—
35	C₃²×C₁₃	—	9	9	no	—
36	C₃²×C₁₃	—	9	27	no	—
37	C₃²×C₁₃	C₃×H(3,𝔽₃)	1	9	yes	—
38	C₃²×C₁₃	C₃×H(3,𝔽₃)	1	3	yes	—
39	C₃²×C₁₃	C₃⁴	1	1	yes	characteristic
40	C₉×C₁₃	—	3	27	no	—
41	C₃⁴	C₃²×C₁₃	1	3	yes	—
42	C₃⁴	C₃²×C₁₃	1	1	yes	characteristic
43	C₃×3₋¹⁺²	—	3	27	no	—
44	C₃×3₋¹⁺²	C₃²×C₁₃	1	9	yes	—
45	C₃×3₋¹⁺²	C₃²×C₁₃	1	18	yes	complemented
46	C₃×H(3,𝔽₃)	—	3	9	no	—
47	C₃×H(3,𝔽₃)	C₃²×C₁₃	1	9	yes	—
48	C₃²×C₉	C₃²×C₁₃	1	9	yes	complemented
49	C₃²⋊C₉	C₃²×C₁₃	1	81	yes	complemented
50	C₃×C₁₃	—	3	3	no	—
51	C₃×C₁₃	—	3	9	no	—
52	C₃×C₁₃	—	9	9	no	—
53	C₃×C₁₃	C₃²×H(3,𝔽₃)	1	1	yes	characteristic
54	C₃×C₁₃	3₋¹⁺⁴	1	3	yes	—
55	C₃³	—	3	9	no	—
56	C₃³	—	9	3	no	—
57	C₃³	—	9	9	no	—
58	C₃³	C₁₃×H(3,𝔽₃)	1	9	yes	—
59	C₃³	C₃³×C₁₃	1	9	yes	—
60	C₃³	C₃³×C₁₃	1	3	yes	—
61	C₃³	C₃³×C₁₃	1	1	yes	characteristic
62	3₋¹⁺²	—	3	27	no	—
63	3₋¹⁺²	—	3	54	no	—
64	H(3,𝔽₃)	—	3	27	no	—
65	C₃×C₉	—	3	27	no	—
66	C₃×C₉	C₃³×C₁₃	1	27	yes	—
67	C₁₃	#10624881	1	1	yes	characteristic, direct product factor, Sylow
68	C₃²	—	3	3	no	—
69	C₃²	—	3	9	no	—
70	C₃²	—	3	9	no	—
71	C₃²	—	3	27	no	—
72	C₃²	—	9	9	no	—
73	C₃²	—	9	27	no	—
74	C₃²	C₃×C₁₃×H(3,𝔽₃)	1	9	yes	—
75	C₃²	C₃×C₁₃×H(3,𝔽₃)	1	3	yes	—
76	C₃²	C₃⁴×C₁₃	1	1	yes	characteristic
77	C₉	—	3	27	no	—
78	C₃	—	3	3	no	—
79	C₃	—	3	9	no	—
80	C₃	—	9	9	no	—
81	C₃	C₃²×C₁₃×H(3,𝔽₃)	1	1	yes	characteristic
82	C₃	C₁₃×3₋¹⁺⁴	1	3	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
1. C₃²×C₁₃×3₋¹⁺²	C₃	semidirect
3. C₁₃×#6893	C₃	semidirect
4. C₁₃×#6891	C₃	semidirect
9. C₃×C₁₃×3₋¹⁺²	C₃²	semidirect
12. C₃²×C₉×C₁₃	C₃²	semidirect
13. C₁₃×C₃²⋊C₉	C₃²	semidirect
14. #10624881	C₁₃	direct (N × H)
27. C₃²×3₋¹⁺²	C₃×C₁₃	semidirect
29. #6893	C₃×C₁₃	semidirect
30. #6891	C₃×C₁₃	semidirect
45. C₃×3₋¹⁺²	C₃²×C₁₃	semidirect
48. C₃²×C₉	C₃²×C₁₃	semidirect
49. C₃²⋊C₉	C₃²×C₁₃	semidirect
67. C₁₃	#10624881	direct (N × H)

Subgroups — C13×#10624881 #23745032

Conjugacy classes of subgroups

Complements

Subgroups — C₁₃×#10624881 #23745032