Subgroups — C₁₃×#10624885 #23745036

Order 9477.

716 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₁₃×3₋¹⁺²	C₃	1	1	yes	maximal, characteristic
2	C₁₃×#6896	C₃	1	27	yes	maximal, complemented
3	C₁₃×#6895	C₃	1	6	yes	maximal, complemented
4	C₁₃×#6891	C₃	1	3	yes	maximal
5	C₁₃×#6887	C₃	1	3	yes	maximal, complemented
6	C₃⁴×C₁₃	C₃²	1	1	yes	characteristic
7	C₃×C₁₃×3₋¹⁺²	—	3	9	no	—
8	C₃×C₁₃×3₋¹⁺²	C₃²	1	9	yes	—
9	C₃×C₁₃×3₋¹⁺²	C₃²	1	9	yes	—
10	C₃²×C₉×C₁₃	C₃²	1	2	yes	—
11	C₃²×C₉×C₁₃	C₃²	1	1	yes	characteristic
12	C₁₃×C₉⋊C₉	C₃²	1	18	yes	complemented
13	C₁₃×C₉⋊C₉	C₃²	1	54	yes	complemented
14	C₁₃×C₃²⋊C₉	C₃²	1	9	yes	—
15	C₁₃×C₃²⋊C₉	C₃²	1	18	yes	—
16	C₉²×C₁₃	C₃²	1	9	yes	complemented
17	#10624885	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
18	C₃³×C₁₃	—	3	3	no	—
19	C₃³×C₁₃	—	9	3	no	—
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	—	9	9	no	—
24	C₃×C₉×C₁₃	—	3	6	no	—
25	C₃×C₉×C₁₃	3₋¹⁺²	1	9	yes	complemented
26	C₃×C₉×C₁₃	C₃³	1	27	yes	—
27	C₃×C₉×C₁₃	C₃³	1	6	yes	—
28	C₃×C₉×C₁₃	C₃³	1	3	yes	—
29	C₃²×3₋¹⁺²	C₃×C₁₃	1	1	yes	characteristic
30	#6896	C₃×C₁₃	1	27	yes	complemented
31	#6895	C₃×C₁₃	1	6	yes	complemented
32	#6891	C₃×C₁₃	1	3	yes	—
33	#6887	C₃×C₁₃	1	3	yes	complemented
34	C₃²×C₁₃	—	3	3	no	—
35	C₃²×C₁₃	—	3	3	no	—
36	C₃²×C₁₃	—	3	3	no	—
37	C₃²×C₁₃	—	3	6	no	—
38	C₃²×C₁₃	—	9	9	no	—
39	C₃²×C₁₃	C₃×3₋¹⁺²	1	3	yes	—
40	C₃²×C₁₃	C₃⁴	1	1	yes	characteristic
41	C₉×C₁₃	—	3	6	no	—
42	C₉×C₁₃	—	3	27	no	—
43	C₉×C₁₃	C₃×3₋¹⁺²	1	9	yes	—
44	C₃⁴	C₃²×C₁₃	1	1	yes	characteristic
45	C₃×3₋¹⁺²	—	3	9	no	—
46	C₃×3₋¹⁺²	C₃²×C₁₃	1	9	yes	—
47	C₃×3₋¹⁺²	C₃²×C₁₃	1	9	yes	—
48	C₃²×C₉	C₃²×C₁₃	1	2	yes	—
49	C₃²×C₉	C₃²×C₁₃	1	1	yes	characteristic
50	C₉⋊C₉	C₃²×C₁₃	1	18	yes	complemented
51	C₉⋊C₉	C₃²×C₁₃	1	54	yes	complemented
52	C₃²⋊C₉	C₃²×C₁₃	1	9	yes	—
53	C₃²⋊C₉	C₃²×C₁₃	1	18	yes	—
54	C₉²	C₃²×C₁₃	1	9	yes	complemented
55	C₃×C₁₃	—	3	3	no	—
56	C₃×C₁₃	—	9	3	no	—
57	C₃×C₁₃	C₃²×3₋¹⁺²	1	1	yes	characteristic
58	C₃×C₁₃	3₋¹⁺⁴	1	3	yes	—
59	C₃³	—	3	3	no	—
60	C₃³	—	9	3	no	—
61	C₃³	C₃³×C₁₃	1	3	yes	—
62	C₃³	C₃³×C₁₃	1	1	yes	characteristic
63	3₋¹⁺²	—	3	27	no	—
64	3₋¹⁺²	—	9	9	no	—
65	C₃×C₉	—	3	6	no	—
66	C₃×C₉	C₁₃×3₋¹⁺²	1	9	yes	complemented
67	C₃×C₉	C₃³×C₁₃	1	27	yes	—
68	C₃×C₉	C₃³×C₁₃	1	6	yes	—
69	C₃×C₉	C₃³×C₁₃	1	3	yes	—
70	C₁₃	#10624885	1	1	yes	characteristic, direct product factor, Sylow
71	C₃²	—	3	3	no	—
72	C₃²	—	3	3	no	—
73	C₃²	—	3	3	no	—
74	C₃²	—	3	6	no	—
75	C₃²	—	9	9	no	—
76	C₃²	C₃×C₁₃×3₋¹⁺²	1	3	yes	—
77	C₃²	C₃⁴×C₁₃	1	1	yes	characteristic
78	C₉	—	3	6	no	—
79	C₉	—	3	27	no	—
80	C₉	C₃×C₁₃×3₋¹⁺²	1	9	yes	—
81	C₃	—	3	3	no	—
82	C₃	—	9	3	no	—
83	C₃	C₃²×C₁₃×3₋¹⁺²	1	1	yes	characteristic
84	C₃	C₁₃×3₋¹⁺⁴	1	3	yes	—

	subgroup	G/H
center, socle	C₃²×C₁₃	C₃⁴
commutator, Frattini, cosocle	C₃²	C₃⁴×C₁₃
prime radical	C₃⁴×C₁₃	C₃²
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×#6896	C₃	semidirect
3. C₁₃×#6895	C₃	semidirect
5. C₁₃×#6887	C₃	semidirect
12. C₁₃×C₉⋊C₉	C₃²	semidirect
13. C₁₃×C₉⋊C₉	C₃²	semidirect
16. C₉²×C₁₃	C₃²	semidirect
17. #10624885	C₁₃	direct (N × H)
25. C₃×C₉×C₁₃	3₋¹⁺²	semidirect
30. #6896	C₃×C₁₃	semidirect
31. #6895	C₃×C₁₃	semidirect
33. #6887	C₃×C₁₃	semidirect
50. C₉⋊C₉	C₃²×C₁₃	semidirect
51. C₉⋊C₉	C₃²×C₁₃	semidirect
54. C₉²	C₃²×C₁₃	semidirect
66. C₃×C₉	C₁₃×3₋¹⁺²	semidirect
70. C₁₃	#10624885	direct (N × H)

Subgroups — C13×#10624885 #23745036

Conjugacy classes of subgroups

Complements

Subgroups — C₁₃×#10624885 #23745036