Subgroups — C₁₃×#10624863 #23745014

Order 9477.

944 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	C₉×C₁₃×3₋¹⁺²	C₃	1	27	yes	maximal, complemented
3	C₁₃×#6887	C₃	1	9	yes	maximal, complemented
4	C₃×C₁₃×C₃²⋊C₉	C₃	1	3	yes	maximal
5	C₃⁴×C₁₃	C₃²	1	1	yes	characteristic
6	C₃×C₁₃×3₋¹⁺²	C₉	1	27	yes	complemented
7	C₃×C₁₃×3₋¹⁺²	C₃²	1	9	yes	—
8	C₃²×C₉×C₁₃	C₃²	1	9	yes	—
9	C₃²×C₉×C₁₃	C₃²	1	3	yes	—
10	C₁₃×C₉⋊C₉	C₃²	1	54	yes	complemented
11	C₁₃×C₃²⋊C₉	C₃²	1	9	yes	—
12	C₁₃×C₃²⋊C₉	C₃²	1	18	yes	—
13	C₉²×C₁₃	C₃²	1	27	yes	complemented
14	#10624863	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
15	C₃³×C₁₃	—	9	3	no	—
16	C₃³×C₁₃	C₃×C₉	1	9	yes	—
17	C₃³×C₁₃	C₃³	1	1	yes	characteristic
18	C₃³×C₁₃	C₃³	1	3	yes	—
19	C₁₃×3₋¹⁺²	C₃×C₉	1	81	yes	complemented
20	C₃×C₉×C₁₃	—	9	9	no	—
21	C₃×C₉×C₁₃	C₃×C₉	1	27	yes	complemented
22	C₃×C₉×C₁₃	C₃³	1	27	yes	—
23	C₃×C₉×C₁₃	C₃³	1	9	yes	—
24	C₃²×3₋¹⁺²	C₃×C₁₃	1	1	yes	characteristic
25	C₉×3₋¹⁺²	C₃×C₁₃	1	27	yes	complemented
26	#6887	C₃×C₁₃	1	9	yes	complemented
27	C₃×C₃²⋊C₉	C₃×C₁₃	1	3	yes	—
28	C₃²×C₁₃	—	3	3	no	—
29	C₃²×C₁₃	—	3	3	no	—
30	C₃²×C₁₃	—	3	6	no	—
31	C₃²×C₁₃	—	9	9	no	—
32	C₃²×C₁₃	C₃²×C₉	1	3	yes	—
33	C₃²×C₁₃	C₃²×C₉	1	9	yes	—
34	C₃²×C₁₃	C₃⁴	1	1	yes	characteristic
35	C₉×C₁₃	—	3	27	no	—
36	C₉×C₁₃	C₃²×C₉	1	27	yes	—
37	C₃⁴	C₃²×C₁₃	1	1	yes	characteristic
38	C₃×3₋¹⁺²	C₉×C₁₃	1	27	yes	complemented
39	C₃×3₋¹⁺²	C₃²×C₁₃	1	9	yes	—
40	C₃²×C₉	C₃²×C₁₃	1	9	yes	—
41	C₃²×C₉	C₃²×C₁₃	1	3	yes	—
42	C₉⋊C₉	C₃²×C₁₃	1	54	yes	complemented
43	C₃²⋊C₉	C₃²×C₁₃	1	9	yes	—
44	C₃²⋊C₉	C₃²×C₁₃	1	18	yes	—
45	C₉²	C₃²×C₁₃	1	27	yes	complemented
46	C₃×C₁₃	—	3	9	no	—
47	C₃×C₁₃	—	3	3	no	—
48	C₃×C₁₃	C₃³×C₉	1	1	yes	characteristic
49	C₃×C₁₃	3₋¹⁺⁴	1	3	yes	—
50	C₃³	—	9	3	no	—
51	C₃³	C₃×C₉×C₁₃	1	9	yes	—
52	C₃³	C₃³×C₁₃	1	1	yes	characteristic
53	C₃³	C₃³×C₁₃	1	3	yes	—
54	3₋¹⁺²	C₃×C₉×C₁₃	1	81	yes	complemented
55	C₃×C₉	—	9	9	no	—
56	C₃×C₉	C₃×C₉×C₁₃	1	27	yes	complemented
57	C₃×C₉	C₃³×C₁₃	1	27	yes	—
58	C₃×C₉	C₃³×C₁₃	1	9	yes	—
59	C₁₃	#10624863	1	1	yes	characteristic, direct product factor, Sylow
60	C₃²	—	3	3	no	—
61	C₃²	—	3	3	no	—
62	C₃²	—	3	6	no	—
63	C₃²	—	9	9	no	—
64	C₃²	C₃²×C₉×C₁₃	1	3	yes	—
65	C₃²	C₃²×C₉×C₁₃	1	9	yes	—
66	C₃²	C₃⁴×C₁₃	1	1	yes	characteristic
67	C₉	—	3	27	no	—
68	C₉	C₃²×C₉×C₁₃	1	27	yes	—
69	C₃	—	3	9	no	—
70	C₃	—	3	3	no	—
71	C₃	C₃³×C₉×C₁₃	1	1	yes	characteristic
72	C₃	C₁₃×3₋¹⁺⁴	1	3	yes	—

	subgroup	G/H
center, socle	C₃²×C₁₃	C₃⁴
commutator	C₃	C₃³×C₉×C₁₃
Frattini, cosocle	C₃²	C₃⁴×C₁₃
prime radical	C₃⁴×C₁₃	C₃²
LCS	G ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₉×C₁₃×3₋¹⁺²	C₃	semidirect
3. C₁₃×#6887	C₃	semidirect
6. C₃×C₁₃×3₋¹⁺²	C₉	semidirect
10. C₁₃×C₉⋊C₉	C₃²	semidirect
13. C₉²×C₁₃	C₃²	semidirect
14. #10624863	C₁₃	direct (N × H)
19. C₁₃×3₋¹⁺²	C₃×C₉	semidirect
21. C₃×C₉×C₁₃	C₃×C₉	semidirect
25. C₉×3₋¹⁺²	C₃×C₁₃	semidirect
26. #6887	C₃×C₁₃	semidirect
38. C₃×3₋¹⁺²	C₉×C₁₃	semidirect
42. C₉⋊C₉	C₃²×C₁₃	semidirect
45. C₉²	C₃²×C₁₃	semidirect
54. 3₋¹⁺²	C₃×C₉×C₁₃	semidirect
56. C₃×C₉	C₃×C₉×C₁₃	semidirect
59. C₁₃	#10624863	direct (N × H)

Subgroups — C13×#10624863 #23745014

Conjugacy classes of subgroups

Complements

Subgroups — C₁₃×#10624863 #23745014