Subgroups — C₁₃×#10624911 #23745062

Order 9477.

596 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#6899	C₃	1	18	yes	maximal, complemented
2	C₁₃×#6897	C₃	1	9	yes	maximal, complemented
3	C₁₃×#6896	C₃	1	9	yes	maximal, complemented
4	C₁₃×#6891	C₃	1	2	yes	maximal
5	C₁₃×#6891	C₃	1	2	yes	maximal
6	C₃⁴×C₁₃	C₃²	1	1	yes	characteristic
7	C₃×C₁₃×3₋¹⁺²	C₃²	1	6	yes	—
8	C₃×C₁₃×3₋¹⁺²	C₃²	1	6	yes	—
9	C₁₃×C₉⋊C₉	C₃²	1	72	yes	complemented
10	C₁₃×C₃²⋊C₉	C₃²	1	6	yes	—
11	C₁₃×C₃²⋊C₉	C₃²	1	6	yes	—
12	C₁₃×C₃²⋊C₉	C₃²	1	6	yes	—
13	C₁₃×C₃²⋊C₉	C₃²	1	6	yes	—
14	C₁₃×C₃²⋊C₉	C₃²	1	12	yes	—
15	C₉²×C₁₃	C₃²	1	9	yes	complemented
16	#10624911	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
17	C₃³×C₁₃	—	9	2	no	—
18	C₃³×C₁₃	—	9	2	no	—
19	C₃³×C₁₃	C₃³	1	1	yes	characteristic
20	C₃³×C₁₃	C₃³	1	2	yes	—
21	C₃³×C₁₃	C₃³	1	1	yes	characteristic
22	C₁₃×3₋¹⁺²	—	9	6	no	—
23	C₁₃×3₋¹⁺²	—	9	6	no	—
24	C₃×C₉×C₁₃	C₃³	1	18	yes	—
25	C₃×C₉×C₁₃	C₃³	1	18	yes	—
26	#6899	C₃×C₁₃	1	18	yes	complemented
27	#6897	C₃×C₁₃	1	9	yes	complemented
28	#6896	C₃×C₁₃	1	9	yes	complemented
29	#6891	C₃×C₁₃	1	2	yes	—
30	#6891	C₃×C₁₃	1	2	yes	—
31	C₃²×C₁₃	—	3	2	no	—
32	C₃²×C₁₃	—	3	2	no	—
33	C₃²×C₁₃	—	3	2	no	—
34	C₃²×C₁₃	—	3	2	no	—
35	C₃²×C₁₃	—	3	2	no	—
36	C₃²×C₁₃	—	3	4	no	—
37	C₃²×C₁₃	—	3	2	no	—
38	C₃²×C₁₃	—	9	9	no	—
39	C₃²×C₁₃	C₃⁴	1	1	yes	characteristic
40	C₉×C₁₃	—	3	18	no	—
41	C₉×C₁₃	—	3	18	no	—
42	C₃⁴	C₃²×C₁₃	1	1	yes	characteristic
43	C₃×3₋¹⁺²	C₃²×C₁₃	1	6	yes	—
44	C₃×3₋¹⁺²	C₃²×C₁₃	1	6	yes	—
45	C₉⋊C₉	C₃²×C₁₃	1	72	yes	complemented
46	C₃²⋊C₉	C₃²×C₁₃	1	6	yes	—
47	C₃²⋊C₉	C₃²×C₁₃	1	6	yes	—
48	C₃²⋊C₉	C₃²×C₁₃	1	6	yes	—
49	C₃²⋊C₉	C₃²×C₁₃	1	6	yes	—
50	C₃²⋊C₉	C₃²×C₁₃	1	12	yes	—
51	C₉²	C₃²×C₁₃	1	9	yes	complemented
52	C₃×C₁₃	—	9	1	no	—
53	C₃×C₁₃	—	9	2	no	—
54	C₃×C₁₃	—	9	1	no	—
55	C₃×C₁₃	3₋¹⁺⁴	1	2	yes	—
56	C₃×C₁₃	3₋¹⁺⁴	1	2	yes	—
57	C₃³	—	9	2	no	—
58	C₃³	—	9	2	no	—
59	C₃³	C₃³×C₁₃	1	1	yes	characteristic
60	C₃³	C₃³×C₁₃	1	2	yes	—
61	C₃³	C₃³×C₁₃	1	1	yes	characteristic
62	3₋¹⁺²	—	9	6	no	—
63	3₋¹⁺²	—	9	6	no	—
64	C₃×C₉	C₃³×C₁₃	1	18	yes	—
65	C₃×C₉	C₃³×C₁₃	1	18	yes	—
66	C₁₃	#10624911	1	1	yes	characteristic, direct product factor, Sylow
67	C₃²	—	3	2	no	—
68	C₃²	—	3	2	no	—
69	C₃²	—	3	2	no	—
70	C₃²	—	3	2	no	—
71	C₃²	—	3	2	no	—
72	C₃²	—	3	4	no	—
73	C₃²	—	3	2	no	—
74	C₃²	—	9	9	no	—
75	C₃²	C₃⁴×C₁₃	1	1	yes	characteristic
76	C₉	—	3	18	no	—
77	C₉	—	3	18	no	—
78	C₃	—	9	1	no	—
79	C₃	—	9	2	no	—
80	C₃	—	9	1	no	—
81	C₃	C₁₃×3₋¹⁺⁴	1	2	yes	—
82	C₃	C₁₃×3₋¹⁺⁴	1	2	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
1. C₁₃×#6899	C₃	semidirect
2. C₁₃×#6897	C₃	semidirect
3. C₁₃×#6896	C₃	semidirect
9. C₁₃×C₉⋊C₉	C₃²	semidirect
15. C₉²×C₁₃	C₃²	semidirect
16. #10624911	C₁₃	direct (N × H)
26. #6899	C₃×C₁₃	semidirect
27. #6897	C₃×C₁₃	semidirect
28. #6896	C₃×C₁₃	semidirect
45. C₉⋊C₉	C₃²×C₁₃	semidirect
51. C₉²	C₃²×C₁₃	semidirect
66. C₁₃	#10624911	direct (N × H)

Subgroups — C13×#10624911 #23745062

Conjugacy classes of subgroups

Complements

Subgroups — C₁₃×#10624911 #23745062