Subgroups — C₁₃×#10624886 #23745037

Order 9477.

728 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×#6895	C₃	1	9	yes	maximal, complemented
3	C₁₃×#6894	C₃	1	27	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	—	3	9	no	—
7	C₃×C₁₃×3₋¹⁺²	C₃²	1	9	yes	—
8	C₃²×C₉×C₁₃	C₃²	1	3	yes	—
9	C₃²×C₉×C₁₃	C₃²	1	9	yes	—
10	C₁₃×C₉⋊C₉	C₃²	1	81	yes	complemented
11	C₁₃×C₃²⋊C₉	C₃²	1	18	yes	—
12	C₁₃×C₃²⋊C₉	C₃²	1	9	yes	—
13	#10624886	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
14	C₃³×C₁₃	—	9	3	no	—
15	C₃³×C₁₃	3₋¹⁺²	1	9	yes	—
16	C₃³×C₁₃	C₃³	1	1	yes	characteristic
17	C₃³×C₁₃	C₃³	1	3	yes	—
18	C₁₃×3₋¹⁺²	—	3	27	no	—
19	C₃×C₉×C₁₃	—	3	9	no	—
20	C₃×C₉×C₁₃	—	9	9	no	—
21	C₃×C₉×C₁₃	C₃³	1	27	yes	—
22	C₃×C₉×C₁₃	C₃³	1	9	yes	—
23	C₃²×3₋¹⁺²	C₃×C₁₃	1	1	yes	characteristic
24	#6895	C₃×C₁₃	1	9	yes	complemented
25	#6894	C₃×C₁₃	1	27	yes	complemented
26	C₃×C₃²⋊C₉	C₃×C₁₃	1	3	yes	—
27	C₃²×C₁₃	—	3	3	no	—
28	C₃²×C₁₃	—	3	3	no	—
29	C₃²×C₁₃	—	3	6	no	—
30	C₃²×C₁₃	—	9	9	no	—
31	C₃²×C₁₃	C₃×3₋¹⁺²	1	3	yes	—
32	C₃²×C₁₃	C₃×3₋¹⁺²	1	9	yes	—
33	C₃²×C₁₃	C₃⁴	1	1	yes	characteristic
34	C₉×C₁₃	—	3	9	no	—
35	C₉×C₁₃	—	3	27	no	—
36	C₃⁴	C₃²×C₁₃	1	1	yes	characteristic
37	C₃×3₋¹⁺²	—	3	9	no	—
38	C₃×3₋¹⁺²	C₃²×C₁₃	1	9	yes	—
39	C₃²×C₉	C₃²×C₁₃	1	3	yes	—
40	C₃²×C₉	C₃²×C₁₃	1	9	yes	—
41	C₉⋊C₉	C₃²×C₁₃	1	81	yes	complemented
42	C₃²⋊C₉	C₃²×C₁₃	1	18	yes	—
43	C₃²⋊C₉	C₃²×C₁₃	1	9	yes	—
44	C₃×C₁₃	—	3	9	no	—
45	C₃×C₁₃	—	3	3	no	—
46	C₃×C₁₃	C₃²×3₋¹⁺²	1	1	yes	characteristic
47	C₃×C₁₃	3₋¹⁺⁴	1	3	yes	—
48	C₃³	—	9	3	no	—
49	C₃³	C₁₃×3₋¹⁺²	1	9	yes	—
50	C₃³	C₃³×C₁₃	1	1	yes	characteristic
51	C₃³	C₃³×C₁₃	1	3	yes	—
52	3₋¹⁺²	—	3	27	no	—
53	C₃×C₉	—	3	9	no	—
54	C₃×C₉	—	9	9	no	—
55	C₃×C₉	C₃³×C₁₃	1	27	yes	—
56	C₃×C₉	C₃³×C₁₃	1	9	yes	—
57	C₁₃	#10624886	1	1	yes	characteristic, direct product factor, Sylow
58	C₃²	—	3	3	no	—
59	C₃²	—	3	3	no	—
60	C₃²	—	3	6	no	—
61	C₃²	—	9	9	no	—
62	C₃²	C₃×C₁₃×3₋¹⁺²	1	3	yes	—
63	C₃²	C₃×C₁₃×3₋¹⁺²	1	9	yes	—
64	C₃²	C₃⁴×C₁₃	1	1	yes	characteristic
65	C₉	—	3	9	no	—
66	C₉	—	3	27	no	—
67	C₃	—	3	9	no	—
68	C₃	—	3	3	no	—
69	C₃	C₃²×C₁₃×3₋¹⁺²	1	1	yes	characteristic
70	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×#6895	C₃	semidirect
3. C₁₃×#6894	C₃	semidirect
10. C₁₃×C₉⋊C₉	C₃²	semidirect
13. #10624886	C₁₃	direct (N × H)
24. #6895	C₃×C₁₃	semidirect
25. #6894	C₃×C₁₃	semidirect
41. C₉⋊C₉	C₃²×C₁₃	semidirect
57. C₁₃	#10624886	direct (N × H)

Subgroups — C13×#10624886 #23745037

Conjugacy classes of subgroups

Complements

Subgroups — C₁₃×#10624886 #23745037