Subgroups — C₁₃×#10624913 #23745064

Order 9477.

596 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#6898	C₃	1	18	yes	maximal, complemented
2	C₁₃×#6896	C₃	1	18	yes	maximal, complemented
3	C₁₃×#6891	C₃	1	4	yes	maximal
4	C₃⁴×C₁₃	C₃²	1	1	yes	characteristic
5	C₃×C₁₃×3₋¹⁺²	C₃²	1	12	yes	—
6	C₁₃×C₉⋊C₉	C₃²	1	72	yes	complemented
7	C₁₃×C₃²⋊C₉	C₃²	1	12	yes	—
8	C₁₃×C₃²⋊C₉	C₃²	1	24	yes	—
9	C₉²×C₁₃	C₃²	1	9	yes	complemented
10	#10624913	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
11	C₃³×C₁₃	—	9	4	no	—
12	C₃³×C₁₃	C₃³	1	2	yes	—
13	C₃³×C₁₃	C₃³	1	2	yes	—
14	C₁₃×3₋¹⁺²	—	9	12	no	—
15	C₃×C₉×C₁₃	C₃³	1	36	yes	—
16	#6898	C₃×C₁₃	1	18	yes	complemented
17	#6896	C₃×C₁₃	1	18	yes	complemented
18	#6891	C₃×C₁₃	1	4	yes	—
19	C₃²×C₁₃	—	3	4	no	—
20	C₃²×C₁₃	—	3	8	no	—
21	C₃²×C₁₃	—	3	4	no	—
22	C₃²×C₁₃	—	9	9	no	—
23	C₃²×C₁₃	C₃⁴	1	1	yes	characteristic
24	C₉×C₁₃	—	3	36	no	—
25	C₃⁴	C₃²×C₁₃	1	1	yes	characteristic
26	C₃×3₋¹⁺²	C₃²×C₁₃	1	12	yes	—
27	C₉⋊C₉	C₃²×C₁₃	1	72	yes	complemented
28	C₃²⋊C₉	C₃²×C₁₃	1	12	yes	—
29	C₃²⋊C₉	C₃²×C₁₃	1	24	yes	—
30	C₉²	C₃²×C₁₃	1	9	yes	complemented
31	C₃×C₁₃	—	9	2	no	—
32	C₃×C₁₃	—	9	2	no	—
33	C₃×C₁₃	3₋¹⁺⁴	1	4	yes	—
34	C₃³	—	9	4	no	—
35	C₃³	C₃³×C₁₃	1	2	yes	—
36	C₃³	C₃³×C₁₃	1	2	yes	—
37	3₋¹⁺²	—	9	12	no	—
38	C₃×C₉	C₃³×C₁₃	1	36	yes	—
39	C₁₃	#10624913	1	1	yes	characteristic, direct product factor, Sylow
40	C₃²	—	3	4	no	—
41	C₃²	—	3	8	no	—
42	C₃²	—	3	4	no	—
43	C₃²	—	9	9	no	—
44	C₃²	C₃⁴×C₁₃	1	1	yes	characteristic
45	C₉	—	3	36	no	—
46	C₃	—	9	2	no	—
47	C₃	—	9	2	no	—
48	C₃	C₁₃×3₋¹⁺⁴	1	4	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×#6898	C₃	semidirect
2. C₁₃×#6896	C₃	semidirect
6. C₁₃×C₉⋊C₉	C₃²	semidirect
9. C₉²×C₁₃	C₃²	semidirect
10. #10624913	C₁₃	direct (N × H)
16. #6898	C₃×C₁₃	semidirect
17. #6896	C₃×C₁₃	semidirect
27. C₉⋊C₉	C₃²×C₁₃	semidirect
30. C₉²	C₃²×C₁₃	semidirect
39. C₁₃	#10624913	direct (N × H)

Subgroups — C13×#10624913 #23745064

Conjugacy classes of subgroups

Complements

Subgroups — C₁₃×#10624913 #23745064