Subgroups — C₁₃×#10624912 #23745063

Order 9477.

596 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#6900	C₃	1	9	yes	maximal, complemented
2	C₁₃×#6898	C₃	1	9	yes	maximal, complemented
3	C₁₃×#6897	C₃	1	18	yes	maximal, complemented
4	C₁₃×#6891	C₃	1	4	yes	maximal
5	C₃⁴×C₁₃	C₃²	1	1	yes	characteristic
6	C₃×C₁₃×3₋¹⁺²	C₃²	1	12	yes	—
7	C₁₃×C₉⋊C₉	C₃²	1	72	yes	complemented
8	C₁₃×C₃²⋊C₉	C₃²	1	24	yes	—
9	C₁₃×C₃²⋊C₉	C₃²	1	12	yes	—
10	C₉²×C₁₃	C₃²	1	9	yes	complemented
11	#10624912	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
12	C₃³×C₁₃	—	9	4	no	—
13	C₃³×C₁₃	C₃³	1	2	yes	—
14	C₃³×C₁₃	C₃³	1	1	yes	characteristic
15	C₃³×C₁₃	C₃³	1	1	yes	characteristic
16	C₁₃×3₋¹⁺²	—	9	12	no	—
17	C₃×C₉×C₁₃	C₃³	1	36	yes	—
18	#6900	C₃×C₁₃	1	9	yes	complemented
19	#6898	C₃×C₁₃	1	9	yes	complemented
20	#6897	C₃×C₁₃	1	18	yes	complemented
21	#6891	C₃×C₁₃	1	4	yes	—
22	C₃²×C₁₃	—	3	4	no	—
23	C₃²×C₁₃	—	3	8	no	—
24	C₃²×C₁₃	—	3	4	no	—
25	C₃²×C₁₃	—	9	9	no	—
26	C₃²×C₁₃	C₃⁴	1	1	yes	characteristic
27	C₉×C₁₃	—	3	36	no	—
28	C₃⁴	C₃²×C₁₃	1	1	yes	characteristic
29	C₃×3₋¹⁺²	C₃²×C₁₃	1	12	yes	—
30	C₉⋊C₉	C₃²×C₁₃	1	72	yes	complemented
31	C₃²⋊C₉	C₃²×C₁₃	1	24	yes	—
32	C₃²⋊C₉	C₃²×C₁₃	1	12	yes	—
33	C₉²	C₃²×C₁₃	1	9	yes	complemented
34	C₃×C₁₃	—	9	1	no	—
35	C₃×C₁₃	—	9	2	no	—
36	C₃×C₁₃	—	9	1	no	—
37	C₃×C₁₃	3₋¹⁺⁴	1	4	yes	—
38	C₃³	—	9	4	no	—
39	C₃³	C₃³×C₁₃	1	2	yes	—
40	C₃³	C₃³×C₁₃	1	1	yes	characteristic
41	C₃³	C₃³×C₁₃	1	1	yes	characteristic
42	3₋¹⁺²	—	9	12	no	—
43	C₃×C₉	C₃³×C₁₃	1	36	yes	—
44	C₁₃	#10624912	1	1	yes	characteristic, direct product factor, Sylow
45	C₃²	—	3	4	no	—
46	C₃²	—	3	8	no	—
47	C₃²	—	3	4	no	—
48	C₃²	—	9	9	no	—
49	C₃²	C₃⁴×C₁₃	1	1	yes	characteristic
50	C₉	—	3	36	no	—
51	C₃	—	9	1	no	—
52	C₃	—	9	2	no	—
53	C₃	—	9	1	no	—
54	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×#6900	C₃	semidirect
2. C₁₃×#6898	C₃	semidirect
3. C₁₃×#6897	C₃	semidirect
7. C₁₃×C₉⋊C₉	C₃²	semidirect
10. C₉²×C₁₃	C₃²	semidirect
11. #10624912	C₁₃	direct (N × H)
18. #6900	C₃×C₁₃	semidirect
19. #6898	C₃×C₁₃	semidirect
20. #6897	C₃×C₁₃	semidirect
30. C₉⋊C₉	C₃²×C₁₃	semidirect
33. C₉²	C₃²×C₁₃	semidirect
44. C₁₃	#10624912	direct (N × H)

Subgroups — C13×#10624912 #23745063

Conjugacy classes of subgroups

Complements

Subgroups — C₁₃×#10624912 #23745063