Subgroups — C₁₃×#10624550 #23744701

Order 9477.

374 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₃×C₉⋊C₉	C₃	1	6	yes	maximal
2	C₃×C₉²×C₁₃	C₃	1	1	yes	maximal, characteristic
3	C₁₃×#6855	C₃	1	6	yes	maximal
4	C₃²×C₉×C₁₃	C₃²	1	9	yes	—
5	C₃²×C₉×C₁₃	C₃²	1	2	yes	—
6	C₃²×C₉×C₁₃	C₃²	1	2	yes	—
7	C₁₃×C₉⋊C₉	—	3	18	no	—
8	C₉²×C₁₃	C₉	1	9	yes	complemented
9	#10624550	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
10	C₃³×C₁₃	C₃³	1	1	yes	characteristic
11	C₃×C₉×C₁₃	—	3	6	no	—
12	C₃×C₉×C₁₃	—	3	18	no	—
13	C₃×C₉×C₁₃	—	3	18	no	—
14	C₃×C₉×C₁₃	C₃×C₉	1	6	yes	—
15	C₃×C₉×C₁₃	C₃×C₉	1	6	yes	—
16	C₃×C₉×C₁₃	3₋¹⁺²	1	18	yes	—
17	C₃×C₉⋊C₉	C₃×C₁₃	1	6	yes	—
18	C₃×C₉²	C₃×C₁₃	1	1	yes	characteristic
19	#6855	C₃×C₁₃	1	6	yes	—
20	C₃²×C₁₃	C₃²×C₉	1	1	yes	characteristic
21	C₃²×C₁₃	C₃×3₋¹⁺²	1	6	yes	—
22	C₃²×C₁₃	#737	1	6	yes	—
23	C₉×C₁₃	—	3	6	no	—
24	C₉×C₁₃	—	9	9	no	—
25	C₉×C₁₃	C₉⋊C₉	1	18	yes	complemented
26	C₃²×C₉	C₃²×C₁₃	1	9	yes	—
27	C₃²×C₉	C₃²×C₁₃	1	2	yes	—
28	C₃²×C₉	C₃²×C₁₃	1	2	yes	—
29	C₉⋊C₉	—	3	18	no	—
30	C₉²	C₉×C₁₃	1	9	yes	complemented
31	C₃×C₁₃	C₃×C₉⋊C₉	1	2	yes	—
32	C₃×C₁₃	#6887	1	2	yes	—
33	C₃×C₁₃	#6896	1	9	yes	—
34	C₃³	C₃³×C₁₃	1	1	yes	characteristic
35	C₃×C₉	—	3	6	no	—
36	C₃×C₉	—	3	18	no	—
37	C₃×C₉	—	3	18	no	—
38	C₃×C₉	C₃×C₉×C₁₃	1	6	yes	—
39	C₃×C₉	C₃×C₉×C₁₃	1	6	yes	—
40	C₃×C₉	C₁₃×3₋¹⁺²	1	18	yes	—
41	C₁₃	#10624550	1	1	yes	characteristic, direct product factor, Sylow
42	C₃²	C₃²×C₉×C₁₃	1	1	yes	characteristic
43	C₃²	C₃×C₁₃×3₋¹⁺²	1	6	yes	—
44	C₃²	C₁₃×#737	1	6	yes	—
45	C₉	—	3	6	no	—
46	C₉	—	9	9	no	—
47	C₉	C₁₃×C₉⋊C₉	1	18	yes	complemented
48	C₃	C₃×C₁₃×C₉⋊C₉	1	2	yes	—
49	C₃	C₁₃×#6887	1	2	yes	—
50	C₃	C₁₃×#6896	1	9	yes	—

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

Complements

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

N	H ≅ G/N	type
8. C₉²×C₁₃	C₉	semidirect
9. #10624550	C₁₃	direct (N × H)
25. C₉×C₁₃	C₉⋊C₉	semidirect
30. C₉²	C₉×C₁₃	semidirect
41. C₁₃	#10624550	direct (N × H)
47. C₉	C₁₃×C₉⋊C₉	semidirect

Subgroups — C13×#10624550 #23744701

Conjugacy classes of subgroups

Complements

Subgroups — C₁₃×#10624550 #23744701