Subgroups — C₁₃×#10624573 #23744724

Order 9477.

338 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₃×C₉⋊C₉	C₃	1	1	yes	maximal, characteristic
2	C₃×C₁₃×C₉⋊C₉	C₃	1	6	yes	maximal
3	C₁₃×#6855	C₃	1	3	yes	maximal
4	C₁₃×#6855	C₃	1	1	yes	maximal, characteristic
5	C₁₃×#6855	C₃	1	2	yes	maximal
6	C₃²×C₉×C₁₃	C₃²	1	1	yes	characteristic
7	C₃²×C₉×C₁₃	C₃²	1	3	yes	—
8	C₃²×C₉×C₁₃	C₃²	1	2	yes	—
9	C₃²×C₉×C₁₃	C₃²	1	1	yes	characteristic
10	C₃²×C₉×C₁₃	C₃²	1	6	yes	—
11	C₁₃×C₉⋊C₉	—	3	18	no	—
12	C₁₃×C₉⋊C₉	—	3	3	no	—
13	#10624573	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
14	C₃³×C₁₃	C₃³	1	1	yes	characteristic
15	C₃×C₉×C₁₃	—	3	6	no	—
16	C₃×C₉×C₁₃	—	3	6	no	—
17	C₃×C₉×C₁₃	—	3	6	no	—
18	C₃×C₉×C₁₃	—	3	2	no	—
19	C₃×C₉×C₁₃	—	3	1	no	—
20	C₃×C₉×C₁₃	—	3	6	no	—
21	C₃×C₉×C₁₃	—	3	1	no	—
22	C₃×C₉×C₁₃	—	3	6	no	—
23	C₃×C₉×C₁₃	—	3	2	no	—
24	C₃×C₉×C₁₃	—	3	3	no	—
25	C₃×C₉×C₁₃	—	3	3	no	—
26	C₃×C₉×C₁₃	—	3	3	no	—
27	C₃×C₉×C₁₃	3₋¹⁺²	1	18	yes	—
28	C₃×C₉×C₁₃	3₋¹⁺²	1	3	yes	—
29	C₃×C₉⋊C₉	C₃×C₁₃	1	1	yes	characteristic
30	C₃×C₉⋊C₉	C₃×C₁₃	1	6	yes	—
31	#6855	C₃×C₁₃	1	3	yes	—
32	#6855	C₃×C₁₃	1	1	yes	characteristic
33	#6855	C₃×C₁₃	1	2	yes	—
34	C₃²×C₁₃	C₃×3₋¹⁺²	1	6	yes	—
35	C₃²×C₁₃	C₃×3₋¹⁺²	1	1	yes	characteristic
36	C₃²×C₁₃	#737	1	2	yes	—
37	C₃²×C₁₃	#737	1	3	yes	—
38	C₃²×C₁₃	#737	1	1	yes	characteristic
39	C₉×C₁₃	—	3	18	no	—
40	C₉×C₁₃	—	3	3	no	—
41	C₉×C₁₃	—	9	3	no	—
42	C₉×C₁₃	—	9	1	no	—
43	C₉×C₁₃	—	9	2	no	—
44	C₃²×C₉	C₃²×C₁₃	1	1	yes	characteristic
45	C₃²×C₉	C₃²×C₁₃	1	3	yes	—
46	C₃²×C₉	C₃²×C₁₃	1	2	yes	—
47	C₃²×C₉	C₃²×C₁₃	1	1	yes	characteristic
48	C₃²×C₉	C₃²×C₁₃	1	6	yes	—
49	C₉⋊C₉	—	3	18	no	—
50	C₉⋊C₉	—	3	3	no	—
51	C₃×C₁₃	#6894	1	6	yes	—
52	C₃×C₁₃	#6895	1	1	yes	characteristic
53	C₃×C₁₃	#6896	1	3	yes	—
54	C₃×C₁₃	#6899	1	1	yes	characteristic
55	C₃×C₁₃	#6900	1	2	yes	—
56	C₃³	C₃³×C₁₃	1	1	yes	characteristic
57	C₃×C₉	—	3	6	no	—
58	C₃×C₉	—	3	6	no	—
59	C₃×C₉	—	3	6	no	—
60	C₃×C₉	—	3	2	no	—
61	C₃×C₉	—	3	1	no	—
62	C₃×C₉	—	3	6	no	—
63	C₃×C₉	—	3	1	no	—
64	C₃×C₉	—	3	6	no	—
65	C₃×C₉	—	3	2	no	—
66	C₃×C₉	—	3	3	no	—
67	C₃×C₉	—	3	3	no	—
68	C₃×C₉	—	3	3	no	—
69	C₃×C₉	C₁₃×3₋¹⁺²	1	18	yes	—
70	C₃×C₉	C₁₃×3₋¹⁺²	1	3	yes	—
71	C₁₃	#10624573	1	1	yes	characteristic, direct product factor, Sylow
72	C₃²	C₃×C₁₃×3₋¹⁺²	1	6	yes	—
73	C₃²	C₃×C₁₃×3₋¹⁺²	1	1	yes	characteristic
74	C₃²	C₁₃×#737	1	2	yes	—
75	C₃²	C₁₃×#737	1	3	yes	—
76	C₃²	C₁₃×#737	1	1	yes	characteristic
77	C₉	—	3	18	no	—
78	C₉	—	3	3	no	—
79	C₉	—	9	3	no	—
80	C₉	—	9	1	no	—
81	C₉	—	9	2	no	—
82	C₃	C₁₃×#6894	1	6	yes	—
83	C₃	C₁₃×#6895	1	1	yes	characteristic
84	C₃	C₁₃×#6896	1	3	yes	—
85	C₃	C₁₃×#6899	1	1	yes	characteristic
86	C₃	C₁₃×#6900	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
13. #10624573	C₁₃	direct (N × H)
71. C₁₃	#10624573	direct (N × H)

Subgroups — C13×#10624573 #23744724

Conjugacy classes of subgroups

Complements

Subgroups — C₁₃×#10624573 #23744724