Subgroups — C₁₃×#10624575 #23744726

Order 9477.

296 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₃×C₉⋊C₉	C₃	1	3	yes	maximal
2	C₃×C₁₃×C₉⋊C₉	C₃	1	1	yes	maximal, characteristic
3	C₁₃×#6855	C₃	1	3	yes	maximal
4	C₁₃×#6855	C₃	1	3	yes	maximal
5	C₁₃×#6855	C₃	1	3	yes	maximal
6	C₃²×C₉×C₁₃	C₃²	1	3	yes	—
7	C₃²×C₉×C₁₃	C₃²	1	3	yes	—
8	C₃²×C₉×C₁₃	C₃²	1	3	yes	—
9	C₃²×C₉×C₁₃	C₃²	1	1	yes	characteristic
10	C₃²×C₉×C₁₃	C₃²	1	3	yes	—
11	C₁₃×C₉⋊C₉	—	3	9	no	—
12	C₁₃×C₉⋊C₉	—	3	3	no	—
13	#10624575	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
14	C₃³×C₁₃	C₃³	1	1	yes	characteristic
15	C₃×C₉×C₁₃	—	3	3	no	—
16	C₃×C₉×C₁₃	—	3	3	no	—
17	C₃×C₉×C₁₃	—	3	3	no	—
18	C₃×C₉×C₁₃	—	3	3	no	—
19	C₃×C₉×C₁₃	—	3	3	no	—
20	C₃×C₉×C₁₃	—	3	3	no	—
21	C₃×C₉×C₁₃	—	3	3	no	—
22	C₃×C₉×C₁₃	—	3	3	no	—
23	C₃×C₉×C₁₃	—	3	3	no	—
24	C₃×C₉×C₁₃	—	3	3	no	—
25	C₃×C₉×C₁₃	—	3	6	no	—
26	C₃×C₉×C₁₃	—	3	3	no	—
27	C₃×C₉×C₁₃	—	3	3	no	—
28	C₃×C₉×C₁₃	—	3	6	no	—
29	C₃×C₉×C₁₃	3₋¹⁺²	1	9	yes	—
30	C₃×C₉×C₁₃	3₋¹⁺²	1	3	yes	—
31	C₃×C₉⋊C₉	C₃×C₁₃	1	3	yes	—
32	C₃×C₉⋊C₉	C₃×C₁₃	1	1	yes	characteristic
33	#6855	C₃×C₁₃	1	3	yes	—
34	#6855	C₃×C₁₃	1	3	yes	—
35	#6855	C₃×C₁₃	1	3	yes	—
36	C₃²×C₁₃	C₃×3₋¹⁺²	1	3	yes	—
37	C₃²×C₁₃	C₃×3₋¹⁺²	1	1	yes	characteristic
38	C₃²×C₁₃	#737	1	3	yes	—
39	C₃²×C₁₃	#737	1	3	yes	—
40	C₃²×C₁₃	#737	1	3	yes	—
41	C₉×C₁₃	—	3	9	no	—
42	C₉×C₁₃	—	3	3	no	—
43	C₉×C₁₃	—	9	3	no	—
44	C₉×C₁₃	—	9	3	no	—
45	C₉×C₁₃	—	9	3	no	—
46	C₃²×C₉	C₃²×C₁₃	1	3	yes	—
47	C₃²×C₉	C₃²×C₁₃	1	3	yes	—
48	C₃²×C₉	C₃²×C₁₃	1	3	yes	—
49	C₃²×C₉	C₃²×C₁₃	1	1	yes	characteristic
50	C₃²×C₉	C₃²×C₁₃	1	3	yes	—
51	C₉⋊C₉	—	3	9	no	—
52	C₉⋊C₉	—	3	3	no	—
53	C₃×C₁₃	#6894	1	3	yes	—
54	C₃×C₁₃	#6895	1	1	yes	characteristic
55	C₃×C₁₃	#6896	1	3	yes	—
56	C₃×C₁₃	#6897	1	3	yes	—
57	C₃×C₁₃	#6899	1	3	yes	—
58	C₃³	C₃³×C₁₃	1	1	yes	characteristic
59	C₃×C₉	—	3	3	no	—
60	C₃×C₉	—	3	3	no	—
61	C₃×C₉	—	3	3	no	—
62	C₃×C₉	—	3	3	no	—
63	C₃×C₉	—	3	3	no	—
64	C₃×C₉	—	3	3	no	—
65	C₃×C₉	—	3	3	no	—
66	C₃×C₉	—	3	3	no	—
67	C₃×C₉	—	3	3	no	—
68	C₃×C₉	—	3	3	no	—
69	C₃×C₉	—	3	6	no	—
70	C₃×C₉	—	3	3	no	—
71	C₃×C₉	—	3	3	no	—
72	C₃×C₉	—	3	6	no	—
73	C₃×C₉	C₁₃×3₋¹⁺²	1	9	yes	—
74	C₃×C₉	C₁₃×3₋¹⁺²	1	3	yes	—
75	C₁₃	#10624575	1	1	yes	characteristic, direct product factor, Sylow
76	C₃²	C₃×C₁₃×3₋¹⁺²	1	3	yes	—
77	C₃²	C₃×C₁₃×3₋¹⁺²	1	1	yes	characteristic
78	C₃²	C₁₃×#737	1	3	yes	—
79	C₃²	C₁₃×#737	1	3	yes	—
80	C₃²	C₁₃×#737	1	3	yes	—
81	C₉	—	3	9	no	—
82	C₉	—	3	3	no	—
83	C₉	—	9	3	no	—
84	C₉	—	9	3	no	—
85	C₉	—	9	3	no	—
86	C₃	C₁₃×#6894	1	3	yes	—
87	C₃	C₁₃×#6895	1	1	yes	characteristic
88	C₃	C₁₃×#6896	1	3	yes	—
89	C₃	C₁₃×#6897	1	3	yes	—
90	C₃	C₁₃×#6899	1	3	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. #10624575	C₁₃	direct (N × H)
75. C₁₃	#10624575	direct (N × H)

Subgroups — C13×#10624575 #23744726

Conjugacy classes of subgroups

Complements

Subgroups — C₁₃×#10624575 #23744726