Subgroups — C₁₃×#10624791 #23744942

Order 9477.

214 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₃×#733	C₃	1	1	yes	maximal, characteristic
2	C₁₃×#6894	C₃	1	3	yes	maximal
3	C₃×C₁₃×C₉⋊C₉	C₃	1	1	yes	maximal, characteristic
4	C₁₃×3₋¹⁺²⋊C₉	C₃	1	6	yes	maximal
5	C₁₃×#6868	C₃	1	2	yes	maximal
6	C₃×C₁₃×3₋¹⁺²	C₃²	1	3	yes	—
7	C₃²×C₉×C₁₃	C₃²	1	1	yes	characteristic
8	C₃²×C₉×C₁₃	C₃²	1	2	yes	—
9	C₃²×C₉×C₁₃	C₃²	1	1	yes	characteristic
10	C₁₃×#733	—	3	3	no	—
11	C₁₃×C₉⋊C₉	—	3	3	no	—
12	C₁₃×C₉⋊C₉	—	3	9	no	—
13	C₁₃×C₃²⋊C₉	C₃²	1	6	yes	—
14	#10624791	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
15	C₃³×C₁₃	C₃³	1	1	yes	characteristic
16	C₁₃×3₋¹⁺²	—	3	3	no	—
17	C₁₃×3₋¹⁺²	—	3	6	no	—
18	C₃×C₉×C₁₃	—	3	1	no	—
19	C₃×C₉×C₁₃	—	3	2	no	—
20	C₃×C₉×C₁₃	—	3	6	no	—
21	C₃×C₉×C₁₃	—	3	2	no	—
22	C₃×C₉×C₁₃	—	3	3	no	—
23	C₃×C₉×C₁₃	—	9	1	no	—
24	C₃×C₉×C₁₃	—	9	2	no	—
25	C₃×C₉×C₁₃	H(3,𝔽₃)	1	3	yes	—
26	C₃×C₉×C₁₃	3₋¹⁺²	1	3	yes	—
27	C₃×#733	C₃×C₁₃	1	1	yes	characteristic
28	#6894	C₃×C₁₃	1	3	yes	—
29	C₃×C₉⋊C₉	C₃×C₁₃	1	1	yes	characteristic
30	3₋¹⁺²⋊C₉	C₃×C₁₃	1	6	yes	—
31	#6868	C₃×C₁₃	1	2	yes	—
32	C₃²×C₁₃	—	3	1	no	—
33	C₃²×C₁₃	—	3	2	no	—
34	C₃²×C₁₃	C₃×H(3,𝔽₃)	1	1	yes	characteristic
35	C₃²×C₁₃	C₃×3₋¹⁺²	1	1	yes	characteristic
36	C₃²×C₁₃	#737	1	2	yes	—
37	C₉×C₁₃	—	3	3	no	—
38	C₉×C₁₃	—	3	3	no	—
39	C₉×C₁₃	—	9	6	no	—
40	C₉×C₁₃	—	9	2	no	—
41	C₉×C₁₃	—	9	3	no	—
42	C₃×3₋¹⁺²	C₃²×C₁₃	1	3	yes	—
43	C₃²×C₉	C₃²×C₁₃	1	1	yes	characteristic
44	C₃²×C₉	C₃²×C₁₃	1	2	yes	—
45	C₃²×C₉	C₃²×C₁₃	1	1	yes	characteristic
46	#733	—	3	3	no	—
47	C₉⋊C₉	—	3	3	no	—
48	C₉⋊C₉	—	3	9	no	—
49	C₃²⋊C₉	C₃²×C₁₃	1	6	yes	—
50	C₃×C₁₃	—	3	1	no	—
51	C₃×C₁₃	—	3	2	no	—
52	C₃×C₁₃	C₉⋊H(3,𝔽₃)	1	1	yes	characteristic
53	C₃×C₁₃	#6912	1	1	yes	characteristic
54	C₃×C₁₃	#6913	1	2	yes	—
55	C₃³	C₃³×C₁₃	1	1	yes	characteristic
56	3₋¹⁺²	—	3	3	no	—
57	3₋¹⁺²	—	3	6	no	—
58	C₃×C₉	—	3	1	no	—
59	C₃×C₉	—	3	2	no	—
60	C₃×C₉	—	3	6	no	—
61	C₃×C₉	—	3	2	no	—
62	C₃×C₉	—	3	3	no	—
63	C₃×C₉	—	9	1	no	—
64	C₃×C₉	—	9	2	no	—
65	C₃×C₉	C₁₃×H(3,𝔽₃)	1	3	yes	—
66	C₃×C₉	C₁₃×3₋¹⁺²	1	3	yes	—
67	C₁₃	#10624791	1	1	yes	characteristic, direct product factor, Sylow
68	C₃²	—	3	1	no	—
69	C₃²	—	3	2	no	—
70	C₃²	C₃×C₁₃×H(3,𝔽₃)	1	1	yes	characteristic
71	C₃²	C₃×C₁₃×3₋¹⁺²	1	1	yes	characteristic
72	C₃²	C₁₃×#737	1	2	yes	—
73	C₉	—	3	3	no	—
74	C₉	—	3	3	no	—
75	C₉	—	9	3	no	—
76	C₉	—	9	2	no	—
77	C₉	—	9	6	no	—
78	C₃	—	3	1	no	—
79	C₃	—	3	2	no	—
80	C₃	C₁₃×C₉⋊H(3,𝔽₃)	1	1	yes	characteristic
81	C₃	C₁₃×#6912	1	1	yes	characteristic
82	C₃	C₁₃×#6913	1	2	yes	—

	subgroup	G/H
center, socle	C₃²×C₁₃	C₃×H(3,𝔽₃)
commutator, Frattini, cosocle	C₃³	C₃³×C₁₃
prime radical	C₃³×C₁₃	C₃³
LCS	G ▷ C₃³ ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃²×C₁₃ ◁ C₃²×C₉×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
14. #10624791	C₁₃	direct (N × H)
67. C₁₃	#10624791	direct (N × H)

Subgroups — C13×#10624791 #23744942

Conjugacy classes of subgroups

Complements

Subgroups — C₁₃×#10624791 #23744942