Subgroups — C₁₃×#10624738 #23744889

Order 9477.

446 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₁₃×3₋¹⁺²	C₃	1	1	yes	maximal, characteristic
2	C₃×C₁₃×#733	C₃	1	9	yes	maximal, complemented
3	C₁₃×#6891	C₃	1	3	yes	maximal
4	C₃⁴×C₁₃	C₃²	1	1	yes	characteristic
5	C₃×C₁₃×3₋¹⁺²	—	3	3	no	—
6	C₃×C₁₃×3₋¹⁺²	—	3	9	no	—
7	C₃×C₁₃×3₋¹⁺²	C₃²	1	9	yes	—
8	C₃²×C₉×C₁₃	C₃²	1	3	yes	—
9	C₁₃×#733	—	3	27	no	—
10	C₁₃×C₃²⋊C₉	—	3	9	no	—
11	#10624738	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
12	C₃³×C₁₃	—	3	3	no	—
13	C₃³×C₁₃	—	9	3	no	—
14	C₃³×C₁₃	H(3,𝔽₃)	1	3	yes	—
15	C₃³×C₁₃	C₃³	1	1	yes	characteristic
16	C₁₃×3₋¹⁺²	—	3	27	no	—
17	C₁₃×3₋¹⁺²	—	3	27	no	—
18	C₃×C₉×C₁₃	—	3	6	no	—
19	C₃×C₉×C₁₃	—	3	3	no	—
20	C₃×C₉×C₁₃	—	3	9	no	—
21	C₃×C₉×C₁₃	H(3,𝔽₃)	1	9	yes	—
22	C₃²×3₋¹⁺²	C₃×C₁₃	1	1	yes	characteristic
23	C₃×#733	C₃×C₁₃	1	9	yes	complemented
24	#6891	C₃×C₁₃	1	3	yes	—
25	C₃²×C₁₃	—	3	3	no	—
26	C₃²×C₁₃	—	3	9	no	—
27	C₃²×C₁₃	—	3	3	no	—
28	C₃²×C₁₃	—	9	9	no	—
29	C₃²×C₁₃	C₃×H(3,𝔽₃)	1	3	yes	—
30	C₃²×C₁₃	C₃×H(3,𝔽₃)	1	1	yes	characteristic
31	C₉×C₁₃	—	3	9	no	—
32	C₉×C₁₃	—	9	9	no	—
33	C₃⁴	C₃²×C₁₃	1	1	yes	characteristic
34	C₃×3₋¹⁺²	—	3	3	no	—
35	C₃×3₋¹⁺²	—	3	9	no	—
36	C₃×3₋¹⁺²	C₃²×C₁₃	1	9	yes	—
37	C₃²×C₉	C₃²×C₁₃	1	3	yes	—
38	#733	—	3	27	no	—
39	C₃²⋊C₉	—	3	9	no	—
40	C₃×C₁₃	—	3	3	no	—
41	C₃×C₁₃	—	9	3	no	—
42	C₃×C₁₃	C₃²⋊H(3,𝔽₃)	1	1	yes	characteristic
43	C₃×C₁₃	#6912	1	3	yes	—
44	C₃³	—	3	3	no	—
45	C₃³	—	9	3	no	—
46	C₃³	C₁₃×H(3,𝔽₃)	1	3	yes	—
47	C₃³	C₃³×C₁₃	1	1	yes	characteristic
48	3₋¹⁺²	—	3	27	no	—
49	3₋¹⁺²	—	3	27	no	—
50	C₃×C₉	—	3	6	no	—
51	C₃×C₉	—	3	3	no	—
52	C₃×C₉	—	3	9	no	—
53	C₃×C₉	C₁₃×H(3,𝔽₃)	1	9	yes	—
54	C₁₃	#10624738	1	1	yes	characteristic, direct product factor, Sylow
55	C₃²	—	3	3	no	—
56	C₃²	—	3	3	no	—
57	C₃²	—	3	9	no	—
58	C₃²	—	9	9	no	—
59	C₃²	C₃×C₁₃×H(3,𝔽₃)	1	3	yes	—
60	C₃²	C₃×C₁₃×H(3,𝔽₃)	1	1	yes	characteristic
61	C₉	—	3	9	no	—
62	C₉	—	9	9	no	—
63	C₃	—	3	3	no	—
64	C₃	—	9	3	no	—
65	C₃	C₁₃×C₃²⋊H(3,𝔽₃)	1	1	yes	characteristic
66	C₃	C₁₃×#6912	1	3	yes	—

	subgroup	G/H
center, socle	C₃²×C₁₃	C₃×H(3,𝔽₃)
commutator, Frattini, cosocle	C₃³	C₃³×C₁₃
prime radical	C₃⁴×C₁₃	C₃²
LCS	G ▷ C₃³ ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃²×C₁₃ ◁ C₃⁴×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃×C₁₃×#733	C₃	semidirect
11. #10624738	C₁₃	direct (N × H)
23. C₃×#733	C₃×C₁₃	semidirect
54. C₁₃	#10624738	direct (N × H)

Subgroups — C13×#10624738 #23744889

Conjugacy classes of subgroups

Complements

Subgroups — C₁₃×#10624738 #23744889