Subgroups — C₁₃×#10624772 #23744923

Order 9477.

356 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	C₁₃×#6891	C₃	1	3	yes	maximal
3	C₁₃×#6868	C₃	1	9	yes	maximal, complemented
4	C₃⁴×C₁₃	C₃²	1	1	yes	characteristic
5	C₃×C₁₃×3₋¹⁺²	—	3	3	no	—
6	C₃×C₁₃×3₋¹⁺²	—	3	3	no	—
7	C₃×C₁₃×3₋¹⁺²	—	3	9	no	—
8	C₃²×C₉×C₁₃	C₃²	1	3	yes	—
9	C₁₃×C₃²⋊C₉	—	3	6	no	—
10	C₁₃×C₃²⋊C₉	C₃²	1	9	yes	—
11	#10624772	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
12	C₃³×C₁₃	—	3	3	no	—
13	C₃³×C₁₃	—	9	2	no	—
14	C₃³×C₁₃	—	9	1	no	—
15	C₃³×C₁₃	H(3,𝔽₃)	1	3	yes	—
16	C₃³×C₁₃	C₃³	1	1	yes	characteristic
17	C₁₃×3₋¹⁺²	—	3	27	no	—
18	C₁₃×3₋¹⁺²	—	9	9	no	—
19	C₃×C₉×C₁₃	—	3	3	no	—
20	C₃×C₉×C₁₃	—	3	6	no	—
21	C₃×C₉×C₁₃	—	3	9	no	—
22	C₃×C₉×C₁₃	3₋¹⁺²	1	9	yes	complemented
23	C₃²×3₋¹⁺²	C₃×C₁₃	1	1	yes	characteristic
24	#6891	C₃×C₁₃	1	3	yes	—
25	#6868	C₃×C₁₃	1	9	yes	complemented
26	C₃²×C₁₃	—	3	2	no	—
27	C₃²×C₁₃	—	3	1	no	—
28	C₃²×C₁₃	—	3	6	no	—
29	C₃²×C₁₃	—	3	3	no	—
30	C₃²×C₁₃	—	3	3	no	—
31	C₃²×C₁₃	—	9	9	no	—
32	C₃²×C₁₃	C₃×H(3,𝔽₃)	1	1	yes	characteristic
33	C₃²×C₁₃	C₃×3₋¹⁺²	1	3	yes	—
34	C₉×C₁₃	—	3	9	no	—
35	C₉×C₁₃	—	9	9	no	—
36	C₃⁴	C₃²×C₁₃	1	1	yes	characteristic
37	C₃×3₋¹⁺²	—	3	3	no	—
38	C₃×3₋¹⁺²	—	3	3	no	—
39	C₃×3₋¹⁺²	—	3	9	no	—
40	C₃²×C₉	C₃²×C₁₃	1	3	yes	—
41	C₃²⋊C₉	—	3	6	no	—
42	C₃²⋊C₉	C₃²×C₁₃	1	9	yes	—
43	C₃×C₁₃	—	3	3	no	—
44	C₃×C₁₃	—	9	3	no	—
45	C₃×C₁₃	#6891	1	1	yes	characteristic
46	C₃×C₁₃	#6911	1	1	yes	characteristic
47	C₃×C₁₃	#6912	1	2	yes	—
48	C₃³	—	3	3	no	—
49	C₃³	—	9	1	no	—
50	C₃³	—	9	2	no	—
51	C₃³	C₁₃×H(3,𝔽₃)	1	3	yes	—
52	C₃³	C₃³×C₁₃	1	1	yes	characteristic
53	3₋¹⁺²	—	3	27	no	—
54	3₋¹⁺²	—	9	9	no	—
55	C₃×C₉	—	3	3	no	—
56	C₃×C₉	—	3	6	no	—
57	C₃×C₉	—	3	9	no	—
58	C₃×C₉	C₁₃×3₋¹⁺²	1	9	yes	complemented
59	C₁₃	#10624772	1	1	yes	characteristic, direct product factor, Sylow
60	C₃²	—	3	1	no	—
61	C₃²	—	3	2	no	—
62	C₃²	—	3	3	no	—
63	C₃²	—	3	3	no	—
64	C₃²	—	3	6	no	—
65	C₃²	—	9	9	no	—
66	C₃²	C₃×C₁₃×H(3,𝔽₃)	1	1	yes	characteristic
67	C₃²	C₃×C₁₃×3₋¹⁺²	1	3	yes	—
68	C₉	—	3	9	no	—
69	C₉	—	9	9	no	—
70	C₃	—	3	3	no	—
71	C₃	—	9	3	no	—
72	C₃	C₁₃×#6891	1	1	yes	characteristic
73	C₃	C₁₃×#6911	1	1	yes	characteristic
74	C₃	C₁₃×#6912	1	2	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
3. C₁₃×#6868	C₃	semidirect
11. #10624772	C₁₃	direct (N × H)
22. C₃×C₉×C₁₃	3₋¹⁺²	semidirect
25. #6868	C₃×C₁₃	semidirect
58. C₃×C₉	C₁₃×3₋¹⁺²	semidirect
59. C₁₃	#10624772	direct (N × H)

Subgroups — C13×#10624772 #23744923

Conjugacy classes of subgroups

Complements

Subgroups — C₁₃×#10624772 #23744923