Subgroups — C₁₃×#10624736 #23744887

Order 9477.

488 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, complemented
2	C₃×C₁₃×#731	C₃	1	9	yes	maximal, complemented
3	C₁₃×#6891	C₃	1	2	yes	maximal, complemented
4	C₁₃×C₃²⋊H(3,𝔽₃)	C₃	1	1	yes	maximal, characteristic
5	C₃⁴×C₁₃	C₃²	1	1	yes	characteristic
6	C₃×C₁₃×3₋¹⁺²	—	3	3	no	—
7	C₃×C₁₃×3₋¹⁺²	—	3	9	no	—
8	C₃×C₁₃×3₋¹⁺²	C₃²	1	6	yes	—
9	C₃×C₁₃×H(3,𝔽₃)	—	3	3	no	—
10	C₃×C₁₃×H(3,𝔽₃)	C₃²	1	3	yes	—
11	C₃²×C₉×C₁₃	C₃²	1	3	yes	—
12	C₁₃×#731	—	3	27	no	—
13	C₁₃×C₃²⋊C₉	—	3	6	no	—
14	#10624736	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
15	C₃³×C₁₃	—	3	3	no	—
16	C₃³×C₁₃	—	3	3	no	—
17	C₃³×C₁₃	—	9	3	no	—
18	C₃³×C₁₃	H(3,𝔽₃)	1	3	yes	—
19	C₃³×C₁₃	C₃³	1	1	yes	characteristic
20	C₁₃×3₋¹⁺²	—	3	27	no	—
21	C₁₃×3₋¹⁺²	—	3	18	no	—
22	C₁₃×H(3,𝔽₃)	—	3	9	no	—
23	C₁₃×H(3,𝔽₃)	—	9	9	no	—
24	C₃×C₉×C₁₃	—	3	6	no	—
25	C₃×C₉×C₁₃	—	3	3	no	—
26	C₃×C₉×C₁₃	—	3	6	no	—
27	C₃×C₉×C₁₃	H(3,𝔽₃)	1	9	yes	complemented
28	C₃²×3₋¹⁺²	C₃×C₁₃	1	1	yes	characteristic, complemented
29	C₃×#731	C₃×C₁₃	1	9	yes	complemented
30	#6891	C₃×C₁₃	1	2	yes	complemented
31	C₃²⋊H(3,𝔽₃)	C₃×C₁₃	1	1	yes	characteristic
32	C₃²×C₁₃	—	3	3	no	—
33	C₃²×C₁₃	—	3	3	no	—
34	C₃²×C₁₃	—	3	3	no	—
35	C₃²×C₁₃	—	3	6	no	—
36	C₃²×C₁₃	—	9	9	no	—
37	C₃²×C₁₃	—	9	3	no	—
38	C₃²×C₁₃	—	9	9	no	—
39	C₃²×C₁₃	C₃×H(3,𝔽₃)	1	3	yes	—
40	C₃²×C₁₃	C₃×H(3,𝔽₃)	1	1	yes	characteristic
41	C₉×C₁₃	—	3	9	no	—
42	C₉×C₁₃	—	9	6	no	—
43	C₃⁴	C₃²×C₁₃	1	1	yes	characteristic
44	C₃×3₋¹⁺²	—	3	3	no	—
45	C₃×3₋¹⁺²	—	3	9	no	—
46	C₃×3₋¹⁺²	C₃²×C₁₃	1	6	yes	—
47	C₃×H(3,𝔽₃)	—	3	3	no	—
48	C₃×H(3,𝔽₃)	C₃²×C₁₃	1	3	yes	—
49	C₃²×C₉	C₃²×C₁₃	1	3	yes	—
50	#731	—	3	27	no	—
51	C₃²⋊C₉	—	3	6	no	—
52	C₃×C₁₃	—	3	3	no	—
53	C₃×C₁₃	—	9	3	no	—
54	C₃×C₁₃	—	27	3	no	—
55	C₃×C₁₃	C₃²⋊H(3,𝔽₃)	1	1	yes	characteristic
56	C₃×C₁₃	#6910	1	3	yes	—
57	C₃³	—	3	3	no	—
58	C₃³	—	3	3	no	—
59	C₃³	—	9	3	no	—
60	C₃³	C₁₃×H(3,𝔽₃)	1	3	yes	—
61	C₃³	C₃³×C₁₃	1	1	yes	characteristic
62	3₋¹⁺²	—	3	27	no	—
63	3₋¹⁺²	—	3	18	no	—
64	H(3,𝔽₃)	—	3	9	no	—
65	H(3,𝔽₃)	—	9	9	no	—
66	C₃×C₉	—	3	6	no	—
67	C₃×C₉	—	3	3	no	—
68	C₃×C₉	—	3	6	no	—
69	C₃×C₉	C₁₃×H(3,𝔽₃)	1	9	yes	complemented
70	C₁₃	#10624736	1	1	yes	characteristic, direct product factor, Sylow
71	C₃²	—	3	3	no	—
72	C₃²	—	3	3	no	—
73	C₃²	—	3	3	no	—
74	C₃²	—	3	6	no	—
75	C₃²	—	9	9	no	—
76	C₃²	—	9	3	no	—
77	C₃²	—	9	9	no	—
78	C₃²	C₃×C₁₃×H(3,𝔽₃)	1	3	yes	—
79	C₃²	C₃×C₁₃×H(3,𝔽₃)	1	1	yes	characteristic
80	C₉	—	3	9	no	—
81	C₉	—	9	6	no	—
82	C₃	—	3	3	no	—
83	C₃	—	9	3	no	—
84	C₃	—	27	3	no	—
85	C₃	C₁₃×C₃²⋊H(3,𝔽₃)	1	1	yes	characteristic
86	C₃	C₁₃×#6910	1	3	yes	—

	subgroup	G/H
center, socle	C₃²×C₁₃	C₃×H(3,𝔽₃)
commutator, Frattini, cosocle	C₃³	C₃³×C₁₃
prime radical	C₁₃×C₃²⋊H(3,𝔽₃)	C₃
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
1. C₃²×C₁₃×3₋¹⁺²	C₃	semidirect
2. C₃×C₁₃×#731	C₃	semidirect
3. C₁₃×#6891	C₃	semidirect
14. #10624736	C₁₃	direct (N × H)
27. C₃×C₉×C₁₃	H(3,𝔽₃)	semidirect
28. C₃²×3₋¹⁺²	C₃×C₁₃	semidirect
29. C₃×#731	C₃×C₁₃	semidirect
30. #6891	C₃×C₁₃	semidirect
69. C₃×C₉	C₁₃×H(3,𝔽₃)	semidirect
70. C₁₃	#10624736	direct (N × H)

Subgroups — C13×#10624736 #23744887

Conjugacy classes of subgroups

Complements

Subgroups — C₁₃×#10624736 #23744887