Subgroups — C₁₃×#10624607 #23744758

Order 9477.

452 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₁₃×3₋¹⁺²	C₃	1	2	yes	maximal
2	C₁₃×#6891	C₃	1	2	yes	maximal
3	C₁₃×#6860	C₃	1	9	yes	maximal, complemented
4	C₃⁴×C₁₃	C₃²	1	1	yes	characteristic
5	C₃×C₁₃×3₋¹⁺²	—	3	2	no	—
6	C₃×C₁₃×3₋¹⁺²	—	3	2	no	—
7	C₃×C₁₃×3₋¹⁺²	—	3	18	no	—
8	C₃×C₁₃×3₋¹⁺²	—	3	2	no	—
9	C₃×C₁₃×3₋¹⁺²	C₃²	1	6	yes	—
10	C₃²×C₉×C₁₃	—	3	2	no	—
11	C₁₃×C₃²⋊C₉	—	3	2	no	—
12	C₁₃×C₃²⋊C₉	—	3	2	no	—
13	C₁₃×C₃²⋊C₉	C₃²	1	6	yes	—
14	#10624607	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
15	C₃³×C₁₃	—	3	6	no	—
16	C₃³×C₁₃	—	9	2	no	—
17	C₃³×C₁₃	H(3,𝔽₃)	1	1	yes	characteristic
18	C₃³×C₁₃	H(3,𝔽₃)	1	2	yes	—
19	C₃³×C₁₃	C₃³	1	1	yes	characteristic
20	C₁₃×3₋¹⁺²	—	3	18	no	—
21	C₁₃×3₋¹⁺²	—	3	18	no	—
22	C₁₃×3₋¹⁺²	—	3	18	no	—
23	C₁₃×3₋¹⁺²	—	9	6	no	—
24	C₃×C₉×C₁₃	—	3	18	no	—
25	C₃×C₉×C₁₃	—	3	6	no	—
26	C₃×C₉×C₁₃	—	3	6	no	—
27	C₃²×3₋¹⁺²	C₃×C₁₃	1	2	yes	—
28	#6891	C₃×C₁₃	1	2	yes	—
29	#6860	C₃×C₁₃	1	9	yes	complemented
30	C₃²×C₁₃	—	3	4	no	—
31	C₃²×C₁₃	—	3	2	no	—
32	C₃²×C₁₃	—	3	2	no	—
33	C₃²×C₁₃	—	3	2	no	—
34	C₃²×C₁₃	—	3	2	no	—
35	C₃²×C₁₃	—	3	2	no	—
36	C₃²×C₁₃	—	9	9	no	—
37	C₃²×C₁₃	AΣL(1,𝔽₂₇)	1	6	yes	—
38	C₃²×C₁₃	C₃×H(3,𝔽₃)	1	1	yes	characteristic
39	C₉×C₁₃	—	3	18	no	—
40	C₉×C₁₃	—	9	6	no	—
41	C₃⁴	C₃²×C₁₃	1	1	yes	characteristic
42	C₃×3₋¹⁺²	—	3	2	no	—
43	C₃×3₋¹⁺²	—	3	2	no	—
44	C₃×3₋¹⁺²	—	3	18	no	—
45	C₃×3₋¹⁺²	—	3	2	no	—
46	C₃×3₋¹⁺²	C₃²×C₁₃	1	6	yes	—
47	C₃²×C₉	—	3	2	no	—
48	C₃²⋊C₉	—	3	2	no	—
49	C₃²⋊C₉	—	3	2	no	—
50	C₃²⋊C₉	C₃²×C₁₃	1	6	yes	—
51	C₃×C₁₃	—	3	6	no	—
52	C₃×C₁₃	—	9	1	no	—
53	C₃×C₁₃	—	9	1	no	—
54	C₃×C₁₃	C₃×AΣL(1,𝔽₂₇)	1	2	yes	—
55	C₃×C₁₃	#6912	1	2	yes	—
56	C₃³	—	3	6	no	—
57	C₃³	—	9	2	no	—
58	C₃³	C₁₃×H(3,𝔽₃)	1	1	yes	characteristic
59	C₃³	C₁₃×H(3,𝔽₃)	1	2	yes	—
60	C₃³	C₃³×C₁₃	1	1	yes	characteristic
61	3₋¹⁺²	—	3	18	no	—
62	3₋¹⁺²	—	3	18	no	—
63	3₋¹⁺²	—	3	18	no	—
64	3₋¹⁺²	—	9	6	no	—
65	C₃×C₉	—	3	18	no	—
66	C₃×C₉	—	3	6	no	—
67	C₃×C₉	—	3	6	no	—
68	C₁₃	#10624607	1	1	yes	characteristic, direct product factor, Sylow
69	C₃²	—	3	2	no	—
70	C₃²	—	3	4	no	—
71	C₃²	—	3	2	no	—
72	C₃²	—	3	2	no	—
73	C₃²	—	3	2	no	—
74	C₃²	—	3	2	no	—
75	C₃²	—	9	9	no	—
76	C₃²	C₁₃×AΣL(1,𝔽₂₇)	1	6	yes	—
77	C₃²	C₃×C₁₃×H(3,𝔽₃)	1	1	yes	characteristic
78	C₉	—	3	18	no	—
79	C₉	—	9	6	no	—
80	C₃	—	3	6	no	—
81	C₃	—	9	1	no	—
82	C₃	—	9	1	no	—
83	C₃	C₃×C₁₃×AΣL(1,𝔽₂₇)	1	2	yes	—
84	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 ▷ C₃² ▷ 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×#6860	C₃	semidirect
14. #10624607	C₁₃	direct (N × H)
29. #6860	C₃×C₁₃	semidirect
68. C₁₃	#10624607	direct (N × H)

Subgroups — C13×#10624607 #23744758

Conjugacy classes of subgroups

Complements

Subgroups — C₁₃×#10624607 #23744758