Subgroups — C₁₃×#10624767 #23744918

Order 9477.

428 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃³×C₉×C₁₃	C₃	1	1	yes	maximal, characteristic
2	C₁₃×#6891	C₃	1	3	yes	maximal
3	C₁₃×#6867	C₃	1	9	yes	maximal, complemented
4	C₃⁴×C₁₃	C₃²	1	1	yes	characteristic
5	C₃×C₁₃×3₋¹⁺²	—	3	3	no	—
6	C₃²×C₉×C₁₃	—	3	3	no	—
7	C₃²×C₉×C₁₃	—	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	#10624767	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
12	C₃³×C₁₃	—	3	9	no	—
13	C₃³×C₁₃	—	3	3	no	—
14	C₃³×C₁₃	H(3,𝔽₃)	1	3	yes	—
15	C₃³×C₁₃	C₃³	1	1	yes	characteristic
16	C₁₃×3₋¹⁺²	—	9	9	no	—
17	C₃×C₉×C₁₃	—	3	27	no	—
18	C₃×C₉×C₁₃	—	3	3	no	—
19	C₃×C₉×C₁₃	—	3	6	no	—
20	C₃×C₉×C₁₃	—	3	9	no	—
21	C₃×C₉×C₁₃	3₋¹⁺²	1	9	yes	complemented
22	C₃³×C₉	C₃×C₁₃	1	1	yes	characteristic
23	#6891	C₃×C₁₃	1	3	yes	—
24	#6867	C₃×C₁₃	1	9	yes	complemented
25	C₃²×C₁₃	—	3	27	no	—
26	C₃²×C₁₃	—	3	3	no	—
27	C₃²×C₁₃	—	3	6	no	—
28	C₃²×C₁₃	—	3	3	no	—
29	C₃²×C₁₃	#731	1	9	yes	—
30	C₃²×C₁₃	C₃×H(3,𝔽₃)	1	1	yes	characteristic
31	C₃²×C₁₃	C₃×3₋¹⁺²	1	3	yes	—
32	C₉×C₁₃	—	3	9	no	—
33	C₉×C₁₃	—	9	9	no	—
34	C₃⁴	C₃²×C₁₃	1	1	yes	characteristic
35	C₃×3₋¹⁺²	—	3	3	no	—
36	C₃²×C₉	—	3	3	no	—
37	C₃²×C₉	—	3	9	no	—
38	C₃²×C₉	C₃²×C₁₃	1	3	yes	—
39	C₃²⋊C₉	—	3	6	no	—
40	C₃²⋊C₉	C₃²×C₁₃	1	9	yes	—
41	C₃×C₁₃	—	3	9	no	—
42	C₃×C₁₃	—	3	3	no	—
43	C₃×C₁₃	#6891	1	1	yes	characteristic
44	C₃×C₁₃	C₃×#731	1	3	yes	—
45	C₃³	—	3	9	no	—
46	C₃³	—	3	3	no	—
47	C₃³	C₁₃×H(3,𝔽₃)	1	3	yes	—
48	C₃³	C₃³×C₁₃	1	1	yes	characteristic
49	3₋¹⁺²	—	9	9	no	—
50	C₃×C₉	—	3	27	no	—
51	C₃×C₉	—	3	3	no	—
52	C₃×C₉	—	3	6	no	—
53	C₃×C₉	—	3	9	no	—
54	C₃×C₉	C₁₃×3₋¹⁺²	1	9	yes	complemented
55	C₁₃	#10624767	1	1	yes	characteristic, direct product factor, Sylow
56	C₃²	—	3	27	no	—
57	C₃²	—	3	3	no	—
58	C₃²	—	3	6	no	—
59	C₃²	—	3	3	no	—
60	C₃²	C₁₃×#731	1	9	yes	—
61	C₃²	C₃×C₁₃×H(3,𝔽₃)	1	1	yes	characteristic
62	C₃²	C₃×C₁₃×3₋¹⁺²	1	3	yes	—
63	C₉	—	3	9	no	—
64	C₉	—	9	9	no	—
65	C₃	—	3	9	no	—
66	C₃	—	3	3	no	—
67	C₃	C₁₃×#6891	1	1	yes	characteristic
68	C₃	C₃×C₁₃×#731	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
3. C₁₃×#6867	C₃	semidirect
11. #10624767	C₁₃	direct (N × H)
21. C₃×C₉×C₁₃	3₋¹⁺²	semidirect
24. #6867	C₃×C₁₃	semidirect
54. C₃×C₉	C₁₃×3₋¹⁺²	semidirect
55. C₁₃	#10624767	direct (N × H)

Subgroups — C13×#10624767 #23744918

Conjugacy classes of subgroups

Complements

Subgroups — C₁₃×#10624767 #23744918