Subgroups — C₁₃×#10624567 #23744718

Order 9477.

524 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	C₃×C₁₃×C₃²⋊C₉	C₃	1	2	yes	maximal
3	C₁₃×#6855	C₃	1	9	yes	maximal, complemented
4	C₃⁴×C₁₃	C₃²	1	1	yes	characteristic
5	C₃×C₁₃×3₋¹⁺²	—	3	6	no	—
6	C₃×C₁₃×3₋¹⁺²	—	3	18	no	—
7	C₃²×C₉×C₁₃	C₃²	1	6	yes	—
8	C₃²×C₉×C₁₃	C₃²	1	6	yes	—
9	C₁₃×C₃²⋊C₉	—	3	6	no	—
10	#10624567	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
11	C₃³×C₁₃	—	3	6	no	—
12	C₃³×C₁₃	—	3	6	no	—
13	C₃³×C₁₃	H(3,𝔽₃)	1	3	yes	—
14	C₃³×C₁₃	C₃³	1	1	yes	characteristic
15	C₁₃×3₋¹⁺²	—	3	54	no	—
16	C₃×C₉×C₁₃	—	3	6	no	—
17	C₃×C₉×C₁₃	—	3	12	no	—
18	C₃×C₉×C₁₃	—	3	6	no	—
19	C₃×C₉×C₁₃	—	3	18	no	—
20	C₃×C₉×C₁₃	3₋¹⁺²	1	18	yes	complemented
21	C₃²×3₋¹⁺²	C₃×C₁₃	1	2	yes	—
22	C₃×C₃²⋊C₉	C₃×C₁₃	1	2	yes	—
23	#6855	C₃×C₁₃	1	9	yes	complemented
24	C₃²×C₁₃	—	3	6	no	—
25	C₃²×C₁₃	—	3	6	no	—
26	C₃²×C₁₃	—	9	9	no	—
27	C₃²×C₁₃	C₃×H(3,𝔽₃)	1	1	yes	characteristic
28	C₃²×C₁₃	C₃×3₋¹⁺²	1	6	yes	—
29	C₃²×C₁₃	#737	1	6	yes	—
30	C₉×C₁₃	—	3	18	no	—
31	C₉×C₁₃	—	9	6	no	—
32	C₃⁴	C₃²×C₁₃	1	1	yes	characteristic
33	C₃×3₋¹⁺²	—	3	6	no	—
34	C₃×3₋¹⁺²	—	3	18	no	—
35	C₃²×C₉	C₃²×C₁₃	1	6	yes	—
36	C₃²×C₉	C₃²×C₁₃	1	6	yes	—
37	C₃²⋊C₉	—	3	6	no	—
38	C₃×C₁₃	—	9	3	no	—
39	C₃×C₁₃	#6891	1	2	yes	—
40	C₃×C₁₃	#6893	1	2	yes	—
41	C₃×C₁₃	#6896	1	9	yes	—
42	C₃³	—	3	6	no	—
43	C₃³	—	3	6	no	—
44	C₃³	C₁₃×H(3,𝔽₃)	1	3	yes	—
45	C₃³	C₃³×C₁₃	1	1	yes	characteristic
46	3₋¹⁺²	—	3	54	no	—
47	C₃×C₉	—	3	6	no	—
48	C₃×C₉	—	3	12	no	—
49	C₃×C₉	—	3	6	no	—
50	C₃×C₉	—	3	18	no	—
51	C₃×C₉	C₁₃×3₋¹⁺²	1	18	yes	complemented
52	C₁₃	#10624567	1	1	yes	characteristic, direct product factor, Sylow
53	C₃²	—	3	6	no	—
54	C₃²	—	3	6	no	—
55	C₃²	—	9	9	no	—
56	C₃²	C₃×C₁₃×H(3,𝔽₃)	1	1	yes	characteristic
57	C₃²	C₃×C₁₃×3₋¹⁺²	1	6	yes	—
58	C₃²	C₁₃×#737	1	6	yes	—
59	C₉	—	3	18	no	—
60	C₉	—	9	6	no	—
61	C₃	—	9	3	no	—
62	C₃	C₁₃×#6891	1	2	yes	—
63	C₃	C₁₃×#6893	1	2	yes	—
64	C₃	C₁₃×#6896	1	9	yes	—

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

Complements

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

N	H ≅ G/N	type
3. C₁₃×#6855	C₃	semidirect
10. #10624567	C₁₃	direct (N × H)
20. C₃×C₉×C₁₃	3₋¹⁺²	semidirect
23. #6855	C₃×C₁₃	semidirect
51. C₃×C₉	C₁₃×3₋¹⁺²	semidirect
52. C₁₃	#10624567	direct (N × H)

Subgroups — C13×#10624567 #23744718

Conjugacy classes of subgroups

Complements

Subgroups — C₁₃×#10624567 #23744718