Subgroups — C₁₃×#10624571 #23744722

Order 9477.

716 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₁₃×3₋¹⁺²	C₃	1	4	yes	maximal
2	C₁₃×#6855	C₃	1	9	yes	maximal, complemented
3	C₃⁴×C₁₃	C₃²	1	1	yes	characteristic
4	C₃×C₁₃×3₋¹⁺²	—	3	12	no	—
5	C₃×C₁₃×3₋¹⁺²	—	3	36	no	—
6	C₃²×C₉×C₁₃	C₃²	1	12	yes	—
7	#10624571	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
8	C₃³×C₁₃	—	3	12	no	—
9	C₃³×C₁₃	H(3,𝔽₃)	1	3	yes	—
10	C₃³×C₁₃	C₃³	1	1	yes	characteristic
11	C₁₃×3₋¹⁺²	—	3	108	no	—
12	C₃×C₉×C₁₃	—	3	12	no	—
13	C₃×C₉×C₁₃	—	3	24	no	—
14	C₃×C₉×C₁₃	3₋¹⁺²	1	36	yes	complemented
15	C₃²×3₋¹⁺²	C₃×C₁₃	1	4	yes	—
16	#6855	C₃×C₁₃	1	9	yes	complemented
17	C₃²×C₁₃	—	3	12	no	—
18	C₃²×C₁₃	—	9	9	no	—
19	C₃²×C₁₃	C₃×H(3,𝔽₃)	1	1	yes	characteristic
20	C₃²×C₁₃	C₃×3₋¹⁺²	1	12	yes	—
21	C₉×C₁₃	—	3	36	no	—
22	C₃⁴	C₃²×C₁₃	1	1	yes	characteristic
23	C₃×3₋¹⁺²	—	3	12	no	—
24	C₃×3₋¹⁺²	—	3	36	no	—
25	C₃²×C₉	C₃²×C₁₃	1	12	yes	—
26	C₃×C₁₃	—	9	3	no	—
27	C₃×C₁₃	#6891	1	4	yes	—
28	C₃×C₁₃	#6900	1	9	yes	—
29	C₃³	—	3	12	no	—
30	C₃³	C₁₃×H(3,𝔽₃)	1	3	yes	—
31	C₃³	C₃³×C₁₃	1	1	yes	characteristic
32	3₋¹⁺²	—	3	108	no	—
33	C₃×C₉	—	3	12	no	—
34	C₃×C₉	—	3	24	no	—
35	C₃×C₉	C₁₃×3₋¹⁺²	1	36	yes	complemented
36	C₁₃	#10624571	1	1	yes	characteristic, direct product factor, Sylow
37	C₃²	—	3	12	no	—
38	C₃²	—	9	9	no	—
39	C₃²	C₃×C₁₃×H(3,𝔽₃)	1	1	yes	characteristic
40	C₃²	C₃×C₁₃×3₋¹⁺²	1	12	yes	—
41	C₉	—	3	36	no	—
42	C₃	—	9	3	no	—
43	C₃	C₁₃×#6891	1	4	yes	—
44	C₃	C₁₃×#6900	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
2. C₁₃×#6855	C₃	semidirect
7. #10624571	C₁₃	direct (N × H)
14. C₃×C₉×C₁₃	3₋¹⁺²	semidirect
16. #6855	C₃×C₁₃	semidirect
35. C₃×C₉	C₁₃×3₋¹⁺²	semidirect
36. C₁₃	#10624571	direct (N × H)

Subgroups — C13×#10624571 #23744722

Conjugacy classes of subgroups

Complements

Subgroups — C₁₃×#10624571 #23744722