Subgroups — C₁₃×#10624564 #23744715

Order 9477.

662 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₁₃×H(3,𝔽₃)	C₃	1	1	yes	maximal, characteristic
2	C₃×C₁₃×C₃²⋊C₉	C₃	1	12	yes	maximal, complemented
3	C₃⁴×C₁₃	C₃²	1	4	yes	—
4	C₃×C₁₃×H(3,𝔽₃)	—	3	12	no	—
5	C₃²×C₉×C₁₃	C₃²	1	9	yes	—
6	C₁₃×C₃²⋊C₉	—	3	36	no	—
7	#10624564	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
8	C₃³×C₁₃	—	3	12	no	—
9	C₃³×C₁₃	—	3	36	no	—
10	C₃³×C₁₃	H(3,𝔽₃)	1	12	yes	—
11	C₃³×C₁₃	C₃³	1	1	yes	characteristic
12	C₁₃×H(3,𝔽₃)	—	3	27	no	—
13	C₃×C₉×C₁₃	—	3	36	no	—
14	C₃²×H(3,𝔽₃)	C₃×C₁₃	1	1	yes	characteristic
15	C₃×C₃²⋊C₉	C₃×C₁₃	1	12	yes	complemented
16	C₃²×C₁₃	—	3	12	no	—
17	C₃²×C₁₃	—	3	36	no	—
18	C₃²×C₁₃	—	9	36	no	—
19	C₃²×C₁₃	C₃×H(3,𝔽₃)	1	4	yes	—
20	C₃²×C₁₃	#737	1	9	yes	—
21	C₉×C₁₃	—	9	9	no	—
22	C₃⁴	C₃²×C₁₃	1	4	yes	—
23	C₃×H(3,𝔽₃)	—	3	12	no	—
24	C₃²×C₉	C₃²×C₁₃	1	9	yes	—
25	C₃²⋊C₉	—	3	36	no	—
26	C₃×C₁₃	—	9	12	no	—
27	C₃×C₁₃	C₃²⋊H(3,𝔽₃)	1	1	yes	characteristic
28	C₃×C₁₃	#6893	1	12	yes	—
29	C₃³	—	3	12	no	—
30	C₃³	—	3	36	no	—
31	C₃³	C₁₃×H(3,𝔽₃)	1	12	yes	—
32	C₃³	C₃³×C₁₃	1	1	yes	characteristic
33	H(3,𝔽₃)	—	3	27	no	—
34	C₃×C₉	—	3	36	no	—
35	C₁₃	#10624564	1	1	yes	characteristic, direct product factor, Sylow
36	C₃²	—	3	12	no	—
37	C₃²	—	3	36	no	—
38	C₃²	—	9	36	no	—
39	C₃²	C₃×C₁₃×H(3,𝔽₃)	1	4	yes	—
40	C₃²	C₁₃×#737	1	9	yes	—
41	C₉	—	9	9	no	—
42	C₃	—	9	12	no	—
43	C₃	C₁₃×C₃²⋊H(3,𝔽₃)	1	1	yes	characteristic
44	C₃	C₁₃×#6893	1	12	yes	—

	subgroup	G/H
center, socle	C₃³×C₁₃	C₃³
commutator, Frattini, cosocle	C₃³	C₃³×C₁₃
prime radical	C₃²×C₁₃×H(3,𝔽₃)	C₃
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. C₃×C₁₃×C₃²⋊C₉	C₃	semidirect
7. #10624564	C₁₃	direct (N × H)
15. C₃×C₃²⋊C₉	C₃×C₁₃	semidirect
35. C₁₃	#10624564	direct (N × H)

Subgroups — C13×#10624564 #23744715

Conjugacy classes of subgroups

Complements

Subgroups — C₁₃×#10624564 #23744715