Subgroups — C₁₃×#10624568 #23744719

Order 9477.

332 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₃×C₃²⋊C₉	C₃	1	4	yes	maximal
2	C₁₃×#6855	C₃	1	9	yes	maximal, complemented
3	C₃⁴×C₁₃	C₃²	1	1	yes	characteristic
4	C₃²×C₉×C₁₃	C₃²	1	12	yes	—
5	C₁₃×C₃²⋊C₉	—	3	12	no	—
6	#10624568	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
7	C₃³×C₁₃	—	3	12	no	—
8	C₃³×C₁₃	H(3,𝔽₃)	1	3	yes	—
9	C₃³×C₁₃	C₃³	1	1	yes	characteristic
10	C₃×C₉×C₁₃	—	3	12	no	—
11	C₃×C₉×C₁₃	—	3	36	no	—
12	C₃×C₃²⋊C₉	C₃×C₁₃	1	4	yes	—
13	#6855	C₃×C₁₃	1	9	yes	complemented
14	C₃²×C₁₃	—	3	12	no	—
15	C₃²×C₁₃	—	9	9	no	—
16	C₃²×C₁₃	C₃×H(3,𝔽₃)	1	1	yes	characteristic
17	C₃²×C₁₃	#737	1	12	yes	—
18	C₉×C₁₃	—	9	12	no	—
19	C₃⁴	C₃²×C₁₃	1	1	yes	characteristic
20	C₃²×C₉	C₃²×C₁₃	1	12	yes	—
21	C₃²⋊C₉	—	3	12	no	—
22	C₃×C₁₃	—	9	3	no	—
23	C₃×C₁₃	#6893	1	4	yes	—
24	C₃×C₁₃	#6897	1	9	yes	—
25	C₃³	—	3	12	no	—
26	C₃³	C₁₃×H(3,𝔽₃)	1	3	yes	—
27	C₃³	C₃³×C₁₃	1	1	yes	characteristic
28	C₃×C₉	—	3	12	no	—
29	C₃×C₉	—	3	36	no	—
30	C₁₃	#10624568	1	1	yes	characteristic, direct product factor, Sylow
31	C₃²	—	3	12	no	—
32	C₃²	—	9	9	no	—
33	C₃²	C₃×C₁₃×H(3,𝔽₃)	1	1	yes	characteristic
34	C₃²	C₁₃×#737	1	12	yes	—
35	C₉	—	9	12	no	—
36	C₃	—	9	3	no	—
37	C₃	C₁₃×#6893	1	4	yes	—
38	C₃	C₁₃×#6897	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

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