Subgroups — C₁₃×#10624554 #23744705

Order 9477.

458 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₃×C₉⋊C₉	C₃	1	12	yes	maximal
2	C₃×C₉²×C₁₃	C₃	1	1	yes	maximal, characteristic
3	C₃²×C₉×C₁₃	C₃²	1	9	yes	—
4	C₃²×C₉×C₁₃	C₃²	1	4	yes	—
5	C₁₃×C₉⋊C₉	—	3	36	no	—
6	C₉²×C₁₃	C₉	1	9	yes	complemented
7	#10624554	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
8	C₃³×C₁₃	C₃³	1	1	yes	characteristic
9	C₃×C₉×C₁₃	—	3	36	no	—
10	C₃×C₉×C₁₃	C₃×C₉	1	12	yes	—
11	C₃×C₉×C₁₃	3₋¹⁺²	1	36	yes	—
12	C₃×C₉⋊C₉	C₃×C₁₃	1	12	yes	—
13	C₃×C₉²	C₃×C₁₃	1	1	yes	characteristic
14	C₃²×C₁₃	C₃²×C₉	1	1	yes	characteristic
15	C₃²×C₁₃	C₃×3₋¹⁺²	1	12	yes	—
16	C₉×C₁₃	—	9	9	no	—
17	C₉×C₁₃	C₉⋊C₉	1	36	yes	complemented
18	C₃²×C₉	C₃²×C₁₃	1	9	yes	—
19	C₃²×C₉	C₃²×C₁₃	1	4	yes	—
20	C₉⋊C₉	—	3	36	no	—
21	C₉²	C₉×C₁₃	1	9	yes	complemented
22	C₃×C₁₃	C₃×C₉⋊C₉	1	4	yes	—
23	C₃×C₁₃	#6900	1	9	yes	—
24	C₃³	C₃³×C₁₃	1	1	yes	characteristic
25	C₃×C₉	—	3	36	no	—
26	C₃×C₉	C₃×C₉×C₁₃	1	12	yes	—
27	C₃×C₉	C₁₃×3₋¹⁺²	1	36	yes	—
28	C₁₃	#10624554	1	1	yes	characteristic, direct product factor, Sylow
29	C₃²	C₃²×C₉×C₁₃	1	1	yes	characteristic
30	C₃²	C₃×C₁₃×3₋¹⁺²	1	12	yes	—
31	C₉	—	9	9	no	—
32	C₉	C₁₃×C₉⋊C₉	1	36	yes	complemented
33	C₃	C₃×C₁₃×C₉⋊C₉	1	4	yes	—
34	C₃	C₁₃×#6900	1	9	yes	—

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