Subgroups — C₃⁴×C₁₃⋊C₉ #23748603

Order 9477.

10232 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃³×C₁₃⋊C₉	C₃	1	120	yes	maximal, direct product factor
2	C₃⁵×C₁₃	C₃	1	1	yes	maximal, characteristic
3	C₃²×C₁₃⋊C₉	C₃²	1	1170	yes	direct product factor
4	C₃⁴×C₁₃	C₉	1	81	yes	complemented
5	C₃⁴×C₁₃	C₃²	1	40	yes	—
6	C₃⁴×C₉	—	13	1	no	maximal, Sylow
7	C₃³×C₁₃	C₃×C₉	1	1080	yes	complemented
8	C₃³×C₁₃	C₃³	1	130	yes	—
9	C₃×C₁₃⋊C₉	C₃³	1	1080	yes	direct product factor
10	C₃⁵	C₁₃⋊C₃	1	1	yes	characteristic
11	C₃³×C₉	—	13	120	no	—
12	C₃²×C₁₃	C₃²×C₉	1	1170	yes	complemented
13	C₃²×C₁₃	C₃⁴	1	40	yes	—
14	C₁₃⋊C₉	C₃⁴	1	81	yes	direct product factor
15	C₃⁴	C₁₃⋊C₉	1	81	yes	direct product factor
16	C₃⁴	C₃×C₁₃⋊C₃	1	40	yes	—
17	C₃²×C₉	—	13	1170	no	—
18	C₃×C₁₃	C₃³×C₉	1	120	yes	complemented
19	C₃×C₁₃	C₃⁵	1	1	yes	characteristic
20	C₃³	C₃×C₁₃⋊C₉	1	1080	yes	direct product factor
21	C₃³	C₃²×C₁₃⋊C₃	1	130	yes	—
22	C₃×C₉	—	13	1080	no	—
23	C₁₃	C₃⁴×C₉	1	1	yes	characteristic, complemented, Sylow
24	C₃²	C₃²×C₁₃⋊C₉	1	1170	yes	direct product factor
25	C₃²	C₃³×C₁₃⋊C₃	1	40	yes	—
26	C₉	—	13	81	no	—
27	C₃	C₃³×C₁₃⋊C₉	1	120	yes	direct product factor
28	C₃	C₃⁴×C₁₃⋊C₃	1	1	yes	characteristic

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