Subgroups — C₃⁴×C₇×C₉ #19100346

Order 5103.

10232 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⁵×C₇	C₃	1	1	yes	maximal, characteristic
2	C₃³×C₇×C₉	C₃	1	120	yes	maximal, direct product factor
3	C₃⁴×C₉	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
4	C₃⁴×C₇	C₉	1	81	yes	direct product factor
5	C₃⁴×C₇	C₃²	1	40	yes	—
6	C₃²×C₇×C₉	C₃²	1	1170	yes	direct product factor
7	C₃⁵	C₃×C₇	1	1	yes	characteristic
8	C₃³×C₉	C₃×C₇	1	120	yes	direct product factor
9	C₃³×C₇	C₃×C₉	1	1080	yes	direct product factor
10	C₃³×C₇	C₃³	1	130	yes	—
11	C₃×C₇×C₉	C₃³	1	1080	yes	direct product factor
12	C₃⁴	C₇×C₉	1	81	yes	direct product factor
13	C₃⁴	C₃²×C₇	1	40	yes	—
14	C₃²×C₉	C₃²×C₇	1	1170	yes	direct product factor
15	C₃²×C₇	C₃²×C₉	1	1170	yes	direct product factor
16	C₃²×C₇	C₃⁴	1	40	yes	—
17	C₇×C₉	C₃⁴	1	81	yes	direct product factor
18	C₃³	C₃×C₇×C₉	1	1080	yes	direct product factor
19	C₃³	C₃³×C₇	1	130	yes	—
20	C₃×C₉	C₃³×C₇	1	1080	yes	direct product factor
21	C₃×C₇	C₃³×C₉	1	120	yes	direct product factor
22	C₃×C₇	C₃⁵	1	1	yes	characteristic
23	C₃²	C₃²×C₇×C₉	1	1170	yes	direct product factor
24	C₃²	C₃⁴×C₇	1	40	yes	—
25	C₉	C₃⁴×C₇	1	81	yes	direct product factor
26	C₇	C₃⁴×C₉	1	1	yes	characteristic, direct product factor, Sylow
27	C₃	C₃³×C₇×C₉	1	120	yes	direct product factor
28	C₃	C₃⁵×C₇	1	1	yes	characteristic

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