Subgroups — C₃³×C₃₁⋊C₉ #21419423

Order 7533.

792 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₃₁⋊C₉	C₃	1	39	yes	maximal, direct product factor
2	C₃⁴×C₃₁	C₃	1	1	yes	maximal, characteristic
3	C₃³×C₃₁	C₉	1	27	yes	complemented
4	C₃³×C₃₁	C₃²	1	13	yes	—
5	C₃×C₃₁⋊C₉	C₃²	1	117	yes	direct product factor
6	C₃²×C₃₁	C₃×C₉	1	117	yes	complemented
7	C₃²×C₃₁	C₃³	1	13	yes	—
8	C₃₁⋊C₉	C₃³	1	27	yes	direct product factor
9	C₃³×C₉	—	31	1	no	maximal, Sylow
10	C₃×C₃₁	C₃²×C₉	1	39	yes	complemented
11	C₃×C₃₁	C₃⁴	1	1	yes	characteristic
12	C₃⁴	C₃₁⋊C₃	1	1	yes	characteristic
13	C₃²×C₉	—	31	39	no	—
14	C₃₁	C₃³×C₉	1	1	yes	characteristic, complemented, Sylow
15	C₃³	C₃₁⋊C₉	1	27	yes	direct product factor
16	C₃³	C₃×C₃₁⋊C₃	1	13	yes	—
17	C₃×C₉	—	31	117	no	—
18	C₃²	C₃×C₃₁⋊C₉	1	117	yes	direct product factor
19	C₃²	C₃²×C₃₁⋊C₃	1	13	yes	—
20	C₉	—	31	27	no	—
21	C₃	C₃²×C₃₁⋊C₉	1	39	yes	direct product factor
22	C₃	C₃³×C₃₁⋊C₃	1	1	yes	characteristic

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