Subgroups — C₃×3₋¹⁺²×C₂₅₁ #35204708

Order 20331.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃³×C₂₅₁	C₃	1	1	yes	maximal, characteristic
2	3₋¹⁺²×C₂₅₁	C₃	1	9	yes	maximal, direct product factor
3	C₃×C₉×C₂₅₁	C₃	1	3	yes	maximal, complemented
4	C₃²×C₂₅₁	—	3	3	no	—
5	C₃²×C₂₅₁	C₃²	1	3	yes	—
6	C₃²×C₂₅₁	C₃²	1	1	yes	characteristic
7	C₉×C₂₅₁	C₃²	1	9	yes	complemented
8	C₃×C₂₅₁	—	3	3	no	—
9	C₃×C₂₅₁	3₋¹⁺²	1	3	yes	direct product factor
10	C₃×C₂₅₁	C₃³	1	1	yes	characteristic
11	C₂₅₁	C₃×3₋¹⁺²	1	1	yes	characteristic, direct product factor, Sylow
12	C₃×3₋¹⁺²	C₂₅₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
13	C₃³	C₃×C₂₅₁	1	1	yes	characteristic
14	3₋¹⁺²	C₃×C₂₅₁	1	9	yes	direct product factor
15	C₃×C₉	C₃×C₂₅₁	1	3	yes	complemented
16	C₃²	—	3	3	no	—
17	C₃²	C₃²×C₂₅₁	1	3	yes	—
18	C₃²	C₃²×C₂₅₁	1	1	yes	characteristic
19	C₉	C₃²×C₂₅₁	1	9	yes	complemented
20	C₃	—	3	3	no	—
21	C₃	3₋¹⁺²×C₂₅₁	1	3	yes	direct product factor
22	C₃	C₃³×C₂₅₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₃²×C₂₅₁	C₃²
commutator, Frattini, cosocle	C₃	C₃³×C₂₅₁
prime radical	C₃³×C₂₅₁	C₃
LCS	G ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃²×C₂₅₁ ◁ G

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

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.