# Extensions 1→N→G→Q→1 with N=C20 and Q=C2×C6

Direct product G=N×Q with N=C20 and Q=C2×C6
dρLabelID
C22×C60240C2^2xC60240,185

Semidirect products G=N:Q with N=C20 and Q=C2×C6
extensionφ:Q→Aut NdρLabelID
C20⋊(C2×C6) = C3×D4×D5φ: C2×C6/C3C22 ⊆ Aut C20604C20:(C2xC6)240,159
C202(C2×C6) = C6×D20φ: C2×C6/C6C2 ⊆ Aut C20120C20:2(C2xC6)240,157
C203(C2×C6) = D5×C2×C12φ: C2×C6/C6C2 ⊆ Aut C20120C20:3(C2xC6)240,156
C204(C2×C6) = D4×C30φ: C2×C6/C6C2 ⊆ Aut C20120C20:4(C2xC6)240,186

Non-split extensions G=N.Q with N=C20 and Q=C2×C6
extensionφ:Q→Aut NdρLabelID
C20.1(C2×C6) = C3×D4⋊D5φ: C2×C6/C3C22 ⊆ Aut C201204C20.1(C2xC6)240,44
C20.2(C2×C6) = C3×D4.D5φ: C2×C6/C3C22 ⊆ Aut C201204C20.2(C2xC6)240,45
C20.3(C2×C6) = C3×Q8⋊D5φ: C2×C6/C3C22 ⊆ Aut C201204C20.3(C2xC6)240,46
C20.4(C2×C6) = C3×C5⋊Q16φ: C2×C6/C3C22 ⊆ Aut C202404C20.4(C2xC6)240,47
C20.5(C2×C6) = C3×D42D5φ: C2×C6/C3C22 ⊆ Aut C201204C20.5(C2xC6)240,160
C20.6(C2×C6) = C3×Q8×D5φ: C2×C6/C3C22 ⊆ Aut C201204C20.6(C2xC6)240,161
C20.7(C2×C6) = C3×Q82D5φ: C2×C6/C3C22 ⊆ Aut C201204C20.7(C2xC6)240,162
C20.8(C2×C6) = C3×C40⋊C2φ: C2×C6/C6C2 ⊆ Aut C201202C20.8(C2xC6)240,35
C20.9(C2×C6) = C3×D40φ: C2×C6/C6C2 ⊆ Aut C201202C20.9(C2xC6)240,36
C20.10(C2×C6) = C3×Dic20φ: C2×C6/C6C2 ⊆ Aut C202402C20.10(C2xC6)240,37
C20.11(C2×C6) = C6×Dic10φ: C2×C6/C6C2 ⊆ Aut C20240C20.11(C2xC6)240,155
C20.12(C2×C6) = C3×C4○D20φ: C2×C6/C6C2 ⊆ Aut C201202C20.12(C2xC6)240,158
C20.13(C2×C6) = D5×C24φ: C2×C6/C6C2 ⊆ Aut C201202C20.13(C2xC6)240,33
C20.14(C2×C6) = C3×C8⋊D5φ: C2×C6/C6C2 ⊆ Aut C201202C20.14(C2xC6)240,34
C20.15(C2×C6) = C6×C52C8φ: C2×C6/C6C2 ⊆ Aut C20240C20.15(C2xC6)240,38
C20.16(C2×C6) = C3×C4.Dic5φ: C2×C6/C6C2 ⊆ Aut C201202C20.16(C2xC6)240,39
C20.17(C2×C6) = C15×D8φ: C2×C6/C6C2 ⊆ Aut C201202C20.17(C2xC6)240,86
C20.18(C2×C6) = C15×SD16φ: C2×C6/C6C2 ⊆ Aut C201202C20.18(C2xC6)240,87
C20.19(C2×C6) = C15×Q16φ: C2×C6/C6C2 ⊆ Aut C202402C20.19(C2xC6)240,88
C20.20(C2×C6) = Q8×C30φ: C2×C6/C6C2 ⊆ Aut C20240C20.20(C2xC6)240,187
C20.21(C2×C6) = C15×C4○D4φ: C2×C6/C6C2 ⊆ Aut C201202C20.21(C2xC6)240,188
C20.22(C2×C6) = C15×M4(2)central extension (φ=1)1202C20.22(C2xC6)240,85

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