# Extensions 1→N→G→Q→1 with N=C6 and Q=C22×C10

Direct product G=N×Q with N=C6 and Q=C22×C10
dρLabelID
C23×C30240C2^3xC30240,208

Semidirect products G=N:Q with N=C6 and Q=C22×C10
extensionφ:Q→Aut NdρLabelID
C6⋊(C22×C10) = S3×C22×C10φ: C22×C10/C2×C10C2 ⊆ Aut C6120C6:(C2^2xC10)240,206

Non-split extensions G=N.Q with N=C6 and Q=C22×C10
extensionφ:Q→Aut NdρLabelID
C6.1(C22×C10) = C10×Dic6φ: C22×C10/C2×C10C2 ⊆ Aut C6240C6.1(C2^2xC10)240,165
C6.2(C22×C10) = S3×C2×C20φ: C22×C10/C2×C10C2 ⊆ Aut C6120C6.2(C2^2xC10)240,166
C6.3(C22×C10) = C10×D12φ: C22×C10/C2×C10C2 ⊆ Aut C6120C6.3(C2^2xC10)240,167
C6.4(C22×C10) = C5×C4○D12φ: C22×C10/C2×C10C2 ⊆ Aut C61202C6.4(C2^2xC10)240,168
C6.5(C22×C10) = C5×S3×D4φ: C22×C10/C2×C10C2 ⊆ Aut C6604C6.5(C2^2xC10)240,169
C6.6(C22×C10) = C5×D42S3φ: C22×C10/C2×C10C2 ⊆ Aut C61204C6.6(C2^2xC10)240,170
C6.7(C22×C10) = C5×S3×Q8φ: C22×C10/C2×C10C2 ⊆ Aut C61204C6.7(C2^2xC10)240,171
C6.8(C22×C10) = C5×Q83S3φ: C22×C10/C2×C10C2 ⊆ Aut C61204C6.8(C2^2xC10)240,172
C6.9(C22×C10) = Dic3×C2×C10φ: C22×C10/C2×C10C2 ⊆ Aut C6240C6.9(C2^2xC10)240,173
C6.10(C22×C10) = C10×C3⋊D4φ: C22×C10/C2×C10C2 ⊆ Aut C6120C6.10(C2^2xC10)240,174
C6.11(C22×C10) = D4×C30central extension (φ=1)120C6.11(C2^2xC10)240,186
C6.12(C22×C10) = Q8×C30central extension (φ=1)240C6.12(C2^2xC10)240,187
C6.13(C22×C10) = C15×C4○D4central extension (φ=1)1202C6.13(C2^2xC10)240,188

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