# Extensions 1→N→G→Q→1 with N=D6 and Q=C22×C10

Direct product G=N×Q with N=D6 and Q=C22×C10
dρLabelID
S3×C23×C10240S3xC2^3xC10480,1211

Semidirect products G=N:Q with N=D6 and Q=C22×C10
extensionφ:Q→Out NdρLabelID
D61(C22×C10) = C2×C10×D12φ: C22×C10/C2×C10C2 ⊆ Out D6240D6:1(C2^2xC10)480,1152
D62(C22×C10) = S3×D4×C10φ: C22×C10/C2×C10C2 ⊆ Out D6120D6:2(C2^2xC10)480,1154
D63(C22×C10) = C2×C10×C3⋊D4φ: C22×C10/C2×C10C2 ⊆ Out D6240D6:3(C2^2xC10)480,1164

Non-split extensions G=N.Q with N=D6 and Q=C22×C10
extensionφ:Q→Out NdρLabelID
D6.1(C22×C10) = C10×C4○D12φ: C22×C10/C2×C10C2 ⊆ Out D6240D6.1(C2^2xC10)480,1153
D6.2(C22×C10) = C10×D42S3φ: C22×C10/C2×C10C2 ⊆ Out D6240D6.2(C2^2xC10)480,1155
D6.3(C22×C10) = C5×D46D6φ: C22×C10/C2×C10C2 ⊆ Out D61204D6.3(C2^2xC10)480,1156
D6.4(C22×C10) = C10×Q83S3φ: C22×C10/C2×C10C2 ⊆ Out D6240D6.4(C2^2xC10)480,1158
D6.5(C22×C10) = C5×Q8.15D6φ: C22×C10/C2×C10C2 ⊆ Out D62404D6.5(C2^2xC10)480,1159
D6.6(C22×C10) = C5×D4○D12φ: C22×C10/C2×C10C2 ⊆ Out D61204D6.6(C2^2xC10)480,1161
D6.7(C22×C10) = C5×Q8○D12φ: C22×C10/C2×C10C2 ⊆ Out D62404D6.7(C2^2xC10)480,1162
D6.8(C22×C10) = S3×C22×C20φ: trivial image240D6.8(C2^2xC10)480,1151
D6.9(C22×C10) = S3×Q8×C10φ: trivial image240D6.9(C2^2xC10)480,1157
D6.10(C22×C10) = C5×S3×C4○D4φ: trivial image1204D6.10(C2^2xC10)480,1160

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