# Extensions 1→N→G→Q→1 with N=D10 and Q=C22×C6

Direct product G=N×Q with N=D10 and Q=C22×C6
dρLabelID
D5×C23×C6240D5xC2^3xC6480,1210

Semidirect products G=N:Q with N=D10 and Q=C22×C6
extensionφ:Q→Out NdρLabelID
D101(C22×C6) = C2×C6×D20φ: C22×C6/C2×C6C2 ⊆ Out D10240D10:1(C2^2xC6)480,1137
D102(C22×C6) = C6×D4×D5φ: C22×C6/C2×C6C2 ⊆ Out D10120D10:2(C2^2xC6)480,1139
D103(C22×C6) = C2×C6×C5⋊D4φ: C22×C6/C2×C6C2 ⊆ Out D10240D10:3(C2^2xC6)480,1149

Non-split extensions G=N.Q with N=D10 and Q=C22×C6
extensionφ:Q→Out NdρLabelID
D10.1(C22×C6) = C6×C4○D20φ: C22×C6/C2×C6C2 ⊆ Out D10240D10.1(C2^2xC6)480,1138
D10.2(C22×C6) = C6×D42D5φ: C22×C6/C2×C6C2 ⊆ Out D10240D10.2(C2^2xC6)480,1140
D10.3(C22×C6) = C3×D46D10φ: C22×C6/C2×C6C2 ⊆ Out D101204D10.3(C2^2xC6)480,1141
D10.4(C22×C6) = C6×Q82D5φ: C22×C6/C2×C6C2 ⊆ Out D10240D10.4(C2^2xC6)480,1143
D10.5(C22×C6) = C3×Q8.10D10φ: C22×C6/C2×C6C2 ⊆ Out D102404D10.5(C2^2xC6)480,1144
D10.6(C22×C6) = C3×D48D10φ: C22×C6/C2×C6C2 ⊆ Out D101204D10.6(C2^2xC6)480,1146
D10.7(C22×C6) = C3×D4.10D10φ: C22×C6/C2×C6C2 ⊆ Out D102404D10.7(C2^2xC6)480,1147
D10.8(C22×C6) = F5×C2×C12φ: C22×C6/C2×C6C2 ⊆ Out D10120D10.8(C2^2xC6)480,1050
D10.9(C22×C6) = C6×C4⋊F5φ: C22×C6/C2×C6C2 ⊆ Out D10120D10.9(C2^2xC6)480,1051
D10.10(C22×C6) = C3×D10.C23φ: C22×C6/C2×C6C2 ⊆ Out D101204D10.10(C2^2xC6)480,1052
D10.11(C22×C6) = C3×D4×F5φ: C22×C6/C2×C6C2 ⊆ Out D10608D10.11(C2^2xC6)480,1054
D10.12(C22×C6) = C3×Q8×F5φ: C22×C6/C2×C6C2 ⊆ Out D101208D10.12(C2^2xC6)480,1056
D10.13(C22×C6) = C6×C22⋊F5φ: C22×C6/C2×C6C2 ⊆ Out D10120D10.13(C2^2xC6)480,1059
D10.14(C22×C6) = F5×C22×C6φ: C22×C6/C2×C6C2 ⊆ Out D10120D10.14(C2^2xC6)480,1205
D10.15(C22×C6) = D5×C22×C12φ: trivial image240D10.15(C2^2xC6)480,1136
D10.16(C22×C6) = C6×Q8×D5φ: trivial image240D10.16(C2^2xC6)480,1142
D10.17(C22×C6) = C3×D5×C4○D4φ: trivial image1204D10.17(C2^2xC6)480,1145

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