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

Direct product G=N×Q with N=C10 and Q=C22×C10
dρLabelID
C22×C102400C2^2xC10^2400,221

Semidirect products G=N:Q with N=C10 and Q=C22×C10
extensionφ:Q→Aut NdρLabelID
C10⋊(C22×C10) = D5×C22×C10φ: C22×C10/C2×C10C2 ⊆ Aut C1080C10:(C2^2xC10)400,219

Non-split extensions G=N.Q with N=C10 and Q=C22×C10
extensionφ:Q→Aut NdρLabelID
C10.1(C22×C10) = C10×Dic10φ: C22×C10/C2×C10C2 ⊆ Aut C1080C10.1(C2^2xC10)400,181
C10.2(C22×C10) = D5×C2×C20φ: C22×C10/C2×C10C2 ⊆ Aut C1080C10.2(C2^2xC10)400,182
C10.3(C22×C10) = C10×D20φ: C22×C10/C2×C10C2 ⊆ Aut C1080C10.3(C2^2xC10)400,183
C10.4(C22×C10) = C5×C4○D20φ: C22×C10/C2×C10C2 ⊆ Aut C10402C10.4(C2^2xC10)400,184
C10.5(C22×C10) = C5×D4×D5φ: C22×C10/C2×C10C2 ⊆ Aut C10404C10.5(C2^2xC10)400,185
C10.6(C22×C10) = C5×D42D5φ: C22×C10/C2×C10C2 ⊆ Aut C10404C10.6(C2^2xC10)400,186
C10.7(C22×C10) = C5×Q8×D5φ: C22×C10/C2×C10C2 ⊆ Aut C10804C10.7(C2^2xC10)400,187
C10.8(C22×C10) = C5×Q82D5φ: C22×C10/C2×C10C2 ⊆ Aut C10804C10.8(C2^2xC10)400,188
C10.9(C22×C10) = Dic5×C2×C10φ: C22×C10/C2×C10C2 ⊆ Aut C1080C10.9(C2^2xC10)400,189
C10.10(C22×C10) = C10×C5⋊D4φ: C22×C10/C2×C10C2 ⊆ Aut C1040C10.10(C2^2xC10)400,190
C10.11(C22×C10) = D4×C50central extension (φ=1)200C10.11(C2^2xC10)400,46
C10.12(C22×C10) = Q8×C50central extension (φ=1)400C10.12(C2^2xC10)400,47
C10.13(C22×C10) = C4○D4×C25central extension (φ=1)2002C10.13(C2^2xC10)400,48
C10.14(C22×C10) = D4×C5×C10central extension (φ=1)200C10.14(C2^2xC10)400,202
C10.15(C22×C10) = Q8×C5×C10central extension (φ=1)400C10.15(C2^2xC10)400,203
C10.16(C22×C10) = C4○D4×C52central extension (φ=1)200C10.16(C2^2xC10)400,204

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