# Extensions 1→N→G→Q→1 with N=C2×C10 and Q=C2×C10

Direct product G=N×Q with N=C2×C10 and Q=C2×C10
dρLabelID
C22×C102400C2^2xC10^2400,221

Semidirect products G=N:Q with N=C2×C10 and Q=C2×C10
extensionφ:Q→Aut NdρLabelID
(C2×C10)⋊(C2×C10) = C5×D4×D5φ: C2×C10/C5C22 ⊆ Aut C2×C10404(C2xC10):(C2xC10)400,185
(C2×C10)⋊2(C2×C10) = D4×C5×C10φ: C2×C10/C10C2 ⊆ Aut C2×C10200(C2xC10):2(C2xC10)400,202
(C2×C10)⋊3(C2×C10) = C10×C5⋊D4φ: C2×C10/C10C2 ⊆ Aut C2×C1040(C2xC10):3(C2xC10)400,190
(C2×C10)⋊4(C2×C10) = D5×C22×C10φ: C2×C10/C10C2 ⊆ Aut C2×C1080(C2xC10):4(C2xC10)400,219

Non-split extensions G=N.Q with N=C2×C10 and Q=C2×C10
extensionφ:Q→Aut NdρLabelID
(C2×C10).(C2×C10) = C5×D42D5φ: C2×C10/C5C22 ⊆ Aut C2×C10404(C2xC10).(C2xC10)400,186
(C2×C10).2(C2×C10) = D4×C50φ: C2×C10/C10C2 ⊆ Aut C2×C10200(C2xC10).2(C2xC10)400,46
(C2×C10).3(C2×C10) = C4○D4×C25φ: C2×C10/C10C2 ⊆ Aut C2×C102002(C2xC10).3(C2xC10)400,48
(C2×C10).4(C2×C10) = C4○D4×C52φ: C2×C10/C10C2 ⊆ Aut C2×C10200(C2xC10).4(C2xC10)400,204
(C2×C10).5(C2×C10) = Dic5×C20φ: C2×C10/C10C2 ⊆ Aut C2×C1080(C2xC10).5(C2xC10)400,83
(C2×C10).6(C2×C10) = C5×C10.D4φ: C2×C10/C10C2 ⊆ Aut C2×C1080(C2xC10).6(C2xC10)400,84
(C2×C10).7(C2×C10) = C5×C4⋊Dic5φ: C2×C10/C10C2 ⊆ Aut C2×C1080(C2xC10).7(C2xC10)400,85
(C2×C10).8(C2×C10) = C5×D10⋊C4φ: C2×C10/C10C2 ⊆ Aut C2×C1080(C2xC10).8(C2xC10)400,86
(C2×C10).9(C2×C10) = C5×C23.D5φ: C2×C10/C10C2 ⊆ Aut C2×C1040(C2xC10).9(C2xC10)400,91
(C2×C10).10(C2×C10) = C10×Dic10φ: C2×C10/C10C2 ⊆ Aut C2×C1080(C2xC10).10(C2xC10)400,181
(C2×C10).11(C2×C10) = D5×C2×C20φ: C2×C10/C10C2 ⊆ Aut C2×C1080(C2xC10).11(C2xC10)400,182
(C2×C10).12(C2×C10) = C10×D20φ: C2×C10/C10C2 ⊆ Aut C2×C1080(C2xC10).12(C2xC10)400,183
(C2×C10).13(C2×C10) = C5×C4○D20φ: C2×C10/C10C2 ⊆ Aut C2×C10402(C2xC10).13(C2xC10)400,184
(C2×C10).14(C2×C10) = Dic5×C2×C10φ: C2×C10/C10C2 ⊆ Aut C2×C1080(C2xC10).14(C2xC10)400,189
(C2×C10).15(C2×C10) = C22⋊C4×C25central extension (φ=1)200(C2xC10).15(C2xC10)400,21
(C2×C10).16(C2×C10) = C4⋊C4×C25central extension (φ=1)400(C2xC10).16(C2xC10)400,22
(C2×C10).17(C2×C10) = Q8×C50central extension (φ=1)400(C2xC10).17(C2xC10)400,47
(C2×C10).18(C2×C10) = C22⋊C4×C52central extension (φ=1)200(C2xC10).18(C2xC10)400,109
(C2×C10).19(C2×C10) = C4⋊C4×C52central extension (φ=1)400(C2xC10).19(C2xC10)400,110
(C2×C10).20(C2×C10) = Q8×C5×C10central extension (φ=1)400(C2xC10).20(C2xC10)400,203

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