Extensions 1→N→G→Q→1 with N=C2×C4 and Q=C5×C10

Direct product G=N×Q with N=C2×C4 and Q=C5×C10
dρLabelID
C2×C10×C20400C2xC10xC20400,201

Semidirect products G=N:Q with N=C2×C4 and Q=C5×C10
extensionφ:Q→Aut NdρLabelID
(C2×C4)⋊1(C5×C10) = C22⋊C4×C52φ: C5×C10/C52C2 ⊆ Aut C2×C4200(C2xC4):1(C5xC10)400,109
(C2×C4)⋊2(C5×C10) = D4×C5×C10φ: C5×C10/C52C2 ⊆ Aut C2×C4200(C2xC4):2(C5xC10)400,202
(C2×C4)⋊3(C5×C10) = C4○D4×C52φ: C5×C10/C52C2 ⊆ Aut C2×C4200(C2xC4):3(C5xC10)400,204

Non-split extensions G=N.Q with N=C2×C4 and Q=C5×C10
extensionφ:Q→Aut NdρLabelID
(C2×C4).1(C5×C10) = C4⋊C4×C52φ: C5×C10/C52C2 ⊆ Aut C2×C4400(C2xC4).1(C5xC10)400,110
(C2×C4).2(C5×C10) = M4(2)×C52φ: C5×C10/C52C2 ⊆ Aut C2×C4200(C2xC4).2(C5xC10)400,112
(C2×C4).3(C5×C10) = Q8×C5×C10φ: C5×C10/C52C2 ⊆ Aut C2×C4400(C2xC4).3(C5xC10)400,203

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