# Extensions 1→N→G→Q→1 with N=C16 and Q=C2×C10

Direct product G=N×Q with N=C16 and Q=C2×C10
dρLabelID
C22×C80320C2^2xC80320,1003

Semidirect products G=N:Q with N=C16 and Q=C2×C10
extensionφ:Q→Aut NdρLabelID
C16⋊(C2×C10) = C5×C16⋊C22φ: C2×C10/C5C22 ⊆ Aut C16804C16:(C2xC10)320,1010
C162(C2×C10) = C10×D16φ: C2×C10/C10C2 ⊆ Aut C16160C16:2(C2xC10)320,1006
C163(C2×C10) = C10×SD32φ: C2×C10/C10C2 ⊆ Aut C16160C16:3(C2xC10)320,1007
C164(C2×C10) = C10×M5(2)φ: C2×C10/C10C2 ⊆ Aut C16160C16:4(C2xC10)320,1004

Non-split extensions G=N.Q with N=C16 and Q=C2×C10
extensionφ:Q→Aut NdρLabelID
C16.(C2×C10) = C5×Q32⋊C2φ: C2×C10/C5C22 ⊆ Aut C161604C16.(C2xC10)320,1011
C16.2(C2×C10) = C5×D32φ: C2×C10/C10C2 ⊆ Aut C161602C16.2(C2xC10)320,176
C16.3(C2×C10) = C5×SD64φ: C2×C10/C10C2 ⊆ Aut C161602C16.3(C2xC10)320,177
C16.4(C2×C10) = C5×Q64φ: C2×C10/C10C2 ⊆ Aut C163202C16.4(C2xC10)320,178
C16.5(C2×C10) = C10×Q32φ: C2×C10/C10C2 ⊆ Aut C16320C16.5(C2xC10)320,1008
C16.6(C2×C10) = C5×C4○D16φ: C2×C10/C10C2 ⊆ Aut C161602C16.6(C2xC10)320,1009
C16.7(C2×C10) = C5×M6(2)central extension (φ=1)1602C16.7(C2xC10)320,175
C16.8(C2×C10) = C5×D4○C16central extension (φ=1)1602C16.8(C2xC10)320,1005

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