# Extensions 1→N→G→Q→1 with N=C8 and Q=C22×C10

Direct product G=N×Q with N=C8 and Q=C22×C10
dρLabelID
C23×C40320C2^3xC40320,1567

Semidirect products G=N:Q with N=C8 and Q=C22×C10
extensionφ:Q→Aut NdρLabelID
C8⋊(C22×C10) = C10×C8⋊C22φ: C22×C10/C10C22 ⊆ Aut C880C8:(C2^2xC10)320,1575
C82(C22×C10) = D8×C2×C10φ: C22×C10/C2×C10C2 ⊆ Aut C8160C8:2(C2^2xC10)320,1571
C83(C22×C10) = SD16×C2×C10φ: C22×C10/C2×C10C2 ⊆ Aut C8160C8:3(C2^2xC10)320,1572
C84(C22×C10) = M4(2)×C2×C10φ: C22×C10/C2×C10C2 ⊆ Aut C8160C8:4(C2^2xC10)320,1568

Non-split extensions G=N.Q with N=C8 and Q=C22×C10
extensionφ:Q→Aut NdρLabelID
C8.1(C22×C10) = C10×C8.C22φ: C22×C10/C10C22 ⊆ Aut C8160C8.1(C2^2xC10)320,1576
C8.2(C22×C10) = C5×D8⋊C22φ: C22×C10/C10C22 ⊆ Aut C8804C8.2(C2^2xC10)320,1577
C8.3(C22×C10) = C10×D16φ: C22×C10/C2×C10C2 ⊆ Aut C8160C8.3(C2^2xC10)320,1006
C8.4(C22×C10) = C10×SD32φ: C22×C10/C2×C10C2 ⊆ Aut C8160C8.4(C2^2xC10)320,1007
C8.5(C22×C10) = C10×Q32φ: C22×C10/C2×C10C2 ⊆ Aut C8320C8.5(C2^2xC10)320,1008
C8.6(C22×C10) = C5×C4○D16φ: C22×C10/C2×C10C2 ⊆ Aut C81602C8.6(C2^2xC10)320,1009
C8.7(C22×C10) = C5×C16⋊C22φ: C22×C10/C2×C10C2 ⊆ Aut C8804C8.7(C2^2xC10)320,1010
C8.8(C22×C10) = C5×Q32⋊C2φ: C22×C10/C2×C10C2 ⊆ Aut C81604C8.8(C2^2xC10)320,1011
C8.9(C22×C10) = Q16×C2×C10φ: C22×C10/C2×C10C2 ⊆ Aut C8320C8.9(C2^2xC10)320,1573
C8.10(C22×C10) = C5×D4○D8φ: C22×C10/C2×C10C2 ⊆ Aut C8804C8.10(C2^2xC10)320,1578
C8.11(C22×C10) = C5×Q8○D8φ: C22×C10/C2×C10C2 ⊆ Aut C81604C8.11(C2^2xC10)320,1580
C8.12(C22×C10) = C10×C4○D8φ: C22×C10/C2×C10C2 ⊆ Aut C8160C8.12(C2^2xC10)320,1574
C8.13(C22×C10) = C5×D4○SD16φ: C22×C10/C2×C10C2 ⊆ Aut C8804C8.13(C2^2xC10)320,1579
C8.14(C22×C10) = C5×Q8○M4(2)φ: C22×C10/C2×C10C2 ⊆ Aut C8804C8.14(C2^2xC10)320,1570
C8.15(C22×C10) = C10×M5(2)central extension (φ=1)160C8.15(C2^2xC10)320,1004
C8.16(C22×C10) = C5×D4○C16central extension (φ=1)1602C8.16(C2^2xC10)320,1005
C8.17(C22×C10) = C10×C8○D4central extension (φ=1)160C8.17(C2^2xC10)320,1569

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