# Extensions 1→N→G→Q→1 with N=D4 and Q=C22×C10

Direct product G=N×Q with N=D4 and Q=C22×C10
dρLabelID
D4×C22×C10160D4xC2^2xC10320,1629

Semidirect products G=N:Q with N=D4 and Q=C22×C10
extensionφ:Q→Out NdρLabelID
D41(C22×C10) = D8×C2×C10φ: C22×C10/C2×C10C2 ⊆ Out D4160D4:1(C2^2xC10)320,1571
D42(C22×C10) = C10×C8⋊C22φ: C22×C10/C2×C10C2 ⊆ Out D480D4:2(C2^2xC10)320,1575
D43(C22×C10) = C4○D4×C2×C10φ: trivial image160D4:3(C2^2xC10)320,1631
D44(C22×C10) = C10×2+ 1+4φ: trivial image80D4:4(C2^2xC10)320,1632

Non-split extensions G=N.Q with N=D4 and Q=C22×C10
extensionφ:Q→Out NdρLabelID
D4.1(C22×C10) = SD16×C2×C10φ: C22×C10/C2×C10C2 ⊆ Out D4160D4.1(C2^2xC10)320,1572
D4.2(C22×C10) = C10×C4○D8φ: C22×C10/C2×C10C2 ⊆ Out D4160D4.2(C2^2xC10)320,1574
D4.3(C22×C10) = C10×C8.C22φ: C22×C10/C2×C10C2 ⊆ Out D4160D4.3(C2^2xC10)320,1576
D4.4(C22×C10) = C5×D8⋊C22φ: C22×C10/C2×C10C2 ⊆ Out D4804D4.4(C2^2xC10)320,1577
D4.5(C22×C10) = C5×D4○D8φ: C22×C10/C2×C10C2 ⊆ Out D4804D4.5(C2^2xC10)320,1578
D4.6(C22×C10) = C5×D4○SD16φ: C22×C10/C2×C10C2 ⊆ Out D4804D4.6(C2^2xC10)320,1579
D4.7(C22×C10) = C5×Q8○D8φ: C22×C10/C2×C10C2 ⊆ Out D41604D4.7(C2^2xC10)320,1580
D4.8(C22×C10) = C10×2- 1+4φ: trivial image160D4.8(C2^2xC10)320,1633
D4.9(C22×C10) = C5×C2.C25φ: trivial image804D4.9(C2^2xC10)320,1634

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