# Extensions 1→N→G→Q→1 with N=D4 and Q=C2×C20

Direct product G=N×Q with N=D4 and Q=C2×C20
dρLabelID
D4×C2×C20160D4xC2xC20320,1517

Semidirect products G=N:Q with N=D4 and Q=C2×C20
extensionφ:Q→Out NdρLabelID
D41(C2×C20) = D8×C20φ: C2×C20/C20C2 ⊆ Out D4160D4:1(C2xC20)320,938
D42(C2×C20) = C5×D8⋊C4φ: C2×C20/C20C2 ⊆ Out D4160D4:2(C2xC20)320,943
D43(C2×C20) = C10×D4⋊C4φ: C2×C20/C2×C10C2 ⊆ Out D4160D4:3(C2xC20)320,915
D44(C2×C20) = C5×C23.36D4φ: C2×C20/C2×C10C2 ⊆ Out D4160D4:4(C2xC20)320,918
D45(C2×C20) = C10×C4≀C2φ: C2×C20/C2×C10C2 ⊆ Out D480D4:5(C2xC20)320,921
D46(C2×C20) = C4○D4×C20φ: trivial image160D4:6(C2xC20)320,1519
D47(C2×C20) = C5×C22.11C24φ: trivial image80D4:7(C2xC20)320,1520
D48(C2×C20) = C5×C23.33C23φ: trivial image160D4:8(C2xC20)320,1522

Non-split extensions G=N.Q with N=D4 and Q=C2×C20
extensionφ:Q→Out NdρLabelID
D4.1(C2×C20) = SD16×C20φ: C2×C20/C20C2 ⊆ Out D4160D4.1(C2xC20)320,939
D4.2(C2×C20) = C5×SD16⋊C4φ: C2×C20/C20C2 ⊆ Out D4160D4.2(C2xC20)320,941
D4.3(C2×C20) = C5×C8○D8φ: C2×C20/C20C2 ⊆ Out D4802D4.3(C2xC20)320,944
D4.4(C2×C20) = C5×C8.26D4φ: C2×C20/C20C2 ⊆ Out D4804D4.4(C2xC20)320,945
D4.5(C2×C20) = C5×C23.24D4φ: C2×C20/C2×C10C2 ⊆ Out D4160D4.5(C2xC20)320,917
D4.6(C2×C20) = C5×C23.37D4φ: C2×C20/C2×C10C2 ⊆ Out D480D4.6(C2xC20)320,919
D4.7(C2×C20) = C5×C42⋊C22φ: C2×C20/C2×C10C2 ⊆ Out D4804D4.7(C2xC20)320,922
D4.8(C2×C20) = C10×C8○D4φ: trivial image160D4.8(C2xC20)320,1569
D4.9(C2×C20) = C5×Q8○M4(2)φ: trivial image804D4.9(C2xC20)320,1570

׿
×
𝔽