Extensions 1→N→G→Q→1 with N=D20 and Q=C2

Direct product G=NxQ with N=D20 and Q=C2
dρLabelID
C2xD2040C2xD2080,37

Semidirect products G=N:Q with N=D20 and Q=C2
extensionφ:Q→Out NdρLabelID
D20:1C2 = D40φ: C2/C1C2 ⊆ Out D20402+D20:1C280,7
D20:2C2 = D4:D5φ: C2/C1C2 ⊆ Out D20404+D20:2C280,15
D20:3C2 = D4xD5φ: C2/C1C2 ⊆ Out D20204+D20:3C280,39
D20:4C2 = Q8:2D5φ: C2/C1C2 ⊆ Out D20404+D20:4C280,42
D20:5C2 = C4oD20φ: trivial image402D20:5C280,38

Non-split extensions G=N.Q with N=D20 and Q=C2
extensionφ:Q→Out NdρLabelID
D20.1C2 = C40:C2φ: C2/C1C2 ⊆ Out D20402D20.1C280,6
D20.2C2 = Q8:D5φ: C2/C1C2 ⊆ Out D20404+D20.2C280,17

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