# Extensions 1→N→G→Q→1 with N=C42 and Q=C3×D5

Direct product G=N×Q with N=C42 and Q=C3×D5
dρLabelID
D5×C4×C12240D5xC4xC12480,664

Semidirect products G=N:Q with N=C42 and Q=C3×D5
extensionφ:Q→Aut NdρLabelID
C421(C3×D5) = (C4×C20)⋊C6φ: C3×D5/C5C6 ⊆ Aut C42806C4^2:1(C3xD5)480,263
C422(C3×D5) = C204D4⋊C3φ: C3×D5/C5C6 ⊆ Aut C42606+C4^2:2(C3xD5)480,262
C423(C3×D5) = D5×C42⋊C3φ: C3×D5/D5C3 ⊆ Aut C42606C4^2:3(C3xD5)480,264
C424(C3×D5) = C3×C42⋊D5φ: C3×D5/C15C2 ⊆ Aut C42240C4^2:4(C3xD5)480,665
C425(C3×D5) = C3×C422D5φ: C3×D5/C15C2 ⊆ Aut C42240C4^2:5(C3xD5)480,669
C426(C3×D5) = C3×D204C4φ: C3×D5/C15C2 ⊆ Aut C421202C4^2:6(C3xD5)480,83
C427(C3×D5) = C12×D20φ: C3×D5/C15C2 ⊆ Aut C42240C4^2:7(C3xD5)480,666
C428(C3×D5) = C3×C204D4φ: C3×D5/C15C2 ⊆ Aut C42240C4^2:8(C3xD5)480,667
C429(C3×D5) = C3×C4.D20φ: C3×D5/C15C2 ⊆ Aut C42240C4^2:9(C3xD5)480,668

Non-split extensions G=N.Q with N=C42 and Q=C3×D5
extensionφ:Q→Aut NdρLabelID
C42.1(C3×D5) = C3×C42.D5φ: C3×D5/C15C2 ⊆ Aut C42480C4^2.1(C3xD5)480,81
C42.2(C3×D5) = C3×C203C8φ: C3×D5/C15C2 ⊆ Aut C42480C4^2.2(C3xD5)480,82
C42.3(C3×D5) = C12×Dic10φ: C3×D5/C15C2 ⊆ Aut C42480C4^2.3(C3xD5)480,661
C42.4(C3×D5) = C3×C202Q8φ: C3×D5/C15C2 ⊆ Aut C42480C4^2.4(C3xD5)480,662
C42.5(C3×D5) = C3×C20.6Q8φ: C3×D5/C15C2 ⊆ Aut C42480C4^2.5(C3xD5)480,663
C42.6(C3×D5) = C12×C52C8central extension (φ=1)480C4^2.6(C3xD5)480,80

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