# Extensions 1→N→G→Q→1 with N=C12 and Q=C3×D5

Direct product G=N×Q with N=C12 and Q=C3×D5
dρLabelID
D5×C3×C12180D5xC3xC12360,91

Semidirect products G=N:Q with N=C12 and Q=C3×D5
extensionφ:Q→Aut NdρLabelID
C121(C3×D5) = C3×D60φ: C3×D5/C15C2 ⊆ Aut C121202C12:1(C3xD5)360,102
C122(C3×D5) = C12×D15φ: C3×D5/C15C2 ⊆ Aut C121202C12:2(C3xD5)360,101
C123(C3×D5) = C32×D20φ: C3×D5/C15C2 ⊆ Aut C12180C12:3(C3xD5)360,92

Non-split extensions G=N.Q with N=C12 and Q=C3×D5
extensionφ:Q→Aut NdρLabelID
C12.1(C3×D5) = C3×Dic30φ: C3×D5/C15C2 ⊆ Aut C121202C12.1(C3xD5)360,100
C12.2(C3×D5) = C3×C153C8φ: C3×D5/C15C2 ⊆ Aut C121202C12.2(C3xD5)360,35
C12.3(C3×D5) = C9×Dic10φ: C3×D5/C15C2 ⊆ Aut C123602C12.3(C3xD5)360,15
C12.4(C3×D5) = C9×D20φ: C3×D5/C15C2 ⊆ Aut C121802C12.4(C3xD5)360,17
C12.5(C3×D5) = C32×Dic10φ: C3×D5/C15C2 ⊆ Aut C12360C12.5(C3xD5)360,90
C12.6(C3×D5) = C9×C52C8central extension (φ=1)3602C12.6(C3xD5)360,2
C12.7(C3×D5) = D5×C36central extension (φ=1)1802C12.7(C3xD5)360,16
C12.8(C3×D5) = C32×C52C8central extension (φ=1)360C12.8(C3xD5)360,33

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