# Extensions 1→N→G→Q→1 with N=C60 and Q=C6

Direct product G=N×Q with N=C60 and Q=C6
dρLabelID
C6×C60360C6xC60360,115

Semidirect products G=N:Q with N=C60 and Q=C6
extensionφ:Q→Aut NdρLabelID
C601C6 = C3×D60φ: C6/C3C2 ⊆ Aut C601202C60:1C6360,102
C602C6 = C12×D15φ: C6/C3C2 ⊆ Aut C601202C60:2C6360,101
C603C6 = C32×D20φ: C6/C3C2 ⊆ Aut C60180C60:3C6360,92
C604C6 = C15×D12φ: C6/C3C2 ⊆ Aut C601202C60:4C6360,97
C605C6 = D5×C3×C12φ: C6/C3C2 ⊆ Aut C60180C60:5C6360,91
C606C6 = S3×C60φ: C6/C3C2 ⊆ Aut C601202C60:6C6360,96
C607C6 = D4×C3×C15φ: C6/C3C2 ⊆ Aut C60180C60:7C6360,116

Non-split extensions G=N.Q with N=C60 and Q=C6
extensionφ:Q→Aut NdρLabelID
C60.1C6 = C3×Dic30φ: C6/C3C2 ⊆ Aut C601202C60.1C6360,100
C60.2C6 = C3×C153C8φ: C6/C3C2 ⊆ Aut C601202C60.2C6360,35
C60.3C6 = C9×Dic10φ: C6/C3C2 ⊆ Aut C603602C60.3C6360,15
C60.4C6 = C9×D20φ: C6/C3C2 ⊆ Aut C601802C60.4C6360,17
C60.5C6 = C32×Dic10φ: C6/C3C2 ⊆ Aut C60360C60.5C6360,90
C60.6C6 = C15×Dic6φ: C6/C3C2 ⊆ Aut C601202C60.6C6360,95
C60.7C6 = C9×C52C8φ: C6/C3C2 ⊆ Aut C603602C60.7C6360,2
C60.8C6 = D5×C36φ: C6/C3C2 ⊆ Aut C601802C60.8C6360,16
C60.9C6 = C32×C52C8φ: C6/C3C2 ⊆ Aut C60360C60.9C6360,33
C60.10C6 = C15×C3⋊C8φ: C6/C3C2 ⊆ Aut C601202C60.10C6360,34
C60.11C6 = D4×C45φ: C6/C3C2 ⊆ Aut C601802C60.11C6360,31
C60.12C6 = Q8×C45φ: C6/C3C2 ⊆ Aut C603602C60.12C6360,32
C60.13C6 = Q8×C3×C15φ: C6/C3C2 ⊆ Aut C60360C60.13C6360,117

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