# Extensions 1→N→G→Q→1 with N=C6 and Q=C6×D5

Direct product G=N×Q with N=C6 and Q=C6×D5
dρLabelID
D5×C62180D5xC6^2360,157

Semidirect products G=N:Q with N=C6 and Q=C6×D5
extensionφ:Q→Aut NdρLabelID
C61(C6×D5) = S3×C6×D5φ: C6×D5/C3×D5C2 ⊆ Aut C6604C6:1(C6xD5)360,151
C62(C6×D5) = C2×C6×D15φ: C6×D5/C30C2 ⊆ Aut C6120C6:2(C6xD5)360,159

Non-split extensions G=N.Q with N=C6 and Q=C6×D5
extensionφ:Q→Aut NdρLabelID
C6.1(C6×D5) = C3×D5×Dic3φ: C6×D5/C3×D5C2 ⊆ Aut C6604C6.1(C6xD5)360,58
C6.2(C6×D5) = C3×S3×Dic5φ: C6×D5/C3×D5C2 ⊆ Aut C61204C6.2(C6xD5)360,59
C6.3(C6×D5) = C3×D30.C2φ: C6×D5/C3×D5C2 ⊆ Aut C61204C6.3(C6xD5)360,60
C6.4(C6×D5) = C3×C15⋊D4φ: C6×D5/C3×D5C2 ⊆ Aut C6604C6.4(C6xD5)360,61
C6.5(C6×D5) = C3×C3⋊D20φ: C6×D5/C3×D5C2 ⊆ Aut C6604C6.5(C6xD5)360,62
C6.6(C6×D5) = C3×C5⋊D12φ: C6×D5/C3×D5C2 ⊆ Aut C61204C6.6(C6xD5)360,63
C6.7(C6×D5) = C3×C15⋊Q8φ: C6×D5/C3×D5C2 ⊆ Aut C61204C6.7(C6xD5)360,64
C6.8(C6×D5) = C3×Dic30φ: C6×D5/C30C2 ⊆ Aut C61202C6.8(C6xD5)360,100
C6.9(C6×D5) = C12×D15φ: C6×D5/C30C2 ⊆ Aut C61202C6.9(C6xD5)360,101
C6.10(C6×D5) = C3×D60φ: C6×D5/C30C2 ⊆ Aut C61202C6.10(C6xD5)360,102
C6.11(C6×D5) = C6×Dic15φ: C6×D5/C30C2 ⊆ Aut C6120C6.11(C6xD5)360,103
C6.12(C6×D5) = C3×C157D4φ: C6×D5/C30C2 ⊆ Aut C6602C6.12(C6xD5)360,104
C6.13(C6×D5) = C9×Dic10central extension (φ=1)3602C6.13(C6xD5)360,15
C6.14(C6×D5) = D5×C36central extension (φ=1)1802C6.14(C6xD5)360,16
C6.15(C6×D5) = C9×D20central extension (φ=1)1802C6.15(C6xD5)360,17
C6.16(C6×D5) = C18×Dic5central extension (φ=1)360C6.16(C6xD5)360,18
C6.17(C6×D5) = C9×C5⋊D4central extension (φ=1)1802C6.17(C6xD5)360,19
C6.18(C6×D5) = D5×C2×C18central extension (φ=1)180C6.18(C6xD5)360,47
C6.19(C6×D5) = C32×Dic10central extension (φ=1)360C6.19(C6xD5)360,90
C6.20(C6×D5) = D5×C3×C12central extension (φ=1)180C6.20(C6xD5)360,91
C6.21(C6×D5) = C32×D20central extension (φ=1)180C6.21(C6xD5)360,92
C6.22(C6×D5) = C3×C6×Dic5central extension (φ=1)360C6.22(C6xD5)360,93
C6.23(C6×D5) = C32×C5⋊D4central extension (φ=1)180C6.23(C6xD5)360,94

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