# Extensions 1→N→G→Q→1 with N=C2×C10 and Q=C3×S3

Direct product G=N×Q with N=C2×C10 and Q=C3×S3
dρLabelID
S3×C2×C30120S3xC2xC30360,158

Semidirect products G=N:Q with N=C2×C10 and Q=C3×S3
extensionφ:Q→Aut NdρLabelID
(C2×C10)⋊1(C3×S3) = C15×S4φ: C3×S3/C3S3 ⊆ Aut C2×C10603(C2xC10):1(C3xS3)360,138
(C2×C10)⋊2(C3×S3) = C3×C5⋊S4φ: C3×S3/C3S3 ⊆ Aut C2×C10606(C2xC10):2(C3xS3)360,139
(C2×C10)⋊3(C3×S3) = A4×D15φ: C3×S3/C3C6 ⊆ Aut C2×C10606+(C2xC10):3(C3xS3)360,144
(C2×C10)⋊4(C3×S3) = C5×S3×A4φ: C3×S3/S3C3 ⊆ Aut C2×C10606(C2xC10):4(C3xS3)360,143
(C2×C10)⋊5(C3×S3) = C15×C3⋊D4φ: C3×S3/C32C2 ⊆ Aut C2×C10602(C2xC10):5(C3xS3)360,99
(C2×C10)⋊6(C3×S3) = C3×C157D4φ: C3×S3/C32C2 ⊆ Aut C2×C10602(C2xC10):6(C3xS3)360,104
(C2×C10)⋊7(C3×S3) = C2×C6×D15φ: C3×S3/C32C2 ⊆ Aut C2×C10120(C2xC10):7(C3xS3)360,159

Non-split extensions G=N.Q with N=C2×C10 and Q=C3×S3
extensionφ:Q→Aut NdρLabelID
(C2×C10).(C3×S3) = C6×Dic15φ: C3×S3/C32C2 ⊆ Aut C2×C10120(C2xC10).(C3xS3)360,103
(C2×C10).2(C3×S3) = Dic3×C30central extension (φ=1)120(C2xC10).2(C3xS3)360,98

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