# Extensions 1→N→G→Q→1 with N=D5×C3×C6 and Q=C2

Direct product G=N×Q with N=D5×C3×C6 and Q=C2
dρLabelID
D5×C62180D5xC6^2360,157

Semidirect products G=N:Q with N=D5×C3×C6 and Q=C2
extensionφ:Q→Out NdρLabelID
(D5×C3×C6)⋊1C2 = C3×C15⋊D4φ: C2/C1C2 ⊆ Out D5×C3×C6604(D5xC3xC6):1C2360,61
(D5×C3×C6)⋊2C2 = C3×C3⋊D20φ: C2/C1C2 ⊆ Out D5×C3×C6604(D5xC3xC6):2C2360,62
(D5×C3×C6)⋊3C2 = C30.12D6φ: C2/C1C2 ⊆ Out D5×C3×C6180(D5xC3xC6):3C2360,68
(D5×C3×C6)⋊4C2 = C327D20φ: C2/C1C2 ⊆ Out D5×C3×C6180(D5xC3xC6):4C2360,69
(D5×C3×C6)⋊5C2 = S3×C6×D5φ: C2/C1C2 ⊆ Out D5×C3×C6604(D5xC3xC6):5C2360,151
(D5×C3×C6)⋊6C2 = C2×D5×C3⋊S3φ: C2/C1C2 ⊆ Out D5×C3×C690(D5xC3xC6):6C2360,152
(D5×C3×C6)⋊7C2 = C32×D20φ: C2/C1C2 ⊆ Out D5×C3×C6180(D5xC3xC6):7C2360,92
(D5×C3×C6)⋊8C2 = C32×C5⋊D4φ: C2/C1C2 ⊆ Out D5×C3×C6180(D5xC3xC6):8C2360,94

Non-split extensions G=N.Q with N=D5×C3×C6 and Q=C2
extensionφ:Q→Out NdρLabelID
(D5×C3×C6).1C2 = C3×D5×Dic3φ: C2/C1C2 ⊆ Out D5×C3×C6604(D5xC3xC6).1C2360,58
(D5×C3×C6).2C2 = D5×C3⋊Dic3φ: C2/C1C2 ⊆ Out D5×C3×C6180(D5xC3xC6).2C2360,65
(D5×C3×C6).3C2 = C2×C323F5φ: C2/C1C2 ⊆ Out D5×C3×C690(D5xC3xC6).3C2360,147
(D5×C3×C6).4C2 = C6×C3⋊F5φ: C2/C1C2 ⊆ Out D5×C3×C6604(D5xC3xC6).4C2360,146
(D5×C3×C6).5C2 = C3×C6×F5φ: C2/C1C2 ⊆ Out D5×C3×C690(D5xC3xC6).5C2360,145
(D5×C3×C6).6C2 = D5×C3×C12φ: trivial image180(D5xC3xC6).6C2360,91

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