# Extensions 1→N→G→Q→1 with N=C23×D5 and Q=C6

Direct product G=N×Q with N=C23×D5 and Q=C6
dρLabelID
D5×C23×C6240D5xC2^3xC6480,1210

Semidirect products G=N:Q with N=C23×D5 and Q=C6
extensionφ:Q→Out NdρLabelID
(C23×D5)⋊1C6 = A4×D20φ: C6/C1C6 ⊆ Out C23×D5606+(C2^3xD5):1C6480,1037
(C23×D5)⋊2C6 = A4×C5⋊D4φ: C6/C1C6 ⊆ Out C23×D5606(C2^3xD5):2C6480,1045
(C23×D5)⋊3C6 = C22×D5×A4φ: C6/C2C3 ⊆ Out C23×D560(C2^3xD5):3C6480,1202
(C23×D5)⋊4C6 = C3×C22⋊D20φ: C6/C3C2 ⊆ Out C23×D5120(C2^3xD5):4C6480,675
(C23×D5)⋊5C6 = C3×C23⋊D10φ: C6/C3C2 ⊆ Out C23×D5120(C2^3xD5):5C6480,730
(C23×D5)⋊6C6 = C2×C6×D20φ: C6/C3C2 ⊆ Out C23×D5240(C2^3xD5):6C6480,1137
(C23×D5)⋊7C6 = C6×D4×D5φ: C6/C3C2 ⊆ Out C23×D5120(C2^3xD5):7C6480,1139
(C23×D5)⋊8C6 = C2×C6×C5⋊D4φ: C6/C3C2 ⊆ Out C23×D5240(C2^3xD5):8C6480,1149

Non-split extensions G=N.Q with N=C23×D5 and Q=C6
extensionφ:Q→Out NdρLabelID
(C23×D5).C6 = C2×A4×F5φ: C6/C1C6 ⊆ Out C23×D53012+(C2^3xD5).C6480,1192
(C23×D5).2C6 = C4×D5×A4φ: C6/C2C3 ⊆ Out C23×D5606(C2^3xD5).2C6480,1036
(C23×D5).3C6 = C3×D5×C22⋊C4φ: C6/C3C2 ⊆ Out C23×D5120(C2^3xD5).3C6480,673
(C23×D5).4C6 = C6×D10⋊C4φ: C6/C3C2 ⊆ Out C23×D5240(C2^3xD5).4C6480,720
(C23×D5).5C6 = C6×C22⋊F5φ: C6/C3C2 ⊆ Out C23×D5120(C2^3xD5).5C6480,1059
(C23×D5).6C6 = F5×C22×C6φ: C6/C3C2 ⊆ Out C23×D5120(C2^3xD5).6C6480,1205
(C23×D5).7C6 = D5×C22×C12φ: trivial image240(C2^3xD5).7C6480,1136

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