# Extensions 1→N→G→Q→1 with N=C23×D5 and Q=S3

Direct product G=N×Q with N=C23×D5 and Q=S3
dρLabelID
S3×C23×D5120S3xC2^3xD5480,1207

Semidirect products G=N:Q with N=C23×D5 and Q=S3
extensionφ:Q→Out NdρLabelID
(C23×D5)⋊1S3 = D10⋊S4φ: S3/C1S3 ⊆ Out C23×D5606(C2^3xD5):1S3480,980
(C23×D5)⋊2S3 = A4⋊D20φ: S3/C1S3 ⊆ Out C23×D5606+(C2^3xD5):2S3480,981
(C23×D5)⋊3S3 = C2×D5×S4φ: S3/C1S3 ⊆ Out C23×D5306+(C2^3xD5):3S3480,1193
(C23×D5)⋊4S3 = (C2×C30)⋊D4φ: S3/C3C2 ⊆ Out C23×D5120(C2^3xD5):4S3480,639
(C23×D5)⋊5S3 = (C2×C6)⋊8D20φ: S3/C3C2 ⊆ Out C23×D5120(C2^3xD5):5S3480,640
(C23×D5)⋊6S3 = C22×C15⋊D4φ: S3/C3C2 ⊆ Out C23×D5240(C2^3xD5):6S3480,1118
(C23×D5)⋊7S3 = C22×C3⋊D20φ: S3/C3C2 ⊆ Out C23×D5240(C2^3xD5):7S3480,1119
(C23×D5)⋊8S3 = C2×D5×C3⋊D4φ: S3/C3C2 ⊆ Out C23×D5120(C2^3xD5):8S3480,1122

Non-split extensions G=N.Q with N=C23×D5 and Q=S3
extensionφ:Q→Out NdρLabelID
(C23×D5).1S3 = D5×A4⋊C4φ: S3/C1S3 ⊆ Out C23×D5606(C2^3xD5).1S3480,979
(C23×D5).2S3 = C2×A4⋊F5φ: S3/C1S3 ⊆ Out C23×D53012+(C2^3xD5).2S3480,1191
(C23×D5).3S3 = C2×D10⋊Dic3φ: S3/C3C2 ⊆ Out C23×D5240(C2^3xD5).3S3480,611
(C23×D5).4S3 = D5×C6.D4φ: S3/C3C2 ⊆ Out C23×D5120(C2^3xD5).4S3480,623
(C23×D5).5S3 = C2×D10.D6φ: S3/C3C2 ⊆ Out C23×D5120(C2^3xD5).5S3480,1072
(C23×D5).6S3 = C23×C3⋊F5φ: S3/C3C2 ⊆ Out C23×D5120(C2^3xD5).6S3480,1206
(C23×D5).7S3 = C22×D5×Dic3φ: trivial image240(C2^3xD5).7S3480,1112

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