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Extensions 1→N→G→Q→1 with N=C2×C30 and Q=S3

Direct product G=N×Q with N=C2×C30 and Q=S3
dρLabelID
S3×C2×C30120S3xC2xC30360,158

Semidirect products G=N:Q with N=C2×C30 and Q=S3
extensionφ:Q→Aut NdρLabelID
(C2×C30)⋊1S3 = C15×S4φ: S3/C1 → S3 ⊆ Aut C2×C30603(C2xC30):1S3360,138
(C2×C30)⋊2S3 = A4⋊D15φ: S3/C1 → S3 ⊆ Aut C2×C30606+(C2xC30):2S3360,141
(C2×C30)⋊3S3 = C3×C5⋊S4φ: S3/C1 → S3 ⊆ Aut C2×C30606(C2xC30):3S3360,139
(C2×C30)⋊4S3 = C5×C3⋊S4φ: S3/C1 → S3 ⊆ Aut C2×C30606(C2xC30):4S3360,140
(C2×C30)⋊5S3 = C15×C3⋊D4φ: S3/C3 → C2 ⊆ Aut C2×C30602(C2xC30):5S3360,99
(C2×C30)⋊6S3 = C62⋊D5φ: S3/C3 → C2 ⊆ Aut C2×C30180(C2xC30):6S3360,114
(C2×C30)⋊7S3 = C22×C3⋊D15φ: S3/C3 → C2 ⊆ Aut C2×C30180(C2xC30):7S3360,161
(C2×C30)⋊8S3 = C3×C15⋊7D4φ: S3/C3 → C2 ⊆ Aut C2×C30602(C2xC30):8S3360,104
(C2×C30)⋊9S3 = C2×C6×D15φ: S3/C3 → C2 ⊆ Aut C2×C30120(C2xC30):9S3360,159
(C2×C30)⋊10S3 = C5×C32⋊7D4φ: S3/C3 → C2 ⊆ Aut C2×C30180(C2xC30):10S3360,109
(C2×C30)⋊11S3 = C3⋊S3×C2×C10φ: S3/C3 → C2 ⊆ Aut C2×C30180(C2xC30):11S3360,160

Non-split extensions G=N.Q with N=C2×C30 and Q=S3
extensionφ:Q→Aut NdρLabelID
(C2×C30).1S3 = C22⋊D45φ: S3/C1 → S3 ⊆ Aut C2×C30906+(C2xC30).1S3360,41
(C2×C30).2S3 = C5×C3.S4φ: S3/C1 → S3 ⊆ Aut C2×C30906(C2xC30).2S3360,40
(C2×C30).3S3 = C2×Dic45φ: S3/C3 → C2 ⊆ Aut C2×C30360(C2xC30).3S3360,28
(C2×C30).4S3 = C45⋊7D4φ: S3/C3 → C2 ⊆ Aut C2×C301802(C2xC30).4S3360,29
(C2×C30).5S3 = C22×D45φ: S3/C3 → C2 ⊆ Aut C2×C30180(C2xC30).5S3360,49
(C2×C30).6S3 = C2×C3⋊Dic15φ: S3/C3 → C2 ⊆ Aut C2×C30360(C2xC30).6S3360,113
(C2×C30).7S3 = C6×Dic15φ: S3/C3 → C2 ⊆ Aut C2×C30120(C2xC30).7S3360,103
(C2×C30).8S3 = C10×Dic9φ: S3/C3 → C2 ⊆ Aut C2×C30360(C2xC30).8S3360,23
(C2×C30).9S3 = C5×C9⋊D4φ: S3/C3 → C2 ⊆ Aut C2×C301802(C2xC30).9S3360,24
(C2×C30).10S3 = D9×C2×C10φ: S3/C3 → C2 ⊆ Aut C2×C30180(C2xC30).10S3360,48
(C2×C30).11S3 = C10×C3⋊Dic3φ: S3/C3 → C2 ⊆ Aut C2×C30360(C2xC30).11S3360,108
(C2×C30).12S3 = Dic3×C30central extension (φ=1)120(C2xC30).12S3360,98

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