# Extensions 1→N→G→Q→1 with N=C2×C10 and Q=S4

Direct product G=N×Q with N=C2×C10 and Q=S4
dρLabelID
C2×C10×S460C2xC10xS4480,1198

Semidirect products G=N:Q with N=C2×C10 and Q=S4
extensionφ:Q→Aut NdρLabelID
(C2×C10)⋊1S4 = C5×C22⋊S4φ: S4/C22S3 ⊆ Aut C2×C10406(C2xC10):1S4480,1200
(C2×C10)⋊2S4 = C244D15φ: S4/C22S3 ⊆ Aut C2×C10406(C2xC10):2S4480,1201
(C2×C10)⋊3S4 = C5×A4⋊D4φ: S4/A4C2 ⊆ Aut C2×C10606(C2xC10):3S4480,1023
(C2×C10)⋊4S4 = C242D15φ: S4/A4C2 ⊆ Aut C2×C10606(C2xC10):4S4480,1034
(C2×C10)⋊5S4 = C22×C5⋊S4φ: S4/A4C2 ⊆ Aut C2×C1060(C2xC10):5S4480,1199

Non-split extensions G=N.Q with N=C2×C10 and Q=S4
extensionφ:Q→Aut NdρLabelID
(C2×C10).1S4 = C5×C42⋊S3φ: S4/C22S3 ⊆ Aut C2×C10603(C2xC10).1S4480,254
(C2×C10).2S4 = C42⋊D15φ: S4/C22S3 ⊆ Aut C2×C10606+(C2xC10).2S4480,258
(C2×C10).3S4 = C5×Q8.D6φ: S4/A4C2 ⊆ Aut C2×C10804(C2xC10).3S4480,1018
(C2×C10).4S4 = Q8⋊Dic15φ: S4/A4C2 ⊆ Aut C2×C10160(C2xC10).4S4480,260
(C2×C10).5S4 = C2×Q8.D15φ: S4/A4C2 ⊆ Aut C2×C10160(C2xC10).5S4480,1027
(C2×C10).6S4 = C2×Q8⋊D15φ: S4/A4C2 ⊆ Aut C2×C1080(C2xC10).6S4480,1028
(C2×C10).7S4 = Q8.D30φ: S4/A4C2 ⊆ Aut C2×C10804(C2xC10).7S4480,1029
(C2×C10).8S4 = C2×A4⋊Dic5φ: S4/A4C2 ⊆ Aut C2×C10120(C2xC10).8S4480,1033
(C2×C10).9S4 = C5×Q8⋊Dic3central extension (φ=1)160(C2xC10).9S4480,256
(C2×C10).10S4 = C10×CSU2(𝔽3)central extension (φ=1)160(C2xC10).10S4480,1016
(C2×C10).11S4 = C10×GL2(𝔽3)central extension (φ=1)80(C2xC10).11S4480,1017
(C2×C10).12S4 = C10×A4⋊C4central extension (φ=1)120(C2xC10).12S4480,1022

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