# Extensions 1→N→G→Q→1 with N=C2×C10 and Q=F5

Direct product G=N×Q with N=C2×C10 and Q=F5
dρLabelID
F5×C2×C1080F5xC2xC10400,214

Semidirect products G=N:Q with N=C2×C10 and Q=F5
extensionφ:Q→Aut NdρLabelID
(C2×C10)⋊1F5 = C102⋊C4φ: F5/C5C4 ⊆ Aut C2×C10100(C2xC10):1F5400,155
(C2×C10)⋊2F5 = C1024C4φ: F5/C5C4 ⊆ Aut C2×C10204+(C2xC10):2F5400,162
(C2×C10)⋊3F5 = C22×C5⋊F5φ: F5/C5C4 ⊆ Aut C2×C10100(C2xC10):3F5400,216
(C2×C10)⋊4F5 = C22×C52⋊C4φ: F5/C5C4 ⊆ Aut C2×C1040(C2xC10):4F5400,217
(C2×C10)⋊5F5 = C5×C22⋊F5φ: F5/D5C2 ⊆ Aut C2×C10404(C2xC10):5F5400,141
(C2×C10)⋊6F5 = D10.D10φ: F5/D5C2 ⊆ Aut C2×C10404(C2xC10):6F5400,148
(C2×C10)⋊7F5 = C22×D5.D5φ: F5/D5C2 ⊆ Aut C2×C1080(C2xC10):7F5400,215

Non-split extensions G=N.Q with N=C2×C10 and Q=F5
extensionφ:Q→Aut NdρLabelID
(C2×C10).1F5 = C2×C25⋊C8φ: F5/C5C4 ⊆ Aut C2×C10400(C2xC10).1F5400,32
(C2×C10).2F5 = C25⋊M4(2)φ: F5/C5C4 ⊆ Aut C2×C102004-(C2xC10).2F5400,33
(C2×C10).3F5 = D25.D4φ: F5/C5C4 ⊆ Aut C2×C101004+(C2xC10).3F5400,34
(C2×C10).4F5 = C22×C25⋊C4φ: F5/C5C4 ⊆ Aut C2×C10100(C2xC10).4F5400,53
(C2×C10).5F5 = C2×C524C8φ: F5/C5C4 ⊆ Aut C2×C10400(C2xC10).5F5400,153
(C2×C10).6F5 = C5213M4(2)φ: F5/C5C4 ⊆ Aut C2×C10200(C2xC10).6F5400,154
(C2×C10).7F5 = C2×C525C8φ: F5/C5C4 ⊆ Aut C2×C1080(C2xC10).7F5400,160
(C2×C10).8F5 = C5214M4(2)φ: F5/C5C4 ⊆ Aut C2×C10404-(C2xC10).8F5400,161
(C2×C10).9F5 = C5×C22.F5φ: F5/D5C2 ⊆ Aut C2×C10404(C2xC10).9F5400,140
(C2×C10).10F5 = C2×C523C8φ: F5/D5C2 ⊆ Aut C2×C1080(C2xC10).10F5400,146
(C2×C10).11F5 = C102.C4φ: F5/D5C2 ⊆ Aut C2×C10404(C2xC10).11F5400,147
(C2×C10).12F5 = C10×C5⋊C8central extension (φ=1)80(C2xC10).12F5400,139

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