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We give a classification of all third-order nonlinear evolution equationswhich admit solvable Lie symmetry algebras $\mathsf{A}$ and which are notlinearized. We have found that there are 48 types of equations for$\dim\mathsf{A}=3$, 88 types for $\dim\mathsf{A}=4$ and there are 55 equationsfor $\dim\mathsf{A}=5$.

Symmetry classification of third-order nonlinear evolution equations. Part II: Solvable algebras