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In this paper, a complete analysis of symmetries and conservation laws forthe charged squashed Kaluza--Klein black hole spacetime in a Riemannian spaceis discussed. First, a comprehensive group analysis of the underlyingspace-time metric using Lie point symmetries are presented and then it the$n$-dimensional optimal system of this space-time metric, for $n=1,\ldots,4$,are computed. It is shown that there is not any $n$-dimensional optimal systemof Lie symmetry subalgebra associated to the system of geodesic for $n\geq5$.Then the point symmetries of the one parameter Lie groups of transformationsthat leave invariant the action integral corresponding to the Lagrangian thatmeans Noether symmetries are found and then the conservation laws associated tothe system of geodesic equations are calculated via Noether's theorem.

Symmetry analysis of the charged squashed Kaluza-Klein black hole metric