We find the symmetry generators for the Friedman equations emanating from a perfect fluid source in the presence of a cosmological constant term. The relevant dynamics are shown to be governed by two coupled, first order ordinary differential equations, the continuity and the quadratic constraint equation. Arbitrary functions appear in the components of the symmetry vector, indicating the infinity of the group. When the equation of state is considered as arbitrary but ab initio given, previously known results are recovered and/or generalized. When the pressure is considered among the dynamical variables, solutions for models with different equations of state are mapped to each other, thus enabling the presentation of solutions to models with complicated equations of state starting from simple known cases.