A nonlinear control system, with n states and m controls (resp. an underdetermined system of n ODEs for n+m variables), is said to be flat if we can find m functions, called a flat output, such that together with their successive time-derivatives along trajectories, they determine the state and the control of the system (resp. determine the evolution of all system's variables). In our talk, we will study and answer the following natural question asked by Rouchon, Martin, and Murray: if a control system is flat and is invariant by an action of a group G of symmetries, does it possess flat outputs that are also invariant under the action of G?