We prove that various subgroups of $Out(F_n)$ — the outer automorphism group of a free group of rank $n$ — such as the stabilizer of the conjugacy class of a rank $n-1$ free factor, are undistorted in $Out(F_n)$. The method of proof is to show that these subgroups are Lipschitz retracts of the ambient group, in fact we construct these retractions in appropriate spaces of trees on which $F_n$ acts.