  We study the effects of symmetry breaking on non-Markovian dynamics in
various system-bath arrangements. It is shown that by breaking certain
symmetries features signaling non-Markovian time evolution disappear within a
finite time t_{g}. We demonstrate numerically that the scaling of t_{g} with
the symmetry breaking strength is different for various types of symmetry. We
provide a mathematical explanation for these differences related to the
spectrum of the total system-bath Hamiltonian and provide arguments that the
scaling properties of t_{g} should be universal.
