  Primitive constant length substitutions generate minimal symbolic dynamical
systems. In this article we present an algorithm which can produce the list of
injective substitutions of the same length that generate topologically
conjugate systems.
  We show that each conjugacy class contains infinitely substitutions which are
not injective. As examples, the Toeplitz conjugacy class contains three
injective substitutions (two on two symbols and one on three symbols), and the
length two Thue-Morse conjugacy class contains twelve substitutions, among
which are two on six symbols. Together, they constitute a list of all primitive
substitutions of length two with infinite minimal systems which are factors of
the Thue-Morse system.
