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In this article we present an algorithm which can produce the list of injective substitutions of the same length that generate topologically conjugate systems.\n  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. 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