In this contribution, we extend the concept of a Petri net morphism to Elementary Object Systems (Eos). Eos are a net-within-nets formalism, that is, we allow the tokens of a Petri net to be Petri nets again. This nested structure has the consequence that even systems defined by very small Petri nets have a quite huge reachability graph. In this contribution, we use automorphism to describe symmetries of the Petri net topology. Since these symmetries carry over to markings as well, this leads to a condensed state space, too.