Symmetry breaking is a well-known method for search reduction. It identifies state-space symmetries prior to search, and prunes symmetric states during search. A recent proposal, star-topology decoupled search, is to search not in the state space, but in a factored version thereof, which avoids the multiplication of states across leaf components in an underlying star-topology structure. We show that, despite the much more complex structure of search states -- so-called decoupled states -- symmetry breaking can be brought to bear in this framework as well. Starting from the notion of structural symmetries over states, we identify a sub-class of such symmetries suitable for star-topology decoupled search, and we show how symmetries from that sub-class induce symmetry relations over decoupled states. We accordingly extend the routines required for search pruning and solution reconstruction. The resulting combined method can be exponentially better than both its components in theory, and this synergetic advantage is also manifested in practice: empirically, our method reliably inherits the best of its base components, and often outperforms them both.