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We evaluate the LHC’s potential of observing Higgs boson decays into light elementary or composite resonances through their hadronic decay channels. We focus on the Higgs boson production processes with the largest cross sections, pp→h and pp→h+jet, with subsequent decays h→ZA or h→Zηc, and comment on the production process pp→hZ. By exploiting track-based jet substructure observables and extrapolating to 3000 fb-1 we find BR(h→ZA)≃BR(h→Zηc)≲0.02 at 95% CL. We interpret this limit in terms of the 2HDM Type 1. We find that searches for h→ZA are complementary to existing measurements and can constrain large parts of the currently allowed parameter space.