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The nearby Hydra cluster (∼50 Mpc) is an ideal laboratory to understand, in detail, the influence of the environment on the morphology and quenching of galaxies in dense environments. We study the Hydra cluster galaxies in the inner regions (1 R 200) of the cluster using data from the Southern Photometric Local Universe Survey, which uses 12 narrow and broad-band filters in the visible region of the spectrum. We analyse structural (Sérsic index, effective radius) and physical (colours, stellar masses, and star formation rates) properties. Based on this analysis, we find that ∼88 per cent of the Hydra cluster galaxies are quenched. Using the Dressler–Schectman test approach, we also find that the cluster shows possible substructures. Our analysis of the phase-space diagram together with densit y- based spatial clustering algorithm indicates that Hydra shows an additional substructure that appears to be in front of the cluster centre, which is still falling into it. Our results, thus, suggest that the Hydra cluster might not be relaxed. We analyse the median Sérsic index as a function of wavelength and find that for red [(u − r) ≥2.3] and earl y- type galaxies it displays a slight increase towards redder filters (13 and 18 per cent, for red and early type, respectively), whereas for blue + green [(u − r)<2.3] galaxies it remains constant. Late-type galaxies show a small decrease of the median Sérsic index towards redder filters. Also, the Sérsic index of galaxies, and thus their structural properties, do not significantly vary as a function of clustercentric distance and density within the cluster; and this is the case regardless of the filter. [ABSTRACT FROM AUTHOR]