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 (1R200) 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 density-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 early-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.CL-D acknowledges scholarship from CONICYT-PFCHA/Doctorado Nacional/2019-21191938. CL-D and AM acknowledge support from FONDECYT Regular grant 1181797. CL-D acknowledges also the support given by the ‘Vicerrectoría de Investigacion de la Universidad de La Serena’ program ‘Apoyo al fortalecimiento de grupos de investigacion’. CL-D and AC acknowledges to Steven Bamford and Boris Haeussler with the MegaMorph project. CL-D and DP acknowledge support from fellowship ‘Becas Doctorales Institucionales ULS’, granted by the ‘Vicerrectoría de Investigacion y Postgrado de la Universidad de La Serena’. AM and DP acknowledge funding from the Max Planck Society through a ‘Partner Group’ grant. DP acknowledges support from FONDECYT Regular grant 1181264. This work has used the computing facilities of the Laboratory of Astroinformatics (Instituto de Astronomia, Geofísica e Ciencias Atmosféricas, Departamento de Astronomia/USP, NAT/Unicsul), whose purchase was made possible by FAPESP (grant 2009/54006-4) and the INCT-A. YJ acknowledges financial support from CONICYT PAI (Concurso Nacional de Inserción en la Academia 2017) No. 79170132 and FONDECYT Iniciación 2018 No. 11180558. LS thanks the FAPESP scholarship grant 2016/21664-2. AAC acknowledges support from FAPERJ (grant E26/203.186/2016), CNPq (grants 304971/2016-2 and 401669/2016-5), and the Universidad de Alicante (contract UATALENTO18-02). AMB thanks the FAPESP scholarship grant 2014/11806-9. RA acknowedges support from ANID FONDECYT Regular grant 1202007
