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We report the largest sample of candidate strong gravitational lensesbelonging to the Survey of Gravitationally-lensed Objects in HSC Imaging forgroup-to-cluster scale (SuGOHI-c) systems. These candidates are compiled fromthe S18A data release of the Hyper Suprime-Cam Subaru Strategic Program(HSC-SSP) Survey. We visually inspect $\sim39,500$ galaxy clusters, selectedfrom several catalogs, overlapping with the Wide, Deep, and UltraDeep fields,spanning the cluster redshift range $0.05<z_{cl}<1.38$. We discover 641candidate lens systems, of which 536 are new. From the full sample, 47 arealmost certainly bonafide lenses, 181 of them are highly probable lenses and413 are possible lens systems. Additionally, we present 131 lens candidates atgalaxy-scale serendipitously discovered during the inspection. We obtainedspectroscopic follow-up of 10 candidates using the X-shooter. With thisfollow-up, we confirm 8 systems as strong gravitational lenses. Of theremaining two, one of the sources is too faint to detect any emission, and theother has a tentative redshift close to the lens redshift, but additional arcsin this system are yet to be observed spectroscopically. Since the HSC-SSP isan ongoing survey, we expect to find $\sim600$ definite or probable lensesusing this procedure and even more if combined with other lens finding methods.

Survey of Gravitationally-lensed Objects in HSC Imaging (SuGOHI). V. Group-to-cluster scale lens search from the HSC-SSP Survey