We report the largest sample of candidate strong gravitational lenses belonging to the Survey of Gravitationally-lensed Objects in HSC Imaging for group-to-cluster scale (SuGOHI-c) systems. These candidates are compiled from the S18A data release of the Hyper Suprime-Cam Subaru Strategic Program (HSC-SSP) Survey. We visually inspect ∼ 39, 500 galaxy clusters, selected from several catalogs, overlapping with the Wide, Deep, and UltraDeep fields, spanning the cluster redshift range 0.05 < z cl < 1.38. We discover 641 candidate lens systems, of which 537 are new. From the full sample, 47 are almost certainly bonafide lenses, 181 of them are highly probable lenses and 413 are possible lens systems. Additionally, we present 131 lens candidates at galaxy-scale serendipitously discovered during the inspection. We obtained spectroscopic follow-up of 10 candidates using the X-shooter. With this followup, we confirm 8 systems as strong gravitational lenses. Out of the remaining two, the lensed sources of one of them was too faint to detect any emission, and the source in the second system has redshift close to the lens but other additional arcs in this system are yet to be tested spectroscopically. Since the HSC-SSP is an ongoing survey, we expect to find ∼ 600 definite or probable lenses using this procedure and more if combined with other lens finding methods.