Ground Level Enhancements (GLEs) recorded by neutron monitor detectors are characterized by a variety of energy spectra of solar energetic particles (SEP), which vary between soft (as in August 1972) and hard (February 1956) ones. The aim of this work is to investigate the statistical relation between the hardness of the energy spectra and the event-integrated intensity. We calculated the event-integrated omnidirectional fluence of protons above 30 MeV (F30) and above 200 MeV (F200) using energy spectra reconstructed from both ground-based and space-borne data. The ratio of the $F_{30}$-to-$F_{200}$ fluences is considered as an index of the hardness of the events spectra. The main results of this study is that all strong events (with the event-integrated intensity greater than 100 %*hr) are characterized by a hard or very hard spectrum, while weak and moderate events do not show any clear pattern between the hardness and the intensity of the event.