  Nearly 70 Ground Level Enhancements (GLEs) of cosmic rays have been recorded
by the worldwide neutron monitor network since the 1950s depicting a big
variety of energy spectra of solar energetic particles (SEP). Here we studied a
statistical relation between the event-integrated intensity of GLEs (calculated
as count-rate relative excess, averaged over all available polar neutron
monitors, and expressed in percent-hours) and the hardness of the solar
particle energy spectra. For each event the integral omnidirectional
event-integrated fluences of particles with energy above 30 MeV ($F_{30}$) and
above 200 MeV ($F_{200}$) were computed using the reconstructed spectra, and
the ratio between the two fluences was considered as a simple index of the
event's hardness. We also provided a justification of the spectrum estimate in
the form of the Band-function, using direct PAMELA data for GLE 71
(17-May-2012). We found that, while there is no clear relation between the
intensity and the hardness for weak events, all strong events with the
intensity greater 100 \%*hr are characterized by a very hard spectrum. This
implies that a hard spectrum can be securely assumed for all extreme GLE
events, e.g., those studied using cosmogenic isotope data in the past.
