HN has an involution whose centralizer is of the form 2.HS.2, where HS is the Higman-Sims group (which is how Harada found it).
Conway and Norton suggested in their 1979 paper that monstrous moonshine is not limited to the monster, but that similar phenomena may be found for other groups.
Larissa Queen and others subsequently found that one can construct the expansions of many Hauptmoduln from simple combinations of dimensions of sporadic groups.
To recall, the prime number 5 plays a special role in the group and for HN, the relevant McKay-Thompson series is
where one can set the constant term a(0) = −6 (OEIS: A007251), and η(τ) is the Dedekind eta function.