Designs from maximal subgroups and conjugacy classes of $\mathrm{PSL}(2,q)$, $q$ odd

In this paper, using a method of construction of $1$-designs which are not necessarily symmetric, introduced by Key and Moori, we determine a number of $1$-designs with interesting parameters from the maximal subgroups and the conjugacy classes of elements of the group $PSL(2,q)$ for $q$ a power of an odd prime.