We obtain some sufficient conditions on the number of non-（sub）normai nonabelian subgroups of a finite group to be solvable, which extend a result of Shi and Zhang in 2011.
A graph is said to be symmetric if its automorphism group acts transitively on its arcs. In this paper, a complete classification of connected pentavalent symmetric graphs of order 16p is given for each prime p. It follows from this result that a connected pentavalent symmetric graph of order 16p exists if and only if p = 2 or 31, and that up to isomorphism, there are three such graphs.
