Non-Pólya Fields with Large Pólya Groups Arising from Lehmer Quintics

In this article we construct a new family of quintic non-Pólya fields with large Pólya groups. We study the upper bound of Pólya numbers of such fields and show that the Pólya numbers never exceed five times the size of its Pólya group. Finally we show that such non-Pólya fields are non-monogenic fields of field index one.