We first discuss the metacyclic group of order 5p its generating subsets in different classes and then give the DCI-properties of them, and prove that metacyclic group of order 55 is not a weak 5-DCI.

• 首先,对5p阶亚循环群的生成子集进行分类给出每一类生成子集的DCI-性,并且证明了5p阶亚循环群是非弱5-DCI的。