Abstract The term fuzzy logic is generic as it can be used to describe the likes of fuzzy arithmetic, fuzzy mathematical programming, fuzzy topology, fuzzy graph theory ad fuzzy data analysis which are customarily called fuzzy set theory. The aspect of pure Mathematics has undergone a lot of dynamic developments over the years. Since inception , the study has been extended to some other important classes of finite abelian and nonabelian groups such as the dihedral , quaternion, semidihedral, and hamiltonian groups. Other different approaches have been so far, applied for the classification. Every finite p-group is nilpotent. The nilpotence property is an hereditary one. Thus, every finite p-group possesses certain remarkable characteristics. Efforts are carefully being intensified to calculate , in this paper, the explicit formulae for the number of distinct fuzzy subgroups of the Cartesian product of the dihedral group of order 25 with a cyclic group of order of an n power of two for, which n ≥ 5.