The Number of Conjugacy Classes of Noncyclic Subgroups of Finite Nilpotent Groups

Let Formula: see text be a finite nilpotent group. We denote by Formula: see text the number of conjugacy classes of noncyclic subgroups of Formula: see text, Formula: see text the number of conjugacy classes of subgroups of Formula: see text. In this paper, we give the formula for Formula: see text, and prove that Formula: see text when the order of Formula: see text is prime power. Moreover, we get the minimum of Formula: see text according to Formula: see text, where Formula: see text is the number of distinct noncyclic Sylow subgroups of Formula: see text.