  This paper deals with the classification of groups $G$ such that power graphs
and proper power graphs of $G$ are line graphs. In fact, we classify all finite
nilpotent groups whose power graphs are line graphs. Also, we categorize all
finite nilpotent groups (except non-abelian $2$-groups) whose proper power
graphs are line graphs. Moreover, we investigate when the proper power graphs
of generalized quaternion groups are line graphs. Besides, we derive a
condition on the order of the dihedral groups for which the proper power graphs
of the dihedral groups are line graphs.
