Given a maximal subgroupMof a finite groupG,a θ completion ofMinGis any subgroupCsuch thatCis not contained inMwhileMG, the core ofMinG, is contained inCandC/MGhas no propor normal subgroup ofG/MG. By using this concept we can reveal the relationship between the concepts of completions and θ-pairs introduced respectively by Deskins, Mukherjee and Bhattacharya. The concept of maximal θ-completions offers a convenience for us to study the Deskins completions in inductions. We obtain in this paper several results which imply a group to be solvable, supersolvable and nilpotent.