利用子群来研究群的结构是研究群的最基本的途径，也是群论研究的永久课题。本项目研究内容共分为两个方面：.第一，研究子群的Hall嵌入性与群结构之间的联系。子群在大群中的状况或满足的关系和条件简称为子群的嵌入性。通过把子群的嵌入性与群的数量性质相结合，我们提出了子群的Hall嵌入性。本项目将借助子群的Hall嵌入性给出新的判定群可解、超可解、p-幂零等重要群类及属于某些饱和群系的新的刻画。.第二，研究群系剩余与群结构之间的联系。找到子群的一些嵌入性质，给出群对群系的剩余；反过来，通过群系剩余的性质给出刻画群的结构与性质的新方法。

It is not only the most principal way to study the structure of finite groups by its subgroups,but also an everlasting topic in the research of the finite groups. The content of this project includes two aspects: . The first aspect is to study the relationship between the Hall embedded properties of subgroups and the structure of finite groups. We introduce the Hall embedded properties of subgroups by combining the embedded properties of subgroups with the quantitative property. New descriptions about a finite group to be solvable, supersolvable, p-nilpotent and belonging some important classes and saturated formation can be given by the Hall embedded properties of subgroups.. The second aspect is to study the relationship between the formation residual and the structure of finite groups.We give the formation residual of finite groups by finding some embedded properties of subgroups; Conversely, we will give some new methods to characterize the structure and properties of finite groups by the properties of the formation residual of finite groups.