The legal definition of parent company refers to a company that owns more than a certain proportion of shares in another company, or a company that can actually control another company through some agreement.
The legal definition of a subsidiary refers to a company in which more than a certain percentage of the shares of a company are held by another company (parent company) or will be actually controlled by another company through some agreement.
It can be seen that the parent-subsidiary company is not determined according to the proportion of shares, but depends on the control right. In practice, the parent company's control over the subsidiary company is embodied in influencing the production and operation decisions of the subsidiary company by appointing and removing board members and making investment decisions.
Therefore, the parent company can judge its subsidiaries through direct shareholding or through the control agreement between them.
In the latter case, if it is judged that one company has realized the control of personnel and finance of another company according to the existing materials, then it can be concluded that the relationship between the two parties is a mother-child relationship.