The fact that a company is controlled by an exempt entity does not mean the company is exempt from income tax. Nor does it mean that the company is taxable. The exemption status of the company will depend on its particular circumstances in light of the legal requirements.
This web page gives examples where we accept a company, which is controlled by an exempt entity, is itself exempt from income tax. It is not an exhaustive list. There will also be many other instances.
The examples are grouped under these exemption categories:
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More information about companies that are controlled by exempt entities is provided in: 
