Under Indian law, the primary types of companies recognized are:
https://www.registerkaro.in/types-of-companies
Private Limited Company:

Members: Minimum of 2 and a maximum of 200 members.
Shares: Shares cannot be freely transferred.
Public Offering: Cannot invite the public to subscribe to its shares.
Public Limited Company:

Members: Minimum of 7 members and no maximum limit.
Shares: Shares can be freely transferred.
Public Offering: Can invite the public to subscribe to its shares.
One Person Company (OPC):

Members: Only one person as a member and sole director.
Purpose: Suited for small businesses and entrepreneurs.
Conversion: Must convert to a private or public company if annual turnover exceeds a certain limit.
Section 8 Company:

Purpose: Formed for promoting commerce, art, science, sports, education, research, social welfare, religion, charity, or any other useful object.
Profit: Prohibits payment of any dividend to its members.
Limited Liability Partnership (LLP):

Members: Requires at least two partners, no upper limit.
Liability: Partners have limited liability.
Hybrid Structure: Combines the benefits of a company and a partnership.
Producer Company:

Members: Formed by primary producers like farmers, artisans, or any other producers.
Purpose: To improve the standard of living and to ensure the prosperity of its members.
Foreign Company:

Definition: A company incorporated outside India that has a place of business in India.
Compliance: Subject to additional regulations and compliance under Indian law.
Dormant Company:

Purpose: For holding assets or intellectual property without significant financial transactions.
Status: Can be classified as dormant by making an application to the Registrar of Companies.
These categories ensure that different types of business activities and organizational structures can be appropriately managed and regulated under Indian law.