Under the Companies Act 2013, there are several registers that companies are required to maintain. Some of the registers that companies need to maintain are:

1. Register of Members: Every company must maintain a register of its members in the prescribed form, which includes details such as the name, address, occupation, and date of becoming a member.
2. Register of Debenture Holders: If a company has issued debentures, it must maintain a register of debenture holders in the prescribed form.
3. Register of Charges: Every company is required to maintain a register of charges, which includes details of all the charges created on the company's assets.
4. Register of Directors and Key Managerial Personnel: Every company must maintain a register of its directors and key managerial personnel, which includes details such as the name, address, date of appointment, and resignation, if any.
5. Register of Contracts or Arrangements in which Directors are Interested: If a director is interested in a contract or arrangement with the company, the company must maintain a register of such contracts or arrangements.
6. Register of Related Party Transactions: Every company must maintain a register of all transactions with related parties.
7. Register of Investments not held in its own name: Every company must maintain a register of all investments made in the name of any person other than the company.
8. Register of Employee Stock Options: Companies issuing employee stock options must maintain a register of the options granted to its employees.

These registers must be maintained at the registered office of the company, and they must be open for inspection by any member or creditor of the company during business hours. The company must also file certain information related to these registers with the Registrar of Companies.