A subsidiary company can hold shares in its holding company:

    (a) as the legal representative of a deceased member of the holding company; or

    (b) as a trustee; or

    (c) if the  subsidiary company is a shareholder even before it became a subsidiary company of the holding company.

Except as mentioned above no company shall, either by itself or through its nominees, hold any shares in its holding company.  As a corollary to it,  no holding company shall allot or transfer its shares to any of its subsidiary companies and any such allotment or transfer of shares of a company to its subsidiary company shall be void.

Where the subsidiary company hold shares in its holding company (a) as the legal representative of a deceased member of the holding company; or (b) as a trustee,  it can vote at a meeting of the holding company in respect of the shares held by it as a legal representative or as a trustee. The subsidiary company cannot vote at the  meeting of the holding company in respect of the shareholding acquired before it became a subsidiary company of the holding company.

Refer :

(1)Section 19 of the Companies Act 2013

(2) Analyzing Subsidiary Company’s Shareholding Rights In Its Parent Company  by Pankaj Tyagi https://corpbiz.io/learning/subsidiary-companys-shareholding-rights-in-its-parent-company/