Yes. A public limited company can become a member of a private limited company,. Since the public company is investing only 30% of the shares of the private company, it would not acquire the status of a holding company.
The procedures to be followed by the public company to subscirbe to the shares of a private company are -
1) if the investment is within the limits specified in 372A the Board Resolution is sufficient. However ensure that the resolution is passed only in the Meetings of the Board as specified in Section 292 of the Companies Act and not by way of circular resolution.
2) If the investment exceeds the limits specified in 372A, convene General Meeting and pass a special resolution.
3) The company may authorise such person as it thinks fit to act as its representative at any meeting of the company as per Section 187(1)(a).
As regards private company
1) Receive the share application and money and allot shares by passing a Board Resolution.
2) File Form 2 with ROC within 30 days of share allotment.