Differences between Companies

public company means registered as LTD co under Cos act 2013, and co in a public sector means a sector which is owned and controlled by the cent govt.
govt co means in which more than half of shares are held by the cent/state govt individually or in aggregate.
govt undertaking means which is regulated under govt control.e.g LIC is a govt undertaking

a subsidiary of public company being a private company is also a public company?

yes that's right

Priya kashyap :Section 2(71)public company" means a company which—

[a] is not a private company *****14[and];

[b] 9[has a minimum paid-up share capital 5[Omitted], as may be prescribed]:

Provided that a company which is a subsidiary of a company, not being a private company, shall be deemed to be public company for the purposes of this Act even where such subsidiary company continues to be a private company in its articles ;