If you work for subsidiary, do you put parent company on resume?

You put what your paycheck says.

You know son... You can put anything you want.

Ask hr

Does not matter. Whatever you think looks best.

No problem with this at all. I see people titling their roles in all manner of ways. Audible, Audible (Amazon), Amazon (Audible), Amazon etc would all be perfectly acceptable. After all, if I want to work for Audible, I apply via Amazon.

Depends on the parent company. If it's brand value is better than subsidiary, then yes. Ex: it's preferable to put AWS rather than Amazon.