How to push to git subtree?

So, with some joint effort with @PhilipKirkbride, here's what we managed to figure out:

You need to put all the details in the command:

git subtree push --prefix=my/folder subtree_origin master

Where master is the branch in the subtree, and subtree_origin is just another remote, which happens to point to your subtree's git repository. You can also type the full repo URL.