Will a subordination show up on an average title report?

Will the subordination show up on an avergae title search or title report, or do you have to do some other kind of research to find it?

Yes, it should be included. Just remember that a title report, even from the best title company, is no guarantee that a subordination agreement or other title issue doesn’t exist. If they were good enough to get these things right every time there would be no reason for title insurance.