she was so tired that she couldn’t think. (Oxford)
Oxford says that-clause above is a subordinate clause expressing a result. Semantically ‘she was tired’ seems to be the main clause, but there also is the possibility ‘she couldn’t think’ might be thought as the main one, and ‘she was tired’ is a subordinate expressing the reason of that-clause.
So the words below that do not use ‘subordinate’ sound to be better explanations for the case. Then on what ground does Oxford say the clause is subordinate?
Cambridge: to introduce a clause that gives further information, although it can often be left out. Longman: to introduce a clause that shows the result of something:
XthatYis a construction, not a word that a dictionary can tell you about. The reason it's subordinate is that it starts with a complementizer that, which marks a subordinate tensed clause. Main clauses do not begin with that. – John Lawler Apr 27 '13 at 23:42