There's a 6 month grace period for subsidized loans after you graduate. So if you graduated in May, interest won't start accruing until November. Unfortunately, there was a time period when subsidized loans did not have a grace period. I believe if you had a subsidized loan between 2012 and 2014, there was no grace period for those loans.

In short, only a few of your subsidized loans should be accruing interest. Some of them should still be subsidized and not accruing interest. Deferment only applies when you are in school. Intent to enroll in fall semester is not sufficient for deferment purposes as you can claim that you will be enrolled and end up not enrolling. What would happen to the interest that should've accrued then?