The code in question is in header.php, line 45.
<?php wp_nav_menu( array( 'theme_location' => 'primary', 'menu_class' => 'nav-menu' ) ); ?>
This is the Codex reference to this function: wp_nav_menu.
From my experience, and some googling, this previous answer has the answer you’re looking for.
If possible, would just adding a class to the sub-menus do the trick instead of adding a div? If so you should be able to just copy and paste the code from the above linked answer and then target the elements with CSS to get the effect you’re after.
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