First, take in consideration that this answer is just to make it work, I am not sure about any implications this may have in security due to every folder being in the public part of your site.
Second, I just tried this with a barebones laravel installation, so I'm not sure if this can have effects later in development (my guess is not, but you never know).
1) Copy all the contents of the public folder in the root laravel folder (which is your subfolder)
2) You can now remove the empty public folder
3) edit index.php and change
// --------------------------------------------------------------
// Set the core Laravel path constants.
// --------------------------------------------------------------
require '../paths.php';
to
// --------------------------------------------------------------
// Set the core Laravel path constants.
// --------------------------------------------------------------
require './paths.php';
4) edit paths.php and change
// --------------------------------------------------------------
// The path to the public directory.
// --------------------------------------------------------------
$paths['public'] = 'public';
to
// --------------------------------------------------------------
// The path to the public directory.
// --------------------------------------------------------------
$paths['public'] = '.';
5) Edit the .htaccess file in the laravel folder to make it redirect no more into public
RewriteEngine on
RewriteCond %{REQUEST_FILENAME} !-f
RewriteCond %{REQUEST_FILENAME} !-d
RewriteRule ^(.*)$ index.php/$1 [L]
