ulx groupallow <group> "ulx god" "^"
ulx groupallow <group> "ulx ungod" "^"
We have FAQs that help cover these, one being "How exactly does can_target work?"
Though that doesn't hit nail on head, it has link to another discussion that covers those.
You can also always type, as superadmin, "ulx usermanagementhelp" in console and see the descriptions of ^, @, and a few others.