Yes, I tried the specific address for iOS and Caldav (https://SUBDOMAIN.DOMAIN.COM:PORT/remote.php/dav/principals/users/USERNAME/) and some more like in this post.
As I read on the Apple site iOS tries to use port 443 and port 8443 as standard. And as I understood several other posts there is no limitation on ports to use as many people seem to use different ports for that purpose. But I did not try the standard ports so far.
Maybe any other ideas?