using apache/nginx as reverse proxy server (map to different ports based on domain name)

Assuming nginx is running on port 82 and you want to serve nginx.domain.com with nginx.

<VirtualHost *:80>

    ServerAdmin me@mydomain.com

    ServerName nginx.domain.com

    ProxyPreserveHost On

    # setup the proxy

    <Proxy *>

        Order allow,deny

        Allow from all

    </Proxy>

    ProxyPass / http://localhost:82/

    ProxyPassReverse / http://localhost:82/

</VirtualHost>

http://serverfault.com/questions/195611/how-do-i-redirect-subdomains-to-a-different-port-on-the-same-server

Now let's reverse the roles, using Nginx as reverse proxy server and Apache as the real server:

https://www.digitalocean.com/community/tutorials/how-to-configure-nginx-as-a-web-server-and-reverse-proxy-for-apache-on-one-ubuntu-14-04-droplet