Resolution
Generally it depends on what services are running on the server. All the ports which can be used by Parallels Plesk Panel/services are listed below:
#20 ftp-data (TCP)
#21 ftp (TCP)
#22 ssh (TCP)
#25 smtp (TCP)
#53 dns (TCP and UDP)
#80 http (web server and Plesk updater) (TCP)
#106 poppassd (for localhost only) (TCP)
#110 pop3 (TCP)
#113 auth (TCP)
#143 imap (TCP)
#443 https (TCP)
#465 smtps (TCP)
#587 mail message submission (TCP)
#990 ftps (TCP)
#993 imaps (TCP)
#995 pop3s (TCP)
#3306 mysql (TCP)
#5224 (outgoing connections only) plesk-license-update (TCP)
#5432 postgres (TCP) – Linux Only
#8443 plesk-https (TCP)
#8447 autoinstaller (TCP)
#8880 plesk-http (TCP)
#9080 tomcat (TCP)
From version 9.0 to version 10.2:
#11443 sw-cp-serverd (TCP)- Linux Only
#11444 sw-cp-serverd (TCP) – Linux Only
Since version 9.0:
#12768 psa-pc-remote (for localhost only) (TCP) – Linux Only, postfix
NOTE: remember to allow local net access.