To test if a given outgoing port is blocked on your network by some malicious middlebox, you can try to telnet into a server that has a service running on that port.
In this example, we use portquiz.net--which is a public service designed for this purpose. It uses iptables' nat table and has all tcp ports open.
# first we verify that we _can_ connect over port 443, which >99% of
# networks won't block; it works
user@personal:~$ time echo 'exit' | telnet portquiz.net 443
Connected to portquiz.net.
Escape character is '^]'.
Connection closed by foreign host.
# next we try to connect over a port that's suspected of being blocked; it fails
user@personal:~$ time echo 'exit' | telnet portquiz.net 22
telnet: Unable to connect to remote host: Connection timed out
Note that the first command exited immediately with the message
Connected to portquiz.net, which indicates that the outgoing port 443 is not being blocked by the network.
The second command, however, says
Unable to connect to remote host: Connection timed out. This shows that--unless there's an issue at portquiz.net--the outgoing port 22 is probably being blocked on your network.
You can take this a step further using nmap to get a list of all the ports that are not blocked by the network. For example:
user@personal:~$ time nmap -p- portquiz.net | grep -i open
21/tcp open ftp
53/tcp open domain
80/tcp open http
143/tcp open imap
443/tcp open https
465/tcp open smtps
587/tcp open submission
993/tcp open imaps
1935/tcp open rtmp
4070/tcp open unknown
In the above command, we can see that all outgoing ports are blocked except 21, 53, 80, 143, 443, 465, 587, 993, 1935, and 4070. In a normal/uncensored network, this list would be much, much longer (probably showing all 65535 ports)