Below is a list of ICMP types and codes. The list is not complete and I have only included those I found somewhat useful.

ICMP types and codes
  • Type 0 - Echo Reply
  • Type 3 - Destination Unreachable
    • Code 0 - Net Unreachable
    • Code 1 - Host Unreachable
    • Code 2 - Protocol Unreachable
    • Code 3 - Port Unreachable
    • Code 4 - Fragmentation Needed and Don't Fragment was Set
    • Code 5 - Source Route Failed
    • Code 6 - Destination Network Unknown
    • Code 7 - Destination Host Unknown
  • Type 5 - Redirect
    • Code 0 - Redirect Datagram for the Network (or subnet)
    • Code 1 - Redirect Datagram for the Host
    • Code 2 - Redirect Datagram for the Type of Service and Network
    • Code 3 - Redirect Datagram for the Type of Service and Host
  • Type 8 - Echo
  • Type 9 - Router Advertisement
    • Code 0 - Normal router advertisement
    • Code 16 - Does not route common traffic
  • Type 10 - Router Selection
  • Type 11 - Time Exceeded
    • Code 0 - Time to Live exceeded in Transit
    • Code 1 - Fragment Reassembly Time Exceeded
  • Type 13 - Timestamp
  • Type 14 - Timestamp Reply

Source: https://www.iana.org/assignments/icm...rameters.xhtml