The PQConnect documentation, specifically the document "INSTALL.md", describes the pq1 portion of the CNAME as a subdomain.

   Please update your DNS A/AAAA records for all domains on this server as follows:

   Existing record:
   Type    Name        Value
   A/AAAA  SUBDOMAIN   IP Address

   New Records:
   Type    Name        Value
   CNAME   SUBDOMAIN   pq1XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX.DOMAIN.TLD
   A/AAAA  pq1XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX  IP Address
   TXT    pq1XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX.DOMAIN.TLD    p=42424
   TXT    ks.pq1XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX.DOMAIN.TLD    ip=IP ADDRESS;p=42425"