One of the more useful operators, the site operator is used to restrict a search to a particular URL or domain name. It is commonly used to search within a known website.
Example: site:americanexpress.com travel
Note that Google matches the domain names from right to left instead of the usual left to right. Therefore, all URLs used with the site operator must end with a valid registered top-level domain name.
Include sub-domains to narrow the search results.
Examples:
site:home.americanexpress.com travel
site:home.americanexpress.com/home travel
Compare the difference in the number of hits between all the above examples.