Is there an official, widely used subject classification?

In addition to the ones @Coder suggests, perhaps the library classification systems:

• Library of Congress
• Dewey Decimal
• Universal Decimal Classification

might be useful?

As @tonysdg says below, there are a variety of other system, too.

These are the possible classification that you could look at:

• Google Scholar --> Metric (a link on the top of the page) --> scroll down to 'view top publications' --> Click categories --> ... explore as per your requirement.

• ACM subject classification (ACM ccs)

• Mathematics subject classification by AMS (Wiki)
• PACS Regular Edition from AIP publishing

Although a bit obsolete, consider also the UNESCO nomenclature. It is international and specifically adapted to research. Also, unlike other systems, it is not restricted to Science and Engineering. For instance, in Spain, you have to specify up to three codes to officially register a PhD Thesis.