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There are several systems for classifying companies within an industry.
The North American Industry Classification System (NAICS) is the latest and most commonly used system. It has a hierarchy that starts with two digit codes for the broadest industries, four digit codes for the major groups within an industry and six digit codes for the company level.
NAICS replaced the Standard Industrial Classification (SIC) system, but the Securities and Exchange Commission still uses SIC instead of NAICS. You will see both in many databases because of this. NAICS is more granular than SIC and is revised every five years. The SIC was last revised in 1987.
One way to identify relevant codes is to look up a major company in a database like Mergent Online. You can also find them using keyword searches in IBISWorld.