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There is more information available on this subject at Capital ship on the English Wikipedia.

Capital ships are a classification of spacecraft, generally encompassing the most important and largest warships with the heaviest firepower and armor. There are usually no formal criteria for the classification, other than the fact that these ships tend to be heavily armed and armored. A capital ship is generally a leading or primary ship in a fleet, battle group, or strike force. Among the UNSC and the Covenant capital ships primarily include battleships, carriers and cruisers.

Covenant

United Nations Space Command

Forerunner