I figured out how to do it:
CivilWarBattles =
Entity["MilitaryConflict", "AmericanCivilWar"][
"AllSubconflicts"]; ClassForCivilWarBattles =
FilteredEntityClass["MilitaryConflict",
EntityFunction[b, MemberQ[CivilWarBattles, b]]];
ContainsExactly[CivilWarBattles][EntityList@ClassForCivilWarBattles]