It doesn't need to break the armour the real killer is the blunt force of the blow (which clubs and maces are better in transmitting to the target than swords or spears) which could break bones and burst internal organs without damaging the armour. Getting hit by a club while wearing chain mail would be little different from being hit whilst wearing nothing. Also IIRC some of the unit descriptions say they used to put pieces of bone or metal into the clubs to allow them to punch holes in armour.
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