Undead Fortitude. If damage reduces the zombie to 0 hit points, it must make a Constitution saving throw with a DC of 5 + the damage taken, unless the damage is radiant or from a critical hit. On a success, the zombie drops to 1 hit point instead.

As long as  the horde has more than half it's hit points it has advantage on saves against turn and destroy undead effects.

Strength in Numbers
A swarm is immune to any spell or magical ability that effect a single target such as hold person or detect thoughts.

A swarm has disadvantage on saving throws for any spell or magical that deal damage in a area of effect such as fireball or shatter.

If the swarm is bloodied it loses its ‘There are many’ attack.

Swarm. The swarm can occupy another creature's space and vice versa, and the swarm can move through any opening large enough for a medium humanoid. The swarm can't regain hit points or gain temporary hit points.

Multiattack. The zombie horde makes one 'there are many'' attacks and one devour attacks.

Devour. Melee Weapon Attack: +7 to hit, reach 5 ft., one target. Hit: 15 (4d4 + 5) slashing damage, or 10 (2d4 + 5) slashing damage if the horde has half of its hit points or fewer, and the target is grappled (escape DC 15). Until this grapple ends, the horde has advantage on attack rolls against the grappled creature. Until the grapple ends, the target is restrained, and takes 7 (2d6) piercing and 7 (2d6) slashing damage at the start of the horde's turn, or 3 (1d6) piercing damage and 3 (1d6) slashing damage if the horde has half of its hit points or fewer.

There are many... Melee Weapon Attack: +7 to hit, reach 5 ft., one target. Hit: 15 (4d4 + 5) slashing damage, or 10 (2d4 + 5) slashing damage if the horde has half of its hit points or fewer,

...and they are always hungry. The horde can make as many opportunity attacks as it wants but not more than one against any single target.