Actually, a .308 Winchester with the 175gr BTHP (Sierra Match King) bullet can still be supersonic at 1000 yards.
With a muzzle velocity of at least 2650 feet per second, the Sierra MK 30cal 175gr bullet will make it out to and slightly beyond 1000 before it goes subsonic. It has a ballistic coefficient of .495-.505.
The 175gr is the standard bullet used on the US military M118LR 'sniper' round. M118 being the military designator for the ammo, 'LR' meaning Long Range.
You can even get a 22 caliber bullet in a .223 Remington (5.56 NATO) out to a 1000 yards maintaining supersonic flight. While many still use the .308 for 1000 yard Service Rifle competition, the AR15 platform in .223 has taken the Farr Trophy (US National Trophy for 1000 yard Service Rifle). This is accomplished by using an 80gr or heavier bullet. The Sierra Match King 22cal (.224") 80gr BTHP is popular, but the Very Low Drag bullets like the Berger 80gr VLD have a much higher ballistic coefficient and can buck the wind better.