The advent of nuclear weapons on the battlefield left the Army very worried. It's understandable; a bomb that could take out an entire city was rightly seen as a game-changer.
Over the years, the Army has shifted its divisional formations, from the "square" formation in World War I (two brigades each with two regiments) to a "triangle" formation (three regiments). But everything changed when the United States Army designed nukes for use on the battlefield, as they presumed the Soviets were going to eventually develop their own.
The solution was a new, pentomic divisional organization. Instead of regiments and battalions, each infantry and airborne division would have five battlegroups, each with five companies of infantry, a mortar battery, and a headquarters unit. Furthermore, each division had two battalions of artillery. Looking at it mathematically, the "triangular" infantry division had three regiments, each with three battalions that had three infantry companies, making for a total of 27 infantry companies. The pentomic structure had 25 infantry companies.
The first unit to adopt this structure was the 101st Airborne Division. As Time Magazine reported in 1957, the Army planned to re-organize 19 infantry and airborne divisions along the pentomic structure.
However, the Army soon found some problems with this structure. The first was that there was a long gap between command tours. The companies were commanded by captains, but you had to be a full colonel to get a "battlegroup." Keeping the same person in charge for so long means command skills will get rusty. It also caused consternation among those concerned with tradition. The "battlegroup" concept placed the storied histories of regiments at risk.
Ultimately, the pentomic structure failed to take hold as growing arsenals made a nuclear war between NATO and the Warsaw Pact unlikely. The Army ended up going back to a triangular structure that used brigades instead of regiments — just in time for the Vietnam War. In the 2000s, the Army shifted to modular brigade combat teams and put four to a division, before dropping that number to three per division in the 2010s.