The nuclear powers
These countries were part of the original Big Five, but eventually eclipsed the other members as they regained all of their prewar territory and were granted full diplomatic relations with the Race (de facto recognition of their independence). This was primarily due to their development of nuclear weapons during the war.
The second-rate powers
These countries were part of the original Big Five but despite preserving their independence they were considered second-rate powers by the end of the war. This was due to the loss of much of their empires and their lack of nuclear weapons.
The afore-mentioned powers were the only countries which participated in coordinating strategy and which were represented at the Peace of Cairo. Members of the Big Five supported neighboring governments which were resisting the Race and anti-collaborationist partisans who opposed governments working with the Race, seeking to replace collaborators with the latter.
Both the Communist and Kuomintang factions of the Chinese sought a seat at the conference, but were flatly rebuffed by Race leaders, who felt that they had securely conquered China. Both factions threatened to make life difficult for the Race in retaliation, but despite living up to this threat China was not represented at the Peace of Cairo.
World War II
When the Conquest Fleet arrived in 1942, the members of the Big Five were engaged in a total war against one another. Faced with the very real threat of conquest by the alien invaders, these nations arranged cease-fires with one another, then periodically participated in strategy conferences in London and other locations. While individual members of the Big Five traded technology and intelligence, and collaborated in some military operations, full cooperation was rare due to geographical distance and/or still-existing ideological tensions. Nazi Germany and the Soviet Union in particular were always seeking to enhance their position vis-à-vis one another as well as the Race.
After two years of fighting, it became clear that the United States, Soviet Union, and Germany, which had built and used atomic bombs, were more powerful and more important than Britain and Japan, which had not. However, all five were represented when Fleetlord Atvar convened a peace conference in Cairo, and all five were granted recognition as sovereign entities by the Race, though only the three nuclear powers were allowed full diplomatic relationships with the Race - until Britain and Japan developed their own atomic weapons after the war.
1944 - 2031
The Big Five had effectively become the Big Three by the 1960s, as the Germans, Soviets and Americans were able by this point to develop their own space programs and - in combination - match the Race's military might. Despite developing its own nuclear weapons Britain never regained its great power status, as various portions of its empire were either lost to the Race or realigned themselves with other powers. Indeed the United Kingdom itself was increasingly becoming a weaker ally of the Reich. Japan, on the other hand, while not rated as highly as the Big Three, retained most of its pre-1944 empire and joined their ranks as a nuclear power in 1965.
Germany temporarily slipped from the ranks of the great powers following its disastrous defeat in the Race-German War of 1965, but by the end of the 20th century had regained much of its former strength. By 2031 the United States and Soviet Union had each built a spaceship capable of interstellar voyages, and both the Germans and Japanese were believed capable of matching this feat. As a result, the Big Three (or Big Four) were now strong enough to threaten the Race's own homeworld.