In addition to Dunbar's number, there's a few other magic numbers that crop up in the statistics of human societies over and over again:
2 - The most basic. Think romantic relationships, best friends, business partners, etc.
6 - The "group." Common chimpanzees patrol in groups of six. Next time you go to a party, notice the maximum number of people that can engage in a conversation. Its nearly always six.
Fun tip based on this: If you want to join a lively conversation, walk up to a group of six people and begin to talk to two of them. The group will naturally fission into two groups of three and four.
30 - The "tribe." This is your extended group of friends, or the maximum number of children that can be put in a classroom. Everyone knows everyone well. This group can be mustered to complete a common task without much trouble.
150 - The "nation." This is Dunbar's magic number, derived from the size of the human neocortex. This is the maximum size a group can reach where everyone has at least a passing relationship with everyone else. It is the last natural group size.
Any group beyond this stretches human social instincts, and requires social constructs such as rules or laws to augment it.