Some of them you mentioned already :
race - the racial make up of the society (it can be informative if the race is coorelated for example with income)
gender - the gender make up of a society, which is usually 50% male and 50% female, but differences from that can cause social problems
class- for example whether the society is more uniform, or whether huge differences between classes exist
other aspects can include
age- can tell us how many people are in a working age
education and literacy - it can help us predict the wealth of the country