Emile Durkheim did a study about suicide rates - he compared the suicide rates between Catholics and Protestants, and found that there was less suicides amongst Catholics, and also that less women committed suicide than men.
He tried to identify why this was the case, and came up with four types of suicide (though applying them to certain instances may not be as clear-cut, it is definitely a good starting point)
He at first split them in terms of integration with outer society. He thought that this affected individuals in two different ways:
Egoistic suicide - too weak integration; people did not have enough social bonds and therefore did not think that their death would affect society, so felt it was easier to do so. (an example of this could potentially be an outlier of society, a drug taker etc.)
Altruistic suicide - this was too much integration, in which the person is so integrated they have no life of their own, the only way to gain back their life is by ending it (in today's society, this can be seen in the suicides of carers, who have extremely high suicide rates, nurses etc.)
He then looked and separated between the amount of regulation that the person had in their life.
Anomic suicide - this is the suicide which is committed through too little regulation in a person's life. This can be seen mostly in cases of dramatic economic and social change (for example, the change in the economy in Greece has affected the once low suicide rate) [Another example could be potentially veterans, who once had a lot of regulation and have then exited the military with no regulation and strict rules to adhere by, losing their sense of direction]
Fatalistic suicide - this is when the person feels that there is too much control in their life - for example in cases where people are incarcerated, and the only escape that they can get (the only way to regain control for themselves) is to commit suicide.
Generally you see anomic suicide paired up with egoistic suicide due to the weak integration & weak regulatory elements, and as a result you also see altruistic and fatalistic suicides paired up. This is not always the case and sometimes you can have cases where all elements are fulfilled to some degree. This is one of the main arguments against Durkheim's theory of suicide as it is difficult to 'box' certain people's suicides depending on their level of integration or regulation they have from society.