Asch's extensive studies found a number of factors affecting conformity rates. One was task difficulty. As the task gets more difficult, with the lines in Asch's study getting closer together in size, people grow less sure of if they are correct and look to others for guidance. Essentially, difficult tasks increase informational social influence. So the more difficult a task is, the more people will conform to the group.
Another factor is anonymity. When everyone gives answers anonymously it avoids social judgement, allowing more freedom to give answers that you truly believe in. In other words, it frees you from declarative social influence as there is no longer a need to fulfill the expectations of others. Therefore anonymity often greatly reduces conformity levels.