Six people in two groups.

There are six people A, B, C, D, E, F which are in each case either in group 1 or group 2. The following statements are given:

- Both A and B are in 1.
- F is in 2, and if E is in 2, then C is also in 2.
- D is in 1 and if F is in 2, then A is also in 2.
- A and E are both in 2.
- D is in 2 and E is in 1, and if C is in 2, then B is in 1.
- D and B are both in 2.
- The statements 1-6 are wrong.

Who is in which group?