Group G consists of 12 elements, with its multiplication table shown below.
| | E | A | B | C | D | F | I | J | K | L | M | N |
|---|----|----|----|----|----|----|----|----|----|----|----|----|
| E | E | A | B | C | D | F | I | J | K | L | M | N |
| A | A | B | E | I | L | K | N | D | M | J | F | C |
| B | B | E | A | N | J | M | C | L | F | D | K | I |
| C | C | K | L | D | E | B | M | I | N | F | J | A |
| D | D | N | F | E | C | L | J | M | A | B | I | K |
| F | F | D | N | K | M | I | E | B | L | C | A | J |
| I | I | M | J | L | A | E | F | N | C | K | D | B |
| J | J | I | M | B | N | D | L | K | E | A | C | F |
| K | K | L | C | M | F | N | A | E | J | I | B | D |
| L | L | C | K | A | I | J | D | F | B | E | N | M |
| M | M | J | I | F | K | C | B | A | D | N | E | L |
| N | N | F | D | J | B | A | K | C | I | M | L | E |
1) Find the inverse elements of each element in group G;
2) Identify which elements commute with all elements in the group;
3) List the order of each element;
4) Find the elements contained in each class of group G;
5) Find all normal subgroups of group G, list their cosets, and indicate which groups their quotient groups are isomorphic to.

Options:
A. 1) $A^{-1} = B, \quad B^{-1} = A, \quad C^{-1} = D, \quad D^{-1} = C, \quad E^{-1} = E, \quad F^{-1} = I, \quad I^{-1} = F, \quad J^{-1} = K, \quad K^{-1} = J, \quad L^{-1} = L, \quad M^{-1} = M, \quad N^{-1} = N$
2) $E$
3) $A = 3, \quad B = 3, \quad C = 3, \quad D = 3, \quad E = 1, \quad F = 3, \quad I = 3, \quad J = 3, \quad K = 3, \quad L = 2, \quad M = 2, \quad N = 2$
4) $\{ E \}, \quad \{ L, M, N \}, \quad \{ A, B, C, D \}, \quad \{ F, I, J, K \}$
5) $\{ E, L, M, N \}; \{ A, C, F, J \}, \{ B, D, I, K \}; C3$
B. 1) $A^{-1} = B, \quad B^{-1} = A, \quad C^{-1} = D, \quad D^{-1} = C, \quad E^{-1} = E, \quad F^{-1} = I, \quad I^{-1} = F, \quad J^{-1} = K, \quad K^{-1} = J, \quad L^{-1} = L, \quad M^{-1} = M, \quad N^{-1} = N$
2) $E$
3) $A = 3, \quad B = 3, \quad C = 3, \quad D = 3, \quad E = 1, \quad F = 3, \quad I = 3, \quad J = 3, \quad K = 3, \quad L = 2, \quad M = 2, \quad N = 2$
4) $\{ E \}, \quad \{ L, M, N \}, \quad \{ A, C, F, J \}, \quad \{ B, D, I, K \}$
5) $\{ E, L, M, N \}; \{ A, C, F, J \}, \{ B, D, I, K \}; C3$
C. 1) $A^{-1} = B, \quad B^{-1} = A, \quad C^{-1} = D, \quad D^{-1} = C, \quad E^{-1} = E, \quad F^{-1} = I, \quad I^{-1} = F, \quad J^{-1} = K, \quad K^{-1} = J, \quad L^{-1} = L, \quad M^{-1} = M, \quad N^{-1} = N$
2) $E$
3) $A = 3, \quad B = 3, \quad C = 3, \quad D = 3, \quad E = 1, \quad F = 3, \quad I = 3, \quad J = 3, \quad K = 3, \quad L = 2, \quad M = 2, \quad N = 2$
4) $\{ E \}, \quad \{ L, M, N \}, \quad \{ A, B, F, J \}, \quad \{ C, D, I, K \}$
5) $\{ E, L, M, N \}; \{ A, C, F, J \}, \{ B, D, I, K \}; C3$
D. 1) $A^{-1} = B, \quad B^{-1} = A, \quad C^{-1} = D, \quad D^{-1} = C, \quad E^{-1} = E, \quad F^{-1} = I, \quad I^{-1} = F, \quad J^{-1} = K, \quad K^{-1} = J, \quad L^{-1} = L, \quad M^{-1} = M, \quad N^{-1} = N$
2) $E$
3) $A = 2, \quad B = 2, \quad C = 2, \quad D = 2, \quad E = 1, \quad F = 2, \quad I = 2, \quad J = 2, \quad K = 2, \quad L = 3, \quad M = 3, \quad N = 3$
4) $\{ E \}, \quad \{ L, M, N \}, \quad \{ A, C, F, J \}, \quad \{ B, D, I, K \}$
5) $\{ E, L, M, N \}; \{ A, C, F, J \}, \{ B, D, I, K \}; C3$
E. 1) $A^{-1} = B, \quad B^{-1} = A, \quad C^{-1} = D, \quad D^{-1} = C, \quad E^{-1} = E, \quad F^{-1} = I, \quad I^{-1} = F, \quad J^{-1} = K, \quad K^{-1} = J, \quad L^{-1} = M, \quad M^{-1} = L, \quad N^{-1} = N$
2) $E$
3) $A = 3, \quad B = 3, \quad C = 3, \quad D = 3, \quad E = 1, \quad F = 3, \quad I = 3, \quad J = 3, \quad K = 3, \quad L = 2, \quad M = 2, \quad N = 2$
4) $\{ E \}, \quad \{ L, M, N \}, \quad \{ A, C, F, J \}, \quad \{ B, D, I, K \}$
5) $\{ E, L, M, N \}; \{ A, C, F, J \}, \{ B, D, I, K \}; C4$
F. 1) $A^{-1} = B, \quad B^{-1} = A, \quad C^{-1} = D, \quad D^{-1} = C, \quad E^{-1} = E, \quad F^{-1} = I, \quad I^{-1} = F, \quad J^{-1} = K, \quad K^{-1} = J, \quad L^{-1} = L, \quad M^{-1} = M, \quad N^{-1} = N$
2) $E, N$
3) $A = 3, \quad B = 3, \quad C = 3, \quad D = 3, \quad E = 1, \quad F = 3, \quad I = 3, \quad J = 3, \quad K = 3, \quad L = 2, \quad M = 2, \quad N = 2$
4) $\{ E \}, \quad \{ L, M, N \}, \quad \{ A, C, F, J \}, \quad \{ B, D, I, K \}$
5) $\{ E, L, M, N \}; \{ A, C, F, J \}, \{ B, D, I, K \}; C3$
G. 1) $A^{-1} = B, \quad B^{-1} = A, \quad C^{-1} = D, \quad D^{-1} = C, \quad E^{-1} = E, \quad F^{-1} = I, \quad I^{-1} = F, \quad J^{-1} = K, \quad K^{-1} = J, \quad L^{-1} = L, \quad M^{-1} = M, \quad N^{-1} = N$
2) $E, L$
3) $A = 3, \quad B = 3, \quad C = 3, \quad D = 3, \quad E = 1, \quad F = 3, \quad I = 3, \quad J = 3, \quad K = 3, \quad L = 2, \quad M = 2, \quad N = 2$
4) $\{ E \}, \quad \{ L, M, N \}, \quad \{ A, C, F, J \}, \quad \{ B, D, I, K \}$
5) $\{ E, L, M, N \}; \{ A, C, F, J \}, \{ B, D, I, K \}; C3$
H. 1) $A^{-1} = B, \quad B^{-1} = A, \quad C^{-1} = D, \quad D^{-1} = C, \quad E^{-1} = E, \quad F^{-1} = I, \quad I^{-1} = F, \quad J^{-1} = K, \quad K^{-1} = J, \quad L^{-1} = L, \quad M^{-1} = M, \quad N^{-1} = N$
2) $E$
3) $A = 3, \quad B = 3, \quad C = 3, \quad D = 3, \quad E = 1, \quad F = 3, \quad I = 3, \quad J = 3, \quad K = 3, \quad L = 2, \quad M = 2, \quad N = 2$
4) $\{ E \}, \quad \{ L, M, N \}, \quad \{ A, C, F, J \}, \quad \{ B, D, I, K \}$
5) $\{ E \}; \{ A, C, F, J \}, \{ B, D, I, K \}; C2$
I. 1) $A^{-1} = B, \quad B^{-1} = A, \quad C^{-1} = D, \quad D^{-1} = C, \quad E^{-1} = E, \quad F^{-1} = I, \quad I^{-1} = F, \quad J^{-1} = K, \quad K^{-1} = J, \quad L^{-1} = L, \quad M^{-1} = M, \quad N^{-1} = N$
2) $E$
3) $A = 3, \quad B = 3, \quad C = 3, \quad D = 3, \quad E = 1, \quad F = 3, \quad I = 3, \quad J = 3, \quad K = 3, \quad L = 2, \quad M = 2, \quad N = 2$
4) $\{ E \}, \quad \{ L, M, N \}, \quad \{ A, C, F, J \}, \quad \{ B, D, I, K \}$
5) $\{ E \}; \{ L, M, N \}, \{ A, C, F, J \}, \{ B, D, I, K \}; C4$
J. 1) $A^{-1} = B, \quad B^{-1} = A, \quad C^{-1} = D, \quad D^{-1} = C, \quad E^{-1} = E, \quad F^{-1} = I, \quad I^{-1} = F, \quad J^{-1} = K, \quad K^{-1} = J, \quad L^{-1} = L, \quad M^{-1} = M, \quad N^{-1} = N$
2) $E$
3) $A = 3, \quad B = 3, \quad C = 3, \quad D = 3, \quad E = 1, \quad F = 3, \quad I = 3, \quad J = 3, \quad K = 3, \quad L = 3, \quad M = 3, \quad N = 3$
4) $\{ E \}, \quad \{ L, M, N \}, \quad \{ A, C, F, J \}, \quad \{ B, D, I, K \}$
5) $\{ E, L, M, N \}; \{ A, C, F, J \}, \{ B, D, I, K \}; C3$
Answer: B