Is there any non-solvable finite group $G$ such that ${\rm cd}(G) =\{1, 3, 4, 5, 6, 10 \}$, where ${\rm cd}(G)$ is the set of irreducible character degrees of $G$. In other words we have that a normal subgroup $M$ of $G$ such that $G/M \cong A_5$. Now, how do we can construct non-solvable finite group $G$ such that ${\rm cd}(G) =\{ 1, 3, 4, 5, a, b\}$ where $6$ divides $a$, $10$ divides $b$, and $(5, a)=(3,b)=1$ ?

Is there any non-solvable finite group $G$ such that ${\rm cd}(G) =\{1, 3, 4, 5, 6, 10 \}$, where ${\rm cd}(G)$ is the set of irreducible character degrees of $G$. In other words we have that a normal subgroup $M$ of $G$ such that $G/M \cong A_5$. Now, how do we can construct a non-solvable finite group $G$ such that ${\rm cd}(G) =\{ 1, 3, 4, 5, a, b\}$ where $6$ divides $a$, $10$ divides $b$, and $(5, a)=(3,b)=1$ ?

Is there any non-solvable group $G$ such that ${\rm cd}(G) =\{1, 3, 4, 5, 6, 10 \}$, where ${\rm cd}(G)$ is the set of irreducible character degrees of $G$. In other words we have that a normal subgroup $M$ of $G$ such that $G/M \cong A_5$. Now, how do we can construct non-solvable group $G$ such that ${\rm cd}(G) =\{ 1, 3, 4, 5, a, b\}$ where $6$ divides $a$, $10$ divides $b$, and $(5, a)=(3,b)=1$ ?

Is there any non-solvable finite group $G$ such that ${\rm cd}(G) =\{1, 3, 4, 5, 6, 10 \}$, where ${\rm cd}(G)$ is the set of irreducible character degrees of $G$. In other words we have that a normal subgroup $M$ of $G$ such that $G/M \cong A_5$. Now, how do we can construct non-solvable finite group $G$ such that ${\rm cd}(G) =\{ 1, 3, 4, 5, a, b\}$ where $6$ divides $a$, $10$ divides $b$, and $(5, a)=(3,b)=1$ ?