Given the octic group $G = \{e, \sigma, \sigma^2, \sigma^3, \beta, \gamma, \delta, t\}$.
Find a subgroup of $G$ that has order $2$ and is a normal subgroup of $G$.
Find a subgroup of $G$ that has order $2$ and is not a normal subgroup of $G$.
Given the octic group $G = \{e, \sigma, \sigma^2, \sigma^3, \beta, \gamma, \delta, t\}$.
Find a subgroup of $G$ that has order $2$ and is a normal subgroup of $G$.
Find a subgroup of $G$ that has order $2$ and is not a normal subgroup of $G$.