Jelly, 6 bytes

*Ɱ4%⁵Q 

A monadic link which accepts an integer and yield a list of integers.

Try it online!

###How?

*Ɱ4%⁵Q - Link: integer, n 4 - four Ɱ - map across (implicit range of [1..4]) with: * - exponentiate ⁵ - ten % - (powers) mod (ten) Q - de-duplicate 

Jelly, 6 bytes

*Ɱ4%⁵Q 

A monadic link which accepts an integer and yield a list of integers.

Try it online!

How?

*Ɱ4%⁵Q - Link: integer, n 4 - four Ɱ - map across (implicit range of [1..4]) with: * - exponentiate ⁵ - ten % - (powers) mod (ten) Q - de-duplicate 

Jelly, 6 bytes

*Ɱ4%⁵Q 

A monadic link which accepts an integer and yield a list of integers.

Try it online!

Jelly, 6 bytes

*Ɱ4%⁵Q 

A monadic link which accepts an integer and yield a list of integers.

Try it online!

###How?

*Ɱ4%⁵Q - Link: integer, n 4 - four Ɱ - map across (implicit range of [1..4]) with: * - exponentiate ⁵ - ten % - (powers) mod (ten) Q - de-duplicate