# Is spin invariant under Parity operator or not?

If I take spin as an angular momentum, which defined as $\overrightarrow{r}\times\overrightarrow{p}$, then it is invariant under parity operation. On my lecture slide, it is also written that spin is an axial vector, which does not change sign under parity operation. But on the book of David Griffth's 'Introduction to elementary particles', when he introduces the famous beta-decay experiment of 60Cobalt, the spin changed direction in its mirror image?

I'm a bit confused now, if anyone can help me that would be very nice!

'Mirror image' ($x,y,z \to x,y,-z$)involves a parity operation ($x,y,z \to -x,-y,-z$)and a rotation ($x,y,z \to -x,-y,z$). The rotation switches the angular momentum direction in Cobalt-60 type experiments. Details depend n where the mirror is placed.