The Spin(10) grand unification has a symmetry breaking of SO(10), or Spin(10).
"The symmetry breaking of SO(10) is usually done with a combination of (( a $45_H$ OR a $54_H$) AND ((a $16_H$ AND a $\overline{16}_H$) OR (a $126_H$ AND a $\overline{126}_H$)) )."
I suppose that 16 has something to do with the 16 spinor representation of SO(10), and 45 has something to do with ${10 \choose 2} = 45$, while 126 has something to do with $\frac{1}{2}{10 \choose 5} = 126$.
What does 54 stands for in the representation theory?
So what are so special about these number: 16,45,54, and 126 in these models? And their roles in the representation theory?