Important Subgroups
It has the branching rules to /Z5.
If the hypercharge is contained within SU(5), this is the conventional Georgi-Glashow model, with the 16 as the matter fields, the 10 as the electroweak Higgs field and the 24 within the 45 as the GUT Higgs field. The superpotential may then include renormalizable terms of the form Tr(45 ⋅ 45); Tr(45 ⋅ 45 ⋅ 45); 10 ⋅ 45 ⋅ 10, 10 ⋅ 16* ⋅ 16 and 16* ⋅ 16. The first three are responsible to the gauge symmetry breaking at low energies and give the Higgs mass, and the latter two give the matter particles masses and their Yukawa couplings to the Higgs.
There is another possible branching, under which the hypercharge is a linear combination of an SU(5) generator and χ. This is known as flipped SU(5).
Another important subgroup is either /Z2 or Z2 ⋊ /Z2 depending upon whether or not the left-right symmetry is broken, yielding the Pati-Salam model, whose branching rule is
Read more about this topic: SO(10) (physics)
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