MIT notes that a teaspoon of the material a neutron star is made of would weigh about 15 times more than the moon. Despite how dense a neutron star is, MIT says that the proton pressure they have calculated has found that a proton contains even higher pressures.
The highly pressurized core of a neutron is generating pressures at its most intense point higher than are found inside a neutron star. The core of the neutron pushes out from the center of the proton, while the portion of the proton surrounding the core pushes in. The two competing pressures stabilize the overall structure of the proton.