At later stages in the life of a star, when it has exhausted its hydrogen fuel, it may fuse other nuclear fuels. This only possible in large massive stars. The ignition of these fuels requires very high temperatures. Helium fusion occurs at temperatures above 100,000,000 Kelvin, and carbon fusion does not begin until the temperature exceeds 600,000,000 Kelvin.
At temperatures above 600,000,000 K, carbon fuses rapidly in a complex network of reactions illustrated in the above diagram, where each arrow represents a different nuclear reaction. The process is complicated because nuclei can react by adding a proton, a neutron, or a helium nucleus or by combning directly with other nuclei. Unstable nuclei can decay by ejecting a proton, a neutron, or a helium nucleus or by splitting into fragments.
Reactions at still higher temeperature scan convert magnesium, aluminium and silicon into yet heavier atoms.
from Michael A. Seeds, Horizons, Exploring the Universe,1991
ed, pp.188-89, diagram from page.191 (Wadsworth Publishing
Chemical Elements page