What are the major subclasses of lipids on the basis of chemical composition?

The major subclasses of lipids are: simple lipids, derived lipids, and compound lipids. 

1. Simple lipids include fats, oils, and waxes. Fats and oils are compounds called triglycerides, consisting of glycerol and three fatty acids. Fatty acids are chains of hydrocarbons with variable lengths and degrees of saturation, terminating in carboxylic acid groups. They can have cis or trans double bonds, leading to diverse fatty acid types. Fats are solid at room temperature and are composed mainly of saturated fatty acids, while oils are liquid and are composed of unsaturated fatty acids. Waxes are esters of long-chain alcohol and fatty acid. The alcohols and acids found in waxes typically have chains ranging from 12-34 carbon atoms. 
2. Derived lipids are those obtained from the breakdown or modification (via hydrolysis) of simple and complex lipids. These lipids make up a large category of biological compounds that exhibit insolubility in water but dissolve in organic solvents. Examples of derived lipids include terpenes, cholesterol, carotenoids, prostaglandins, and fat-soluble vitamins. 
3. Compound lipids include phospholipid and glycolipids. Phospholipids form fatty acids, phosphoric acid, glycerol, amino alcohol sphingosine, and nitrogen-containing alcohol upon hydrolysis. They can be further classified into glycerophospholipids or sphingophospholipids based on the alcohol group associated with them (glycerol or sphingosine). Upon hydrolysis, glycolipids produce fatty acids, glycerol, sphingosine and a carbohydrate. Other compound lipids include amino lipids, lipoproteins and sulfolipids.