What organic functional groups are present in urethane?

Urethane is a general description that can pertain to carbamates, ethyl carbamates or polyurethane. It has a general structure of R-O-C(=O)-N-(R or H)

R denotes a sub chains or constituents

The functional groups that are present in urethane are The ester group; R-O-C(=O)-R' and an amine; RN(R' or H)2

An example of urethane is the ethyl carbamate, CH3CH2-O-C(=O)-NH2, that has an ethyl substituent in the ester area and a primary amine. 

**Types of amine

Primary: one R group is attached; RNH2
Secondary: two R groups are attached; RR'NH
Tertiary: three R groups are attached; RR'R''N

How do the functional groups affect the properties of urethane? 

Urethane is another name for ethyl carbamate.  This is a chemical that is composed of one central carbon that contains an ethyl ester.  Attached to this carbon is also an amine (NH2).  The combination of ester and amine allow for urethane molecules to form amide bonds together and form long polymeric chains (polyurethane).  These two functional groups also give urethane a very high polarity which allows it to be soluble in many organic solvents.  Because of this high polarity, pure, anhydrous (without any water) urethane is a crystalline solid with a relatively high melting point for such a small chemical compound.