Chevvron, the system changed last week and I've only looked at the bits I'm using at present but, we have Class A from either F180 or F245 and above depending on radar availability I think.
Below A, is usually Class C leading into Class D or Class C control zones with E underlying the C and G underlying that; or Class E leading into G
Leading into non-towered Class G aerodromes is usually a layer of Class E from F245 to F180.
Along the J Curve (Cairns down the east coast to Adelaide) there's Class E below C down to about A085 (8500' AMSL [our flight levels start at F110]).
To give some examples; Mackay (YBMK) is a Class D towered aerodrome 22125-1100z daily. Outside these hours the tower closes and airspace up to A045 is reclassified Class G. BN centre has one on radar from about circuit height.
Alice Springs (YBAS) has no radar within cooee (a bloody long way). It has Class C steps with E underlying, running into a Class D tower zone, which gets reclassified Class G when the tower is closed at night. It is possible to avoid Class E (non radar) and descend wholly in A/C/D.
Ayers Rock (YAYE), has Class G Airspace to F180, E from F180 to F245 then A. It also has a CAGRO, Certified Air Ground Radio Operator, who provides known traffic info, weather at the field, and the like. S/He doesn't provide a separation service, it's info only.