Liverpool have won the european cup five times in their history
Liverpool FC have won the Carling cup six times.
Liverpool Football Club has won the Community Shield Cup fifteen times.
7 times 6times
If by super cup, you mean the EUFA Super Cup; then they have won it 3 times.
8th including 2012 cup
It is Liverpool.
Liverpool FC have won the European Cup a record 5 times ; 1977, 1978, 1981, 1984 and 2005.