Hodge numbers for CICYs with symmetries of order divisible by 4

We compute the Hodge numbers for the quotients of complete intersection Calabi-Yau three-folds by groups of orders divisible by 4. We make use of the polynomial deformation method and the counting of invariant Kahler classes. The quotients studied here have been obtained in the automated classification of V. Braun. Although the computer search found the freely acting groups, the Hodge numbers of the quotients were not calculated. The freely acting groups, G, that arise in the classification are either Z2 or contain Z4, Z2*Z2, Z3 or Z5 as a subgroup. The Hodge numbers for the quotients for which the group G contains Z3 or Z5 have been computed previously. This paper deals with the remaining cases, for which G⊇Z4 or G⊇Z2*Z2. We also compute the Hodge numbers for 99 of the 166 CICY's which have Z2 quotients.