Saving contacts to phone google contacts

[Guest quantitum]

I have display system group contacts selected on my GT540 android 2.1. I enter new contact information and press done. When I search the contact it is not on the phone and not on google online contacts either. I try it again and again and contact is not saved on phone google contacts. I can save the contact on Phone Sync or SIM. Why can't it be saved on phone Google Contacts??? Can it be done???