Strawberries without runners

I`ve got  strawberries which I`ve had for for a number of years and forgotten the variety. They they don`t produce runners so I wonder if anyone might know what they might be.
I have transplanted them a couple of times and because they have a great taste I want to divide and transplant. Would be grateful for any tip on the best time to do this and advice on the dividing. They are quite big so how may divisions should I try? Thanks

I'd not heard of strawberries without runners!