Can my employer suspend me for a week for being late without warning?

I thought I was suppose to come in at 5:30p.m. but in reality I should of been there at 4:30p.m. and my boss told me to go home and later sent me a text suspending me for a week. Is that legal? I am late slot but usually only by 5-10 min tops and it's an ongoing joke at work. He has never written me up or anything until yesterday when I showed up an hour late and told him it was an honest mistake that I got the time wrong. Not only did he send me home, later I got to this text.1/4 Yesterday you were late. You thought you were supposed to be there at 530. You were scheduled at 430. With that said you were once again even late for wh2/4 at you thought was your scheduled time.
We can not have our employees being late. I can't remember the last time you were on time.
You work hard when y3/4 ou are there but, we need to know that we can depend on you.
As a result we are suspending you for this week. Prior to your return we would like you to 4/4 call us or come in so that we can have you understand our expectations.