Is this a Wild Strawberry Plant?

I started my small scale Strawberry Garden this year. I planted 1 Pineberry plant, (which is starting to grow nicely I think I got a runner going) and about 10 Quinault's ( which are also going crazy). I was interested in crossbreeding these things indoors to create my own yard variety. So I went hunting for Wild strawberry plants in my yard. I heard the wild strawberries (even though they are really small) Are the best flavored you can get.  Im pretty sure I found what I believe to be about 5 or so small wild strawberry plants. Then I found this beast. This thing is a monster. It has about a 1 foot radius on it already. I dug it up with a shovel so I wouldn't hurt the root structure, BUT this thing has a large Tap root on it. My strawberry plants I planted were just small bundles of roots with a crown, I did not see a tap root like this. I accidently broke the tip on it when I lifted the plug of dirt out the ground. The plant is recovering and is doing well since I put it in a pot, I pulled out all the grass and clovers from the plug manually. In the pictures it is hard to see, but the leaves have the little red tips. The leaves are not as wide as my other strawberry plants and thing has a very wild growth patter. The stems are super thick and this thing is really growing like some kind of monkey grass wildness. I have never seen a strawberry plant picture online that looks like this. I live in NY State. This thing was just growing in the  yard. It grew low to the ground so my lawn mower didn't destroy it. Its like it adapted itself to avoid the blades. Is this a wild Strawberry plant or rare variety or is it some other kind of weed. If it is strawberry, im going to be trying to breed with it for fun, the genetics look very different on this thing.
Any thoughts on these pictures. This is the plant in question. Thanks.

I believe you have a rough cinquefoil. It's a weed, distantly related to strawberry, but doesn't make berries. Hope that helps.

It does not look even slightly like the wild strawberries from this area.  They are smoother edged and very low growing.  If the lawn mower is set at medium height it is possible to mow over them and never disturb a plant.  ( I have some in my lawn that have been there for a decade.)  As my elevation is too low they almost never produce but they do grow.

This is what the small wild strawberry plants I found in the yard look like, I even clipped one back a bit and put it inside the house under a light to experiment with it. They do not look like the monster plant though and it was on the other side of the yard. I do not believe these little babies are runners from it.
These little wild ones are obviosly different.

If this big weed is a cinquefoil, can strawberries crossbreed with it? Would it be possible to graft another strawberry plant onto a cinquefoil? Im definitely going to keep the large plant and bring it up to top health. It might still have pretty flowers on it and look good if its spoiled and taken care of.

Those second ones are definitely wild strawberries. That would be interesting to see what you get with a cross to the wild strawberry. The cinquefoil is potentilla norvegica, brought to the u.s. by Norwegian pioneers for medicine. What is the white flower? I like to collect and propagate wild plants as well.

Hello Dan, Those are actually little blue flowers. The light might make it look white. These are as best as I can tell, called, Forget Me Not. They spread pretty good and they look good when they take over a yard. Im trying to get rid of all my grass so im keeping nice stuff like this that is wild and native and good looking so I can stop using the lawn mover :) Just collecting stuff now that I want to make yard patches with and ill put a walkway between all these different things that I let grow wild. Im done with grass. its so boring.

The entire side yard between me and my neighbor is wild strawberries. It's been 10 years but they entirely pushed out the grass and they look lovely. Still, I had not considered transplanting into my front yard. I definitely will now. Thanks for this thread!

Lee, wild strawberries aren’t usually that aggressive. It is possible, but most of the plants in yards that people call wild strawberries are actually Mock Strawberries. They have red berries but don’t taste good. They look very similar.

https://en.m.wikipedia.org/wiki/Mock_strawberry

Do your plants have yellow or white blooms?

Musk strawberries make great ground cover in shade. They are taller and more aggressive than domestic strawberries and much more aggressive than our wild strawberries. They don’t produce for several years and mine haven’t produced hardly anything yet after around four years. They do have a very different and interesting flavor. They look great. They seem to be totally disease resistant.  I wonder if they could be crossed with either domesticated varieties or Fragaria virginiana?

http://www.fruitipedia.com/2018/12/musk-strawberry_fragaria-moschata/