The ornamental design for a large toothbrushcaddy, as shown and described.
FIG. 1 is a top perspective view of the large toothbrush caddy showing my new design.
FIG. 2 is a front view thereof.
FIG. 3 is a back view thereof.
FIG. 4 is a side view thereof.
FIG. 5 is another side view thereof.
FIG. 6 is a top view thereof.
FIG. 7 is a bottom view thereof.
FIG. 8 is a front top perspective exploded view thereof; and,
FIG. 9 is a back top perspective exploded view thereof.
The broken lines in the drawings illustrate portions of the large toothbrush caddy which form no part of the claimed design and the dot dash broken lines show a bracket.