The invention claimed is:1. A vent plug for a lead-acid battery comprising:a head portion;a cylindrical portion extending from the head portion; anda filter provided inside the cylindrical portion,wherein, in a case where an end portion of the cylindrical portion on the head portion side is defined as a first end portion, and an end portion of the cylindrical portion on a side opposite to the first end portion is defined as a second end portion,the cylindrical portion includes:a cylinder portion;a screw thread portion having a spiral shape and provided on an outer peripheral surface of the cylinder portion;a slit; anda through hole that allows an inside and an outside of the cylinder portion to communicate with each other,wherein the filter is disposed at a position where the through hole is provided in an axial direction of the cylindrical portion,wherein, in a case where a circumferential position where a start end portion, which is an end portion of the screw thread portion on the second end portion side, is located is defined as a first circumferential position, and a screw thread located closer to the first end portion side from the start end portion than the start end portion at the first circumferential position and located closest to the second end portion side is defined as a first-peripheral screw thread portion, the screw thread portion intersects the slit only at the first-peripheral screw thread portion when the cylindrical portion is viewed in a plan view from a radially outer side of the cylinder portion, andwherein the first peripheral screw thread portion is cut out and divided by the slit where the screw thread portion intersects the slit.2. The vent plug for a lead-acid battery according to claim 1, further comprising a splash-proof body having a plurality of splash-proof plates,wherein a distance between an end portion of the splash-proof plate and the first end portion is smaller than a distance between the first end portion and the start end portion in the axial direction.3. The vent plug for a lead-acid battery according to claim 1, further comprising a splash-proof body having a plurality of splash-proof plates,wherein a distance between an end portion of the splash-proof plate and the first end portion is smaller than a distance between the end portion of the screw thread portion and the first end portion in the axial direction.4. The vent plug for a lead-acid battery according to claim 1,wherein when viewed in the plan view from the radially outer side of the cylinder portion, a top portion of the slit is higher than a peak of the first peripheral screw thread portion where the screw thread portion intersects the slit.5. The vent plug for a lead-acid battery according to claim 1, further comprising a splash-proof body having a plurality of splash-proof plates,wherein when a distance from a bottom portion of the slit to a top portion of the slit in the axial direction is h1, a distance from the second end portion to an end portion of the splash-proof plate in the axial direction is h2, and a pitch of the screw thread portion is α, h1, h2, and α satisfy a following relational expression:h1<h2<h1+α.6. A lead-acid battery comprising the vent plug according to claim 1.
