A direct nuclear blast - nothing. However it is said that cockroaches would possibly survive radiation where other animals would be killed.
There is a possibility for a cockroach to live and die. A cockroach will die from the initial blast, meaning the cockroach will die from the fiery explosion. A cockroach will survive the radiation of the blast, but not the actual blast itself.
none
Twinkies
only by being far far away
Only by being a safe distance away.
Not within the 5 PSI max overpressure range.
Anyone that has not been kiled in the blast, has a change on surving.
Cockroaches would out-survive humans when being exposed to increased levels of radiation. However, most other insects can out-survive cockroaches, and some microbes can out-survive insects. A reason most insects can endure high levels of radiation is that their cells divide less frequently. Radiation interferes with the way cells divide. Every division multiplies the damage caused by radiation. If a cell divides less frequently, accumulation of damage will occur with less speed. Insects are thus less affected by radiation.
Insects have higher LD50 for radiation exposure than mammals. LD50 is defined as the dose of something toxic that results in 50% fatality in the exposed group. However insects would have similar problems to mammals surviving the thermal effects.
It is highly unlikely that anything directly at the site of a nuclear blast would survive due to the extreme heat, pressure, and radiation. However, some organisms like extremophiles have shown the capability to survive in extremely harsh conditions and may have a chance of surviving indirectly through protective mechanisms.
Insects in general have a higher LD50 for ionizing radiation than do mammals. But nothing is unique about cockroaches. Other effects like the blast and heat will kill them as easily as anything else.
No cockroaches are one of the few organisms able to survive nuclear explosions. Scorpions cannot.