Without using any external package, you could do (for even)
res = df[(as.numeric(substr(df$Timestamp, 18, 19)) %% 2) == 0,]
For testing purposes, I used a small subset of your dataframe:
df = data.frame(Timestamp = c("2013-04-01 00:00:00", "2013-04-01 00:00:01", "2013-04-01 00:00:02", "2013-04-01 00:00:03", "2013-04-01 00:00:04"), C01 = rep(0,5), C02 = rep(1,5))
df$Timestamp = as.POSIXct(df$Timestamp)
Here is what you obtain (for even):
#> res
# Timestamp C01 C02
#1 2013-04-01 00:00:00 0 1
#3 2013-04-01 00:00:02 0 1
#5 2013-04-01 00:00:04 0 1
For odd, the same logic is applied by replacing ==0
by ==1