New Zealand had 1499 cases of COVID-19 before eliminating transmission of the virus. Extensive contract tracing during the outbreak has resulted in a dataset of epidemiologically linked cases. This data contains useful information about the transmission dynamics of the virus, its dependence on factors such as age, and its response to different control measures. We use Monte-Carlo network construction techniques to provide an estimate of the number of secondary cases for every individual infected during the outbreak. We then apply standard statistical techniques to quantify differences between groups of individuals. Children under 10 years old are significantly under-represented in the case data. Children infected fewer people on average and had a lower probability of transmitting the disease in comparison to adults and the elderly. Imported cases infected fewer people on average and also had a lower probability of transmitting than domestically acquired cases. Superspreading is a significant contributor to the epidemic dynamics, with 20% of cases among adults responsible for 65-85% of transmission. Subclinical cases infected fewer individuals than clinical cases. After controlling for outliers serial intervals were approximated with a normal distribution (μ = 4.4 days, σ = 4.7 days). Border controls and strong social distancing measures, particularly when targeted at superspreading, play a significant role in reducing the spread of COVID-19.