Teams Harry Conway played for
| Main FC | New South Wales (2015/16-2021/22) |
| South Australia (2022/23) | |
| Main ListA | New South Wales (2016/17-2019/20) |
| South Australia (2022/23) | |
| Main Twenty20 | Adelaide Strikers (2019/20-2022/23) |
| Other FC | Cricket Australia XI (2017/18) |
| Australia A (2020/21) | |
| Under-19 ODI | Australia Under-19s (2011/12-2012) |
| Under-19 World Cup | Australia Under-19s (2012) |
| Big Bash League | Adelaide Strikers (2019/20-2022/23) |
| Sheffield Shield | New South Wales (2015/16-2021/22) |
| South Australia (2022/23) | |
| Miscellaneous | Northern District (2010/11-2015/16) |
| New South Wales Under-19s (2011/12) | |
| Australia Under-19s (2012) | |
| New South Wales Country Origin (2013/14) | |
| New South Wales XI (2013/14) | |
| New South Wales Under-23s (2013/14-2016/17) | |
| Australian Capital Territory (2014/15) | |
| Cricket Australia XI (2014/15) | |
| Australian XI (2014/15) | |
| New South Wales Second XI (2016/17) | |
| Australia Prime Minister's XI (2016/17) | |
| New South Wales Metropolitan Under-23s (2017/18-2018/19) |
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