If you were able to max out your 401(k) -- that is, contributing $19,500, or $26,000 if you're 50 or older -- in the midst of one of the most chaotic years any of us have ever lived through, hats off to you. And if you'd like to save even more, all the better, but you should consider a different account so you can earn the most tax breaks on your savings. Here are three possibilities.

1. IRA

You can open an IRA on your own with any broker, and you may contribute up to $6,000 per year, or $7,000 if you're 50 or older. Some IRAs may enable you to automatically transfer a certain amount of money from your bank account to your IRA on a regular schedule. Otherwise, you can make a lump-sum deposit if you have enough cash. 

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IRAs give you more freedom to invest your money how you choose than 401(k)s. You can put your money in stocks, bonds, mutual funds, exchange-traded funds (ETFs), and more and adjust your portfolio as often as you feel is necessary. This also gives you more control over how much you pay in fees.

Another plus is that you can choose between a traditional IRA, which you fund with pre-tax dollars, and a Roth IRA, which you fund with after-tax dollars. Some 401(k)s may offer you this option as well, but not all companies have Roth 401(k)s. If you'd rather pay taxes now to avoid taxes on your withdrawals in retirement, consider placing your extra savings in a Roth IRA.

2. Health savings account (HSA)

A health savings account (HSA) is intended for medical savings, but you can also use it for retirement savings. You must have a high-deductible health insurance plan -- one with a deductible of $1,400 or more for an individual or $2,800 or more for a family -- to contribute to an HSA. Individuals may set aside up to $3,550 in 2020, while families may save up to $7,100. These limits will rise by $50 and $100, respectively, for 2021.

Contributions to your HSA reduce your taxable income for the year, like most 401(k) contributions. But withdrawals work a little differently. Medical withdrawals are always tax- and penalty-free. You can also make non-medical withdrawals, though you'll owe taxes on these, along with a 20% penalty if you're under 65.

3. Taxable brokerage account

A taxable brokerage account also isn't intended for retirement savings, and it doesn't provide the same tax benefits as the accounts above. But there are no limits on how much you can contribute to one or what you can invest your money in. You're also free to withdraw your funds at any time without paying a penalty.

If you plan to use your taxable brokerage account to save for retirement, you should aim to hold your assets for at least a year before you sell them. Then, they become subject to long-term capital gains tax, rather than short-term capital gains tax, which is the same as your income tax bracket. Long-term capital gains tax brackets range from 0% to 20%, depending on your income, but you usually end up paying less than you would if you'd owed short-term capital gains tax on your withdrawals.

You don't have to choose just one of the account types above. You could put some retirement savings in an HSA and then switch to an IRA, or vice versa. Or you could contribute some money to all three types of accounts. Weigh the pros and cons of each of them and decide what makes the most sense for your situation.