Segment Information - Financial Information Regarding Reportable Segments (Details) $ in Millions	3 Months Ended	12 Months Ended
	Dec. 27, 2020 USD ($) segment	Dec. 27, 2020 USD ($) segment	Dec. 29, 2019 USD ($)	Dec. 30, 2018 USD ($)
Segment Reporting [Abstract]
Number of operating segments | segment	2	2
Number of reportable segments | segment	2	2
Segment Reporting Information [Line Items]
Revenues		$ 1,384.9	$ 1,436.8	$ 1,326.8
Operating expenses:
Selling, general and administrative		144.9	142.4	123.8
Depreciation and amortization		81.1	88.4	97.4
Total operating expenses		1,072.9	1,119.0	1,042.4
Operating profit		312.0	317.8	284.4
Interest expense, net		56.0	55.7	38.7
Other (income) expense, net		(1.0)	(0.1)	(0.5)
Intercompany income (expense)		0.0
Income before income taxes		257.0	262.2	246.2
Income taxes		62.2	69.0	62.5
Net income		194.8	193.2	183.7
Total assets	$ 2,528.9	2,528.9	2,151.2	1,488.5
Capital expenditures		69.8	68.5	66.7
Long-lived assets	1,126.6	1,126.6	982.8
Service revenues
Segment Reporting Information [Line Items]
Revenues		1,233.1	1,303.8	1,219.6
Operating expenses:
Cost of service and vehicle sales		721.7	780.1	729.4
Vehicle sales
Segment Reporting Information [Line Items]
Revenues		151.8	133.0	107.2
Operating expenses:
Cost of service and vehicle sales		125.2	108.1	91.8
U.S.
Operating expenses:
Long-lived assets	1,040.8	1,040.8	923.3
Foreign
Operating expenses:
Long-lived assets	85.8	85.8	59.5
United States
Segment Reporting Information [Line Items]
Revenues		1,215.1	1,266.1	1,185.1
Operating expenses:
Selling, general and administrative		135.0	131.3	111.9
Depreciation and amortization		74.3	81.8	90.5
Total operating expenses		933.7	981.5	929.3
Operating profit		281.4	284.6	255.8
Interest expense, net		56.2	55.7	38.6
Other (income) expense, net		(0.7)	(0.2)	(0.8)
Intercompany income (expense)		(8.0)
Income before income taxes		233.9	229.1	218.0
Income taxes		56.9	59.7	54.7
Net income		177.0	169.4	163.3
Total assets	2,341.1	2,341.1	1,963.4	1,344.3
Capital expenditures		52.3	64.2	63.0
United States | Service revenues
Segment Reporting Information [Line Items]
Revenues		1,134.4	1,196.2	1,123.9
Operating expenses:
Cost of service and vehicle sales		659.8	714.4	674.1
United States | Vehicle sales
Segment Reporting Information [Line Items]
Revenues		80.7	69.9	61.2
Operating expenses:
Cost of service and vehicle sales		64.6	54.0	52.8
International
Segment Reporting Information [Line Items]
Revenues		169.8	170.7	141.7
Operating expenses:
Selling, general and administrative		9.9	11.1	11.9
Depreciation and amortization		6.8	6.6	6.9
Total operating expenses		139.2	137.5	113.1
Operating profit		30.6	33.2	28.6
Interest expense, net		(0.2)	0.0	0.1
Other (income) expense, net		(0.3)	0.1	0.3
Intercompany income (expense)		8.0
Income before income taxes		23.1	33.1	28.2
Income taxes		5.3	9.3	7.8
Net income		17.8	23.8	20.4
Total assets	$ 187.8	187.8	187.8	144.2
Capital expenditures		17.5	4.3	3.7
International | Service revenues
Segment Reporting Information [Line Items]
Revenues		98.7	107.6	95.7
Operating expenses:
Cost of service and vehicle sales		61.9	65.7	55.3
International | Vehicle sales
Segment Reporting Information [Line Items]
Revenues		71.1	63.1	46.0
Operating expenses:
Cost of service and vehicle sales		$ 60.6	$ 54.1	$ 39.0