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Business segments - Schedule of Segment Reporting Results By Segment (Details) $ in Thousands | 3 Months Ended | 12 Months Ended
--- | --- | ---
Sep. 30, 2020 USD ($) | Jun. 30, 2020 USD ($) | Mar. 31, 2020 USD ($) | Dec. 31, 2019 USD ($) | Sep. 30, 2019 USD ($) | Jun. 30, 2019 USD ($) | Mar. 31, 2019 USD ($) | Dec. 31, 2018 USD ($) | Sep. 30, 2020 USD ($) segment | Sep. 30, 2019 USD ($) | Sep. 30, 2018 USD ($)
Segment Reporting [Abstract] |  |  |  |  |  |  |  |  |  |  |
Number of business segments | segment |  |  |  |  |  |  |  |  | 3 |  |
Financial information for each of the Company's business segments |  |  |  |  |  |  |  |  |  |  |
Revenue | $ 923,836 | $ 901,337 | $ 818,135 | $ 818,229 | $ 754,966 | $ 730,710 | $ 736,520 | $ 664,619 | $ 3,461,537 | $ 2,886,815 | $ 2,392,236
Gross profit | 196,851 | 185,603 | 153,098 | 175,450 | 168,250 | 174,247 | 169,422 | 159,265 | 711,002 | 671,184 | 594,385
Selling, general and administrative expense |  |  |  |  |  |  |  |  | 387,090 | 321,023 | 285,241
Operating income | 84,523 | 87,309 | 37,311 | 79,135 | 77,576 | 83,594 | 81,801 | 74,136 | 288,278 | 317,107 | 295,483
Amortization of intangible assets |  |  |  |  |  |  |  |  | (35,634) | (33,054) | (10,308)
Gain on sale of a business |  |  |  |  |  |  |  |  | 1,718 | 0 | 0
Depreciation and amortization |  |  |  |  |  |  |  |  | 64,527 | 52,404 | 51,884
Segment Reconciling Items |  |  |  |  |  |  |  |  |  |  |
Financial information for each of the Company's business segments |  |  |  |  |  |  |  |  |  |  |
Selling, general and administrative expense |  |  |  |  |  |  |  |  | 4,358 | 2,676 | 2,844
Amortization of intangible assets | (8,900) | (8,712) | (8,934) | (9,088) | (9,028) | (9,049) | (9,519) | (5,458) | (35,634) | (33,054) | (10,308)
Restructuring costs |  |  |  |  |  |  |  |  | 0 | 0 | (3,353)
Acquisition-related expenses | (459) | (150) | (3,377) | (635) | 0 | 0 | 0 | (2,691) | (4,621) | (2,691) | (947)
Gain on sale of a business | 12 | 1,706 | 0 | 0 |  |  |  |  | 1,718 | 0 | 0
Other |  |  |  |  |  |  |  |  | 263 | 15 | (1,897)
U.S. Services |  |  |  |  |  |  |  |  |  |  |
Financial information for each of the Company's business segments |  |  |  |  |  |  |  |  |  |  |
Revenue |  |  |  |  |  |  |  |  | 1,329,274 | 1,176,488 |
U.S. Services | Operating segments |  |  |  |  |  |  |  |  |  |  |
Financial information for each of the Company's business segments |  |  |  |  |  |  |  |  |  |  |
Revenue | 371,345 | 336,950 | 308,698 | 312,281 | 300,406 | 291,132 | 290,737 | 294,213 | 1,329,274 | 1,176,488 | 1,213,911
Gross profit | 92,199 | 93,029 | 85,454 | 89,590 | 83,154 | 86,664 | 86,260 | 88,031 | 360,272 | 344,109 | 359,624
Selling, general and administrative expense |  |  |  |  |  |  |  |  | 132,489 | 123,275 | 140,990
Operating income | 62,343 | 61,033 | 46,215 | 58,192 | 53,832 | 54,250 | 56,860 | 55,892 | 227,783 | 220,834 | 218,634
Depreciation and amortization |  |  |  |  |  |  |  |  | 20,951 | 18,466 | 20,963
U.S. Federal Services |  |  |  |  |  |  |  |  |  |  |
Financial information for each of the Company's business segments |  |  |  |  |  |  |  |  |  |  |
Revenue |  |  |  |  |  |  |  |  | 1,633,337 | 1,111,197 |
U.S. Federal Services | Operating segments |  |  |  |  |  |  |  |  |  |  |
Financial information for each of the Company's business segments |  |  |  |  |  |  |  |  |  |  |
Revenue | 423,232 | 450,143 | 393,391 | 366,571 | 312,179 | 292,295 | 289,736 | 216,987 | 1,633,337 | 1,111,197 | 478,911
Gross profit | 86,423 | 84,723 | 76,958 | 70,821 | 66,586 | 66,803 | 60,696 | 47,985 | 318,925 | 242,070 | 126,698
Selling, general and administrative expense |  |  |  |  |  |  |  |  | 186,023 | 126,128 | 69,312
Operating income | 31,855 | 39,233 | 30,232 | 31,582 | 31,090 | 33,907 | 29,592 | 21,353 | 132,902 | 115,942 | 57,386
Depreciation and amortization |  |  |  |  |  |  |  |  | 25,153 | 16,802 | 8,478
Outside the U.S. |  |  |  |  |  |  |  |  |  |  |
Financial information for each of the Company's business segments |  |  |  |  |  |  |  |  |  |  |
Revenue |  |  |  |  |  |  |  |  | 498,926 | 599,130 |
Outside the U.S. | Operating segments |  |  |  |  |  |  |  |  |  |  |
Financial information for each of the Company's business segments |  |  |  |  |  |  |  |  |  |  |
Revenue | 129,259 | 114,244 | 116,046 | 139,377 | 142,381 | 147,283 | 156,047 | 153,419 | 498,926 | 599,130 | 699,414
Gross profit | 18,229 | 7,851 | (9,314) | 15,039 | 18,510 | 20,780 | 22,466 | 23,249 | 31,805 | 85,005 | 108,063
Selling, general and administrative expense |  |  |  |  |  |  |  |  | 65,938 | 68,944 | 72,095
Operating income | $ (584) | $ (5,817) | $ (26,718) | $ (1,014) | $ 2,157 | $ 4,989 | $ 4,474 | $ 4,441 | (34,133) | 16,061 | 35,968
Depreciation and amortization |  |  |  |  |  |  |  |  | $ 18,423 | $ 17,136 | $ 22,443

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