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Schedule II - Condensed Financial Information of Registrant - Condensed Statements of Cash Flows of Registrant (Details) - USD ($)
$ in Millions
 3 Months Ended 12 Months Ended
Sep. 30, 2016
Jun. 30, 2016
Mar. 31, 2016
Dec. 31, 2015
Sep. 30, 2015
Jun. 30, 2015
Mar. 31, 2015
Dec. 31, 2014
Sep. 30, 2016
Sep. 30, 2015
Sep. 30, 2014
Cash flows from operating activities:                      
Net (loss) income $ 36.2 $ (93.0) $ 15.9 $ 7.0 $ (127.1) $ (41.4) $ (237.5) $ (106.4) $ (33.9) $ (512.4) $ 101.7
Adjustments to reconcile net income (loss) to operating cash flows from continuing operations:                      
Depreciation and amortization                 183.7 171.0 158.2
Stock-based compensation                 78.0 72.6 73.7
Amortization of debt issuance costs                 18.3 17.2 16.2
Amortization of debt discount                 2.8 4.8 4.6
Write-off of discounts and debt issuance costs on retired debt                 5.8 12.8 9.2
Changes in operating assets and liabilities:                      
Net change in cash due to continuing operating activities                 913.3 316.8 704.1
Cash flows from investing activities:                      
Proceeds from investments sold, matured or repaid                 53.7 86.6 54.9
Cost of investments acquired                 (5.2) (5.4) (101.7)
Capital expenditures                 (95.4) (90.6) (75.5)
Net change in cash due to continuing investing activities                 (891.4) (2,141.3) (1,941.9)
Cash flows from financing activities:                      
Dividends paid on preferred stock                     (28.6)
Payments of Debt Issuance Costs                 (9.3) (44.8) (15.8)
Common stock repurchased                   (22.2) (65.8)
Share based award tax withholding payments                 (28.7) (21.0) (31.5)
Other financing activities, net                 1.3 4.1 2.8
Net change in cash due to continuing financing activities                 148.7 1,730.8 666.0
Cash and cash equivalents at beginning of period       661.2       728.8 661.2 728.8 677.0
Cash and cash equivalents at end of period 497.3       661.2       497.3 661.2 728.8
HGI                      
Cash flows from operating activities:                      
Net (loss) income                 (198.8) (556.8) (10.3)
Adjustments to reconcile net income (loss) to operating cash flows from continuing operations:                      
Depreciation and amortization                 0.3 0.5 0.2
Stock-based compensation                 13.7 25.0 27.0
Amortization of debt issuance costs                 2.7 4.4 3.5
Amortization of debt discount                 3.3 1.8 1.5
Equity in net income of subsidiaries                 214.8 357.2 (207.7)
Dividends from subsidiaries                 63.5 65.7 118.0
Deferred income taxes                 205.8 0.0 0.0
Loss from the change in the fair value of the equity conversion feature of preferred stock                 0.0 0.0 12.7
Gain On Contingent Purchase Price Adjustment                 0.0 (8.5) (0.5)
Changes in operating assets and liabilities:                      
Accounts payable and accrued and other current liabilities                 (5.4) (35.4) 43.5
Other operating                 1.8 64.4 (0.7)
Net change in cash due to continuing operating activities                 (109.9) (81.7) (12.8)
Cash flows from investing activities:                      
Capital contributions to consolidated subsidiaries                 (2.9) (406.4) (115.5)
Capital expenditures                 (0.1) (1.2) (0.3)
Net change in cash due to continuing investing activities                 (3.0) (407.6) (115.8)
Cash flows from financing activities:                      
Dividends paid on preferred stock                 0.0 0.0 (28.6)
Proceeds from senior secured notes                 0.0 409.6 400.0
Payments of Debt Issuance Costs                 0.0 (6.8) (10.4)
Common stock repurchased                 0.0 (22.1) (65.6)
Share based award tax withholding payments                 (17.8) (18.3) (6.5)
Other financing activities, net                 4.4 4.1 2.8
Net change in cash due to continuing financing activities                 (13.4) 366.5 291.7
Net change in cash and cash equivalents                 (126.3) (122.8) 163.1
Cash and cash equivalents at beginning of period       $ 297.2       $ 420.0 297.2 420.0 256.9
Cash and cash equivalents at end of period $ 170.9       $ 297.2       $ 170.9 $ 297.2 $ 420.0