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Keyed in multiple places:

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Key to Solidago, Key A: Key to "thyrsiflorous goldenrods" -- with stem leaves dominant and cylindrical inflorescences [subgenus Solidago, sections Thyrsiflorae (mostly) and an Erectae]

Asteraceae

Solidago

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1 Outer phyllaries appressed; [subgenus Solidago; section Erectae]
1 Outer phyllaries with squarrose tips; [subgenus Solidago; section Thyrsiflorae].
  2 Leaves oblanceolate-obovate, often short acuminate at the apex; mid-stem leaves 8-14 cm long, 18-40 mm wide, the margins sharply serrate on at least the upper 2/3
  2 Leaves narrowly to broadly elliptic (or less commonly slightly oblanceolate), acute at the apex; mid-stem leaves 3-8 (-10) cm long, 8-25 mm wide, margins entire to shallowly serrate on only the upper ½ to 2/3.
    3 Middle and inner series phyllaries glabrous, usually minutely glandular or resinous and shiny; mid and upper stem leaves usually narrowly lanceolate, rarely broadly lanceolate to ovate, green to shiny silvery; [MO to LA west to e. KS to se. and c. TX, disjunct in n. COA]
    3 Middle and inner series phyllaries sparsely to moderately strigose, sometimes minutely glandular; mid and upper stem leaves lanceolate-elliptic to ovate-elliptic; [NC to n. FL west to AL; e. KS, e. OK, c. TX westwards]
      4 Involucres at anthesis (6-) avg. 7.5 (-8) mm high; [NC to n. FL west to AL, disjunct in e. TX]
      4 Involucres at anthesis (4.3-) avg. 5.3 (-7) mm high; [e. KS, e. OK, c. TX westwards]
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Key to Solidago, Key O: Key to "erect goldenrods" -- with basally disposed leaves and elongate, cylindrical inflorescences (subgenus Solidago, section Erectae]

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1 Phyllaries very narrow, ca. 0.5 (-0.75) mm wide, linear-lanceolate, very gradually tapering to a pointed or minutely rounded tip; [subgenus Solidago, section Erectae, series Puberulae].
  2 Stems glabrous proximally up to mid-stem; rays mostly 6-9; inner phyllaries usually striate with 2 prominent secondary veins
  2 Stems finely hairy throughout with minute strigillose hairs; rays mostly 9-16; inner phyllaries not striate.
    3 Leaves 20-50 (-60) per stem; midstem leaves usually 4-5 cm long; phyllaries attenuate; [Mountains and Piedmont of GA northward, and Coastal Plain from VA northward]
    3 Leaves (20-) 50-120 per stem; midstem leaves usually 1-4 cm long; phyllaries acute to acuminate; [Coastal Plain from DE southward]
1 Phyllaries broader, (0.75-) 1.0-1.5 mm wide at mid-length, ovate to lanceolate, acute to obtuse or broadly rounded; [subgenus Solidago, section Erectae, series Erectae].
(c) Ware, Richard & Teresa - CC-BY-NC, permission granted to NCBG
      4 Rays white
      4 Rays yellow (may turn pale yellow with age).
        5 Involucres (6-) avg. 7.2 (-9.5) mm high
        5 Involucres 3.5-6.5 mm high.
          6 Leaves and stems sparsely to densely hairy with long, spreading (to less typically appressed) hairs
          6 Leaves and upper stems glabrous or nearly so, the lower stems often somewhat hairy with short hairs (often feeling slightly scabrous).
(c) Ware, Richard & Teresa - CC-BY-NC, permission granted to NCBG
             7 Inflorescence thyrsiform, very slender, usually linear in outline but sometimes with a few widely spaced elongate branches; cypsela bodies 2.2-3.0 mm long; ray flowers often pale yellow; [MA to se. IN, south to GA and MS, mostly avoiding the Coastal Plain southward]
(c) Fleming, Gary P.
(c) Pogacnik, Shaun - CC-BY-NC, permission granted to NCBG
             7 Inflorescence panicle-like, usually with several to many ascending branches and ovoid in outline; cypsela bodies 1.1-2.0 mm long; ray florets golden yellow; [MA to GA, west to SD and scattered south from CO to ne. NM].
(c) Graeff, Alex - CC-BY-NC-ND, permission granted to NCBG
               8 Mid-stem leaves 0.4-1.5 (-2.0) cm wide; basal leaves 0.8-2.0 cm wide, entire or slightly serrate, present or absent at flowering
(c) Faulkner, Erin - CC-BY-NC, permission granted to NCBG
               8 Mid-stem leaves usually > 2 cm wide; basal leaves (2.0-) 3.0-5.5 cm wide, coarsely serrate, present at flowering