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Keyed in multiple places:

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Key to Solidago, Key D: Key to "rugosa goldenrods" -- with pinnately-veined stem leaves dominant and well-developed paniculiform inflorescences [subgenus Pleiactila; section Venosae]

Asteraceae

Solidago

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1 Larger leaves 1-2× as long as wide, 2-7 cm wide; [IL & MO south to AR]; [subgenus Pleiactila, section Venosae, subsection Drummondiani]
1 Larger leaves 2-5+× as long as wide, 0.6-4 cm wide; [collectively widespread]
  2 Leaf venation not notably reticulate; plants to 12 dm tall, from a compact caudex; [subgenus Pleiactila, section Venosae, subsection Ulmifoliae].
    3 Leaves sparsely hirsute below, at least on the midvein and larger lateral veins
      4 Midstems densely pubescent; midstem leaves with attenuate to rounded bases; midvein of phyllaries as wide or wider than the tissue on each side (midveins of phyllaries equal or greater than 1/3 the phyllary width; [mainly Interior Highlands of AR and MO, rarely disjunct eastwards]
      4 Midstems glabrous to sparsely pubescent; midstem leaves acuminate; midvein of phyllaries narrower than the tissue on each side (midveins of phyllaries 1/3 to 1/5 the phyllary width); [widespread in our region]
  2 Leaves pinnately veined and also forming a prominent reticulum, the veins (primary, secondary, and tertiary) very evidently raised on the undersurface (less obviously so in S. fistulosa); plants to 30 (-40) dm tall, from long-creeping rhizomes, thus forming clonal patches; [subgenus Pleiactila, section Venosae, subsection Venosae].
        5 Mid-stem leaves sessile, somewhat clasping; leaf margins nearly entire to obscurely serrulate; leaves planar
        5 Mid-stem leaves subsessile, not clasping; leaf margins strongly serrate; leaves rugose.
          6 Involucres 4-6 mm high; broader phyllaries 0.7-1.2 mm wide; stems glabrous below the inflorescence; mid-stem leaves elliptic (widest near the middle)
          6 Involucres (2-) 2.5-3.5 (4.5) mm high; phyllaries mostly < 0.5 mm wide; stems hairy or glabrous below the inflorescence; mid-stem leaves lanceolate to ovate (widest below the middle).
             7 Leaves relatively thin, not very rugose, usually sharply serrate, the apices acuminate, glabrous or soft-hairy on the surfaces; rays (4-) 5-12 (-13).
               8 Stem glabrous throughout (except for scattered hairs in inflorescence), stem with striate ridges decurrent from leaf bases; leaf blades appressed serrate (teeth short), blades glabrous beneath except for sparse, short, appressed, straight hairs; early blooming (1 month earlier than S. rugosa in same area); [permanently saturated, ± forested wetlands with Sphagnum moss, such as red maple-Atlantic white cedar swamps, streamhead pocosins, montane bogs]
               8 Stem pubescent with crinkly hairs throughout (occasional plants varying to glabrate below), stem without striate ridges decurrent from leaf bases; leaf blades sharply serrate (teeth coarse), blades villous to crinkly hairy beneath; late blooming (ca. 1 month later than S. aestivalis in same area); [dry to moist fields, meadows, and other open habitats]
             7 Leaves relatively thick and firm, strongly rugose, usually subentire to bluntly serrate, the apices often only acute, slightly to strongly scabrous or stiffly-hairy on the surfaces; rays 4-9.
                 9 Inflorescences narrow, the lower lateral branches only slightly exceeding the subtending leaves; leaves sparsely pubescent; [of the Southern Appalachians]
                 9 Inflorescences broad, the lower lateral branches generally much longer than the subtending leaves; leaves moderately to densely pubescent; [collectively widespread].
                   10 Upper stem leaves lanceolate to elliptic, not much reduced relative to leaves lower on the stem
                   10 Upper stem leaves ovate, much reduced relative to leaves lower on the stem
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Key to Solidago, Key E: Key to "tall goldenrods" -- with 3-veined stem leaves dominant and secund paniculiform inflorescences [subgenus Pleiactila; section Unilaterales (in part)]

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1 Upper stem (above the midpoint, up to the branches of the inflorescence) glabrous.
  2 Plants to 20 dm tall; basal leaves never present; mid-stem leaves averaging 4-6× as long as wide; upper stem usually slightly to moderately glaucous as well as glabrous; [widespread]; [subgenus Pleiactilis, section Unilaterales, subsection Serotinae]
  2 Plants to 10 dm tall; basal leaves withering or not before flowering (if not, also keyed elsewhere), often with associated sterile offshoots with basal leaves; mid-stem leaves averaging 5-10× as long as wide; upper stem glabrous, green; [KY, TN, and MS westwards].
    3 Rootstock short and branched, not producing creeping rhizomes; ray flowers 5-8; receptacle lacking intercalated green bracts (resembling phyllaries) inward from the rays; mid and upper stem leaves usually lacking axillary fascicles of smaller leaves; [subgenus Pleiactilis, section Unilaterales, subsection Radulae]
    3 Rootstock producing creeping rhizomes; ray flowers 7-13; receptacle often with a few intercalated green bracts (resembling phyllaries) inward from the rays; mid and upper stem leaves usually with axillary fascicles of smaller leaves; [subgenus Pleiactilis, section Unilaterales, subsection Junceae]
1 Upper stem hairy (above the midpoint, up to the branches of the inflorescence), variously puberulent, strigillose to strigose, villous, or scabrous.
      4 Midstem leaf blades 1-4 (-5)× as long as wide, the base attenuated to a winged petiole (at least in leaves of the lower midstem(; plants 1-10 dm tall; [collectively in IL, MO, AR, and LA westwards, disjunct eastwards in KY, NC, SC, GA, and AL]
        5 Leaf margins coarsely serrate; midstem leaf blades mostly 1.3-2× as long as wide; leaf surfaces evenly short villous; [IL & MO south to AR]; [subgenus Pleiactilis, section Venosae, subsection Drummondiani]
        5 Leaf margins entire to finely serrate; midstem leaf blades mostly 2-4 (-5)× as long as wide; leaf surface vestiture appressed to scabrous; [subgenus Pleiactilis, section Unilaterales, subsection Radulae].
          6 Leaf surfaces with appressed (strigillose) hairs; upper stem vestiture densely strigose, the stems appearing grayish-green; rhizomes long-creeping, the plants forming clonal patches; [OK and nc. TX westwards and northwestwards]
          6 Leaf surfaces scabrous; upper stem vestiture scabrous to loosely puberulent, the stems appearing green or dingy green; rhizomes short (less commonly moderately creeping); [se. KS, OK, and TX eastwards]
      4 Midstem leaf blades 4-20× as long as wide, the base sessile and cuneate to rounded; plants 3-20 dm tall; [collectively widespread].
             7 Rays 2-8; midstem leaves 4-15 mm wide, mostly 6-20× as long as wide, either twisted at base or not.
               8 Larger mid-stem leaves lanceolate to narrowly elliptic, 7-10 cm long, 10-15 mm wide; leaves not twisted; [KY and s. IN]; [subgenus Pleiactilis, section Unilaterales, subsection Canadensae]
               8 Larger mid-stem leaves linear to lance-linear, 2-9 cm wide, 2-7 (-10) mm wide; leaves either twisted at base or not; [either OK and westwards, or Coastal Plain from VA to FL west to TX and AR].
                 9 Leaves 4-9 cm long, 4-5 mm wide; [inland provinces, OK and westwards]; [subgenus Pleiactilis, section Unilaterales, subsection Radulae]
                 9 Leaves 2-7 cm long, 2-7 (-10) mm wide; [Coastal Plain, VA to FL west to TX and AR]; [subgenus Pleiactilis, section Unilaterales, subsection Tortifoliae]
             7 Rays 4-17 (-24); midstem leaves 5-30 mm wide, 4-12× as long as wide, not twisted at base.
                   10 Midstem leaves mostly 8-12× as long as wide.
                     11 Rays 10-15; [wet pine savanna and marsh habitats, Coastal Plain of NC, SC, GA, FL, AL, and MS]; [subgenus Pleiactilis, section Unilaterales, subsection Tortifoliae]
                     11 Rays 7-11; [riverscour habitats, inland provinces of PA, MD, DC, VA, WV, IN, KY, TN]; [subgenus Pleiactilis, section Unilaterales, subsection Canadensae]
                   10 Midstem leaves mostly 4-6× as long as wide; [subgenus Pleiactilis, section Unilaterales, subsection Canadensae].
(c) McClosky, Daniel - CC-BY
                       12 Mid-stem leaves serrate, the teeth 3-8 (-10) per side, the largest > 1.5 mm long; involucres 1.7-2.5 (-3.0) mm high.
                       12 Mid-stem leaves entire to serrulate, the teeth usually 0-6 per side (up to 14); involucres (2.5-) 3-4.5 mm high.
                            14 Stem densely and closely villous-tomentose; leaves densely and evenly short pilose above and beneath; [western]
                            14 Stem short pilose to puberulent; leaves usually noticeably less hairy above than beneath and often darker colored above, with ascending-appressed hairs on the upper surfaces; [collectively widespread].
                              15 Upper surface of the leaves moderately to densely pubescent with short, curved to spreading hairs; [western]
                              15 Upper surface of the leaves sparsely to moderately roughened with minute bulbous-based hairs (stouter and shorter than the hairs on the lower surface), or glabrous except along the veins; [collectively widespread].
                                16 Inflorescence broad; upper stem leaves not reduced in size relative to the mid-stem leaves; [broadly eastern]