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Keyed in multiple places:

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Key to Parthenium

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1 Leaves pinnatifid to bipinnatifid, the primary sinuses extending 9/10 or more of the way to the midrib; leaves thin in texture; pappus of 2 petaloid scales; [section Parthenium].
  2 Annuals (rarely persisting); leaf blades (1-)2-pinnately lobed, scabrellous below and seldom accompanied with erect hairs 1-2 mm long
  2 Biennials (sometimes flowering first year or persisting); leaf blades ± pinnately lobed, strigillose below and usually accompanied with erect hairs 1-2 mm long
1 Leaves toothed (pinnatifid or sinuous-margined in forms of P. integrifolium var. mabryanum, the sinuses extending up to 3/4 of the way to the midrib); leaves somewhat thick in texture; pappus of 2-3 weak awns; [native perennials]; [section Partheniastrum].
    3 Plants arising from a short caudex surmounting a system of fleshy-thickened but tough roots; stems glabrous or with short, appressed pubescence < 1 mm long; cauline leaves seldom auriculate-clasping, the upper cauline leaves typically sessile or petiolate, the lower cauline leaves petiolate, the petioles winged or not; blades of basal leaves (4-) 6-21 (-27) cm long, (1.4-) 2-12 (-13.5) cm wide.
      4 Blades of basal leaves ovate-lanceolate, (4-) 6-12 (-20) cm long, (3-) 4-8 (-9.5) cm wide, coarsely toothed but never undulately lobed; heads mostly 5-7 mm across, usually (18-) 90-180 (-400) per inflorescence; [widespread in our area]
      4 Blades of basal leaves linear-lanceolate to ovate-lanceolate, (6-) 7-12 (-13.5) cm long, (1.4-) 2-4 (-4.5 cm) wide, coarsely toothed and sometimes also undulately lobed throughout their length; heads mostly 4-6 mm across, usually (30) 40-75 (-85) per inflorescence; [of Coastal Plain and eastern Piedmont of VA, NC, and SC]
    3 Plants arising from a long, even-width, 3-5(-6) mm wide, branching, woody or lignescent rhizome; stems either with coarse, spreading pubescence 1-3 mm long or puberulous or strigose with hairs < 1 mm long; cauline leaves all auriculate-clasping, the upper cauline leaves sessile and auriculate-clasping, the lower cauline leaves with winged petioles, the wings expanded at the base; blades of basal leaves 11-18 (-20) cm long, 5-8 cm wide.
        5 Leaves stiffly to loosely, sparsely to densely villous on both sides with thin, white hairs arising from a slender, non-pedestaled base; stems hirsute-pilose with white hairs 1-3 mm long; heads 4-7 mm in diameter
        5 Leaves hispid with short, basally erect hairs, each arising from a “pedestal” of 2-4 concentric rings of glassy cells; stems either sparsely to densely hirsute-villous with white hairs 1-2 mm long, or merely puberulous or strigose with minute, appressed hairs 0.1-0.8 mm long; heads 7-10 mm in diameter

Key to Asteraceae, Key L: Herbaceous composites with the leaves alternate or basal and the heads radiate, the rays white, pink, purple, and the 0 pappus

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1 Rays primarily pink or purple, not white-tinged (flowers viewed from above, adaxial surface of the rays).
  2 Receptacles epaleate; leaves pinnatisect; [waif, ne. US]
  2 Receptacles paleate; leaves simple or bladeless; [widespread natives]
    3 Leaves without blades (the petioles terete, appearing Juncus-like); ray florets pink or purplish; disc florets fewer (60-120+), the corollas usually yellowish; [wet pinelands and seepages]
    3 Leaves broad and conspicuous; ray florets purple; disc florets many (200+), the corollas pink, green, red, purple, or yellow colored; [plants of prairies and similar habitats]
1 Rays primarily white to white-tinged or yellow throughout (lamina of the ray with at least some white basally if not uniformly yellow).
      4 Disc florets functionally staminate (thus cypselae only forming from ray florets)
      4 Disc florets bisexual, fertile.
        5 Leaves entire or toothed, but not deeply pinnatisect; sometimes with smaller rounded lobes (Leucanthemum basal leaves can have deeper, round lobes); plants usually not aromatic.
          6 Stem internodes usually winged (at least proximally)
          6 Stems not winged.
             7 Leaves primarily basal, the cauline leaves absent or fewer and much reduced in size from basal leaves; abaxial surface of the ray laminae white or sometimes pink-tinged (on live plants) but lacking a prominent colored midstripe.
               8 Leaves strigose, the margins crenate-serrate; roots not red-tipped; abaxial surface of ray laminae often pink or purple tinged, flowers closing at night
               8 Leaves glabrous (or faces sparsely hairy), the margins entire or toothed; roots usually red-tipped; rays drying pinkish but abaxial surface not conspicuously pink tinged on live plants
             7 Plants with well-developed cauline leaves, the margins entire or sometimes toothed (usually entire in Aphanostephus, occasionally deeply lobed); abaxial surface of the ray lamina sometimes white, but often with a prominent purple or blue midstripe (except Leucanthemum, which merely dries pink)
                 9 Flowering heads smaller, arranged in corymbiform or paniculiform arrays; ray florets with diminuitive laminae (0.3-5.0 mm long), heads thus sometimes superficially appearing disciform (rays sometimes double in horticultural forms as in Achillea ptarmica)
                   10 Plants aromatic; leaves linear to narrowly lanceolate, the surfaces glabrous or sparsely hairy; pales more or less folded but lacking distal papillae; cypselae not shed along with subtending phyllary and disc florets; [tribe Anthemideae]
                   10 Plants not aromatic; leaves variously shaped, at least some usually lyrate or oblanceolate (not all linear), the surfaces hairy and gland-dotted (at least abaxially); pales distally pappilate or fimbriate; cypselae shed along with subtending phyllary and 2 disc florets each invested in a pale; [tribe Heliantheae]
                 9 Flowering heads larger, singular on scapes (if in 2's or 3's, these large and not in broad corymbiform arrays), rays prominent, the laminae usually > 10 mm long
                     11 Rays white abaxially (drying pinkish); receptacles broadly convex, not pitted; plants rhizomatous perennials; pappus absent; [tribe Anthemideae]
                     11 Rays white or with prominent blue or purple midstripe (sometimes present after drying); receptacles conic, pitted; plants tap-rooted annuals (except Astranthium riddellii); pappus absent, coroniform, or of scales; [tribe Astereae]
                       12 Phyllaries scarious margined; cypselae 4-angled and with 4-12 thick ribs, pappus absent, of scales or coroniform; ray florets closing distally at night
                       12 Phyllaries sometimes hyaline but not scarious margined; cypselae compressed, lacking prominent ribs (though sometimes glochidiate), pappus absent or short coroniform; ray florets not closing at night
        5 Leaves deeply lobed or pinnatisect, the ultimate segments linear or if rounded, the sinuses of the lobes nearly reaching the midrib (pinnatifid); plants typically aromatic (except Tripleurospermum and Parthenium); [tribe Anthemideae].
                          13 Receptacles paleate (chaffy or with apparent bracts), the pales sometimes distally fimbriate or papillate (Parthenium).
                            14 Stem internodes usually winged
                            14 Stems not winged.
                              15 Rays (the laminae) white with conspicuous yellow coloration at the bases
                              15 Rays primarily white to white-tinged (without strong yellow color at the base of the laminae) or yellow throughout (lamina of the ray with at least some white basally; if rays are white).
                                16 Flowering heads smaller, arranged in corymbiform or paniculiform arrays; ray florets with diminuitive laminae (0.3-5.0 mm long); ray and disc florets both white or white-ish.
                                  17 Plants usually aromatic; pales more or less folded but not distally fimbriate or papillate; cypselae not shed along with phyllary and disc florets; [tribe Anthemideae]
                                  17 Plants not aromatic (at least not conspicuously so); pales distally fimbriate or papillate; cypselae shed along with subtending phyllary and 2 disc florets each invested in a pale; [tribe Heliantheae]
                                16 Flowering heads larger, arranged mostly singular at the ends of scapes, not in broad corymbiform arrays (except Tripleurospermum, which has larger heads and prominent rays), ray laminae prominent; ray and disc florets differing in color (rays typically white; discs typically yellow).
                                    18 Plants annual, erect or decumbent, ill-scented or not; ultimate leaf margins dentate to lobed; cypsela ribs usually 9-10 (sometimes lacking); [widespread non-natives]
                                    18 Plants perennial and prostrate (mat-forming), aromatic; ultimate leaf margins entire; cypsela ribs weak; [waif, ne. US]
                          13 Receptacles epaleate (lacking chaff).
                                       19 Ultimate leaf lobes broad, ovate-shaped (not linear)
                                       19 Ultimate leaf lobes linear.
                                         20 Plants usually aromatic; maturing flowering heads with deflexed ray laminae; cypsela 5-ribbed, lacking apical resin sacs
                                         20 Plants not aromatic; ray laminae not deflexed; cypsela with 3 ribs and 1-5 abaxial-apical resin sacs
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