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Keyed in multiple places:

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Key A2: pteridophytes and lycophytes growing as floating or rooted aquatics

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1 Plant with at least some leaves palmately or pinnately lobed or 1-4× pinnately divided (‘fern-like’) and > 2 cm long
1 Plant either a floating aquatic with leaves <5 cm long, or with clover-like or linear leaves.
..2 Plant a floating aquatic
..2 Plant a rooted aquatic.
....3 Plant clover-like, with 4 leaf segments borne terminally
....3 Leaves linear.
......4 Plants cormose or with short rhizomes; leaves numerous, undivided leaves
......4 Plants with creeping rhizomes; leaves few, reduced to a winged petiole

Key C1: floating aquatics

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1 Individual leaves > 2 cm wide.
..2 Leaves obovate, cuneate at the base, sessile, pale green; plants floating because of “unwettable” leaf surfaces
..2 Leaves orbicular, cordate or truncate at the base, petiolate, dark green; plants floating because of petioles inflated as bladders, or inflated cells centrally located on each leaf.
....3 Petiole terete, not air-filled; plants floating because of inflated cells centrally located on each leaf (most easily seen on the lower surface)
....3 Petiole conspicuously expanded into an air-filled bladder; plants floating because of petioles inflated as bladders
1 Individual leaves or “fronds” < 2 cm wide, or leaves absent.
......4 Submersed portions of the plant with small (< 4 mm in diameter) bladder-traps
......4 Submersed portions of plant lacking small bladder traps.
........5 Plants dichotomously forked, upper surface of leaves velvety or variously hairy
........5 Plants unbranched, or if branched, irregularly so; upper surface of leaves glabrous, waxy.
..........6 Plant thalloid; flowers embedded in the thallus in reproductive pouches
..........6 Plant with well-differentiated stems and leaves, the leaves obviously and alternately spaced along a well-developed stem; flowers axillary
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