1. Stem epidermal cells differentiated, large, hyaline, more or less thin-walled........................................2
1. Stem epidermal cells not differentiated, small, more or less thick-walled............................................. 5
2. Plants medium-sized; outer epidermal cell walls somewhat thick-walled...............................................3
2. Plants small, slender; outer epidermal cell walls thin-walled.................................................................4
3. Autoicous; leaf apex shortly acuminate; leaf margins smooth below middle, conspicuously serrulate above; alar parts of stem leaves excavated, consisting of few quadrate or rounded oblong, hyaline and thin-walled cells; sporophytes common...................................................................................7. H. fertile
3. Dioicous or polyoicous; leaf apex long acuminate; leaf margins entire; alar parts of stem leaves not excavated, consisting of one large, hyaline, thin-walled cell and 3–4 small, quadrate cells; sporophytes uncommon............................................................................................. 2. H. callichroum
4. Stem leaves widely ovate-lanceolate, slenderly acuminate, falcate-secund; alar cells numerous, small, subquadrate; median leaf cells 39–80 µm long....................................................9. H. hamulosum
4. Stem leaves narrowly ovate-lanceolate, not strongly falcate-secund; alar cells inconspicuously differentiated, few; median leaf cells 50–100 µm long.................. 17. H. subimponens subsp. ulophyllum
5. Alar cells conspicuously differentiated, numerous, quadrate (6–15 cells along the margins) ......................6
5. Alar cells inconspicuously or little differentiated (fewer than 6 cells along the margins) ............................. 9
6. Leaves with long apices, usually concave-secund; leaf margins serrulate..................................................7
6. Leaves with short apices; leaf margins dentate........................................................................................8
7. Stems regularly bipinnately branched; leaf margins plane.................................18. H. submolluscum
7. Stems irregularly or pinnately branched; leaf margins revolute from base to leaf apex......... 15. H. revolutum
8. Plants medium-sized; leaves widely ovate-lanceolate; leaf cells linear-rhomboid; alar parts not sharply delimited from leaf cells at base...........................................................................20. H. vaucheri
8. Plants small to large; leaves oblong-lanceolate; leaf cells elongate-rhomboid; alar parts sharply delimited from leaf cells at base...................................................................................... 4. H. cupressiforme
9. Plants small, slender.....................................................................................................................10
9. Plants medium-sized to robust.......................................................................................................12
10. Pseudoparaphyllia numerous, growing on the stems and branches; leaf margins entire; alar cells quadrate, thin-walled; plants autoicous;............................................................................ 14. H. recurvatum
10. Pseudoparaphyllia sparse; leaf margins serrulate; alar cells quadrate or oblong-quadrate, thick-walled; plants either autoicous or dioicous......................................................................................................11
11. Branches julaceous; leaves broadly oblong-lanceolate, acuminate or abruptly long-apiculate; leaf margins serrulate in the upper half; alar cells not tinged; plants autoicous......................................... 12. H. pallescens
11. Branches complanate; leaves broadly oblong or triangularly lanceolate, acuminate, gradually apiculate; leaf margins serrulate throughout; alar cells reddish brown; plants dioicous.................................... 3. H. circinale
12. Plants rigid, large; stems regularly or sparsely pinnately to bipinnately branched; capsules ca. 4 mm long
........................................................................................................................10. H. macrogynum
12. Plants soft, medium-sized; irregularly pinnately branched; capsules less than 3.5 mm long................13
13. Stem leaves 2–3 mm long; rather shortly acuminate, falcate............................................................14
13. Stem leaves 1.0–2.5 mm long; slenderly long-acuminate, strongly falcate to circinate.........................17
14. Plants short; autoicous; perichaetial leaves erect, very long (up to 8 mm); capsules rather small; setae 1.5–2.5 cm long; almost exclusively confined to limestone................................................ 1. H. calcicola
14. Plants elongate; dioicous; perichaetial leaves shorter (less than 5 mm); capsules large; setae longer than 2.5 cm; rarely on limestone.................................................................................................................. 15
15. Stems irregularly and loosely branched; leaves plicate; leaf margins sometimes revolute below; perichaetial leaves not plicate; operculum long-beaked............................................................ 8. H. fujiyamae
15. Stems regularly pinnately branched; leaves scarcely or only slightly plicate; leaf margins plane; perichaetial leaves strongly plicate; operculum obtuse or shortly beaked..................................................... 16
16. Plants usually tinged with reddish or golden color, often lustrous; leaves not or only slightly cordate at base; leaf cells 60–90 µm long, alar cells quadrate, few (1–2 along the margin); capsules rounded at base, straight or slightly arcuate; spores 25–30 µm in diameter......................................... 16. H. sakuraii
16. Plants usually not tinged; leaves cordate or subcordate at base; leaf cells 40–60 µm long; alar cells quadrate, 2–4 along the margin; capsules narrowed at base, arcuate; spores 12–18 µm in diameter......13. H. plumaeforme
17. Central strand of stem absent; alar parts of stem leaves not excavated, consisting of small or somewhat enlarged, colored and more or less thick-walled cells; capsules nearly erect to inclined; perichaetial leaves not plicate; spores smooth........................................................................................19. H. tristo-viride
17. Central strand of stems developed; alar parts of stem leaves excavated, consisting of strongly enlarged, hyaline and thin-walled cells; capsules inclined to horizontal, arcuate; perichaetial leaves plicate; spores papillose...................................................................................................................................18
18. Plants dioicous; leaves not tinged at base; alar cells not differentiated; capsules rounded at base, straight or only slightly arcuate; operculum with a small beak........................................... 11. H. oldhamii
18. Plants autoicous; leaves usually tinged with brownish color at base; alar cells differentiated; capsules narrowed at base, arcuate; operculum obtuse to apiculate......................................................................... 19
19. Plants small; branches not clearly complanate; stem leaves less than 2 mm long; alar cells subquadrate, 3–5 along the margin; median leaf cells ca. 2–3 µm wide; capsules not exceeding 2.3 mm long.........................
.......................................................................................................................5. H. densirameum
19. Plants medium-sized, rarely smaller; branches complanate; stem leaves often longer than 2 mm; alar cells large, hyaline, subquadrate (ca. 2 cells along the margin); median leaf cells ca. 3–5 µm wide; capsules longer than 2.3 mm............................................................................................................................. 6. H. fauriei