Finite Group DatabasebetaFinite Group DatabasebetaOrder 17100.
144 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 48 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D5×AGL(1,𝔽19) |
| commutator, hypocenter | C5×C19 | C22×C5×C9 |
| Frattini | C1 | G |
| Fitting, socle | C52×C19 | C22×C9 |
| prime radical | C5×D5×D19⋊C3 | C3 |
| cosocle | C5×C19⋊C3 | C22×C3×C5 |
| LCS | G ▷ C5×C19 | |
| UCS | C1 ◁ C5 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C5×D5×#4296 | C2 | semidirect |
| 2. C5×C5⋊AGL(1,𝔽19) | C2 | semidirect |
| 3. C52×AGL(1,𝔽19) | C2 | semidirect |
| 5. C52×#4296 | C22 | semidirect |
| 7. D5×AGL(1,𝔽19) | C5 | direct (N × H) |
| 11. C5×D5×D19 | C9 | semidirect |
| 13. C5⋊AGL(1,𝔽19) | C2×C5 | semidirect |
| 14. D5×#4296 | C2×C5 | semidirect |
| 17. C5×AGL(1,𝔽19) | D5 | direct (N × H) |
| 18. C5×AGL(1,𝔽19) | C2×C5 | semidirect |
| 22. C5×D95 | C2×C9 | semidirect |
| 23. C5×D5×C19 | C2×C9 | semidirect |
| 24. C52×D19 | C2×C9 | semidirect |
| 27. C5×#4296 | C2×D5 | semidirect |
| 28. C5×#4296 | C22×C5 | semidirect |
| 37. C52×C19 | C22×C9 | semidirect |
| 42. D5×D19 | C5×C9 | semidirect |
| 45. AGL(1,𝔽19) | C5×D5 | direct (N × H) |
| 53. D95 | C2×C5×C9 | semidirect |
| 56. C5×D19 | C9×D5 | semidirect |
| 57. C5×D19 | C2×C5×C9 | semidirect |
| 58. D5×C19 | C2×C5×C9 | semidirect |
| 61. #4296 | C2×C5×D5 | semidirect |
| 70. C5×C19 | C2×C9×D5 | semidirect |
| 71. C5×C19 | C22×C5×C9 | semidirect |
| 86. C5×D5 | AGL(1,𝔽19) | direct (N × H) |
| 92. D19 | C5×C9×D5 | semidirect |
| 101. C52 | C2×AGL(1,𝔽19) | semidirect |
| 104. C19 | C2×C5×C9×D5 | semidirect |
| 118. D5 | C5×AGL(1,𝔽19) | direct (N × H) |
| 124. C5 | D5×AGL(1,𝔽19) | direct (N × H) |
| 125. C5 | C2×C5×AGL(1,𝔽19) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×D5×#4296 | 2 |
| C5×C5⋊AGL(1,𝔽19) | 2 |
| C52×AGL(1,𝔽19) | 2 |
| C5×D5×D19⋊C3 | 3 |
| C2×C5×AGL(1,𝔽19) | 5 |
| D5×AGL(1,𝔽19) | 5 |
| C2×C5×C9×D5 | 19 |