Finite Group DatabasebetaFinite Group DatabasebetaOrder 17100.
240 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 75 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | C5⋊D5×D19⋊C3 |
| commutator, hypocenter | C52×C19 | C22×C9 |
| Fitting, socle, cosocle | C3×C52×C19 | C22×C3 |
| prime radical | C3×D19×C5⋊D5 | C3 |
| LCS | G ▷ C52×C19 | |
| UCS | C1 ◁ C3 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C5⋊D5×#4294 | C2 | semidirect |
| 2. C5⋊(C5⋊(#4294⋊C2)) | C2 | semidirect |
| 3. C52×#4294⋊C2 | C2 | semidirect |
| 5. C52×#4294 | C22 | semidirect |
| 12. D19×C5⋊D5 | C9 | semidirect |
| 19. C5×#4294⋊C2 | D5 | semidirect |
| 20. C5×#4294⋊C2 | D5 | semidirect |
| 21. C5×#4294⋊C2 | D5 | semidirect |
| 26. C5⋊D95 | C2×C9 | semidirect |
| 27. C19×C5⋊D5 | C2×C9 | semidirect |
| 28. C52×D19 | C2×C9 | semidirect |
| 30. C5×#4294 | C2×D5 | semidirect |
| 31. C5×#4294 | C2×D5 | semidirect |
| 32. C5×#4294 | C2×D5 | semidirect |
| 43. C52×C19 | C22×C9 | semidirect |
| 52. #4294⋊C2 | C5⋊D5 | direct (N × H) |
| 62. C5×D19 | C9×D5 | semidirect |
| 63. C5×D19 | C9×D5 | semidirect |
| 64. C5×D19 | C9×D5 | semidirect |
| 71. #4294 | C2×C5⋊D5 | semidirect |
| 79. C5×C19 | C2×C9×D5 | semidirect |
| 80. C5×C19 | C2×C9×D5 | semidirect |
| 81. C5×C19 | C2×C9×D5 | semidirect |
| 99. C5⋊D5 | #4294⋊C2 | direct (N × H) |
| 105. D19 | C9×C5⋊D5 | semidirect |
| 116. C52 | C2×#4294⋊C2 | semidirect |
| 120. C19 | C2×C9×C5⋊D5 | semidirect |
| 141. C5 | D5×#4294⋊C2 | semidirect |
| 142. C5 | D5×#4294⋊C2 | semidirect |
| 143. C5 | D5×#4294⋊C2 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5⋊D5×#4294 | 2 |
| C5⋊(C5⋊(#4294⋊C2)) | 2 |
| C52×#4294⋊C2 | 2 |
| C3×D19×C5⋊D5 | 3 |
| D5×#4294⋊C2 | 5 |
| C2×C9×C5⋊D5 | 19 |