Finite Group DatabasebetaFinite Group DatabasebetaOrder 1760.
328 conjugacy classes of subgroups; only the 174 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 174 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4×C5 | C22×D11 |
| commutator, cosocle | C2×C11 | C24×C5 |
| Frattini | C2 | C23×C5×D11 |
| Fitting | C5×C11×#41 | C2 |
| socle | C2×C5×C11 | C24 |
| hypercenter | C5×#41 | D11 |
| hypocenter | C11 | C2×C5×#41 |
| LCS | G ▷ C2×C11 ▷ C11 | |
| UCS | C1 ◁ C4×C5 ◁ C5×#41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C5×C11×#41 | C2 | semidirect |
| 2. C5×#4343 | C2 | semidirect |
| 3. C5×Q8×D11 | C2 | semidirect |
| 4. C5×#4341 | C2 | semidirect |
| 5. C5×D4×D11 | C2 | semidirect |
| 6. C5×#4339 | C2 | semidirect |
| 7. C2×C4×C5×D11 | C2 | semidirect |
| 9. C5×Q8×C11 | C22 | semidirect |
| 10. C5×D4×C11 | C22 | semidirect |
| 11. C2×C4×C5×C11 | C22 | semidirect |
| 12. C5×C22⋊D11 | C22 | semidirect |
| 13. C2×C5×Dic11 | C22 | semidirect |
| 14. C5×D44 | C22 | semidirect |
| 17. C4×C5×D11 | C22 | semidirect |
| 18. C4×C5×D11 | C22 | semidirect |
| 19. C5×Dic22 | C22 | semidirect |
| 20. #41×D11 | C5 | direct (N × H) |
| 29. C11×#41 | C2×C5 | semidirect |
| 30. #4343 | C2×C5 | semidirect |
| 31. Q8×D11 | C2×C5 | semidirect |
| 32. #4341 | C2×C5 | semidirect |
| 33. D4×D11 | C2×C5 | semidirect |
| 34. #4339 | C2×C5 | semidirect |
| 35. C2×C4×D11 | C2×C5 | semidirect |
| 40. C5×D11 | #41 | direct (N × H) |
| 42. Q8×C11 | C22×C5 | semidirect |
| 43. D4×C11 | C22×C5 | semidirect |
| 44. C2×C4×C11 | C22×C5 | semidirect |
| 45. C22⋊D11 | C22×C5 | semidirect |
| 46. C2×Dic11 | C22×C5 | semidirect |
| 47. D44 | C22×C5 | semidirect |
| 50. C4×D11 | C22×C5 | semidirect |
| 51. C4×D11 | C22×C5 | semidirect |
| 52. Dic22 | C22×C5 | semidirect |
| 56. C5×#41 | D11 | direct (N × H) |
| 60. C5×C11 | C2×#41 | semidirect |
| 71. C5×Q8 | C2×D11 | semidirect |
| 74. C5×D4 | C2×D11 | semidirect |
| 80. C2×C4×C5 | C2×D11 | semidirect |
| 85. D11 | C5×#41 | direct (N × H) |
| 97. #41 | C5×D11 | direct (N × H) |
| 101. C11 | C2×C5×#41 | semidirect |
| 108. Q8 | C2×C5×D11 | semidirect |
| 111. D4 | C2×C5×D11 | semidirect |
| 117. C2×C4 | C2×C5×D11 | semidirect |
| 118. C5 | #41×D11 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×C11×#41 | 2 |
| C5×#4343 | 2 |
| C5×Q8×D11 | 2 |
| C5×#4341 | 2 |
| C5×D4×D11 | 2 |
| C5×#4339 | 2 |
| C2×C4×C5×D11 | 2 |
| #41×D11 | 5 |
| C2×C5×#41 | 11 |