Finite Group DatabasebetaFinite Group DatabasebetaOrder 1760.
328 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 112 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×D5×D11 |
| commutator, socle, cosocle | C2×C5×C11 | C24 |
| Fitting | C5×D4×C11 | C22 |
| hypercenter | D4 | D5×D11 |
| hypocenter | C5×C11 | C2×#41 |
| LCS | G ▷ C2×C5×C11 ▷ C5×C11 | |
| UCS | C1 ◁ C2 ◁ D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11725033 | C2 | semidirect |
| 2. D4×D5×C11 | C2 | semidirect |
| 3. C5×#4341 | C2 | semidirect |
| 4. D5×C22⋊D11 | C2 | semidirect |
| 5. #11724999 | C2 | semidirect |
| 6. C2×D5×Dic11 | C2 | semidirect |
| 7. #11724997 | C2 | semidirect |
| 8. C4×D5×D11 | C2 | semidirect |
| 9. #11724989 | C2 | semidirect |
| 10. #11724985 | C2 | semidirect |
| 11. D5×Dic22 | C2 | semidirect |
| 14. C5×D4×C11 | C22 | semidirect |
| 15. C22⋊D55 | C22 | semidirect |
| 16. C2×Dic55 | C22 | semidirect |
| 17. C4×D55 | C22 | semidirect |
| 18. Dic110 | C22 | semidirect |
| 19. C11×C22⋊D5 | C22 | semidirect |
| 20. C11×D20 | C22 | semidirect |
| 22. C5×C22⋊D11 | C22 | semidirect |
| 23. C2×C5×Dic11 | C22 | semidirect |
| 24. C4×C5×D11 | C22 | semidirect |
| 25. C5×Dic22 | C22 | semidirect |
| 26. #89170 | C22 | semidirect |
| 27. #89169 | C22 | semidirect |
| 28. #89167 | C22 | semidirect |
| 29. #89166 | C22 | semidirect |
| 32. D5×Dic11 | C22 | semidirect |
| 33. D5×Dic11 | C22 | semidirect |
| 34. Dic5×D11 | C22 | semidirect |
| 57. #4341 | D5 | direct (N × H) |
| 66. D5×C11 | #41 | semidirect |
| 71. D4×C11 | C2×D5 | semidirect |
| 76. C22⋊D11 | C2×D5 | semidirect |
| 82. C2×Dic11 | C2×D5 | semidirect |
| 86. C4×D11 | C2×D5 | semidirect |
| 89. Dic22 | C2×D5 | semidirect |
| 96. D4×D5 | D11 | semidirect |
| 101. C5×C11 | C2×#41 | semidirect |
| 119. C5×D4 | C2×D11 | semidirect |
| 124. C22⋊D5 | C2×D11 | semidirect |
| 128. D20 | C2×D11 | semidirect |
| 169. C11 | D5×#41 | semidirect |
| 175. D5 | #4341 | direct (N × H) |
| 187. D4 | D5×D11 | semidirect |
| 199. C5 | C2×#4341 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11725033 | 2 |
| D4×D5×C11 | 2 |
| C5×#4341 | 2 |
| D5×C22⋊D11 | 2 |
| #11724999 | 2 |
| C2×D5×Dic11 | 2 |
| #11724997 | 2 |
| C4×D5×D11 | 2 |
| #11724989 | 2 |
| #11724985 | 2 |
| D5×Dic22 | 2 |
| C2×#4341 | 5 |
| D5×#41 | 11 |