Finite Group DatabasebetaFinite Group DatabasebetaOrder 1760.
332 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 108 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 | C23×C5×C11 | C22 |
| hypercenter | C23 | D5×D11 |
| hypocenter | C5×C11 | H(5,𝔽2) |
| LCS | G ▷ C2×C5×C11 ▷ C5×C11 | |
| UCS | C1 ◁ C2 ◁ C23 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C22⋊D55 | C2 | semidirect |
| 2. C2×C11×C22⋊D5 | C2 | semidirect |
| 3. C2×C5×C22⋊D11 | C2 | semidirect |
| 4. #11725007 | C2 | semidirect |
| 5. D5×C22⋊D11 | C2 | semidirect |
| 6. D11×C22⋊D5 | C2 | semidirect |
| 7. #11724999 | C2 | semidirect |
| 8. #11724997 | C2 | semidirect |
| 9. #11724996 | C2 | semidirect |
| 10. C23×C5×C11 | C22 | semidirect |
| 11. C22×D55 | C22 | semidirect |
| 12. C22×D5×C11 | C22 | semidirect |
| 13. C22×C5×D11 | C22 | semidirect |
| 14. C2×D5×D11 | C22 | semidirect |
| 15. C22⋊D55 | C22 | semidirect |
| 16. C22⋊D55 | C22 | semidirect |
| 17. C2×Dic55 | C22 | semidirect |
| 18. C11×C22⋊D5 | C22 | semidirect |
| 19. C11×C22⋊D5 | C22 | semidirect |
| 20. C2×C11×Dic5 | C22 | semidirect |
| 21. C5×C22⋊D11 | C22 | semidirect |
| 22. C5×C22⋊D11 | C22 | semidirect |
| 23. C2×C5×Dic11 | C22 | semidirect |
| 24. #89170 | C22 | semidirect |
| 25. #89169 | C22 | semidirect |
| 26. #89168 | C22 | semidirect |
| 27. #89167 | C22 | semidirect |
| 28. #89166 | C22 | semidirect |
| 29. D5×Dic11 | C22 | semidirect |
| 30. Dic5×D11 | C22 | semidirect |
| 49. C2×C22⋊D11 | D5 | semidirect |
| 64. C23×C11 | C2×D5 | semidirect |
| 67. C22×D11 | C2×D5 | semidirect |
| 75. C22⋊D11 | C2×D5 | semidirect |
| 76. C22⋊D11 | C2×D5 | semidirect |
| 79. C2×Dic11 | C2×D5 | semidirect |
| 87. C2×C22⋊D5 | D11 | semidirect |
| 93. C5×C11 | H(5,𝔽2) | semidirect |
| 109. C23×C5 | C2×D11 | semidirect |
| 112. C22×D5 | C2×D11 | semidirect |
| 120. C22⋊D5 | C2×D11 | semidirect |
| 121. C22⋊D5 | C2×D11 | semidirect |
| 124. C2×Dic5 | C2×D11 | semidirect |
| 160. C11 | #4144 | semidirect |
| 172. C23 | D5×D11 | semidirect |
| 189. C5 | #67037 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C22⋊D55 | 2 |
| C2×C11×C22⋊D5 | 2 |
| C2×C5×C22⋊D11 | 2 |
| #11725007 | 2 |
| D5×C22⋊D11 | 2 |
| D11×C22⋊D5 | 2 |
| #11724999 | 2 |
| #11724997 | 2 |
| #11724996 | 2 |
| #67037 | 5 |
| #4144 | 11 |