Finite Group DatabasebetaFinite Group DatabasebetaOrder 1760.
328 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 110 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×Q8×C11 | C22 |
| hypercenter | Q8 | D5×D11 |
| hypocenter | C5×C11 | C2×#41 |
| LCS | G ▷ C2×C5×C11 ▷ C5×C11 | |
| UCS | C1 ◁ C2 ◁ Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. Q8×D55 | C2 | semidirect |
| 2. C11×#713 | C2 | semidirect |
| 3. C5×#4343 | C2 | semidirect |
| 4. #11724994 | C2 | semidirect |
| 5. C4×D5×D11 | C2 | semidirect |
| 6. #11724989 | C2 | semidirect |
| 7. #11724982 | C2 | semidirect |
| 9. C5×Q8×C11 | C22 | semidirect |
| 11. Dic110 | C22 | semidirect |
| 12. C11×D20 | C22 | semidirect |
| 13. C4×D5×C11 | C22 | semidirect |
| 14. C5×D44 | C22 | semidirect |
| 15. C4×C5×D11 | C22 | semidirect |
| 16. #89167 | C22 | semidirect |
| 18. D5×Dic11 | C22 | semidirect |
| 19. Dic5×D11 | C22 | semidirect |
| 30. #4343 | D5 | semidirect |
| 38. D55 | #41 | semidirect |
| 42. Q8×C11 | C2×D5 | semidirect |
| 47. D44 | C2×D5 | semidirect |
| 51. C4×D11 | C2×D5 | semidirect |
| 54. #713 | D11 | semidirect |
| 60. C5×C11 | C2×#41 | semidirect |
| 70. C5×Q8 | C2×D11 | semidirect |
| 75. D20 | C2×D11 | semidirect |
| 79. C4×D5 | C2×D11 | semidirect |
| 101. C11 | D5×#41 | semidirect |
| 108. Q8 | D5×D11 | semidirect |
| 118. C5 | #41×D11 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D55 | 2 |
| C11×#713 | 2 |
| C5×#4343 | 2 |
| #11724994 | 2 |
| C4×D5×D11 | 2 |
| #11724989 | 2 |
| #11724982 | 2 |
| #41×D11 | 5 |
| D5×#41 | 11 |