Finite Group DatabasebetaFinite Group DatabasebetaOrder 1760.
328 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 121 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4 | C22×D55 |
| commutator, socle, cosocle | C2×C5×C11 | C24 |
| Frattini | C2 | C23×D55 |
| Fitting | C5×C11×#41 | C2 |
| hypercenter | #41 | D55 |
| hypocenter | C5×C11 | C2×#41 |
| LCS | G ▷ C2×C5×C11 ▷ C5×C11 | |
| UCS | C1 ◁ C4 ◁ #41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C5×C11×#41 | C2 | semidirect |
| 2. #11725035 | C2 | semidirect |
| 3. Q8×D55 | C2 | semidirect |
| 4. #11725033 | C2 | semidirect |
| 5. D4×D55 | C2 | semidirect |
| 6. #11725031 | C2 | semidirect |
| 7. C2×C4×D55 | C2 | semidirect |
| 9. C5×Q8×C11 | C22 | semidirect |
| 10. C5×D4×C11 | C22 | semidirect |
| 11. C2×C4×C5×C11 | C22 | semidirect |
| 12. C22⋊D55 | C22 | semidirect |
| 13. C2×Dic55 | C22 | semidirect |
| 14. D220 | C22 | semidirect |
| 17. C4×D55 | C22 | semidirect |
| 18. C4×D55 | C22 | semidirect |
| 19. Dic110 | C22 | semidirect |
| 29. C11×#41 | D5 | semidirect |
| 40. D55 | #41 | direct (N × H) |
| 42. Q8×C11 | C2×D5 | semidirect |
| 43. D4×C11 | C2×D5 | semidirect |
| 44. C2×C4×C11 | C2×D5 | semidirect |
| 53. C5×#41 | D11 | semidirect |
| 60. C5×C11 | C2×#41 | semidirect |
| 70. C5×Q8 | C2×D11 | semidirect |
| 71. C5×D4 | C2×D11 | semidirect |
| 72. C2×C4×C5 | C2×D11 | semidirect |
| 97. #41 | D55 | direct (N × H) |
| 101. C11 | D5×#41 | semidirect |
| 108. Q8 | C2×D55 | semidirect |
| 111. D4 | C2×D55 | semidirect |
| 117. C2×C4 | C2×D55 | 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 |
|---|---|
| C5×C11×#41 | 2 |
| #11725035 | 2 |
| Q8×D55 | 2 |
| #11725033 | 2 |
| D4×D55 | 2 |
| #11725031 | 2 |
| C2×C4×D55 | 2 |
| #41×D11 | 5 |
| D5×#41 | 11 |