Finite Group DatabasebetaFinite Group DatabasebetaOrder 1760.
120 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 44 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C2×D5×D11 |
| commutator, socle, cosocle | C22×C5×C11 | C23 |
| Fitting, prime radical | C23×C5×C11 | C22 |
| hypercenter | C23 | D5×D11 |
| hypocenter | C5×C11 | #126 |
| LCS | G ▷ C22×C5×C11 ▷ C5×C11 | |
| UCS | C1 ◁ C22 ◁ C23 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #11724889 | C2 | semidirect |
| 5. #11724888 | C2 | semidirect |
| 6. Dic11⋊Dic5 | C2 | semidirect |
| 7. Dic5×Dic11 | C2 | semidirect |
| 52. C5×C11 | #126 | semidirect |
| 92. C11 | #4025 | semidirect |
| 104. C5 | #66932 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22⋊Dic55 | 2 |
| C11×C22⋊Dic5 | 2 |
| C5×C22⋊Dic11 | 2 |
| #11724889 | 2 |
| #11724888 | 2 |
| Dic11⋊Dic5 | 2 |
| Dic5×Dic11 | 2 |
| #66932 | 5 |
| #4025 | 11 |