Finite Group DatabasebetaFinite Group DatabasebetaOrder 1760.
188 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 54 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 | C23×C5×C11 | C22 |
| hypercenter | C23 | D5×D11 |
| hypocenter | C5×C11 | #121 |
| 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 |
|---|---|---|
| 1. C22×Dic55 | C2 | semidirect |
| 2. C2×C11×C22⋊D5 | C2 | semidirect |
| 3. C2×C5×C22⋊D11 | C2 | semidirect |
| 4. C2×#89167 | C2 | semidirect |
| 5. #11724888 | C2 | semidirect |
| 6. #11724885 | C2 | semidirect |
| 7. (C2×D11)⋊Dic5 | C2 | semidirect |
| 22. C22×C5×C11 | D4 | semidirect |
| 31. Dic55 | D4 | semidirect |
| 36. C2×C22⋊D11 | D5 | semidirect |
| 61. C2×C22⋊D5 | D11 | semidirect |
| 66. C5×C11 | #121 | semidirect |
| 72. C22×C11 | C22⋊D5 | semidirect |
| 104. C22×C5 | C22⋊D11 | semidirect |
| 120. C11 | #4085 | semidirect |
| 138. C5 | #66992 | semidirect |
| 147. C22 | #89167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic55 | 2 |
| C2×C11×C22⋊D5 | 2 |
| C2×C5×C22⋊D11 | 2 |
| C2×#89167 | 2 |
| #11724888 | 2 |
| #11724885 | 2 |
| (C2×D11)⋊Dic5 | 2 |
| #66992 | 5 |
| #4085 | 11 |