Finite Group DatabasebetaFinite Group DatabasebetaOrder 1760.
260 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 60 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 | #120 |
| 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. C23×C5×D11 | C2 | semidirect |
| 2. C2×C22⋊D55 | C2 | semidirect |
| 3. C2×#89168 | C2 | semidirect |
| 4. C11×C22⋊Dic5 | C2 | semidirect |
| 5. (C2×D11)⋊Dic5 | C2 | semidirect |
| 7. C22×D55 | C22 | semidirect |
| 12. C2×Dic55 | C22 | semidirect |
| 13. C2×C11×Dic5 | C22 | semidirect |
| 17. C22×C5×C11 | D4 | semidirect |
| 24. C2×C5×D11 | D4 | semidirect |
| 27. C23×D11 | D5 | semidirect |
| 51. C22⋊Dic5 | D11 | semidirect |
| 52. C5×C11 | #120 | semidirect |
| 54. C22×C11 | C22⋊D5 | semidirect |
| 61. C2×D11 | C22⋊D5 | semidirect |
| 72. C2×Dic5 | C2×D11 | semidirect |
| 84. C22×C5 | D44 | semidirect |
| 95. C11 | #4099 | semidirect |
| 110. C5 | #66935 | semidirect |
| 118. C22 | #89168 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C5×D11 | 2 |
| C2×C22⋊D55 | 2 |
| C2×#89168 | 2 |
| C11×C22⋊Dic5 | 2 |
| (C2×D11)⋊Dic5 | 2 |
| #66935 | 5 |
| #4099 | 11 |