Finite Group DatabasebetaFinite Group DatabasebetaOrder 1760.
156 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 156 conjugacy classes of subgroups — too many to draw. Only its 55 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 | C22×D55 |
| commutator, socle, cosocle | C22×C5×C11 | C23 |
| Fitting, prime radical | C2×C5×D4×C11 | C2 |
| hypercenter | C2×D4 | D55 |
| hypocenter | C5×C11 | #123 |
| LCS | G ▷ C22×C5×C11 ▷ C5×C11 | |
| UCS | C1 ◁ C22 ◁ C2×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C22×Dic55 | C2 | semidirect |
| 3. C22⋊Dic55 | C2 | semidirect |
| 4. C22⋊Dic55 | C2 | semidirect |
| 5. #11724930 | C2 | semidirect |
| 44. C5×C11 | #123 | semidirect |
| 78. C11 | #4081 | semidirect |
| 90. C5 | #66988 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×D4×C11 | 2 |
| C22×Dic55 | 2 |
| C22⋊Dic55 | 2 |
| #11724930 | 2 |
| #66988 | 5 |
| #4081 | 11 |