Finite Group DatabasebetaFinite Group DatabasebetaOrder 1760.
292 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 108 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×D5×D11 |
| commutator, socle, cosocle | C2×C5×C11 | C24 |
| Fitting | C2×C4×C5×C11 | C22 |
| hypercenter | C2×C4 | D5×D11 |
| hypocenter | C5×C11 | 2−1+4 |
| LCS | G ▷ C2×C5×C11 ▷ C5×C11 | |
| UCS | C1 ◁ C2 ◁ C2×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×Dic110 | C2 | semidirect |
| 2. C11×#709 | C2 | semidirect |
| 3. C5×#4339 | C2 | semidirect |
| 4. #11724997 | C2 | semidirect |
| 5. #11724989 | C2 | semidirect |
| 6. D5×Dic22 | C2 | semidirect |
| 7. #11724982 | C2 | semidirect |
| 8. D11×Dic10 | C2 | semidirect |
| 39. #4339 | D5 | semidirect |
| 68. #709 | D11 | semidirect |
| 71. C5×C11 | 2−1+4 | semidirect |
| 117. C11 | #4150 | semidirect |
| 138. C5 | #67043 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Dic110 | 2 |
| C11×#709 | 2 |
| C5×#4339 | 2 |
| #11724997 | 2 |
| #11724989 | 2 |
| D5×Dic22 | 2 |
| #11724982 | 2 |
| D11×Dic10 | 2 |
| #67043 | 5 |
| #4150 | 11 |