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 | C5×Q8×C11 | C22 |
| hypercenter | Q8 | D5×D11 |
| hypocenter | C5×C11 | 2−1+4 |
| LCS | G ▷ C2×C5×C11 ▷ C5×C11 | |
| UCS | C1 ◁ C2 ◁ Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. Q8×D55 | C2 | semidirect |
| 2. Q8×D5×C11 | C2 | semidirect |
| 3. C5×#4343 | C2 | semidirect |
| 4. #11724988 | C2 | semidirect |
| 5. #11724983 | C2 | semidirect |
| 6. #11724982 | C2 | semidirect |
| 7. D11×Dic10 | C2 | semidirect |
| 30. #4343 | D5 | semidirect |
| 54. Q8×D5 | D11 | semidirect |
| 59. C5×C11 | 2−1+4 | semidirect |
| 98. C11 | #4150 | semidirect |
| 115. C5 | #67040 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D55 | 2 |
| Q8×D5×C11 | 2 |
| C5×#4343 | 2 |
| #11724988 | 2 |
| #11724983 | 2 |
| #11724982 | 2 |
| D11×Dic10 | 2 |
| #67040 | 5 |
| #4150 | 11 |