Finite Group DatabasebetaFinite Group DatabasebetaOrder 1760.
328 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 116 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | D5×D11 |
| commutator, cosocle | C2×C5×C11 | C24 |
| Frattini | C2 | C22×D5×D11 |
| Fitting | C2×C4×C5×C11 | C22 |
| socle | C22×C5×C11 | C23 |
| hypocenter | C5×C11 | C2×#41 |
| LCS | G ▷ C2×C5×C11 ▷ C5×C11 | |
| UCS | C1 ◁ C2×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C4×D55 | C2 | semidirect |
| 2. C2×C4×D5×C11 | C2 | semidirect |
| 3. C2×C4×C5×D11 | C2 | semidirect |
| 4. C2×#89170 | C2 | semidirect |
| 5. C2×#89169 | C2 | semidirect |
| 6. C2×#89168 | C2 | semidirect |
| 7. C2×#89167 | C2 | semidirect |
| 8. #11724988 | C2 | direct (N × H) |
| 14. C4×D55 | C22 | semidirect |
| 16. C4×D5×C11 | C22 | semidirect |
| 18. C4×C5×D11 | C22 | semidirect |
| 19. #89170 | C22 | semidirect |
| 20. #89169 | C22 | semidirect |
| 21. #89168 | C22 | semidirect |
| 22. #89167 | C22 | semidirect |
| 41. C2×C4×D11 | D5 | semidirect |
| 44. C2×C5×C11 | #41 | semidirect |
| 61. C4×D11 | C2×D5 | semidirect |
| 69. C2×C4×D5 | D11 | semidirect |
| 71. C5×C11 | C2×#41 | semidirect |
| 95. C4×D5 | C2×D11 | semidirect |
| 99. C2×C11 | #709 | semidirect |
| 122. C11 | C2×#709 | semidirect |
| 124. C2×C5 | #4339 | semidirect |
| 142. C5 | C2×#4339 | semidirect |
| 157. C2 | #11724988 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D55 | 2 |
| C2×C4×D5×C11 | 2 |
| C2×C4×C5×D11 | 2 |
| C2×#89170 | 2 |
| C2×#89169 | 2 |
| C2×#89168 | 2 |
| C2×#89167 | 2 |
| #11724988 | 2 |
| C2×#4339 | 5 |
| C2×#709 | 11 |