Finite Group DatabasebetaFinite Group DatabasebetaOrder 1760.
188 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 71 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C4×D55 | C2 | semidirect |
| 3. C42×C5×C11 | C2 | semidirect |
| 4. #11724932 | C2 | semidirect |
| 5. C4⋊Dic55 | C2 | semidirect |
| 11. D220 | C4 | direct (N × H) |
| 17. C2×D55 | C2×C4 | semidirect |
| 19. C4×C5×C11 | C2×C4 | semidirect |
| 20. C4×C5×C11 | D4 | semidirect |
| 24. C42×C11 | D5 | semidirect |
| 41. C42×C5 | D11 | semidirect |
| 44. C5×C11 | C4×D4 | semidirect |
| 50. C4×C11 | C4×D5 | semidirect |
| 51. C4×C11 | D20 | semidirect |
| 70. C4×C5 | C4×D11 | semidirect |
| 71. C4×C5 | D44 | semidirect |
| 77. C42 | D55 | semidirect |
| 78. C11 | C4×D20 | semidirect |
| 90. C5 | C4×D44 | semidirect |
| 97. C4 | C4×D55 | semidirect |
| 98. C4 | D220 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D220 | 2 |
| C2×C4×D55 | 2 |
| C42×C5×C11 | 2 |
| #11724932 | 2 |
| C4⋊Dic55 | 2 |
| C4×D44 | 5 |
| C4×D20 | 11 |