Finite Group DatabasebetaFinite Group DatabasebetaOrder 1760.
260 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 74 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 |
|---|---|---|
| 1. C23×D5×C11 | C2 | semidirect |
| 2. C2×C11×C22⋊D5 | C2 | semidirect |
| 3. C2×C11×D20 | C2 | semidirect |
| 4. C5×C11×C22⋊C4 | C2 | semidirect |
| 5. C11×#685 | C2 | semidirect |
| 10. C22×D5×C11 | C22 | semidirect |
| 11. C2×C4×C5×C11 | C22 | semidirect |
| 13. C2×C11×Dic5 | C22 | semidirect |
| 17. C22×C5×C11 | D4 | semidirect |
| 24. C2×D5×C11 | D4 | semidirect |
| 31. C11×C22⋊C4 | D5 | semidirect |
| 32. #4028 | C11 | direct (N × H) |
| 46. C2×C4×C11 | C2×D5 | semidirect |
| 47. C23×D5 | C2×C11 | semidirect |
| 48. C2×C22⋊D5 | C2×C11 | semidirect |
| 49. C2×D20 | C2×C11 | semidirect |
| 50. C5×C22⋊C4 | C2×C11 | semidirect |
| 51. #685 | C2×C11 | semidirect |
| 52. C5×C11 | #120 | semidirect |
| 60. C22×C11 | D20 | semidirect |
| 68. C22×D5 | C22×C11 | semidirect |
| 69. C2×C4×C5 | C22×C11 | semidirect |
| 71. C2×Dic5 | C22×C11 | semidirect |
| 80. C22×C5 | D4×C11 | semidirect |
| 87. C2×D5 | D4×C11 | semidirect |
| 94. C22⋊C4 | D5×C11 | semidirect |
| 95. C11 | #4028 | direct (N × H) |
| 109. C2×C4 | C2×D5×C11 | semidirect |
| 110. C5 | C11×#120 | semidirect |
| 118. C22 | C11×D20 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D5×C11 | 2 |
| C2×C11×C22⋊D5 | 2 |
| C2×C11×D20 | 2 |
| C5×C11×C22⋊C4 | 2 |
| C11×#685 | 2 |
| C11×#120 | 5 |
| #4028 | 11 |