Finite Group DatabasebetaFinite Group DatabasebetaOrder 1120.
136 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 58 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. C5×#1157 | C2 | semidirect |
| 2. C2×C5×D28 | C2 | semidirect |
| 3. C5×C7×M16 | C2 | semidirect |
| 4. C5×D56 | C2 | semidirect |
| 5. C5×#1132 | C2 | semidirect |
| 11. C5×D28 | C22 | semidirect |
| 13. C5×Dic14 | C22 | semidirect |
| 14. C5×C7×C8 | C22 | semidirect |
| 15. #6471 | C5 | direct (N × H) |
| 24. #1157 | C2×C5 | semidirect |
| 25. C2×D28 | C2×C5 | semidirect |
| 26. C7×M16 | C2×C5 | semidirect |
| 27. D56 | C2×C5 | semidirect |
| 28. #1132 | C2×C5 | semidirect |
| 33. C5×M16 | D7 | semidirect |
| 43. D28 | C22×C5 | semidirect |
| 45. Dic14 | C22×C5 | semidirect |
| 46. C7×C8 | C22×C5 | semidirect |
| 55. C5×C8 | C2×D7 | semidirect |
| 56. C5×C7 | AGL(1,ℤ/8) | semidirect |
| 76. M16 | C5×D7 | semidirect |
| 93. C8 | C2×C5×D7 | semidirect |
| 94. C7 | C5×AGL(1,ℤ/8) | semidirect |
| 95. C5 | #6471 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#1157 | 2 |
| C2×C5×D28 | 2 |
| C5×C7×M16 | 2 |
| C5×D56 | 2 |
| C5×#1132 | 2 |
| #6471 | 5 |
| C5×AGL(1,ℤ/8) | 7 |