Finite Group DatabasebetaFinite Group DatabasebetaOrder 1120.
124 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 44 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. #10587987 | C2 | semidirect |
| 2. C5×#1157 | C2 | semidirect |
| 3. C2×C7×#168 | C2 | semidirect |
| 4. #10587851 | C2 | semidirect |
| 5. #10587847 | C2 | semidirect |
| 6. #10587846 | C2 | semidirect |
| 7. #10587842 | C2 | semidirect |
| 29. #1157 | D5 | semidirect |
| 41. C2×#168 | D7 | semidirect |
| 68. C5×C7 | #135 | semidirect |
| 110. C7 | #4096 | semidirect |
| 111. C5 | #6467 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10587987 | 2 |
| C5×#1157 | 2 |
| C2×C7×#168 | 2 |
| #10587851 | 2 |
| #10587847 | 2 |
| #10587846 | 2 |
| #10587842 | 2 |
| #6467 | 5 |
| #4096 | 7 |