Finite Group DatabasebetaFinite Group DatabasebetaOrder 1120.
148 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 148 conjugacy classes of subgroups — too many to draw. Only its 50 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. C2×#63308 | C2 | semidirect |
| 3. #10587900 | C2 | semidirect |
| 5. C5×C4⋊Dic7 | C2 | semidirect |
| 6. #10587858 | C2 | semidirect |
| 22. C2×C7×D5 | Q8 | semidirect |
| 33. C4⋊Dic7 | D5 | semidirect |
| 65. C5×C7 | C22⋊Q8 | semidirect |
| 80. C2×D5 | Dic14 | semidirect |
| 111. C7 | #4042 | semidirect |
| 112. C5 | #6441 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63308 | 2 |
| C2×D5×Dic7 | 2 |
| #10587900 | 2 |
| C7×#685 | 2 |
| C5×C4⋊Dic7 | 2 |
| #10587858 | 2 |
| #10587855 | 2 |
| #6441 | 5 |
| #4042 | 7 |