Finite Group DatabasebetaFinite Group DatabasebetaOrder 1120.
152 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 82 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. C5×C7×C4⋊C4 | C2 | semidirect |
| 4. C7×C4⋊Dic5 | C2 | semidirect |
| 5. C4×C7×Dic5 | C2 | semidirect |
| 11. C4×C7×D5 | C4 | semidirect |
| 13. #4038 | C7 | direct (N × H) |
| 24. C7×C4⋊C4 | D5 | semidirect |
| 28. C5×C4⋊C4 | C2×C7 | semidirect |
| 30. C4⋊Dic5 | C2×C7 | semidirect |
| 31. C4×Dic5 | C2×C7 | semidirect |
| 47. C4×D5 | C4×C7 | semidirect |
| 48. C5×C7 | #117 | semidirect |
| 68. C4⋊C4 | C7×D5 | semidirect |
| 85. C7 | #4038 | direct (N × H) |
| 86. C5 | C7×#117 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C7×D5 | 2 |
| C5×C7×C4⋊C4 | 2 |
| C7×#685 | 2 |
| C7×C4⋊Dic5 | 2 |
| C4×C7×Dic5 | 2 |
| C7×#117 | 5 |
| #4038 | 7 |