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. C5×C4⋊Dic7 | C2 | semidirect |
| 5. C4×C5×Dic7 | C2 | semidirect |
| 11. C4×C5×D7 | C4 | semidirect |
| 12. #6455 | C5 | direct (N × H) |
| 23. C7×C4⋊C4 | C2×C5 | semidirect |
| 25. C4⋊Dic7 | C2×C5 | semidirect |
| 26. C4×Dic7 | C2×C5 | semidirect |
| 29. C5×C4⋊C4 | D7 | semidirect |
| 41. C4×D7 | C4×C5 | semidirect |
| 48. C5×C7 | #117 | semidirect |
| 68. C4⋊C4 | C5×D7 | semidirect |
| 85. C7 | C5×#117 | semidirect |
| 86. C5 | #6455 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C5×D7 | 2 |
| C5×C7×C4⋊C4 | 2 |
| C5×(C2×D7)⋊C4 | 2 |
| C5×C4⋊Dic7 | 2 |
| C4×C5×Dic7 | 2 |
| #6455 | 5 |
| C5×#117 | 7 |