Finite Group DatabasebetaFinite Group DatabasebetaOrder 1120.
120 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 120 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×C7×C4⋊C4 | C2 | semidirect |
| 5. C7×C4⋊Dic5 | C2 | semidirect |
| 6. C7×#683 | C2 | semidirect |
| 7. C4×C7×Dic5 | C2 | semidirect |
| 16. #4044 | C7 | direct (N × H) |
| 29. C7×C4⋊C4 | D5 | semidirect |
| 34. C5×C4⋊C4 | C2×C7 | semidirect |
| 38. C4⋊Dic5 | C2×C7 | semidirect |
| 39. #683 | C2×C7 | semidirect |
| 40. C4×Dic5 | C2×C7 | semidirect |
| 59. C5×C7 | #126 | semidirect |
| 83. C4⋊C4 | C7×D5 | semidirect |
| 103. C7 | #4044 | direct (N × H) |
| 104. C5 | C7×#126 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×C7×C4⋊C4 | 2 |
| C7×#685 | 2 |
| C7×C4⋊Dic5 | 2 |
| C7×#683 | 2 |
| C4×C7×Dic5 | 2 |
| C7×#126 | 5 |
| #4044 | 7 |