Finite Group DatabasebetaFinite Group DatabasebetaOrder 1120.
188 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 86 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. C2×C4×C5×D7 | C2 | semidirect |
| 3. C5×C7×C4⋊C4 | C2 | semidirect |
| 4. C5×(C2×D7)⋊C4 | C2 | semidirect |
| 5. C4×C5×Dic7 | C2 | semidirect |
| 11. C5×D28 | C4 | semidirect |
| 13. #6456 | C5 | direct (N × H) |
| 18. C2×C5×D7 | C2×C4 | semidirect |
| 20. C4×C5×C7 | C2×C4 | semidirect |
| 22. C5×Dic7 | D4 | semidirect |
| 24. C2×C4×D7 | C2×C5 | semidirect |
| 25. C7×C4⋊C4 | C2×C5 | semidirect |
| 26. (C2×D7)⋊C4 | C2×C5 | semidirect |
| 27. C4×Dic7 | C2×C5 | semidirect |
| 30. C5×C4⋊C4 | D7 | semidirect |
| 42. D28 | C4×C5 | semidirect |
| 51. C5×C7 | C4×D4 | semidirect |
| 56. C2×D7 | C2×C4×C5 | semidirect |
| 58. C4×C7 | C2×C4×C5 | semidirect |
| 60. Dic7 | C5×D4 | semidirect |
| 68. C4×C5 | C4×D7 | semidirect |
| 71. C4⋊C4 | C5×D7 | semidirect |
| 89. C7 | C4×C5×D4 | semidirect |
| 90. C5 | #6456 | direct (N × H) |
| 98. C4 | C4×C5×D7 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×D28 | 2 |
| C2×C4×C5×D7 | 2 |
| C5×C7×C4⋊C4 | 2 |
| C5×(C2×D7)⋊C4 | 2 |
| C4×C5×Dic7 | 2 |
| #6456 | 5 |
| C4×C5×D4 | 7 |