Finite Group DatabasebetaFinite Group DatabasebetaOrder 1120.
188 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 66 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×C5×C22⋊D7 | C2 | semidirect |
| 2. C2×C5×C22⋊D7 | C2 | semidirect |
| 3. C2×C5×D28 | C2 | semidirect |
| 4. C2×C4×C5×D7 | C2 | semidirect |
| 5. C5×C7×C22⋊C4 | C2 | semidirect |
| 6. C5×(C2×D7)⋊C4 | C2 | semidirect |
| 7. C5×Dic7⋊C4 | C2 | semidirect |
| 19. #6447 | C5 | direct (N × H) |
| 30. C2×C5×D7 | D4 | semidirect |
| 34. C5×Dic7 | D4 | semidirect |
| 35. C2×C22⋊D7 | C2×C5 | semidirect |
| 36. C2×C22⋊D7 | C2×C5 | semidirect |
| 37. C2×D28 | C2×C5 | semidirect |
| 38. C2×C4×D7 | C2×C5 | semidirect |
| 39. C7×C22⋊C4 | C2×C5 | semidirect |
| 40. (C2×D7)⋊C4 | C2×C5 | semidirect |
| 41. Dic7⋊C4 | C2×C5 | semidirect |
| 48. C5×C22⋊C4 | D7 | semidirect |
| 77. C5×C7 | #121 | semidirect |
| 88. C2×D7 | C5×D4 | semidirect |
| 92. Dic7 | C5×D4 | semidirect |
| 113. C22⋊C4 | C5×D7 | semidirect |
| 137. C7 | C5×#121 | semidirect |
| 138. C5 | #6447 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×C22⋊D7 | 2 |
| C2×C5×D28 | 2 |
| C2×C4×C5×D7 | 2 |
| C5×C7×C22⋊C4 | 2 |
| C5×(C2×D7)⋊C4 | 2 |
| C5×Dic7⋊C4 | 2 |
| #6447 | 5 |
| C5×#121 | 7 |