Finite Group DatabasebetaFinite Group DatabasebetaOrder 1120.
260 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 74 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. C23×C5×D7 | C2 | semidirect |
| 2. C2×C5×C22⋊D7 | C2 | semidirect |
| 3. C2×C5×D28 | C2 | semidirect |
| 4. C5×C7×C22⋊C4 | C2 | semidirect |
| 5. C5×(C2×D7)⋊C4 | C2 | semidirect |
| 10. C22×C5×D7 | C22 | semidirect |
| 11. C2×C4×C5×C7 | C22 | semidirect |
| 13. C2×C5×Dic7 | C22 | semidirect |
| 15. #6445 | C5 | direct (N × H) |
| 18. C22×C5×C7 | D4 | semidirect |
| 25. C2×C5×D7 | D4 | semidirect |
| 28. C23×D7 | C2×C5 | semidirect |
| 29. C2×C22⋊D7 | C2×C5 | semidirect |
| 30. C2×D28 | C2×C5 | semidirect |
| 31. C7×C22⋊C4 | C2×C5 | semidirect |
| 32. (C2×D7)⋊C4 | C2×C5 | semidirect |
| 37. C5×C22⋊C4 | D7 | semidirect |
| 47. C22×D7 | C22×C5 | semidirect |
| 48. C2×C4×C7 | C22×C5 | semidirect |
| 50. C2×Dic7 | C22×C5 | semidirect |
| 60. C2×C4×C5 | C2×D7 | semidirect |
| 61. C5×C7 | #120 | semidirect |
| 64. C22×C7 | C5×D4 | semidirect |
| 71. C2×D7 | C5×D4 | semidirect |
| 81. C22×C5 | D28 | semidirect |
| 89. C22⋊C4 | C5×D7 | semidirect |
| 108. C2×C4 | C2×C5×D7 | semidirect |
| 109. C7 | C5×#120 | semidirect |
| 110. C5 | #6445 | direct (N × H) |
| 118. C22 | C5×D28 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C5×D7 | 2 |
| C2×C5×C22⋊D7 | 2 |
| C2×C5×D28 | 2 |
| C5×C7×C22⋊C4 | 2 |
| C5×(C2×D7)⋊C4 | 2 |
| #6445 | 5 |
| C5×#120 | 7 |