Finite Group DatabasebetaFinite Group DatabasebetaOrder 1120.
188 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 188 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. C22×C4×C5×C7 | C2 | semidirect |
| 2. C2×C5×C22⋊D7 | C2 | semidirect |
| 3. C2×C5×D28 | C2 | semidirect |
| 4. C5×(C2×D7)⋊C4 | C2 | semidirect |
| 5. C5×C4⋊Dic7 | C2 | semidirect |
| 14. #6493 | C5 | direct (N × H) |
| 18. C22×C5×C7 | D4 | semidirect |
| 24. C4×C5×C7 | D4 | semidirect |
| 26. C22×C4×C7 | C2×C5 | semidirect |
| 27. C2×C22⋊D7 | C2×C5 | semidirect |
| 28. C2×D28 | C2×C5 | semidirect |
| 29. (C2×D7)⋊C4 | C2×C5 | semidirect |
| 30. C4⋊Dic7 | C2×C5 | semidirect |
| 33. C22×C4×C5 | D7 | semidirect |
| 57. C5×C7 | #121 | semidirect |
| 61. C22×C7 | C5×D4 | semidirect |
| 67. C4×C7 | C5×D4 | semidirect |
| 74. C22×C5 | D28 | semidirect |
| 78. C4×C5 | C22⋊D7 | semidirect |
| 81. C22×C4 | C5×D7 | semidirect |
| 102. C7 | C5×#121 | semidirect |
| 103. C5 | #6493 | direct (N × H) |
| 109. C22 | C5×D28 | semidirect |
| 113. C4 | C5×C22⋊D7 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×C5×C7 | 2 |
| C2×C5×C22⋊D7 | 2 |
| C2×C5×D28 | 2 |
| C5×(C2×D7)⋊C4 | 2 |
| C5×C4⋊Dic7 | 2 |
| #6493 | 5 |
| C5×#121 | 7 |