Finite Group DatabasebetaFinite Group DatabasebetaOrder 1120.
312 conjugacy classes of subgroups; only the 132 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 132 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×Dic70 | C2 | semidirect |
| 3. C2×C5×Dic14 | C2 | semidirect |
| 4. C2×#63308 | C2 | semidirect |
| 6. D5×Dic14 | C2 | direct (N × H) |
| 10. Dic70 | C22 | semidirect |
| 14. C5×Dic14 | C22 | semidirect |
| 15. #63308 | C22 | semidirect |
| 20. C2×C7×D5 | Q8 | semidirect |
| 31. C2×Dic14 | D5 | direct (N × H) |
| 38. C2×C5×C7 | C2×Q8 | semidirect |
| 40. C7×D5 | C2×Q8 | semidirect |
| 50. Dic14 | C2×D5 | direct (N × H) |
| 61. C5×C7 | C22×Q8 | semidirect |
| 71. C2×D5 | Dic14 | direct (N × H) |
| 84. C2×C7 | Q8×D5 | semidirect |
| 86. C2×C5 | C2×Dic14 | semidirect |
| 88. D5 | C2×Dic14 | direct (N × H) |
| 99. C7 | C2×Q8×D5 | semidirect |
| 100. C5 | C22×Dic14 | semidirect |
| 109. C2 | D5×Dic14 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Dic70 | 2 |
| C2×C4×C7×D5 | 2 |
| C2×C5×Dic14 | 2 |
| C2×#63308 | 2 |
| C2×D5×Dic7 | 2 |
| D5×Dic14 | 2 |
| C22×Dic14 | 5 |
| C2×Q8×D5 | 7 |