Finite Group DatabasebetaFinite Group DatabasebetaOrder 1120.
140 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 140 conjugacy classes of subgroups — too many to draw. Only its 62 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 |
|---|---|---|
| 15. #63308 | C4 | semidirect |
| 23. C5×Dic7 | Q8 | semidirect |
| 59. C5×C7 | C4×Q8 | semidirect |
| 67. Dic7 | Dic10 | semidirect |
| 98. C7 | C4×Dic10 | semidirect |
| 99. C5 | #6450 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63308 | 2 |
| #10587900 | 2 |
| C7×#683 | 2 |
| C4×C5×Dic7 | 2 |
| Dic7⋊Dic5 | 2 |
| Dic5×Dic7 | 2 |
| #6450 | 5 |
| C4×Dic10 | 7 |