Finite Group DatabasebetaFinite Group DatabasebetaOrder 1120.
140 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 140 conjugacy classes of subgroups — too many to draw. Only its 52 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 |
|---|---|---|
| 9. Dic70 | C4 | semidirect |
| 11. C5×Dic14 | C4 | semidirect |
| 12. #63308 | C4 | semidirect |
| 18. C7⋊AGL(1,𝔽5) | Q8 | semidirect |
| 44. Dic14 | AGL(1,𝔽5) | semidirect |
| 53. C5×C7 | C4×Q8 | semidirect |
| 90. C7 | Q8×AGL(1,𝔽5) | semidirect |
| 91. C5 | #6450 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D5×Dic14 | 2 |
| C4×C7⋊AGL(1,𝔽5) | 2 |
| C7×C4⋊AGL(1,𝔽5) | 2 |
| Dic7⋊AGL(1,𝔽5) | 2 |
| AGL(1,𝔽5)×Dic7 | 2 |
| #6450 | 5 |
| Q8×AGL(1,𝔽5) | 7 |