Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
242 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 242 conjugacy classes of subgroups — too many to draw. Only its 56 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. #11717224 | C2 | semidirect |
| 2. C2×C5×D40 | C2 | semidirect |
| 3. C5×#3944 | C2 | semidirect |
| 4. #11716589 | C2 | semidirect |
| 5. #11716587 | C2 | semidirect |
| 9. #87802 | C22 | semidirect |
| 10. #87801 | C22 | semidirect |
| 14. C5×#672 | C22 | semidirect |
| 31. C2×D40 | D5 | semidirect |
| 35. #3944 | D5 | semidirect |
| 67. #672 | C2×D5 | semidirect |
| 105. C52 | #509 | semidirect |
| 156. C5 | #65197 | semidirect |
| 157. C5 | #65436 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11717224 | 2 |
| C2×C5×D40 | 2 |
| C5×#3944 | 2 |
| #11716589 | 2 |
| #11716587 | 2 |
| #65436 | 5 |
| #65197 | 5 |