Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
256 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 256 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. C2×#87801 | C2 | semidirect |
| 2. C5×#4050 | C2 | semidirect |
| 3. C5×#3944 | C2 | semidirect |
| 4. #11716590 | C2 | semidirect |
| 5. #11716587 | C2 | semidirect |
| 11. C5×Dic20 | C22 | semidirect |
| 12. C5×D40 | C22 | semidirect |
| 14. C5×#672 | C22 | semidirect |
| 28. #4050 | D5 | semidirect |
| 35. #3944 | D5 | semidirect |
| 56. Dic20 | C2×D5 | semidirect |
| 63. D40 | C2×D5 | semidirect |
| 66. #672 | C2×D5 | semidirect |
| 103. C52 | #509 | semidirect |
| 154. C5 | #65197 | semidirect |
| 155. C5 | #65482 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87801 | 2 |
| C5×#4050 | 2 |
| C5×#3944 | 2 |
| #11716590 | 2 |
| #11716587 | 2 |
| #65482 | 5 |
| #65197 | 5 |