Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
224 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 224 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×#87802 | C2 | semidirect |
| 3. C5×#3944 | C2 | semidirect |
| 4. #11716592 | C2 | semidirect |
| 5. #11716589 | C2 | semidirect |
| 35. #3944 | D5 | semidirect |
| 101. C52 | #510 | semidirect |
| 146. C5 | #65198 | semidirect |
| 147. C5 | #65484 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87802 | 2 |
| C5×#4050 | 2 |
| C5×#3944 | 2 |
| #11716592 | 2 |
| #11716589 | 2 |
| #65484 | 5 |
| #65198 | 5 |