Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
440 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 2. #11717210 | C2 | semidirect |
| 3. C52×#102 | C2 | semidirect |
| 4. #11716699 | C2 | semidirect |
| 5. #11716688 | C2 | semidirect |
| 6. #11716682 | C2 | semidirect |
| 7. #11716676 | C2 | semidirect |
| 37. C5×#102 | D5 | semidirect |
| 92. #102 | C5⋊D5 | semidirect |
| 94. C52 | #490 | semidirect |
| 139. C5 | #65053 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11717260 | 2 |
| #11717210 | 2 |
| C52×#102 | 2 |
| #11716699 | 2 |
| #11716688 | 2 |
| #11716682 | 2 |
| #11716676 | 2 |
| #65053 | 5 |