Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
480 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 125 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. C2×#87810 | C2 | semidirect |
| 3. #11717244 | C2 | semidirect |
| 4. C2×#87804 | C2 | semidirect |
| 5. #11716699 | C2 | semidirect |
| 6. #11716677 | C2 | semidirect |
| 7. #11716674 | C2 | semidirect |
| 37. #6029 | D4 | semidirect |
| 100. C52 | #468 | semidirect |
| 148. C5 | #65331 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C52×#121 | 2 |
| C2×#87810 | 2 |
| #11717244 | 2 |
| C2×#87804 | 2 |
| #11716699 | 2 |
| #11716677 | 2 |
| #11716674 | 2 |
| #65331 | 5 |