Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
648 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 648 conjugacy classes of subgroups — too many to draw. Only its 127 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×#87900 | C2 | semidirect |
| 2. C52×#121 | C2 | semidirect |
| 3. C2×#87810 | C2 | semidirect |
| 4. C2×#87809 | C2 | semidirect |
| 5. C22⋊#6029 | C2 | semidirect |
| 6. #11716677 | C2 | semidirect |
| 7. #11716676 | C2 | semidirect |
| 38. C4⋊(C5⋊D5) | D4 | semidirect |
| 41. #6045 | D4 | semidirect |
| 45. C5×#121 | D5 | semidirect |
| 111. #121 | C5⋊D5 | semidirect |
| 115. C52 | #449 | semidirect |
| 172. C5 | #65326 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87900 | 2 |
| C52×#121 | 2 |
| C2×#87810 | 2 |
| C2×#87809 | 2 |
| C22⋊#6029 | 2 |
| #11716677 | 2 |
| #11716676 | 2 |
| #65326 | 5 |