Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
616 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 616 conjugacy classes of subgroups — too many to draw. Only its 179 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. C52×#117 | C2 | semidirect |
| 3. C2×#87804 | C2 | semidirect |
| 4. #11716672 | C2 | semidirect |
| 9. #87900 | C4 | semidirect |
| 11. C2×C4⋊(C5⋊D5) | C4 | semidirect |
| 13. C2×#6045 | C4 | semidirect |
| 16. C42×C52 | C22 | semidirect |
| 18. #87804 | C22 | semidirect |
| 41. C5×#117 | D5 | semidirect |
| 67. C42×C5 | C2×D5 | semidirect |
| 98. #117 | C5⋊D5 | semidirect |
| 100. C52 | #421 | semidirect |
| 127. C42 | C2×C5⋊D5 | semidirect |
| 152. C5 | #65294 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87900 | 2 |
| C52×#117 | 2 |
| C2×#87804 | 2 |
| #11716672 | 2 |
| #65294 | 5 |