Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
352 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 352 conjugacy classes of subgroups — too many to draw. Only its 144 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 |
|---|---|---|
| 4. #11716595 | C2 | semidirect |
| 5. Dic5×#168 | C2 | semidirect |
| 8. #87804 | C4 | semidirect |
| 13. C5×#681 | C4 | semidirect |
| 25. #6029 | C2×C4 | semidirect |
| 26. C5×#168 | C2×C4 | semidirect |
| 45. C5×Dic5 | M16 | semidirect |
| 62. #681 | Dic5 | direct (N × H) |
| 96. #168 | C2×Dic5 | semidirect |
| 102. C52 | C4×M16 | semidirect |
| 124. Dic5 | #681 | direct (N × H) |
| 154. C5 | C4×#681 | semidirect |
| 155. C5 | M16×Dic5 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87804 | 2 |
| C2×C4×C5×Dic5 | 2 |
| C2×C5×#681 | 2 |
| #11716595 | 2 |
| Dic5×#168 | 2 |
| M16×Dic5 | 5 |
| C4×#681 | 5 |