Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
299 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 299 conjugacy classes of subgroups — too many to draw. Only its 121 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 |
|---|---|---|
| 3. #11716845 | C2 | semidirect |
| 4. C4×#6032 | C2 | semidirect |
| 9. #87849 | C4 | direct (N × H) |
| 26. #6032 | C2×C4 | semidirect |
| 41. C4×C52 | M16 | semidirect |
| 43. C5×Dic5 | M16 | semidirect |
| 98. C52 | C4×M16 | semidirect |
| 116. C4×C5 | #681 | semidirect |
| 118. C4×C5 | #700 | semidirect |
| 121. Dic5 | #681 | semidirect |
| 155. C5 | C4×#681 | semidirect |
| 156. C5 | C4×#700 | semidirect |
| 165. C4 | #87849 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87849 | 2 |
| C42×C5×D5 | 2 |
| #11716845 | 2 |
| C4×#6032 | 2 |
| C4×#700 | 5 |
| C4×#681 | 5 |