Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
392 conjugacy classes of subgroups; only the 190 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 190 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. C5×#3935 | C2 | semidirect |
| 4. C4×C5×#168 | C2 | semidirect |
| 10. C5×#681 | C4 | direct (N × H) |
| 13. C4×#681 | C5 | direct (N × H) |
| 21. C5×#168 | C2×C4 | semidirect |
| 29. #3935 | C2×C5 | semidirect |
| 30. C4×#168 | C2×C5 | semidirect |
| 36. C4×C52 | M16 | semidirect |
| 55. #681 | C4×C5 | direct (N × H) |
| 83. #168 | C2×C4×C5 | semidirect |
| 88. C52 | C4×M16 | semidirect |
| 104. C4×C5 | #681 | direct (N × H) |
| 107. C4×C5 | C5×M16 | semidirect |
| 135. C5 | C4×#681 | direct (N × H) |
| 136. C5 | C4×C5×M16 | semidirect |
| 141. C4 | C5×#681 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C42×C52 | 2 |
| C2×C5×#681 | 2 |
| C5×#3935 | 2 |
| C4×C5×#168 | 2 |
| C4×C5×M16 | 5 |
| C4×#681 | 5 |