Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
268 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 78 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. C5×#4016 | C2 | semidirect |
| 3. C5×#3967 | C2 | semidirect |
| 5. C4×C5×#168 | C2 | semidirect |
| 14. #65345 | C5 | direct (N × H) |
| 27. #4016 | C2×C5 | semidirect |
| 31. #3967 | C2×C5 | semidirect |
| 33. C4×#168 | C2×C5 | semidirect |
| 90. C52 | #488 | semidirect |
| 136. C5 | #65345 | direct (N × H) |
| 137. C5 | C5×#488 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C52×#124 | 2 |
| C5×#4016 | 2 |
| C5×#3967 | 2 |
| C5×#3964 | 2 |
| C4×C5×#168 | 2 |
| C5×#488 | 5 |
| #65345 | 5 |