Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
266 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 266 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 |
|---|---|---|
| 3. C5×#3967 | C2 | semidirect |
| 4. C5×#3967 | C2 | semidirect |
| 6. C5×#3940 | C2 | semidirect |
| 7. C5×#3939 | C2 | semidirect |
| 20. #65334 | C5 | direct (N × H) |
| 44. #3967 | C2×C5 | semidirect |
| 45. #3967 | C2×C5 | semidirect |
| 47. #3940 | C2×C5 | semidirect |
| 48. #3939 | C2×C5 | semidirect |
| 134. C52 | #485 | semidirect |
| 203. C5 | #65334 | direct (N × H) |
| 204. C5 | C5×#485 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C52×C22⋊Q8 | 2 |
| C5×#4072 | 2 |
| C5×#3967 | 2 |
| C5×C22⋊#168 | 2 |
| C5×#3940 | 2 |
| C5×#3939 | 2 |
| C5×#485 | 5 |
| #65334 | 5 |