Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
384 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 126 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. C2×C52×M16 | C2 | semidirect |
| 3. C22×C5×#168 | C2 | semidirect |
| 4. C5×#3952 | C2 | semidirect |
| 17. #65418 | C5 | direct (N × H) |
| 35. C2×C5×M16 | D5 | semidirect |
| 36. C2×C5×M16 | C2×C5 | semidirect |
| 38. C22×#168 | C2×C5 | semidirect |
| 40. #3952 | C2×C5 | semidirect |
| 115. C2×M16 | C5×D5 | semidirect |
| 118. C52 | #408 | semidirect |
| 180. C5 | #65418 | direct (N × H) |
| 181. C5 | C5×#408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#709 | 2 |
| C2×C52×M16 | 2 |
| C22×C5×#168 | 2 |
| C5×#3952 | 2 |
| C5×#408 | 5 |
| #65418 | 5 |