Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
304 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 112 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 |
|---|---|---|
| 4. #11716616 | C2 | semidirect |
| 5. #11716614 | C2 | semidirect |
| 13. C2×C5×#168 | C4 | semidirect |
| 67. C2×#168 | Dic5 | semidirect |
| 103. C52 | #427 | semidirect |
| 156. C5 | #65287 | semidirect |
| 157. C5 | #65395 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11717246 | 2 |
| C5×#4072 | 2 |
| C22×C5×#168 | 2 |
| #11716616 | 2 |
| #11716614 | 2 |
| #65395 | 5 |
| #65287 | 5 |