Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
312 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 312 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 |
| 14. C5×#681 | C4 | semidirect |
| 27. C5×#168 | C2×C4 | semidirect |
| 72. #681 | Dic5 | semidirect |
| 105. #168 | C2×Dic5 | semidirect |
| 111. C52 | #428 | semidirect |
| 174. C5 | #65253 | semidirect |
| 175. C5 | #65410 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11717246 | 2 |
| C2×C5×C4⋊Dic5 | 2 |
| C2×C5×#681 | 2 |
| #11716616 | 2 |
| #11716614 | 2 |
| #65410 | 5 |
| #65253 | 5 |