Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
288 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 68 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×#4015 | C2 | semidirect |
| 3. C2×#87775 | C2 | semidirect |
| 5. #11716670 | C2 | semidirect |
| 34. #4015 | D5 | semidirect |
| 97. C52 | #497 | semidirect |
| 143. C5 | #65349 | semidirect |
| 144. C5 | #65375 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4021 | 2 |
| C5×#4015 | 2 |
| C2×#87775 | 2 |
| C2×#87772 | 2 |
| #11716670 | 2 |
| #65375 | 5 |
| #65349 | 5 |