Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
282 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 282 conjugacy classes of subgroups — too many to draw. Only its 72 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. #11716608 | C2 | semidirect |
| 107. C52 | #484 | semidirect |
| 166. C5 | #65011 | semidirect |
| 167. C5 | #65259 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11717244 | 2 |
| C2×C5×C4⋊Dic5 | 2 |
| C5×C22⋊#168 | 2 |
| #11716616 | 2 |
| #11716608 | 2 |
| #65259 | 5 |
| #65011 | 5 |