Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
238 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 238 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 |
|---|---|---|
| 129. C52 | #487 | semidirect |
| 188. C5 | #64970 | semidirect |
| 189. C5 | #65081 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11717036 | 2 |
| #11716983 | 2 |
| #11716683 | 2 |
| C5×#3948 | 2 |
| C5×C8×Dic5 | 2 |
| #11716608 | 2 |
| #11716607 | 2 |
| #65081 | 5 |
| #64970 | 5 |