Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
264 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 88 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 |
|---|---|---|
| 22. C5×#168 | Q8 | semidirect |
| 82. #168 | Dic10 | semidirect |
| 87. C52 | #500 | semidirect |
| 131. C5 | #64971 | semidirect |
| 132. C5 | #65367 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11717189 | 2 |
| C5×#4015 | 2 |
| C4×C5×#168 | 2 |
| #11716616 | 2 |
| #65367 | 5 |
| #64971 | 5 |