Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
266 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 96 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. C4⋊#6029 | C2 | semidirect |
| 5. C5×C4⋊#168 | C2 | semidirect |
| 6. #11716612 | C2 | semidirect |
| 7. #11716612 | C2 | semidirect |
| 50. C4⋊#168 | D5 | semidirect |
| 134. C52 | #424 | semidirect |
| 200. C5 | #65128 | semidirect |
| 201. C5 | #65288 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4018 | 2 |
| C2×#87768 | 2 |
| C2×D5×#168 | 2 |
| C4⋊#6029 | 2 |
| C5×C4⋊#168 | 2 |
| #11716612 | 2 |
| #65288 | 5 |
| #65128 | 5 |