Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
304 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 104 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. #11716617 | C2 | semidirect |
| 5. #11716615 | C2 | semidirect |
| 8. #87804 | C4 | semidirect |
| 27. #6029 | C2×C4 | semidirect |
| 108. C52 | #428 | semidirect |
| 169. C5 | #65253 | semidirect |
| 170. C5 | #65284 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87804 | 2 |
| C5×#4072 | 2 |
| C2×C5×C4⋊Dic5 | 2 |
| #11716617 | 2 |
| #11716615 | 2 |
| #65284 | 5 |
| #65253 | 5 |