Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
290 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 81 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 |
|---|---|---|
| 3. C4⋊#6034 | C2 | semidirect |
| 4. C4⋊#6033 | C2 | semidirect |
| 5. #11716783 | C2 | semidirect |
| 46. C4×C52 | M16 | semidirect |
| 52. C5×Dic5 | M16 | semidirect |
| 115. C52 | #423 | semidirect |
| 129. C4×C5 | #700 | semidirect |
| 130. C4×C5 | #704 | semidirect |
| 141. Dic5 | #700 | semidirect |
| 178. C5 | #65681 | semidirect |
| 179. C5 | #65758 | semidirect |
| 190. C4 | #87834 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87834 | 2 |
| C4×D5×Dic5 | 2 |
| C4⋊#6034 | 2 |
| C4⋊#6033 | 2 |
| #11716783 | 2 |
| #65758 | 5 |
| #65681 | 5 |