Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
267 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 267 conjugacy classes of subgroups — too many to draw. Only its 80 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. #11716847 | C2 | semidirect |
| 4. C5×#4004 | C2 | semidirect |
| 5. #11716759 | C2 | semidirect |
| 36. #4004 | D5 | semidirect |
| 48. C5×Dic5 | M16 | semidirect |
| 49. C5×Dic5 | M16 | semidirect |
| 112. C52 | #423 | semidirect |
| 135. Dic5 | #676 | semidirect |
| 136. Dic5 | #704 | semidirect |
| 174. C5 | #65126 | semidirect |
| 175. C5 | #65758 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87828 | 2 |
| C4×D5×Dic5 | 2 |
| #11716847 | 2 |
| C5×#4004 | 2 |
| #11716759 | 2 |
| #65758 | 5 |
| #65126 | 5 |