Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
320 conjugacy classes of subgroups; only the 134 normal subgroups are shown.
This group has 320 conjugacy classes of subgroups — too many to draw. Only its 134 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. C5×#3946 | C2 | semidirect |
| 15. #65407 | C5 | direct (N × H) |
| 34. #3946 | C2×C5 | semidirect |
| 42. C5×Dic5 | M16 | semidirect |
| 98. C52 | #423 | semidirect |
| 120. Dic5 | C5×M16 | semidirect |
| 150. C5 | #65407 | direct (N × H) |
| 151. C5 | C5×#423 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C52×M16 | 2 |
| C2×C4×C5×Dic5 | 2 |
| C2×C5×#681 | 2 |
| C5×#3946 | 2 |
| C5×#423 | 5 |
| #65407 | 5 |