Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
216 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 86 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 |
|---|---|---|
| 20. #65145 | C5 | direct (N × H) |
| 29. C52×C8 | Q8 | semidirect |
| 30. C5×#168 | Q8 | semidirect |
| 105. C5×C8 | Dic10 | semidirect |
| 106. C5×C8 | C5×Q8 | semidirect |
| 107. #168 | C5×Q8 | semidirect |
| 115. C52 | #501 | semidirect |
| 168. C8 | C5×Dic10 | semidirect |
| 170. C5 | #65145 | direct (N × H) |
| 171. C5 | C5×#501 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4036 | 2 |
| C5×#4034 | 2 |
| C52×#106 | 2 |
| C5×#3950 | 2 |
| C5×#3947 | 2 |
| C5×#3940 | 2 |
| C5×#3939 | 2 |
| C5×#501 | 5 |
| #65145 | 5 |