Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
216 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 72 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 |
|---|---|---|
| 29. C52×C8 | Q8 | semidirect |
| 30. C5×#168 | Q8 | semidirect |
| 105. C5×C8 | Dic10 | semidirect |
| 106. C5×C8 | Dic10 | semidirect |
| 107. #168 | Dic10 | semidirect |
| 115. C52 | #501 | semidirect |
| 168. C8 | #6039 | semidirect |
| 170. C5 | #64991 | semidirect |
| 171. C5 | #65145 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11717036 | 2 |
| #11716988 | 2 |
| #11716685 | 2 |
| C5×#3949 | 2 |
| C5×#3947 | 2 |
| #11716616 | 2 |
| #11716614 | 2 |
| #65145 | 5 |
| #64991 | 5 |