Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
290 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 290 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 |
|---|---|---|
| 19. #87776 | C4 | direct (N × H) |
| 52. C4×C52 | Q16 | semidirect |
| 132. C52 | C4×Q16 | semidirect |
| 144. C4×C5 | Dic20 | semidirect |
| 145. C4×C5 | #689 | semidirect |
| 193. C5 | C4×Dic20 | semidirect |
| 194. C5 | C4×#689 | semidirect |
| 201. C4 | #87776 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#6045 | 2 |
| C4×C5×Dic10 | 2 |
| C2×#87776 | 2 |
| C4×C5×#168 | 2 |
| #11716616 | 2 |
| #11716608 | 2 |
| #11716607 | 2 |
| C4×#689 | 5 |
| C4×Dic20 | 5 |