Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
600 conjugacy classes of subgroups; only the 251 normal subgroups are shown.
This group has 600 conjugacy classes of subgroups — too many to draw. Only its 251 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. #11716702 | C2 | semidirect |
| 7. C2×C52×Q8 | C4 | semidirect |
| 43. C2×C5×Q8 | Dic5 | semidirect |
| 72. C52 | #419 | semidirect |
| 83. C2×Q8 | #1039 | semidirect |
| 107. C5 | #65514 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C52×Q8 | 2 |
| #11717246 | 2 |
| C2×#87804 | 2 |
| #11716702 | 2 |
| #65514 | 5 |