Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
480 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 66 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 |
|---|---|---|
| 2. #11717451 | C2 | semidirect |
| 3. #11716904 | C2 | semidirect |
| 4. C2×C52×D4 | C4 | semidirect |
| 6. C22×#1039 | C4 | semidirect |
| 10. C2×#6045 | C4 | semidirect |
| 43. C2×C5×D4 | AGL(1,𝔽5) | semidirect |
| 92. C52 | #410 | semidirect |
| 116. C2×D4 | #1044 | semidirect |
| 144. C5 | #65771 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87902 | 2 |
| #11717451 | 2 |
| #11716904 | 2 |
| #65771 | 5 |