Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
240 conjugacy classes of subgroups; only the 27 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 27 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. #11716906 | C2 | semidirect |
| 3. #11716879 | C2 | semidirect |
| 4. C23×C5×D5 | C4 | semidirect |
| 9. C5×C22⋊Dic5 | C4 | semidirect |
| 45. C23×D5 | AGL(1,𝔽5) | semidirect |
| 58. C22⋊Dic5 | AGL(1,𝔽5) | semidirect |
| 96. C52 | AΣL(1,𝔽16) | semidirect |
| 163. C5 | #64864 | semidirect |
| 164. C5 | #64934 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11717095 | 2 |
| #11716906 | 2 |
| #11716879 | 2 |
| #64934 | 5 |
| #64864 | 5 |