Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
992 conjugacy classes of subgroups; only the 275 normal subgroups are shown.
This group has 992 conjugacy classes of subgroups — too many to draw. Only its 275 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 |
|---|---|---|
| 1. C52×2−1+4 | C2 | semidirect |
| 2. #11717523 | C2 | semidirect |
| 3. #11717271 | C2 | semidirect |
| 4. #11717270 | C2 | semidirect |
| 5. #11717268 | C2 | semidirect |
| 6. C2×#87812 | C2 | semidirect |
| 7. #11717262 | C2 | semidirect |
| 42. C5×2−1+4 | D5 | semidirect |
| 95. 2−1+4 | C5⋊D5 | semidirect |
| 101. C52 | #578 | semidirect |
| 146. C5 | #66172 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C52×2−1+4 | 2 |
| #11717523 | 2 |
| #11717271 | 2 |
| #11717270 | 2 |
| #11717268 | 2 |
| C2×#87812 | 2 |
| #11717262 | 2 |
| #66172 | 5 |