Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
392 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 108 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 |
|---|---|---|
| 3. C5×#3935 | C2 | semidirect |
| 4. #11716594 | C2 | semidirect |
| 11. #87769 | C4 | semidirect |
| 20. C5×#168 | C2×C4 | semidirect |
| 26. #3935 | D5 | semidirect |
| 33. #1039 | M16 | semidirect |
| 66. #168 | C4×D5 | semidirect |
| 71. C52 | C4×M16 | semidirect |
| 108. C5 | #64996 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C42×C5⋊D5 | 2 |
| C2×#87769 | 2 |
| C5×#3935 | 2 |
| #11716594 | 2 |
| #64996 | 5 |