Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
392 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 120 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. C4×C5×#168 | C2 | semidirect |
| 4. #11716596 | C2 | semidirect |
| 11. #87769 | C4 | direct (N × H) |
| 20. C5×#168 | C2×C4 | semidirect |
| 26. C4×#168 | D5 | semidirect |
| 30. C4×C52 | M16 | semidirect |
| 66. #168 | C4×D5 | semidirect |
| 71. C52 | C4×M16 | semidirect |
| 80. C4×C5 | #676 | semidirect |
| 108. C5 | C4×#676 | semidirect |
| 114. C4 | #87769 | direct (N × H) |
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 |
| C4×C5×#168 | 2 |
| #11716596 | 2 |
| C4×#676 | 5 |