Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
328 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 84 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. C5×#4015 | C2 | semidirect |
| 3. C2×#87772 | C2 | semidirect |
| 4. C4×#6029 | C2 | semidirect |
| 21. #6029 | D4 | semidirect |
| 27. #4015 | D5 | semidirect |
| 34. C4×C52 | SD16 | semidirect |
| 80. C52 | #492 | semidirect |
| 91. C4×C5 | #687 | semidirect |
| 92. C4×C5 | #688 | semidirect |
| 120. C5 | #65365 | semidirect |
| 121. C5 | #65374 | semidirect |
| 126. C4 | #87772 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4020 | 2 |
| C5×#4015 | 2 |
| C2×#87772 | 2 |
| C4×#6029 | 2 |
| #65374 | 5 |
| #65365 | 5 |