Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
392 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 88 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×#87774 | C2 | semidirect |
| 4. C4×C5×#168 | C2 | semidirect |
| 21. C5×#168 | D4 | semidirect |
| 28. #4015 | D5 | semidirect |
| 30. C4×#168 | D5 | semidirect |
| 34. C4×C52 | SD16 | semidirect |
| 78. #168 | D20 | semidirect |
| 83. C52 | #492 | semidirect |
| 96. C4×C5 | #677 | semidirect |
| 97. C4×C5 | #688 | semidirect |
| 126. C5 | #64982 | semidirect |
| 127. C5 | #65374 | semidirect |
| 132. C4 | #87774 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11717194 | 2 |
| C5×#4015 | 2 |
| C2×#87774 | 2 |
| C4×C5×#168 | 2 |
| #65374 | 5 |
| #64982 | 5 |