Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
324 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 124 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. #11716670 | C2 | semidirect |
| 4. C5×#3935 | C2 | semidirect |
| 5. Dic5×#168 | C2 | semidirect |
| 13. #87768 | C4 | semidirect |
| 23. #6029 | C2×C4 | semidirect |
| 24. C5×#168 | C2×C4 | semidirect |
| 34. #3935 | D5 | semidirect |
| 42. C5×Dic5 | M16 | semidirect |
| 85. #168 | C4×D5 | semidirect |
| 91. C52 | C4×M16 | semidirect |
| 107. Dic5 | #681 | semidirect |
| 135. C5 | #64996 | semidirect |
| 136. C5 | C4×#681 | 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×#87768 | 2 |
| #11716670 | 2 |
| C5×#3935 | 2 |
| Dic5×#168 | 2 |
| C4×#681 | 5 |
| #64996 | 5 |