Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
294 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 76 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. C4×C5×Dic10 | C2 | semidirect |
| 3. C2×#87772 | C2 | semidirect |
| 4. C4⋊#6029 | C2 | semidirect |
| 5. #11716603 | C2 | semidirect |
| 29. C5×Dic10 | D4 | semidirect |
| 36. C4×Dic10 | D5 | semidirect |
| 47. C4×C52 | SD16 | semidirect |
| 105. Dic10 | D20 | semidirect |
| 114. C52 | #460 | semidirect |
| 132. C4×C5 | #687 | semidirect |
| 133. C4×C5 | #688 | semidirect |
| 175. C5 | #65316 | semidirect |
| 176. C5 | #65364 | semidirect |
| 184. 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 |
| C4×C5×Dic10 | 2 |
| C2×#87772 | 2 |
| C4⋊#6029 | 2 |
| #11716603 | 2 |
| #65364 | 5 |
| #65316 | 5 |