Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
364 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 364 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×#87774 | C2 | semidirect |
| 4. C5×C4⋊#168 | C2 | semidirect |
| 5. #11716605 | C2 | semidirect |
| 29. C5×Dic10 | D4 | semidirect |
| 37. C4×Dic10 | D5 | semidirect |
| 41. C4⋊#168 | D5 | semidirect |
| 47. C4×C52 | SD16 | semidirect |
| 112. Dic10 | D20 | semidirect |
| 120. C52 | #460 | semidirect |
| 141. C4×C5 | #677 | semidirect |
| 142. C4×C5 | #688 | semidirect |
| 185. C5 | #65137 | semidirect |
| 186. C5 | #65316 | semidirect |
| 194. C4 | #87774 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11717194 | 2 |
| C4×C5×Dic10 | 2 |
| C2×#87774 | 2 |
| C5×C4⋊#168 | 2 |
| #11716605 | 2 |
| #65316 | 5 |
| #65137 | 5 |