Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
418 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 66 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 |
|---|---|---|
| 1. C2×#87871 | C2 | semidirect |
| 2. #11717215 | C2 | semidirect |
| 3. C2×#87774 | C2 | semidirect |
| 4. C2×#87771 | C2 | semidirect |
| 5. C5×#3942 | C2 | semidirect |
| 6. C5×#3941 | C2 | semidirect |
| 7. #11716598 | C2 | semidirect |
| 38. C5×D20 | D4 | semidirect |
| 40. C5×Dic10 | D4 | semidirect |
| 58. #3942 | D5 | semidirect |
| 59. #3941 | D5 | semidirect |
| 153. D20 | D20 | semidirect |
| 162. Dic10 | D20 | semidirect |
| 174. C52 | #449 | semidirect |
| 269. C5 | #65070 | semidirect |
| 270. C5 | #65100 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87871 | 2 |
| #11717215 | 2 |
| C2×#87774 | 2 |
| C2×#87771 | 2 |
| C5×#3942 | 2 |
| C5×#3941 | 2 |
| #11716598 | 2 |
| #65100 | 5 |
| #65070 | 5 |