Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
392 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 392 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×#87870 | C2 | semidirect |
| 2. C2×#87800 | C2 | semidirect |
| 3. #11717027 | C2 | semidirect |
| 4. C2×#87771 | C2 | semidirect |
| 5. C5×#3953 | C2 | semidirect |
| 6. C5×#3952 | C2 | semidirect |
| 7. #11716608 | C2 | semidirect |
| 33. #6045 | D4 | semidirect |
| 37. C5×D20 | D4 | semidirect |
| 56. #3953 | D5 | semidirect |
| 57. #3952 | D5 | semidirect |
| 149. D20 | D20 | semidirect |
| 171. C52 | #449 | semidirect |
| 261. C5 | #65023 | semidirect |
| 262. C5 | #65070 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87870 | 2 |
| C2×#87800 | 2 |
| #11717027 | 2 |
| C2×#87771 | 2 |
| C5×#3953 | 2 |
| C5×#3952 | 2 |
| #11716608 | 2 |
| #65070 | 5 |
| #65023 | 5 |