Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
275 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 275 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×#87829 | C2 | semidirect |
| 2. C2×#87827 | C2 | semidirect |
| 4. #11716845 | C2 | semidirect |
| 5. C5×#4004 | C2 | semidirect |
| 6. #11716754 | C2 | semidirect |
| 7. #11716754 | C2 | semidirect |
| 36. #6032 | D4 | semidirect |
| 45. #4004 | D5 | semidirect |
| 59. C2×C5⋊D5 | M16 | semidirect |
| 142. C52 | #435 | semidirect |
| 222. C5 | #65125 | semidirect |
| 223. C5 | #65704 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87829 | 2 |
| C2×#87827 | 2 |
| #11717013 | 2 |
| #11716845 | 2 |
| C5×#4004 | 2 |
| #11716754 | 2 |
| #65704 | 5 |
| #65125 | 5 |