Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
808 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 808 conjugacy classes of subgroups — too many to draw. Only its 120 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. C22×#6036 | C2 | semidirect |
| 3. C2×C5×C22⋊Dic5 | C2 | semidirect |
| 4. C2×#87779 | C2 | semidirect |
| 5. #11716620 | C2 | semidirect |
| 10. C2×C22⋊(C5⋊D5) | C4 | semidirect |
| 23. C23×C52 | C2×C4 | semidirect |
| 33. C2×#1039 | C2×C4 | semidirect |
| 39. C2×C5×Dic5 | D4 | semidirect |
| 45. C2×C22⋊Dic5 | D5 | semidirect |
| 63. C2×C5⋊D5 | C22⋊C4 | semidirect |
| 109. C23×C5 | C4×D5 | semidirect |
| 142. C2×Dic5 | C22⋊D5 | semidirect |
| 149. C52 | #386 | semidirect |
| 229. C23 | #6036 | semidirect |
| 243. C5 | #65245 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C22⋊(C5⋊D5) | 2 |
| C22×#6036 | 2 |
| C2×C5×C22⋊Dic5 | 2 |
| C2×#87779 | 2 |
| #11716620 | 2 |
| #65245 | 5 |