Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
407 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 407 conjugacy classes of subgroups — too many to draw. Only its 105 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. C2×#87849 | C2 | semidirect |
| 3. C22⋊#6032 | C2 | semidirect |
| 4. #11716846 | C2 | semidirect |
| 13. C2×#6032 | C22 | semidirect |
| 44. C22×C52 | M16 | semidirect |
| 52. C2×C5×D5 | M16 | semidirect |
| 127. C52 | #407 | semidirect |
| 143. C22×C5 | #681 | semidirect |
| 144. C22×C5 | #700 | semidirect |
| 152. C2×D5 | #681 | semidirect |
| 208. C5 | #65496 | semidirect |
| 209. C5 | #65756 | semidirect |
| 219. C22 | #87849 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×C5×D5 | 2 |
| C2×#87849 | 2 |
| C22⋊#6032 | 2 |
| #11716846 | 2 |
| #65756 | 5 |
| #65496 | 5 |