Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
257 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 257 conjugacy classes of subgroups — too many to draw. Only its 83 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×#87849 | C2 | semidirect |
| 3. #11716846 | C2 | semidirect |
| 4. C4⋊#6032 | C2 | semidirect |
| 5. C4×#6032 | C2 | semidirect |
| 27. #6032 | D4 | semidirect |
| 43. C4×C52 | M16 | semidirect |
| 100. C52 | #436 | semidirect |
| 117. C4×C5 | #681 | semidirect |
| 118. C4×C5 | #700 | semidirect |
| 154. C5 | #65301 | semidirect |
| 155. C5 | #65705 | semidirect |
| 164. C4 | #87849 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87849 | 2 |
| C5×#4039 | 2 |
| #11716846 | 2 |
| C4⋊#6032 | 2 |
| C4×#6032 | 2 |
| #65705 | 5 |
| #65301 | 5 |