Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
480 conjugacy classes of subgroups; only the 136 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 136 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 |
|---|---|---|
| 4. #11716608 | C2 | direct (N × H) |
| 9. C2×#6045 | C4 | semidirect |
| 27. #6045 | C2×C4 | semidirect |
| 78. C2×C52 | #103 | semidirect |
| 122. C52 | C2×#103 | semidirect |
| 164. C2×C5 | #3942 | semidirect |
| 165. C2×C5 | #3948 | semidirect |
| 186. C5 | C2×#3942 | semidirect |
| 187. C5 | C2×#3948 | semidirect |
| 197. C2 | #11716608 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6045 | 2 |
| C2×C5×C4⋊Dic5 | 2 |
| C22×C5×#168 | 2 |
| #11716608 | 2 |
| C2×#3948 | 5 |
| C2×#3942 | 5 |