Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
888 conjugacy classes of subgroups; only the 253 normal subgroups are shown.
This group has 888 conjugacy classes of subgroups — too many to draw. Only its 253 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. C4×C52×Q8 | C2 | semidirect |
| 3. #11717264 | C2 | semidirect |
| 6. #11717209 | C2 | semidirect |
| 7. #11717208 | C2 | semidirect |
| 10. C4×#6045 | C2 | semidirect |
| 11. C4×#6045 | C2 | semidirect |
| 50. C4×C5⋊D5 | Q8 | semidirect |
| 53. C4×C5×Q8 | D5 | semidirect |
| 131. C4×Q8 | C5⋊D5 | semidirect |
| 134. C52 | #533 | semidirect |
| 193. C5 | #65912 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C52×Q8 | 2 |
| #11717266 | 2 |
| #11717264 | 2 |
| #11717217 | 2 |
| #11717216 | 2 |
| #11717209 | 2 |
| #11717208 | 2 |
| #11717192 | 2 |
| C42×C5⋊D5 | 2 |
| C4×#6045 | 2 |
| #65912 | 5 |