Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
424 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 82 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. #11717441 | C2 | semidirect |
| 3. #11716878 | C2 | semidirect |
| 4. #11716864 | C2 | semidirect |
| 5. C8×#1043 | C2 | semidirect |
| 12. C52×Q16 | C4 | semidirect |
| 13. #87811 | C4 | semidirect |
| 14. #87801 | C4 | semidirect |
| 45. C5×Q16 | AGL(1,𝔽5) | semidirect |
| 69. C52 | #443 | semidirect |
| 77. Q16 | #1043 | semidirect |
| 100. C5 | #65740 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11717441 | 2 |
| #11717239 | 2 |
| #11716878 | 2 |
| #11716864 | 2 |
| C8×#1043 | 2 |
| #65740 | 5 |