Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
328 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 328 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 |
|---|---|---|
| 4. #11716885 | C2 | semidirect |
| 5. C8×#1043 | C2 | semidirect |
| 6. #11716764 | C2 | semidirect |
| 7. #11716761 | C2 | semidirect |
| 14. #87834 | C4 | semidirect |
| 17. C5×#676 | C4 | semidirect |
| 18. #87768 | C4 | semidirect |
| 29. #6034 | C2×C4 | semidirect |
| 30. #6033 | C2×C4 | semidirect |
| 31. C52×C8 | C2×C4 | semidirect |
| 32. #6029 | C2×C4 | semidirect |
| 33. C5×#168 | C2×C4 | semidirect |
| 46. #1043 | M16 | semidirect |
| 64. #676 | AGL(1,𝔽5) | semidirect |
| 89. C5×C8 | C2×AGL(1,𝔽5) | semidirect |
| 92. #168 | C2×AGL(1,𝔽5) | semidirect |
| 100. C52 | C4×M16 | semidirect |
| 145. C8 | D5⋊AGL(1,𝔽5) | semidirect |
| 147. C5 | M16×AGL(1,𝔽5) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D5⋊AGL(1,𝔽5) | 2 |
| #11717361 | 2 |
| #11716909 | 2 |
| #11716885 | 2 |
| C8×#1043 | 2 |
| #11716764 | 2 |
| #11716761 | 2 |
| M16×AGL(1,𝔽5) | 5 |