Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
294 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 110 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. #11716732 | C2 | semidirect |
| 5. AGL(1,𝔽5)×#168 | C2 | semidirect |
| 8. #87853 | C4 | semidirect |
| 9. #87849 | C4 | semidirect |
| 14. #87804 | C4 | semidirect |
| 15. C5×#681 | C4 | semidirect |
| 16. #87768 | C4 | semidirect |
| 30. #6032 | C2×C4 | semidirect |
| 31. #6029 | C2×C4 | semidirect |
| 32. C5×#168 | C2×C4 | semidirect |
| 48. C5×AGL(1,𝔽5) | M16 | semidirect |
| 73. #681 | AGL(1,𝔽5) | direct (N × H) |
| 110. #168 | C2×AGL(1,𝔽5) | semidirect |
| 116. C52 | C4×M16 | semidirect |
| 127. AGL(1,𝔽5) | #681 | direct (N × H) |
| 176. C5 | C4×#681 | semidirect |
| 177. 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 |
|---|---|
| D5⋊#681 | 2 |
| C2×C4×C5×AGL(1,𝔽5) | 2 |
| D5×#681 | 2 |
| #11716732 | 2 |
| AGL(1,𝔽5)×#168 | 2 |
| M16×AGL(1,𝔽5) | 5 |
| C4×#681 | 5 |