Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
327 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 327 conjugacy classes of subgroups — too many to draw. Only its 74 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 |
|---|---|---|
| 2. D5⋊#681 | C2 | semidirect |
| 3. C5×#4130 | C2 | semidirect |
| 4. #11716739 | C2 | semidirect |
| 5. C2×#6045 | C4 | semidirect |
| 6. C2×C5×D20 | C4 | semidirect |
| 12. #87870 | C4 | semidirect |
| 15. #87849 | C22 | semidirect |
| 19. C4×C5×AGL(1,𝔽5) | C22 | semidirect |
| 43. #4130 | D5 | semidirect |
| 74. C2×D20 | AGL(1,𝔽5) | semidirect |
| 83. C4×AGL(1,𝔽5) | C2×D5 | semidirect |
| 144. C52 | #421 | semidirect |
| 220. C5 | #65294 | semidirect |
| 221. C5 | #65769 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87870 | 2 |
| D5⋊#681 | 2 |
| C5×#4130 | 2 |
| #11716739 | 2 |
| #65769 | 5 |
| #65294 | 5 |