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. #11717425 | C2 | semidirect |
| 3. C5×D5⋊M16 | C2 | semidirect |
| 4. #11716738 | C2 | semidirect |
| 5. C2×#6045 | C4 | semidirect |
| 6. C2×C5×D20 | C4 | semidirect |
| 12. #87870 | C4 | semidirect |
| 16. C4×#1042 | C22 | semidirect |
| 18. C5×#700 | C22 | semidirect |
| 44. D5⋊M16 | D5 | semidirect |
| 74. C2×D20 | AGL(1,𝔽5) | semidirect |
| 84. #700 | C2×D5 | semidirect |
| 144. C52 | #421 | semidirect |
| 220. C5 | #65428 | 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 |
| #11717425 | 2 |
| C5×D5⋊M16 | 2 |
| #11716738 | 2 |
| #65769 | 5 |
| #65428 | 5 |