Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
382 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 382 conjugacy classes of subgroups — too many to draw. Only its 64 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. C5×#4144 | C2 | semidirect |
| 2. C5×#4086 | C2 | semidirect |
| 3. #11716941 | C2 | semidirect |
| 4. #11716700 | C2 | semidirect |
| 5. #11716610 | C2 | semidirect |
| 12. C2×C5×D20 | C22 | semidirect |
| 13. #87804 | C22 | semidirect |
| 14. C4×C5×Dic5 | C22 | semidirect |
| 30. C5×D20 | D4 | semidirect |
| 32. C5×Dic10 | D4 | semidirect |
| 35. #4144 | D5 | semidirect |
| 38. #4086 | D5 | semidirect |
| 69. C2×D20 | C2×D5 | semidirect |
| 75. C4×Dic5 | C2×D5 | semidirect |
| 113. D20 | C22⋊D5 | semidirect |
| 115. Dic10 | C22⋊D5 | semidirect |
| 124. C52 | #453 | semidirect |
| 189. C5 | #65366 | semidirect |
| 190. C5 | #65530 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4144 | 2 |
| C5×#4086 | 2 |
| #11716941 | 2 |
| #11716700 | 2 |
| #11716610 | 2 |
| #65530 | 5 |
| #65366 | 5 |