Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
280 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 82 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. C2×C52×Q16 | C2 | semidirect |
| 4. C5×#3967 | C2 | semidirect |
| 5. C5×#3949 | C2 | semidirect |
| 16. #65478 | C5 | direct (N × H) |
| 29. C2×C5×Q16 | D5 | semidirect |
| 30. C2×C5×Q16 | C2×C5 | semidirect |
| 37. #3967 | C2×C5 | semidirect |
| 38. #3949 | C2×C5 | semidirect |
| 99. C2×Q16 | C5×D5 | semidirect |
| 104. C52 | #470 | semidirect |
| 154. C5 | #65478 | direct (N × H) |
| 155. C5 | C5×#470 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C52×Q16 | 2 |
| C5×#4092 | 2 |
| C2×C5×#676 | 2 |
| C5×#3967 | 2 |
| C5×#3949 | 2 |
| C5×#470 | 5 |
| #65478 | 5 |