Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
320 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 320 conjugacy classes of subgroups — too many to draw. Only its 86 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 |
| 2. C5×#4093 | C2 | semidirect |
| 3. C2×C5×#688 | C2 | semidirect |
| 5. C5×C8×Dic5 | C2 | semidirect |
| 16. #65480 | C5 | direct (N × H) |
| 28. C2×C5×Q16 | D5 | semidirect |
| 29. C2×C5×Q16 | C2×C5 | semidirect |
| 33. #4093 | C2×C5 | semidirect |
| 34. C2×#688 | C2×C5 | semidirect |
| 37. C8×Dic5 | C2×C5 | semidirect |
| 95. C2×Q16 | C5×D5 | semidirect |
| 100. C52 | #495 | semidirect |
| 147. C5 | #65480 | direct (N × H) |
| 148. C5 | C5×#495 | 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×#4093 | 2 |
| C2×C5×#688 | 2 |
| C2×C5×D40 | 2 |
| C5×C8×Dic5 | 2 |
| C5×#495 | 5 |
| #65480 | 5 |