Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
688 conjugacy classes of subgroups; only the 382 normal subgroups are shown.
This group has 688 conjugacy classes of subgroups — too many to draw. Only its 382 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. C5×Q8×Dic5 | C2 | semidirect |
| 4. C2×C52×Q8 | C4 | semidirect |
| 11. #66146 | C5 | direct (N × H) |
| 22. Q8×Dic5 | C2×C5 | semidirect |
| 31. C2×C5×Q8 | Dic5 | semidirect |
| 32. C2×C5×Q8 | C4×C5 | semidirect |
| 65. C52 | #519 | semidirect |
| 80. C2×Q8 | C5×Dic5 | semidirect |
| 101. C5 | #66146 | direct (N × H) |
| 102. C5 | C5×#519 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C52×Q8 | 2 |
| C5×Q8×Dic5 | 2 |
| C5×#4072 | 2 |
| C5×#519 | 5 |
| #66146 | 5 |