Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
448 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 118 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. C2×C5×#683 | C2 | semidirect |
| 3. C52×#95 | C2 | semidirect |
| 10. #64965 | C5 | direct (N × H) |
| 24. C2×#683 | C2×C5 | semidirect |
| 26. C5×#95 | D5 | semidirect |
| 27. C5×#95 | C2×C5 | semidirect |
| 78. #95 | C5×D5 | semidirect |
| 79. C52 | #396 | semidirect |
| 127. C5 | #64965 | direct (N × H) |
| 128. C5 | C5×#396 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#685 | 2 |
| C2×C5×#683 | 2 |
| C52×#95 | 2 |
| C5×#396 | 5 |
| #64965 | 5 |