Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
818 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 818 conjugacy classes of subgroups — too many to draw. Only its 159 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 |
|---|---|---|
| 3. C5×#1394 | C2 | semidirect |
| 4. #10598190 | C2 | semidirect |
| 5. #10598135 | C2 | semidirect |
| 18. D5×#101 | C4 | semidirect |
| 51. C5×#101 | C2×C4 | semidirect |
| 54. #3968 | C2×C4 | semidirect |
| 63. #1394 | D5 | direct (N × H) |
| 220. #101 | C4×D5 | semidirect |
| 312. D5 | #1394 | direct (N × H) |
| 364. C5 | C2×#1394 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D5×#101 | 2 |
| D5×#391 | 2 |
| C5×#1394 | 2 |
| #10598190 | 2 |
| #10598135 | 2 |
| C2×#1394 | 5 |