Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
230 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 79 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. C5×#1579 | C2 | semidirect |
| 4. #10598255 | C2 | semidirect |
| 6. #10597955 | C2 | semidirect |
| 7. #10597933 | C2 | semidirect |
| 37. #3960 | C8 | semidirect |
| 47. #1579 | D5 | semidirect |
| 56. C5×Q16 | C2×C8 | semidirect |
| 74. #672 | C2×C8 | semidirect |
| 146. Q16 | C8×D5 | semidirect |
| 189. C5 | #12065 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#1579 | 2 |
| #10601706 | 2 |
| #10598870 | 2 |
| #10598255 | 2 |
| #10597956 | 2 |
| #10597955 | 2 |
| #10597933 | 2 |
| #12065 | 5 |