Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
552 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 101 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×C5×#473 | C2 | semidirect |
| 2. C22×#3960 | C2 | semidirect |
| 4. #10602854 | C2 | semidirect |
| 5. C2×#64781 | C2 | semidirect |
| 6. C2×#64715 | C2 | semidirect |
| 7. #10598220 | C2 | semidirect |
| 41. C2×C5×Q16 | D4 | semidirect |
| 64. C5×#108 | D4 | semidirect |
| 75. C2×#672 | D4 | semidirect |
| 77. C2×#473 | D5 | semidirect |
| 211. C2×Q16 | C22⋊D5 | semidirect |
| 241. #108 | C22⋊D5 | semidirect |
| 365. C5 | #13321 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#473 | 2 |
| C22×#3960 | 2 |
| #10615530 | 2 |
| #10602854 | 2 |
| C2×#64781 | 2 |
| C2×#64715 | 2 |
| #10598220 | 2 |
| #13321 | 5 |