Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
552 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 99 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. C22×#3932 | C2 | semidirect |
| 2. C2×#65185 | C2 | semidirect |
| 4. C2×#64728 | C2 | semidirect |
| 5. C2×#64715 | C2 | semidirect |
| 6. #10601447 | C2 | semidirect |
| 7. C5×#1382 | C2 | semidirect |
| 45. C2×Dic20 | D4 | semidirect |
| 65. C2×C5×C16 | D4 | semidirect |
| 67. C5×#108 | D4 | semidirect |
| 82. #1382 | D5 | semidirect |
| 239. C2×C16 | D20 | semidirect |
| 241. #108 | D20 | semidirect |
| 365. C5 | #13321 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#3932 | 2 |
| C2×#65185 | 2 |
| #10610914 | 2 |
| C2×#64728 | 2 |
| C2×#64715 | 2 |
| #10601447 | 2 |
| C5×#1382 | 2 |
| #13321 | 5 |