Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
238 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 104 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. Q8×#674 | C2 | semidirect |
| 4. Q8⋊#674 | C2 | semidirect |
| 6. #10598522 | C2 | semidirect |
| 7. C8×#674 | C2 | semidirect |
| 55. C5×SD16 | C16 | semidirect |
| 75. #674 | SD16 | direct (N × H) |
| 93. C5×Q8 | C2×C16 | semidirect |
| 105. C5×C8 | C2×C16 | semidirect |
| 148. SD16 | #674 | direct (N × H) |
| 175. Q8 | C2×#674 | semidirect |
| 193. C8 | C2×#674 | semidirect |
| 194. C5 | C16×SD16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#674 | 2 |
| D4×#674 | 2 |
| SD16×#168 | 2 |
| Q8⋊#674 | 2 |
| D4⋊#674 | 2 |
| #10598522 | 2 |
| C8×#674 | 2 |
| C16×SD16 | 5 |