Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
790 conjugacy classes of subgroups; only the 154 normal subgroups are shown.
This group has 790 conjugacy classes of subgroups — too many to draw. Only its 154 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 |
|---|---|---|
| 18. C5×H(3,ℤ/4) | C4 | semidirect |
| 19. #64777 | C4 | semidirect |
| 20. #64751 | C4 | semidirect |
| 95. C2×C5×C8 | C4⋊C4 | semidirect |
| 98. C42×C5 | C4⋊C4 | semidirect |
| 104. C4×Dic5 | C4⋊C4 | semidirect |
| 106. C2×#168 | C4⋊C4 | semidirect |
| 123. H(3,ℤ/4) | AGL(1,𝔽5) | semidirect |
| 245. C2×C8 | C4⋊AGL(1,𝔽5) | semidirect |
| 264. C42 | C4⋊AGL(1,𝔽5) | semidirect |
| 308. C5 | #11335 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10617409 | 2 |
| #10617128 | 2 |
| #10604753 | 2 |
| #10604376 | 2 |
| D5×H(3,ℤ/4) | 2 |
| #11335 | 5 |