Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
551 conjugacy classes of subgroups; only the 276 normal subgroups are shown.
This group has 551 conjugacy classes of subgroups — too many to draw. Only its 276 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 |
|---|---|---|
| 2. C5×Q8×AGL(1,𝔽5) | C2 | semidirect |
| 4. C2×C52×Q8 | C4 | semidirect |
| 5. C5×Q8×D5 | C4 | semidirect |
| 8. C2×C5×Dic10 | C4 | semidirect |
| 12. #66262 | C5 | direct (N × H) |
| 24. Q8×AGL(1,𝔽5) | C2×C5 | semidirect |
| 39. C2×C5×Q8 | C4×C5 | semidirect |
| 40. C2×C5×Q8 | AGL(1,𝔽5) | semidirect |
| 42. Q8×D5 | C4×C5 | semidirect |
| 45. C2×Dic10 | C4×C5 | semidirect |
| 78. C52 | #519 | semidirect |
| 98. C2×Q8 | C5×AGL(1,𝔽5) | semidirect |
| 122. C5 | C5×#519 | semidirect |
| 123. C5 | #66262 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×Q8×D5 | 2 |
| C5×Q8×AGL(1,𝔽5) | 2 |
| C5×#4130 | 2 |
| #66262 | 5 |
| C5×#519 | 5 |