Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
239 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 239 conjugacy classes of subgroups — too many to draw. Only its 92 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 |
|---|---|---|
| 6. C5×C4⋊AGL(1,𝔽5) | C4 | semidirect |
| 7. C2×C52×C8 | C4 | semidirect |
| 8. C2×C5×#168 | C4 | semidirect |
| 10. #64893 | C5 | direct (N × H) |
| 40. C4⋊AGL(1,𝔽5) | C4×C5 | semidirect |
| 44. C2×C5×C8 | C4×C5 | semidirect |
| 45. C2×C5×C8 | AGL(1,𝔽5) | semidirect |
| 48. C2×#168 | C4×C5 | semidirect |
| 80. C52 | #340 | semidirect |
| 106. C2×C8 | C5×AGL(1,𝔽5) | semidirect |
| 133. C5 | C5×#340 | semidirect |
| 134. C5 | #64893 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×C4⋊AGL(1,𝔽5) | 2 |
| C2×C5×C8×D5 | 2 |
| #64893 | 5 |
| C5×#340 | 5 |