Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
179 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 179 conjugacy classes of subgroups — too many to draw. Only its 45 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 |
|---|---|---|
| 5. C2×C52×Q8 | C4 | semidirect |
| 9. C5×C4⋊Dic5 | C4 | semidirect |
| 42. C2×C5×Q8 | Dic5 | semidirect |
| 43. C2×C5×Q8 | AGL(1,𝔽5) | semidirect |
| 52. C4⋊Dic5 | Dic5 | semidirect |
| 89. C52 | #328 | semidirect |
| 113. C2×Q8 | #1042 | semidirect |
| 145. C5 | #64758 | semidirect |
| 146. C5 | #64926 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4092 | 2 |
| #11716849 | 2 |
| #11716846 | 2 |
| #64926 | 5 |
| #64758 | 5 |