Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
117 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 117 conjugacy classes of subgroups — too many to draw. Only its 37 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 |
|---|---|---|
| 71. C52 | #362 | semidirect |
| 105. C5 | #64785 | semidirect |
| 106. C5 | #64910 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×D5×Q16 | 2 |
| #11716838 | 2 |
| #11716833 | 2 |
| #64910 | 5 |
| #64785 | 5 |