Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
311 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 311 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 3. #11716848 | C2 | semidirect |
| 68. C5×D5 | #101 | semidirect |
| 101. C52 | C2×#101 | semidirect |
| 140. D5 | #3968 | semidirect |
| 155. C5 | C2×#3968 | semidirect |
| 156. C5 | D5⋊#101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×Q8×D5 | 2 |
| D5⋊#681 | 2 |
| #11716848 | 2 |
| D5⋊#101 | 5 |
| C2×#3968 | 5 |