Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
316 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 72 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 |
|---|---|---|
| 1. #11717189 | C2 | semidirect |
| 3. C2×#87776 | C2 | semidirect |
| 5. C5×#3935 | C2 | semidirect |
| 37. #3935 | D5 | semidirect |
| 100. C52 | #497 | semidirect |
| 147. C5 | #65004 | semidirect |
| 148. C5 | #65349 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11717189 | 2 |
| C5×#4021 | 2 |
| C2×#87776 | 2 |
| C2×#87773 | 2 |
| C5×#3935 | 2 |
| #65349 | 5 |
| #65004 | 5 |