Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
264 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 66 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. C2×#87775 | C2 | semidirect |
| 5. #11716674 | C2 | semidirect |
| 6. C5×#3942 | C2 | semidirect |
| 7. #11716607 | C2 | semidirect |
| 49. #3942 | D5 | semidirect |
| 56. C2×C5×D5 | Q16 | semidirect |
| 139. C52 | #467 | semidirect |
| 148. C2×D5 | #689 | semidirect |
| 207. C5 | #65102 | semidirect |
| 208. C5 | #65340 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4043 | 2 |
| #11716974 | 2 |
| C2×#87775 | 2 |
| C2×D5×#168 | 2 |
| #11716674 | 2 |
| C5×#3942 | 2 |
| #11716607 | 2 |
| #65340 | 5 |
| #65102 | 5 |