Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
456 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 127 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. C2×#87802 | C2 | semidirect |
| 4. C52×#107 | C2 | semidirect |
| 5. #11716677 | C2 | semidirect |
| 30. C5×#107 | D5 | semidirect |
| 35. C2×C5⋊D5 | Q16 | semidirect |
| 69. #107 | C5⋊D5 | semidirect |
| 71. C52 | #467 | semidirect |
| 105. C5 | #65176 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87802 | 2 |
| C2×C8×C5⋊D5 | 2 |
| #11717217 | 2 |
| C52×#107 | 2 |
| #11716677 | 2 |
| #65176 | 5 |