Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
480 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 141 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. #11717189 | C2 | semidirect |
| 4. C52×C4⋊C8 | C2 | semidirect |
| 5. #11716683 | C2 | semidirect |
| 32. C5×C4⋊C8 | D5 | semidirect |
| 39. C4×C52 | SD16 | semidirect |
| 74. C4⋊C8 | C5⋊D5 | semidirect |
| 76. C52 | #461 | semidirect |
| 82. C4×C5 | #677 | semidirect |
| 113. C5 | #65130 | semidirect |
| 121. C4 | #87800 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87800 | 2 |
| C4×C4⋊(C5⋊D5) | 2 |
| #11717189 | 2 |
| C52×C4⋊C8 | 2 |
| #11716683 | 2 |
| #65130 | 5 |