Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
672 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 672 conjugacy classes of subgroups — too many to draw. Only its 111 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. #11717517 | C2 | semidirect |
| 2. #11717260 | C2 | semidirect |
| 3. #11717228 | C2 | semidirect |
| 4. C52×#100 | C2 | semidirect |
| 5. #11716692 | C2 | semidirect |
| 12. C2×C4⋊(C5⋊D5) | C22 | semidirect |
| 13. C52×M16 | C22 | semidirect |
| 14. C4×#1039 | C22 | semidirect |
| 29. C4⋊(C5⋊D5) | D4 | semidirect |
| 31. #6045 | D4 | semidirect |
| 36. C5×#100 | D5 | semidirect |
| 55. C5×M16 | C2×D5 | semidirect |
| 84. #100 | C5⋊D5 | semidirect |
| 85. C52 | #453 | semidirect |
| 105. M16 | C2×C5⋊D5 | semidirect |
| 127. C5 | #65036 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11717517 | 2 |
| #11717260 | 2 |
| #11717228 | 2 |
| C52×#100 | 2 |
| #11716692 | 2 |
| #65036 | 5 |