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. C52×#127 | C2 | semidirect |
| 3. #11717252 | C2 | semidirect |
| 4. #11716700 | C2 | semidirect |
| 5. #11716672 | C2 | semidirect |
| 8. C2×C52×D4 | C22 | semidirect |
| 13. C42×C52 | C22 | semidirect |
| 16. #87804 | C22 | semidirect |
| 29. C4⋊(C5⋊D5) | D4 | semidirect |
| 31. #6045 | D4 | semidirect |
| 34. C5×#127 | D5 | semidirect |
| 50. C2×C5×D4 | C2×D5 | semidirect |
| 55. C42×C5 | C2×D5 | semidirect |
| 82. #127 | C5⋊D5 | semidirect |
| 85. C52 | #453 | semidirect |
| 102. C2×D4 | C2×C5⋊D5 | semidirect |
| 106. C42 | C2×C5⋊D5 | semidirect |
| 127. C5 | #65366 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11717517 | 2 |
| C52×#127 | 2 |
| #11717252 | 2 |
| #11716700 | 2 |
| #11716672 | 2 |
| #65366 | 5 |