Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
294 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 106 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 |
|---|---|---|
| 4. #11716733 | C2 | semidirect |
| 5. #11716731 | C2 | semidirect |
| 11. C5×#704 | C4 | semidirect |
| 12. C5×#700 | C4 | semidirect |
| 14. #87804 | C4 | semidirect |
| 15. C5×#681 | C4 | semidirect |
| 16. #87768 | C4 | semidirect |
| 30. C5×#170 | C2×C4 | semidirect |
| 31. #6029 | C2×C4 | semidirect |
| 32. C5×#168 | C2×C4 | semidirect |
| 48. #1042 | M16 | semidirect |
| 57. #704 | Dic5 | semidirect |
| 61. #700 | Dic5 | semidirect |
| 74. #681 | AGL(1,𝔽5) | semidirect |
| 104. #170 | C2×Dic5 | semidirect |
| 110. #168 | C2×AGL(1,𝔽5) | semidirect |
| 116. C52 | C4×M16 | semidirect |
| 176. C5 | M16×Dic5 | semidirect |
| 177. C5 | M16×AGL(1,𝔽5) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×#1042 | 2 |
| C5×D5⋊M16 | 2 |
| D5×#681 | 2 |
| #11716733 | 2 |
| #11716731 | 2 |
| M16×AGL(1,𝔽5) | 5 |
| M16×Dic5 | 5 |