Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
248 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 74 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 |
|---|---|---|
| 2. #11716933 | C2 | semidirect |
| 3. #11716682 | C2 | semidirect |
| 4. C5×#3951 | C2 | semidirect |
| 5. #11716609 | C2 | semidirect |
| 11. C5×Dic20 | C4 | semidirect |
| 12. C5×D40 | C4 | semidirect |
| 13. C5×#677 | C4 | semidirect |
| 35. #3951 | D5 | semidirect |
| 63. Dic20 | Dic5 | semidirect |
| 64. D40 | Dic5 | semidirect |
| 65. #677 | Dic5 | semidirect |
| 102. C52 | #444 | semidirect |
| 148. C5 | #65183 | semidirect |
| 149. C5 | #65486 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4050 | 2 |
| #11716933 | 2 |
| #11716682 | 2 |
| C5×#3951 | 2 |
| #11716609 | 2 |
| #65486 | 5 |
| #65183 | 5 |