Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
522 conjugacy classes of subgroups; only the 130 normal subgroups are shown.
This group has 522 conjugacy classes of subgroups — too many to draw. Only its 130 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. C5×#4072 | C2 | semidirect |
| 3. C5×#4070 | C2 | semidirect |
| 5. #11717074 | C2 | semidirect |
| 6. #11717018 | C2 | semidirect |
| 7. #11716991 | C2 | semidirect |
| 8. #11716990 | C2 | semidirect |
| 9. #11716986 | C2 | semidirect |
| 10. #11716961 | C2 | semidirect |
| 11. #11716954 | C2 | semidirect |
| 60. #4072 | D5 | semidirect |
| 61. #4070 | D5 | semidirect |
| 204. C52 | #552 | semidirect |
| 304. C5 | #65863 | semidirect |
| 305. C5 | #65973 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C22⋊(C5⋊D5) | 2 |
| C5×#4072 | 2 |
| C5×#4070 | 2 |
| #11717093 | 2 |
| #11717074 | 2 |
| #11717018 | 2 |
| #11716991 | 2 |
| #11716990 | 2 |
| #11716986 | 2 |
| #11716961 | 2 |
| #11716954 | 2 |
| #65973 | 5 |
| #65863 | 5 |