Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
153 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 153 conjugacy classes of subgroups — too many to draw. Only its 55 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. C25×#125 | C2 | semidirect |
| 5. #11716356 | C2 | semidirect |
| 6. #11716355 | C2 | semidirect |
| 7. C4⋊#6014 | C2 | semidirect |
| 78. #125 | D25 | semidirect |
| 85. C25 | #478 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C25×#125 | 2 |
| C4×D100 | 2 |
| #11716358 | 2 |
| #11716356 | 2 |
| #11716355 | 2 |
| C4⋊#6014 | 2 |
| #65355 | 5 |