Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
944 conjugacy classes of subgroups; only the 215 normal subgroups are shown.
This group has 944 conjugacy classes of subgroups — too many to draw. Only its 215 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×C5⋊D5 |
| commutator, socle, cosocle | C22×C52 | C24 |
| Fitting | C52×#124 | C2 |
| hypercenter | #124 | C5⋊D5 |
| hypocenter | C52 | #555 |
| LCS | G ▷ C22×C52 ▷ C52 | |
| UCS | C1 ◁ C22 ◁ #124 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C52×#124 | C2 | semidirect |
| 2. #11717267 | C2 | semidirect |
| 3. #11717264 | C2 | semidirect |
| 4. #11717259 | C2 | semidirect |
| 5. #11717205 | C2 | semidirect |
| 6. #11717204 | C2 | semidirect |
| 7. #11717201 | C2 | semidirect |
| 8. #11717197 | C2 | semidirect |
| 9. #11717192 | C2 | semidirect |
| 49. C5×#124 | D5 | semidirect |
| 118. #124 | C5⋊D5 | semidirect |
| 124. C52 | #555 | semidirect |
| 181. C5 | #66004 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C52×#124 | 2 |
| #11717267 | 2 |
| #11717264 | 2 |
| #11717259 | 2 |
| #11717205 | 2 |
| #11717204 | 2 |
| #11717201 | 2 |
| #11717197 | 2 |
| #11717192 | 2 |
| #66004 | 5 |