Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
944 conjugacy classes of subgroups; only the 243 normal subgroups are shown.
This group has 944 conjugacy classes of subgroups — too many to draw. Only its 243 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×C4⋊Q8 | C2 |
| hypercenter | C4⋊Q8 | C5⋊D5 |
| hypocenter | C52 | #555 |
| LCS | G ▷ C22×C52 ▷ C52 | |
| UCS | C1 ◁ C22 ◁ C4⋊Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C52×C4⋊Q8 | C2 | semidirect |
| 2. #11717267 | C2 | semidirect |
| 3. #11717215 | C2 | semidirect |
| 4. #11717212 | C2 | semidirect |
| 5. C4×C4⋊(C5⋊D5) | C2 | semidirect |
| 26. C5×C4⋊Q8 | D5 | semidirect |
| 62. C4⋊Q8 | C5⋊D5 | semidirect |
| 67. C52 | #555 | semidirect |
| 98. C5 | #66068 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C52×C4⋊Q8 | 2 |
| #11717267 | 2 |
| #11717215 | 2 |
| #11717212 | 2 |
| C4×C4⋊(C5⋊D5) | 2 |
| #66068 | 5 |