Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
704 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 704 conjugacy classes of subgroups — too many to draw. Only its 144 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C2×D52 |
| commutator | C22×C52 | C22×C4 |
| Fitting, prime radical | C24×C52 | C22 |
| socle, cosocle | C23×C52 | C23 |
| hypercenter | C24 | D52 |
| hypocenter | C52 | #380 |
| LCS | G ▷ C22×C52 ▷ C52 | |
| UCS | C1 ◁ C23 ◁ C24 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C2×#87781 | C2 | semidirect |
| 4. #11716620 | C2 | semidirect |
| 7. C22×#1039 | C4 | semidirect |
| 38. C22×C52 | C4⋊C4 | semidirect |
| 45. #1039 | C22⋊C4 | semidirect |
| 101. C52 | #380 | semidirect |
| 116. C22×C5 | #683 | semidirect |
| 163. C5 | #65231 | semidirect |
| 168. C22 | #87781 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#1039 | 2 |
| C2×C5×C22⋊Dic5 | 2 |
| C2×#87781 | 2 |
| #11716620 | 2 |
| #65231 | 5 |