Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
776 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 776 conjugacy classes of subgroups — too many to draw. Only its 114 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, socle, cosocle | C23×C52 | C23 |
| Fitting | C22×C4×C52 | C22 |
| hypercenter | C22×C4 | D52 |
| hypocenter | C52 | #392 |
| LCS | G ▷ C23×C52 ▷ C52 | |
| UCS | C1 ◁ C23 ◁ C22×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×C5×D20 | C2 | semidirect |
| 2. C22×#6038 | C2 | semidirect |
| 3. C2×#87808 | C2 | semidirect |
| 4. C2×#87778 | C2 | semidirect |
| 5. C5×#3963 | C2 | semidirect |
| 25. C22×C5⋊D5 | D4 | semidirect |
| 32. C22×C5×D5 | D4 | semidirect |
| 34. C2×C4×C52 | D4 | semidirect |
| 39. C2×C5×Dic5 | D4 | semidirect |
| 45. C22×D20 | D5 | semidirect |
| 52. #3963 | D5 | semidirect |
| 140. C22×D5 | C22⋊D5 | semidirect |
| 149. C2×C4×C5 | D20 | semidirect |
| 150. C2×C4×C5 | C22⋊D5 | semidirect |
| 160. C2×Dic5 | D20 | semidirect |
| 168. C52 | #392 | semidirect |
| 274. C2×C4 | #6038 | semidirect |
| 276. C5 | #64960 | semidirect |
| 277. C5 | #65512 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×D20 | 2 |
| C22×#6038 | 2 |
| C2×#87808 | 2 |
| C2×#87778 | 2 |
| C5×#3963 | 2 |
| #65512 | 5 |
| #64960 | 5 |