Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
432 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 88 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×#6038 |
| commutator, cosocle | C2×C4×C52 | C23 |
| Frattini | C2×C4 | C2×D52 |
| Fitting | C42×C52 | C22 |
| socle | C22×C52 | C2×D4 |
| hypercenter | C42 | D52 |
| hypocenter | C52 | #493 |
| LCS | G ▷ C2×C4×C52 ▷ C2×C52 ▷ C52 | |
| UCS | C1 ◁ C22 ◁ C42 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11717194 | C2 | semidirect |
| 2. C5×#4020 | C2 | semidirect |
| 3. C2×#87771 | C2 | semidirect |
| 4. C4×C5×#168 | C2 | semidirect |
| 22. C5×#168 | D4 | semidirect |
| 29. #4020 | D5 | semidirect |
| 31. C4×#168 | D5 | semidirect |
| 37. C4×C52 | D8 | semidirect |
| 83. #168 | D20 | semidirect |
| 88. C52 | #493 | semidirect |
| 104. C4×C5 | D40 | semidirect |
| 105. C4×C5 | #686 | semidirect |
| 136. C5 | #64984 | semidirect |
| 137. C5 | #65362 | semidirect |
| 143. C4 | #87771 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11717194 | 2 |
| C5×#4020 | 2 |
| C2×#87771 | 2 |
| C4×C5×#168 | 2 |
| #65362 | 5 |
| #64984 | 5 |