Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
177 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 177 conjugacy classes of subgroups — too many to draw. Only its 87 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22×C25 | C2×D4 |
| commutator | C2×C4 | C23×C25 |
| Frattini, cosocle | C2×C4×C5 | C23×C5 |
| socle | C22×C5 | C2×C5×D4 |
| prime radical | C5×#127 | C2×C5 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C25 ◁ C42×C25 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C25×C4⋊Q8 | C2 | semidirect |
| 3. C25×#102 | C2 | semidirect |
| 4. C4×C8×C25 | C2 | semidirect |
| 44. #486 | C25 | direct (N × H) |
| 59. C4⋊Q8 | C2×C25 | semidirect |
| 61. #102 | C2×C25 | semidirect |
| 62. C4×C8 | C2×C25 | semidirect |
| 63. C25 | #486 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C25×C4⋊Q8 | 2 |
| C25×#127 | 2 |
| C25×#102 | 2 |
| C4×C8×C25 | 2 |
| C5×#486 | 5 |