Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
244 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 244 conjugacy classes of subgroups — too many to draw. Only its 53 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C23 | D52⋊C2 |
| commutator | #1039 | C42 |
| Fitting, socle, prime radical | C23×C52 | D4 |
| cosocle | C22×#1039 | C22 |
| hypocenter | C52 | #340 |
| LCS | G ▷ #1039 ▷ C2×C52 ▷ C52 | |
| UCS | C1 ◁ C23 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 6. C2×#6034 | C4 | semidirect |
| 8. #87781 | C4 | semidirect |
| 64. C52 | #340 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6034 | 2 |
| C2×#87781 | 2 |
| #340 | 25 |