Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
384 conjugacy classes of subgroups; only the 232 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 232 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C22×C52 | C2×D4 |
| commutator, Frattini, cosocle | C2×C4 | C23×C52 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C52 ◁ C42×C52 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 15. C5×#477 | C5 | direct (N × H) |
| 18. C52×Q8 | Q8 | semidirect |
| 48. #477 | C52 | direct (N × H) |
| 54. C5×Q8 | C5×Q8 | semidirect |
| 67. C52 | #477 | direct (N × H) |
| 90. Q8 | C52×Q8 | semidirect |
| 98. C5 | C5×#477 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C52×C4⋊Q8 | 2 |
| C4×C52×Q8 | 2 |
| C52×#107 | 2 |
| C52×C4⋊C8 | 2 |
| C52×#103 | 2 |
| C5×#477 | 5 |