Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
952 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 952 conjugacy classes of subgroups — too many to draw. Only its 221 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 | C22×C5⋊D5 |
| commutator, socle, cosocle | C23×C52 | C23 |
| Fitting, prime radical | C22×C52×D4 | C2 |
| hypercenter | C22×D4 | C5⋊D5 |
| hypocenter | C52 | #394 |
| LCS | G ▷ C23×C52 ▷ C52 | |
| UCS | C1 ◁ C23 ◁ C22×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C22⋊#1039 | C2 | semidirect |
| 3. C2×C22⋊#1039 | C2 | semidirect |
| 4. C2×#87806 | C2 | semidirect |
| 5. #11716698 | C2 | semidirect |
| 35. C2×#1039 | D4 | semidirect |
| 98. C52 | #394 | semidirect |
| 150. C5 | #65511 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C52×D4 | 2 |
| C2×C22⋊#1039 | 2 |
| C2×#87806 | 2 |
| #11716698 | 2 |
| #65511 | 5 |