Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
630 conjugacy classes of subgroups; only the 150 normal subgroups are shown.
This group has 630 conjugacy classes of subgroups — too many to draw. Only its 150 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D52 |
| commutator, socle, cosocle | C22×C52 | C24 |
| Fitting | C52×C4⋊C4 | C22 |
| prime radical | C2×#6037 | C22 |
| hypercenter | C4⋊C4 | D52 |
| hypocenter | C52 | D4×Q8 |
| LCS | G ▷ C22×C52 ▷ C52 | |
| UCS | C1 ◁ C22 ◁ C4⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×D5×Dic10 | C2 | semidirect |
| 2. #11717207 | C2 | semidirect |
| 3. C5×#4043 | C2 | semidirect |
| 4. #11717037 | C2 | semidirect |
| 7. #11717014 | C2 | semidirect |
| 8. #11716985 | C2 | semidirect |
| 33. #6045 | D4 | semidirect |
| 39. #6037 | Q8 | semidirect |
| 46. #4043 | D5 | semidirect |
| 56. C2×C5×D5 | C2×Q8 | semidirect |
| 61. #1039 | C2×Q8 | semidirect |
| 134. C52 | D4×Q8 | semidirect |
| 142. C2×D5 | Q8×D5 | semidirect |
| 197. C5 | #65966 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D5×Dic10 | 2 |
| #11717207 | 2 |
| C5×#4043 | 2 |
| #11717037 | 2 |
| #11717020 | 2 |
| C4×#6037 | 2 |
| #11717014 | 2 |
| #11716985 | 2 |
| #65966 | 5 |