Finite Group Databasebeta

← C2×C5×C3⋊(C3⋊(C3⋊D3)) #13108569

Subgroups — C2×C5×C3⋊(C3⋊(C3⋊D3)) #13108569

Order 1620.

2120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C34×C5C211yesmaximal, characteristic, complemented
2C5×C3⋊(C3⋊(C3⋊D3))C212yesmaximal, direct product factor
3C2×C5×C3⋊(C3⋊D3)—340nomaximal
4C34×C5C2211yescharacteristic, complemented, Hall
5C2×C3⋊(C3⋊(C3⋊D3))C511yesmaximal, characteristic, direct product factor, Hall
6C2×C33×C5D3140yescomplemented
7C5×C3⋊(C3⋊D3)—380no—
8C2×C5×C3⋊D3—9130no—
9C2×C34C2×C511yescharacteristic, complemented
10C3⋊(C3⋊(C3⋊D3))C2×C512yesdirect product factor
11C33×C5C2×D3140yescomplemented
12C2×C3⋊(C3⋊D3)—340no—
13C2×C32×C5C3⋊D31130yescomplemented
14C5×C3⋊D3—9260no—
15C34C22×C511yescharacteristic, complemented, Sylow
16C2×C5×D3—2740no—
17C2×C33C5×D3140yescomplemented
18C3⋊(C3⋊D3)—380no—
19C32×C5C2×C3⋊D31130yescomplemented
20C2×C3⋊D3—9130no—
21C2×C3×C5C3⋊(C3⋊D3)140yescomplemented
22C5×D3—2780no—
23C33C2×C5×D3140yescomplemented
24C22×C5—811noHall
25C2×C32C5×C3⋊D31130yescomplemented
26C3⋊D3—9260no—
27C3×C5C2×C3⋊(C3⋊D3)140yescomplemented
28C2×D3—2740no—
29C2×C5—812no—
30C2×C5C3⋊(C3⋊(C3⋊D3))11yescharacteristic, direct product factor
31C32C2×C5×C3⋊D31130yescomplemented
32C2×C3C5×C3⋊(C3⋊D3)140yescomplemented
33D3—2780no—
34C5C2×C3⋊(C3⋊(C3⋊D3))11yescharacteristic, direct product factor, Sylow
35C22—811noSylow
36C3C2×C5×C3⋊(C3⋊D3)140yescomplemented
37C2—812no—
38C2C5×C3⋊(C3⋊(C3⋊D3))11yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C5C3⋊(C3⋊(C3⋊D3))
commutator, cosocle, hypocenterC34C22×C5
FrattiniC1G
Fitting, socleC2×C34×C5C2
LCSG ▷ C34
UCSC1 ◁ C2×C5

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×C34×C5C2semidirect
2. C5×C3⋊(C3⋊(C3⋊D3))C2direct (N × H)
4. C34×C5C22semidirect
5. C2×C3⋊(C3⋊(C3⋊D3))C5direct (N × H)
6. C2×C33×C5D3semidirect
9. C2×C34C2×C5semidirect
10. C3⋊(C3⋊(C3⋊D3))C2×C5direct (N × H)
11. C33×C5C2×D3semidirect
13. C2×C32×C5C3⋊D3semidirect
15. C34C22×C5semidirect
17. C2×C33C5×D3semidirect
19. C32×C5C2×C3⋊D3semidirect
21. C2×C3×C5C3⋊(C3⋊D3)semidirect
23. C33C2×C5×D3semidirect
25. C2×C32C5×C3⋊D3semidirect
27. C3×C5C2×C3⋊(C3⋊D3)semidirect
30. C2×C5C3⋊(C3⋊(C3⋊D3))direct (N × H)
31. C32C2×C5×C3⋊D3semidirect
32. C2×C3C5×C3⋊(C3⋊D3)semidirect
34. C5C2×C3⋊(C3⋊(C3⋊D3))direct (N × H)
36. C3C2×C5×C3⋊(C3⋊D3)semidirect
38. C2C5×C3⋊(C3⋊(C3⋊D3))direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×C34×C52
C5×C3⋊(C3⋊(C3⋊D3))2
C2×C5×C3⋊(C3⋊D3)3
C2×C3⋊(C3⋊(C3⋊D3))5