Finite Group Databasebeta

← C2×C5×(C13⋊D13)⋊C7 #37556841

Subgroups — C2×C5×(C13⋊D13)⋊C7 #37556841

Order 23660.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×C132⋊C7C211yesmaximal, characteristic, complemented
2C5×(C13⋊D13)⋊C7C212yesmaximal, direct product factor
3C5×C132⋊C7C2211yescharacteristic, complemented, Hall
4C2×(C13⋊D13)⋊C7C511yesmaximal, characteristic, direct product factor, Hall
5C2×C5×C13⋊D13C711yesmaximal, characteristic, complemented, Hall
6C2×C132⋊C7C2×C511yescharacteristic, complemented
7(C13⋊D13)⋊C7C2×C512yesdirect product factor
8C2×C5×C132C2×C711yescharacteristic, complemented
9C5×C13⋊D13C2×C712yescomplemented
10C132⋊C7C22×C511yescharacteristic, complemented, Hall
11C5×C132C22×C711yescharacteristic, complemented, Hall
12C2×C13⋊D13C5×C711yescharacteristic, complemented, Hall
13C2×C132C2×C5×C711yescharacteristic, complemented
14C13⋊D13C2×C5×C712yescomplemented
15C2×C5×D13—912no—
16C132C22×C5×C711yescharacteristic, complemented, Sylow
17C22×C5×C7—1691nomaximal, Hall
18C2×C5×C13—72no—
19C5×D13—914no—
20C2×C5×C7—1692no—
21C2×C5×C7—1691no—
22C5×C13—72no—
23C2×D13—912no—
24C5×C7—1691noHall
25C22×C7—1691noHall
26C2×C13—72no—
27D13—914no—
28C22×C5—11831noHall
29C2×C7—1692no—
30C2×C7—1691no—
31C13—72no—
32C2×C5—11832no—
33C2×C5(C13⋊D13)⋊C711yescharacteristic, direct product factor
34C7—1691noSylow
35C5C2×(C13⋊D13)⋊C711yescharacteristic, direct product factor, Sylow
36C22—11831noSylow
37C2—11832no—
38C2C5×(C13⋊D13)⋊C711yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C5(C13⋊D13)⋊C7
commutator, cosocle, hypocenterC132C22×C5×C7
FrattiniC1G
Fitting, socleC2×C5×C132C2×C7
LCSG ▷ C132
UCSC1 ◁ C2×C5

Complements

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

NH ≅ G/Ntype
1. C2×C5×C132⋊C7C2semidirect
2. C5×(C13⋊D13)⋊C7C2direct (N × H)
3. C5×C132⋊C7C22semidirect
4. C2×(C13⋊D13)⋊C7C5direct (N × H)
5. C2×C5×C13⋊D13C7semidirect
6. C2×C132⋊C7C2×C5semidirect
7. (C13⋊D13)⋊C7C2×C5direct (N × H)
8. C2×C5×C132C2×C7semidirect
9. C5×C13⋊D13C2×C7semidirect
10. C132⋊C7C22×C5semidirect
11. C5×C132C22×C7semidirect
12. C2×C13⋊D13C5×C7semidirect
13. C2×C132C2×C5×C7semidirect
14. C13⋊D13C2×C5×C7semidirect
16. C132C22×C5×C7semidirect
33. C2×C5(C13⋊D13)⋊C7direct (N × H)
35. C5C2×(C13⋊D13)⋊C7direct (N × H)
38. C2C5×(C13⋊D13)⋊C7direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×C132⋊C72
C5×(C13⋊D13)⋊C72
C2×(C13⋊D13)⋊C75
C2×C5×C13⋊D137
C22×C5×C7169