Finite Group Databasebeta

← C5×C7×C22⋊(C73⋊C3) #44501451

Subgroups — C5×C7×C22⋊(C73⋊C3) #44501451

Order 30660.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C5×C7×C73C311yesmaximal, characteristic, complemented, Hall
2C5×C7×C73⋊C3—41nomaximal, Hall
3C7×C22⋊(C73⋊C3)C511yesmaximal, characteristic, direct product factor, Hall
4C2×C5×C7×C73—31no—
5C5×C22⋊(C73⋊C3)C711yesmaximal, characteristic, direct product factor, Hall
6C5×C7×C73A411yescharacteristic, complemented, Hall
7C22×C7×C73C3×C511yescharacteristic, complemented, Hall
8C7×C73⋊C3—41noHall
9C22×C5×C73C3×C711yescharacteristic, complemented, Hall
10C5×C73⋊C3—41noHall
11C2×C7×C73—31no—
12C22⋊(C73⋊C3)C5×C711yescharacteristic, direct product factor, Hall
13C2×C5×C73—31no—
14C7×C73C5×A411yescharacteristic, complemented, Hall
15C5×C7×A4—731nomaximal, Hall
16C5×C73C7×A411yescharacteristic, complemented, Hall
17C22×C73C3×C5×C711yescharacteristic, complemented, Hall
18C73⋊C3—41noHall
19C2×C73—31no—
20C22×C5×C7C73⋊C311yescharacteristic, complemented, Hall
21C3×C5×C7—2921noHall
22C7×A4—731noHall
23C73C5×C7×A411yescharacteristic, complemented, Sylow
24C2×C5×C7—31no—
25C5×A4—731noHall
26C5×C7C22⋊(C73⋊C3)11yescharacteristic, direct product factor, Hall
27C22×C7C5×C73⋊C311yescharacteristic, complemented, Hall
28C3×C7—2921noHall
29C22×C5C7×C73⋊C311yescharacteristic, complemented, Hall
30C3×C5—2921noHall
31C2×C7—31no—
32A4—731noHall
33C2×C5—31no—
34C7C5×C22⋊(C73⋊C3)11yescharacteristic, direct product factor, Sylow
35C5C7×C22⋊(C73⋊C3)11yescharacteristic, direct product factor, Sylow
36C22C5×C7×C73⋊C311yescharacteristic, complemented, Sylow
37C3—2921noSylow
38C2—31no—
subgroupG/H
center, hypercenterC5×C7C22⋊(C73⋊C3)
commutator, cosocle, hypocenterC22×C73C3×C5×C7
FrattiniC1G
Fitting, socleC22×C5×C7×C73C3
LCSG ▷ C22×C73
UCSC1 ◁ C5×C7

Complements

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

NH ≅ G/Ntype
1. C22×C5×C7×C73C3semidirect
3. C7×C22⋊(C73⋊C3)C5direct (N × H)
5. C5×C22⋊(C73⋊C3)C7direct (N × H)
6. C5×C7×C73A4semidirect
7. C22×C7×C73C3×C5semidirect
9. C22×C5×C73C3×C7semidirect
12. C22⋊(C73⋊C3)C5×C7direct (N × H)
14. C7×C73C5×A4semidirect
16. C5×C73C7×A4semidirect
17. C22×C73C3×C5×C7semidirect
20. C22×C5×C7C73⋊C3semidirect
23. C73C5×C7×A4semidirect
26. C5×C7C22⋊(C73⋊C3)direct (N × H)
27. C22×C7C5×C73⋊C3semidirect
29. C22×C5C7×C73⋊C3semidirect
34. C7C5×C22⋊(C73⋊C3)direct (N × H)
35. C5C7×C22⋊(C73⋊C3)direct (N × H)
36. C22C5×C7×C73⋊C3semidirect

Maximal subgroups

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

subgroupindex
C22×C5×C7×C733
C5×C7×C73⋊C34
C7×C22⋊(C73⋊C3)5
C5×C22⋊(C73⋊C3)7
C5×C7×A473