Finite Group Databasebeta

← C4×C5×(C43⋊C3)⋊C7 #31825331

Subgroups — C4×C5×(C43⋊C3)⋊C7 #31825331

Order 18060.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×(C43⋊C3)⋊C7C211yesmaximal, characteristic
2C4×C5×C43⋊C7C311yesmaximal, characteristic, complemented, Hall
3C5×(C43⋊C3)⋊C7C411yescharacteristic, direct product factor, Hall
4C4×(C43⋊C3)⋊C7C511yesmaximal, characteristic, direct product factor, Hall
5C2×C5×C43⋊C7C2×C311yescharacteristic
6C4×C5×C43⋊C3C711yesmaximal, characteristic, complemented, Hall
7C2×(C43⋊C3)⋊C7C2×C511yescharacteristic
8C5×C43⋊C7C3×C411yescharacteristic, complemented, Hall
9C2×C5×C43⋊C3C2×C711yescharacteristic
10C4×C43⋊C7C3×C511yescharacteristic, complemented, Hall
11(C43⋊C3)⋊C7C4×C511yescharacteristic, direct product factor, Hall
12C4×C5×C43C3×C711yescharacteristic, complemented, Hall
13C5×C43⋊C3C4×C711yescharacteristic, complemented, Hall
14C2×C43⋊C7C2×C3×C511yescharacteristic
15C4×C43⋊C3C5×C711yescharacteristic, complemented, Hall
16C2×C5×C43C2×C3×C711yescharacteristic
17C3×C4×C5×C7—431nomaximal, Hall
18C43⋊C7C3×C4×C511yescharacteristic, complemented, Hall
19C2×C43⋊C3C2×C5×C711yescharacteristic
20C5×C43C3×C4×C711yescharacteristic, complemented, Hall
21C2×C3×C5×C7—431no—
22C4×C43C3×C5×C711yescharacteristic, complemented, Hall
23C4×C5×C7—431noHall
24C43⋊C3C4×C5×C711yescharacteristic, complemented, Hall
25C3×C5×C7—431noHall
26C2×C43C2×C3×C5×C711yescharacteristic
27C3×C4×C7—431noHall
28C2×C5×C7—431no—
29C3×C4×C5—3011noHall
30C43C3×C4×C5×C711yescharacteristic, complemented, Sylow
31C2×C3×C7—431no—
32C5×C7—431noHall
33C2×C3×C5—3011no—
34C4×C7—431noHall
35C3×C7—431noHall
36C4×C5(C43⋊C3)⋊C711yescharacteristic, direct product factor, Hall
37C3×C5—3011noHall
38C2×C7—431no—
39C3×C4—3011noHall
40C2×C5C2×(C43⋊C3)⋊C711yescharacteristic
41C7—431noSylow
42C2×C3—3011no—
43C5C4×(C43⋊C3)⋊C711yescharacteristic, direct product factor, Sylow
44C4C5×(C43⋊C3)⋊C711yescharacteristic, direct product factor, Sylow
45C3—3011noSylow
46C2C2×C5×(C43⋊C3)⋊C711yescharacteristic
subgroupG/H
center, hypercenterC4×C5(C43⋊C3)⋊C7
commutator, hypocenterC43C3×C4×C5×C7
FrattiniC2C2×C5×(C43⋊C3)⋊C7
FittingC4×C5×C43C3×C7
socleC2×C5×C43C2×C3×C7
prime radicalC2×C5×(C43⋊C3)⋊C7C2
cosocleC2×C43C2×C3×C5×C7
LCSG ▷ C43
UCSC1 ◁ C4×C5

Complements

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

NH ≅ G/Ntype
2. C4×C5×C43⋊C7C3semidirect
3. C5×(C43⋊C3)⋊C7C4direct (N × H)
4. C4×(C43⋊C3)⋊C7C5direct (N × H)
6. C4×C5×C43⋊C3C7semidirect
8. C5×C43⋊C7C3×C4semidirect
10. C4×C43⋊C7C3×C5semidirect
11. (C43⋊C3)⋊C7C4×C5direct (N × H)
12. C4×C5×C43C3×C7semidirect
13. C5×C43⋊C3C4×C7semidirect
15. C4×C43⋊C3C5×C7semidirect
18. C43⋊C7C3×C4×C5semidirect
20. C5×C43C3×C4×C7semidirect
22. C4×C43C3×C5×C7semidirect
24. C43⋊C3C4×C5×C7semidirect
30. C43C3×C4×C5×C7semidirect
36. C4×C5(C43⋊C3)⋊C7direct (N × H)
43. C5C4×(C43⋊C3)⋊C7direct (N × H)
44. C4C5×(C43⋊C3)⋊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×(C43⋊C3)⋊C72
C4×C5×C43⋊C73
C4×(C43⋊C3)⋊C75
C4×C5×C43⋊C37
C3×C4×C5×C743