Finite Group Databasebeta

← C2×C5×(C127⋊C3)⋊C7 #40998673

Subgroups — C2×C5×(C127⋊C3)⋊C7 #40998673

Order 26670.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×(C127⋊C3)⋊C7C211yesmaximal, characteristic, direct product factor, Hall
2C2×C5×C127⋊C7C311yesmaximal, characteristic, complemented, Hall
3C2×(C127⋊C3)⋊C7C511yesmaximal, characteristic, direct product factor, Hall
4C5×C127⋊C7C2×C311yescharacteristic, complemented, Hall
5C2×C5×C127⋊C3C711yesmaximal, characteristic, complemented, Hall
6(C127⋊C3)⋊C7C2×C511yescharacteristic, direct product factor, Hall
7C5×C127⋊C3C2×C711yescharacteristic, complemented, Hall
8C2×C127⋊C7C3×C511yescharacteristic, complemented, Hall
9C2×C5×C127C3×C711yescharacteristic, complemented, Hall
10C127⋊C7C2×C3×C511yescharacteristic, complemented, Hall
11C2×C127⋊C3C5×C711yescharacteristic, complemented, Hall
12C5×C127C2×C3×C711yescharacteristic, complemented, Hall
13C127⋊C3C2×C5×C711yescharacteristic, complemented, Hall
14C2×C127C3×C5×C711yescharacteristic, complemented, Hall
15C2×C3×C5×C7—1271nomaximal, Hall
16C127C2×C3×C5×C711yescharacteristic, complemented, Sylow
17C3×C5×C7—1271noHall
18C2×C5×C7—1271noHall
19C2×C3×C7—1271noHall
20C5×C7—1271noHall
21C2×C3×C5—8891noHall
22C3×C7—1271noHall
23C3×C5—8891noHall
24C2×C7—1271noHall
25C2×C5(C127⋊C3)⋊C711yescharacteristic, direct product factor, Hall
26C7—1271noSylow
27C2×C3—8891noHall
28C5C2×(C127⋊C3)⋊C711yescharacteristic, direct product factor, Sylow
29C3—8891noSylow
30C2C5×(C127⋊C3)⋊C711yescharacteristic, direct product factor, Sylow
subgroupG/H
center, hypercenterC2×C5(C127⋊C3)⋊C7
commutator, cosocle, hypocenterC127C2×C3×C5×C7
FrattiniC1G
Fitting, socleC2×C5×C127C3×C7
LCSG ▷ C127
UCSC1 ◁ C2×C5

Complements

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

NH ≅ G/Ntype
1. C5×(C127⋊C3)⋊C7C2direct (N × H)
2. C2×C5×C127⋊C7C3semidirect
3. C2×(C127⋊C3)⋊C7C5direct (N × H)
4. C5×C127⋊C7C2×C3semidirect
5. C2×C5×C127⋊C3C7semidirect
6. (C127⋊C3)⋊C7C2×C5direct (N × H)
7. C5×C127⋊C3C2×C7semidirect
8. C2×C127⋊C7C3×C5semidirect
9. C2×C5×C127C3×C7semidirect
10. C127⋊C7C2×C3×C5semidirect
11. C2×C127⋊C3C5×C7semidirect
12. C5×C127C2×C3×C7semidirect
13. C127⋊C3C2×C5×C7semidirect
14. C2×C127C3×C5×C7semidirect
16. C127C2×C3×C5×C7semidirect
25. C2×C5(C127⋊C3)⋊C7direct (N × H)
28. C5C2×(C127⋊C3)⋊C7direct (N × H)
30. C2C5×(C127⋊C3)⋊C7direct (N × H)

Maximal subgroups

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

subgroupindex
C5×(C127⋊C3)⋊C72
C2×C5×C127⋊C73
C2×(C127⋊C3)⋊C75
C2×C5×C127⋊C37
C2×C3×C5×C7127