Finite Group Databasebeta

← D7×(C151⋊C3)⋊C5 #44540296

Subgroups — D7×(C151⋊C3)⋊C5 #44540296

Order 31710.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×(C151⋊C3)⋊C5C211yesmaximal, characteristic, complemented, Hall
2D7×C151⋊C5C311yesmaximal, characteristic, complemented, Hall
3D7×C151⋊C3C511yesmaximal, characteristic, complemented, Hall
4C7×C151⋊C5C2×C311yescharacteristic, complemented, Hall
5C2×(C151⋊C3)⋊C5—71nomaximal, Hall
6C7×C151⋊C3C2×C511yescharacteristic, complemented, Hall
7(C151⋊C3)⋊C5D711yescharacteristic, direct product factor, Hall
8D7×C151C3×C511yescharacteristic, complemented, Hall
9C2×C151⋊C5—71noHall
10C7×C151C2×C3×C511yescharacteristic, complemented, Hall
11C2×C151⋊C3—71noHall
12C151⋊C5C3×D711yescharacteristic, complemented, Hall
13C151⋊C3C5×D711yescharacteristic, complemented, Hall
14C2×C151—71noHall
15C3×C5×D7—1511nomaximal, Hall
16C151C3×C5×D711yescharacteristic, complemented, Sylow
17C3×C5×C7—1511noHall
18C5×D7—1511noHall
19C3×D7—1511noHall
20C5×C7—1511noHall
21C2×C3×C5—10571noHall
22C3×C7—1511noHall
23C3×C5—1511noHall
24D7(C151⋊C3)⋊C511yescharacteristic, direct product factor, Hall
25C2×C5—10571noHall
26C7C2×(C151⋊C3)⋊C511yescharacteristic, complemented, Sylow
27C2×C3—10571noHall
28C5—1511noSylow
29C3—1511noSylow
30C2—71noSylow
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC7×C151C2×C3×C5
LCSG ▷ C7×C151
UCSC1

Complements

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

NH ≅ G/Ntype
1. C7×(C151⋊C3)⋊C5C2semidirect
2. D7×C151⋊C5C3semidirect
3. D7×C151⋊C3C5semidirect
4. C7×C151⋊C5C2×C3semidirect
6. C7×C151⋊C3C2×C5semidirect
7. (C151⋊C3)⋊C5D7direct (N × H)
8. D7×C151C3×C5semidirect
10. C7×C151C2×C3×C5semidirect
12. C151⋊C5C3×D7semidirect
13. C151⋊C3C5×D7semidirect
16. C151C3×C5×D7semidirect
24. D7(C151⋊C3)⋊C5direct (N × H)
26. C7C2×(C151⋊C3)⋊C5semidirect

Maximal subgroups

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

subgroupindex
C7×(C151⋊C3)⋊C52
D7×C151⋊C53
D7×C151⋊C35
C2×(C151⋊C3)⋊C57
C3×C5×D7151