Finite Group Databasebeta

← C2×C23×C52⋊C9 #23780353

Subgroups — C2×C23×C52⋊C9 #23780353

Order 10350.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C52⋊C9C211yesmaximal, characteristic, direct product factor, Hall
2C2×C3×C52×C23C311yesmaximal, characteristic
3C3×C52×C23C2×C311yescharacteristic
4C2×C52×C23C911yescharacteristic, complemented, Hall
5C2×C3×C5×C23—32no—
6C52×C23C2×C911yescharacteristic, complemented, Hall
7C2×C52⋊C9C2311yesmaximal, characteristic, direct product factor, Hall
8C2×C9×C23—251nomaximal, Hall
9C3×C5×C23—32no—
10C2×C5×C23—32no—
11C52⋊C9C2×C2311yescharacteristic, direct product factor, Hall
12C9×C23—251noHall
13C2×C3×C52C3×C2311yescharacteristic
14C2×C3×C23C52⋊C311yescharacteristic
15C5×C23—32no—
16C3×C52C2×C3×C2311yescharacteristic
17C3×C23C2×C52⋊C311yescharacteristic
18C2×C52C9×C2311yescharacteristic, complemented, Hall
19C2×C23C52⋊C911yescharacteristic, direct product factor, Hall
20C2×C3×C5—32no—
21C52C2×C9×C2311yescharacteristic, complemented, Sylow
22C23C2×C52⋊C911yescharacteristic, direct product factor, Sylow
23C2×C9—251noHall
24C3×C5—32no—
25C2×C5—32no—
26C9—251noSylow
27C2×C3C23×C52⋊C311yescharacteristic
28C5—32no—
29C3C2×C23×C52⋊C311yescharacteristic
30C2C23×C52⋊C911yescharacteristic, direct product factor, Sylow
subgroupG/H
center, hypercenterC2×C3×C23C52⋊C3
commutator, hypocenterC52C2×C9×C23
FrattiniC3C2×C23×C52⋊C3
Fitting, socle, prime radicalC2×C3×C52×C23C3
cosocleC3×C52C2×C3×C23
LCSG ▷ C52
UCSC1 ◁ C2×C3×C23

Complements

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

NH ≅ G/Ntype
1. C23×C52⋊C9C2direct (N × H)
4. C2×C52×C23C9semidirect
6. C52×C23C2×C9semidirect
7. C2×C52⋊C9C23direct (N × H)
11. C52⋊C9C2×C23direct (N × H)
18. C2×C52C9×C23semidirect
19. C2×C23C52⋊C9direct (N × H)
21. C52C2×C9×C23semidirect
22. C23C2×C52⋊C9direct (N × H)
30. C2C23×C52⋊C9direct (N × H)