Finite Group Databasebeta

← (C5⋊D5)⋊C3×C29⋊C7 #44478554

Subgroups — (C5⋊D5)⋊C3×C29⋊C7 #44478554

Order 30450.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C52⋊C3×C29⋊C7C211yesmaximal, characteristic, complemented, Hall
2C5⋊D5×C29⋊C7C311yesmaximal, characteristic, complemented, Hall
3C52×C29⋊C7C2×C311yescharacteristic, complemented, Hall
4C29×(C5⋊D5)⋊C3C711yesmaximal, characteristic, complemented, Hall
5C29×C52⋊C3C2×C711yescharacteristic, complemented, Hall
6D5×C29⋊C7—152no—
7C29×C5⋊D5C3×C711yescharacteristic, complemented, Hall
8C2×C3×C29⋊C7—251nomaximal, Hall
9C7×(C5⋊D5)⋊C3—291nomaximal, Hall
10C5×C29⋊C7—32no—
11C52×C29C2×C3×C711yescharacteristic, complemented, Hall
12C3×C29⋊C7—251noHall
13C7×C52⋊C3—291noHall
14C2×C29⋊C7—251noHall
15C7×C5⋊D5—291noHall
16D5×C29—152no—
17C29⋊C7(C5⋊D5)⋊C311yescharacteristic, direct product factor, Hall
18C52×C7—291noHall
19C2×C3×C29—251noHall
20(C5⋊D5)⋊C3C29⋊C711yescharacteristic, direct product factor, Hall
21C5×C29—32no—
22C3×C29—251noHall
23C52⋊C3C2×C29⋊C711yescharacteristic, complemented, Hall
24C7×D5—4352no—
25C2×C29—251noHall
26C5⋊D5C3×C29⋊C711yescharacteristic, complemented, Hall
27C2×C3×C7—7251noHall
28C5×C7—872no—
29C29C7×(C5⋊D5)⋊C311yescharacteristic, complemented, Sylow
30C52C2×C3×C29⋊C711yescharacteristic, complemented, Sylow
31C3×C7—7251noHall
32C2×C7—7251noHall
33D5—152no—
34C7—291noSylow
35C2×C3—251noHall
36C5—32no—
37C3—251noSylow
38C2—251noSylow
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC52×C29C2×C3×C7
LCSG ▷ C52×C29
UCSC1

Complements

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

NH ≅ G/Ntype
1. C52⋊C3×C29⋊C7C2semidirect
2. C5⋊D5×C29⋊C7C3semidirect
3. C52×C29⋊C7C2×C3semidirect
4. C29×(C5⋊D5)⋊C3C7semidirect
5. C29×C52⋊C3C2×C7semidirect
7. C29×C5⋊D5C3×C7semidirect
11. C52×C29C2×C3×C7semidirect
17. C29⋊C7(C5⋊D5)⋊C3direct (N × H)
20. (C5⋊D5)⋊C3C29⋊C7direct (N × H)
23. C52⋊C3C2×C29⋊C7semidirect
26. C5⋊D5C3×C29⋊C7semidirect
29. C29C7×(C5⋊D5)⋊C3semidirect
30. C52C2×C3×C29⋊C7semidirect

Maximal subgroups

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

subgroupindex
C52⋊C3×C29⋊C72
C5⋊D5×C29⋊C73
C29×(C5⋊D5)⋊C37
C2×C3×C29⋊C725
C7×(C5⋊D5)⋊C329