Finite Group Databasebeta

← C2×(C5⋊D5)⋊(C61⋊C3) #32913082

Subgroups — C2×(C5⋊D5)⋊(C61⋊C3) #32913082

Order 18300.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C52⋊(C61⋊C3)C211yesmaximal, characteristic, complemented
2(C5⋊D5)⋊(C61⋊C3)C212yesmaximal, direct product factor
3C2×C5⋊D5×C61C311yesmaximal, characteristic, complemented, Hall
4C52⋊(C61⋊C3)C2211yescharacteristic, complemented, Hall
5C5⋊D5×C61C2×C312yescomplemented
6C2×C52×C61C2×C311yescharacteristic, complemented
7C52×C61C22×C311yescharacteristic, complemented, Hall
8C2×D5×C61—152no—
9C22×C61⋊C3—251nomaximal, Hall
10C2×C5×C61—32no—
11D5×C61—154no—
12C2×C61⋊C3—252no—
13C2×C61⋊C3—501no—
14C5×C61—32no—
15C2×(C5⋊D5)⋊C3—611nomaximal, Hall
16C22×C61—251noHall
17C61⋊C3—501noHall
18C2×C52⋊C3—611no—
19(C5⋊D5)⋊C3—612no—
20C2×C61—252no—
21C2×C61(C5⋊D5)⋊C311yescharacteristic, complemented
22C2×C5⋊D5C61⋊C311yescharacteristic, complemented, Hall
23C52⋊C3—611noHall
24C61C2×(C5⋊D5)⋊C311yescharacteristic, complemented, Sylow
25C2×C52C2×C61⋊C311yescharacteristic, complemented
26C5⋊D5C2×C61⋊C312yescomplemented
27C52C22×C61⋊C311yescharacteristic, complemented, Sylow
28C2×D5—152no—
29C22×C3—15251noHall
30C2×C5—32no—
31D5—154no—
32C2×C3—15252no—
33C2×C3—15251no—
34C5—32no—
35C22—251noSylow
36C3—15251noSylow
37C2—252no—
38C2(C5⋊D5)⋊(C61⋊C3)11yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2(C5⋊D5)⋊(C61⋊C3)
commutator, cosocle, hypocenterC52×C61C22×C3
FrattiniC1G
Fitting, socleC2×C52×C61C2×C3
LCSG ▷ C52×C61
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. C2×C52⋊(C61⋊C3)C2semidirect
2. (C5⋊D5)⋊(C61⋊C3)C2direct (N × H)
3. C2×C5⋊D5×C61C3semidirect
4. C52⋊(C61⋊C3)C22semidirect
5. C5⋊D5×C61C2×C3semidirect
6. C2×C52×C61C2×C3semidirect
7. C52×C61C22×C3semidirect
21. C2×C61(C5⋊D5)⋊C3semidirect
22. C2×C5⋊D5C61⋊C3semidirect
24. C61C2×(C5⋊D5)⋊C3semidirect
25. C2×C52C2×C61⋊C3semidirect
26. C5⋊D5C2×C61⋊C3semidirect
27. C52C22×C61⋊C3semidirect
38. C2(C5⋊D5)⋊(C61⋊C3)direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C52⋊(C61⋊C3)2
(C5⋊D5)⋊(C61⋊C3)2
C2×C5⋊D5×C613
C22×C61⋊C325
C2×(C5⋊D5)⋊C361