Finite Group Databasebeta

← C3⋊#22604861 #42124786

Subgroups — C3⋊#22604861 #42124786

Order 27900.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×(C5⋊D5)⋊(C31⋊C3)C211yesmaximal, characteristic
2C3⋊(C31⋊#1043)C311yesmaximal, characteristic, complemented
3#22604861—31nomaximal
4C3×C52⋊(C31⋊C3)C411yescharacteristic, complemented, Hall
5C3×C31×C5⋊D5C2×C311yescharacteristic
6(C5⋊D5)⋊(C31⋊C3)—21no—
7(C5⋊D5)⋊(C31⋊C3)D311yescharacteristic
8C31⋊#1043—31noHall
9C52⋊(C31⋊C3)—21no—
10C52⋊(C31⋊C3)Dic311yescharacteristic, complemented
11C3×C52×C31C3×C411yescharacteristic, complemented
12C3⋊(C31⋊AGL(1,𝔽5))—152no—
13C31×C5⋊D5C3×D311yescharacteristic
14C3⋊((C31⋊C3)⋊C4)—251nomaximal, Hall
15C3×D5×C31—152no—
16C3⋊(#1043⋊C3)—311nomaximal, Hall
17C52×C31C3×Dic311yescharacteristic, complemented, Hall
18C31⋊AGL(1,𝔽5)—452no—
19C2×C3×C31⋊C3—251no—
20C3×C5×C31—32no—
21C3×(C5⋊D5)⋊C3—311no—
22Dic93—251no—
23(C31⋊C3)⋊C4—751no—
24D5×C31—152no—
25C3⋊#1043—311no—
26#1043⋊C3—931no—
27C3×C31⋊C3—251noHall
28C3×C52⋊C3—311noHall
29C2×C3×C31—251no—
30C2×C31⋊C3—251no—
31C2×C31⋊C3—501no—
32C5×C31—32no—
33C3×C5⋊D5D31⋊C311yescharacteristic
34(C5⋊D5)⋊C3—311no—
35(C5⋊D5)⋊C3—621no—
36Dic31—751noHall
37#1043—931noHall
38C3×C31#1043⋊C311yescharacteristic, complemented
39C31⋊C3—251no—
40C31⋊C3—501no—
41C3×C52(C31⋊C3)⋊C411yescharacteristic, complemented
42C52⋊C3—311no—
43C52⋊C3—621no—
44C2×C31—251no—
45ΓL(1,𝔽16)—4652no—
46C5⋊D5C3⋊(D31⋊C3)11yescharacteristic
47C3×Dic3—7751noHall
48C31C3⋊(#1043⋊C3)11yescharacteristic, complemented, Sylow
49C3×D5—152no—
50C52C3⋊((C31⋊C3)⋊C4)11yescharacteristic, complemented, Sylow
51AGL(1,𝔽5)—13952no—
52C2×C32—7751no—
53C3×C5—32no—
54C3×C4—23251no—
55Dic3—7751no—
56D5—152no—
57C32—7751noSylow
58C2×C3—7751no—
59C2×C3—15501no—
60C2×C3—251no—
61C5—32no—
62C4—23251noSylow
63C3—7751no—
64C3—15501no—
65C3#2260486111yescharacteristic, complemented
66C2—251no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC3×C52×C31C3×C4
prime radicalC3×(C5⋊D5)⋊(C31⋊C3)C2
cosocleC3×C31×C5⋊D5C2×C3
LCSG ▷ C3×C52×C31
UCSC1

Complements

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

NH ≅ G/Ntype
2. C3⋊(C31⋊#1043)C3semidirect
4. C3×C52⋊(C31⋊C3)C4semidirect
10. C52⋊(C31⋊C3)Dic3semidirect
11. C3×C52×C31C3×C4semidirect
17. C52×C31C3×Dic3semidirect
38. C3×C31#1043⋊C3semidirect
41. C3×C52(C31⋊C3)⋊C4semidirect
48. C31C3⋊(#1043⋊C3)semidirect
50. C52C3⋊((C31⋊C3)⋊C4)semidirect
65. C3#22604861semidirect

Maximal subgroups

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

subgroupindex
C3×(C5⋊D5)⋊(C31⋊C3)2
C3⋊(C31⋊#1043)3
#226048613
C3⋊((C31⋊C3)⋊C4)25
C3⋊(#1043⋊C3)31