Finite Group Databasebeta

← (C31⋊C3)⋊(#1043⋊C3) #42124686

Subgroups — (C31⋊C3)⋊(#1043⋊C3) #42124686

Order 27900.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31⋊C3×(C5⋊D5)⋊C3C211yesmaximal, characteristic
2#22604863C311yesmaximal, characteristic, complemented
3#22604861C312yesmaximal, complemented
4(C31⋊C3)⋊#1043C311yesmaximal, characteristic, complemented
5C52⋊C3×C31⋊C3C411yescharacteristic, complemented, Hall
6(C5⋊D5)⋊(C31⋊C3)C2×C312yes—
7C31×(C5⋊D5)⋊C3C2×C311yescharacteristic
8C5⋊D5×C31⋊C3C2×C311yescharacteristic
9C31⋊#1043C3211yescharacteristic, complemented, Hall
10C52⋊(C31⋊C3)C3×C412yescomplemented
11C31×C52⋊C3C3×C411yescharacteristic, complemented
12C52×C31⋊C3C3×C411yescharacteristic, complemented
13(C31⋊C3)⋊AGL(1,𝔽5)—152no—
14C31×C5⋊D5C2×C3211yescharacteristic
15C3×(C31⋊C3)⋊C4—251nomaximal, Hall
16D5×C31⋊C3—152no—
17C3×#1043⋊C3—311nomaximal, Hall
18C52×C31C32×C411yescharacteristic, complemented, Hall
19C31⋊AGL(1,𝔽5)—152no—
20C2×C3×C31⋊C3—251no—
21C5×C31⋊C3—32no—
22C3×(C5⋊D5)⋊C3—311no—
23C3×Dic31—251no—
24(C31⋊C3)⋊C4—251no—
25(C31⋊C3)⋊C4—252no—
26D5×C31—152no—
27C3×#1043—311no—
28#1043⋊C3—312no—
29#1043⋊C3—311no—
30C3×C31⋊C3—251noHall
31C3×C52⋊C3—311noHall
32C2×C3×C31—251no—
33C2×C31⋊C3—252no—
34C2×C31⋊C3—251no—
35C5×C31—32no—
36C3×C5⋊D5—311no—
37(C5⋊D5)⋊C3—312no—
38(C5⋊D5)⋊C3D31⋊C311yescharacteristic
39Dic31—251noHall
40#1043—311noHall
41C3×C31—251no—
42C31⋊C3—252no—
43C31⋊C3#1043⋊C311yescharacteristic, complemented
44C3×C52—311no—
45C52⋊C3—312no—
46C52⋊C3(C31⋊C3)⋊C411yescharacteristic, complemented
47C2×C31—251no—
48C3×AGL(1,𝔽5)—4652no—
49C5⋊D5C3×D31⋊C311yescharacteristic
50C32×C4—7751noHall
51C31C3×#1043⋊C311yescharacteristic, complemented, Sylow
52C3×D5—4652no—
53C52C3×(C31⋊C3)⋊C411yescharacteristic, complemented, Sylow
54AGL(1,𝔽5)—4652no—
55C2×C32—7751no—
56C3×C5—932no—
57C3×C4—7751no—
58C3×C4—7752no—
59C3×C4—7751no—
60D5—152no—
61C32—7751noSylow
62C2×C3—7752no—
63C2×C3—7751no—
64C2×C3—251no—
65C5—32no—
66C4—7751noSylow
67C3—7752no—
68C3—251no—
69C3—311no—
70C2—251no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC52×C31C32×C4
prime radicalC31⋊C3×(C5⋊D5)⋊C3C2
cosocleC31×C5⋊D5C2×C32
LCSG ▷ C52×C31
UCSC1

Complements

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

NH ≅ G/Ntype
2. #22604863C3semidirect
3. #22604861C3semidirect
4. (C31⋊C3)⋊#1043C3semidirect
5. C52⋊C3×C31⋊C3C4semidirect
9. C31⋊#1043C32semidirect
10. C52⋊(C31⋊C3)C3×C4semidirect
11. C31×C52⋊C3C3×C4semidirect
12. C52×C31⋊C3C3×C4semidirect
18. C52×C31C32×C4semidirect
43. C31⋊C3#1043⋊C3semidirect
46. C52⋊C3(C31⋊C3)⋊C4semidirect
51. C31C3×#1043⋊C3semidirect
53. C52C3×(C31⋊C3)⋊C4semidirect

Maximal subgroups

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

subgroupindex
C31⋊C3×(C5⋊D5)⋊C32
#226048633
#226048613
(C31⋊C3)⋊#10433
C3×(C31⋊C3)⋊C425
C3×#1043⋊C331