Finite Group Databasebeta

← C2×#28358426 #42124530

Subgroups — C2×#28358426 #42124530

Order 27900.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C52⋊(C31⋊C9)C211yesmaximal, characteristic, complemented
2#28358426C212yesmaximal, direct product factor
3C2×C3×C5⋊D155C311yesmaximal, characteristic
4C52⋊(C31⋊C9)C2211yescharacteristic, complemented, Hall
5C3×C5⋊D155C2×C312yes—
6C2×C3×C52×C31C2×C311yescharacteristic
7C2×C5⋊D155C911yescharacteristic, complemented, Hall
8C3×C52×C31C22×C311yescharacteristic
9C2×C3×D155—152no—
10C2×C52×C31C2×C911yescharacteristic, complemented
11C5⋊D155C2×C912yescomplemented
12C2×D31⋊C9—251nomaximal, Hall
13C2×C3×C5×C31—32no—
14C3×D155—154no—
15C2×(C5⋊D5)⋊C9—311nomaximal, Hall
16C52×C31C22×C911yescharacteristic, complemented, Hall
17C2×D155—152no—
18C2×C31⋊C9—251no—
19D31⋊C9—252no—
20C3×C5×C31—32no—
21C2×C52⋊C9—311no—
22(C5⋊D5)⋊C9—312no—
23C2×C3×D31—251no—
24C2×C5×C31—32no—
25D155—154no—
26C2×C3×C5⋊D5—311no—
27C31⋊C9—251noHall
28C52⋊C9—311noHall
29C2×C3×C31(C5⋊D5)⋊C311yescharacteristic
30C3×D31—252no—
31C5×C31—32no—
32C2×C3×C52D31⋊C311yescharacteristic
33C3×C5⋊D5—312no—
34C2×D31—251noHall
35C2×C5⋊D5—311noHall
36C3×C31C2×(C5⋊D5)⋊C311yescharacteristic
37C3×C52C2×D31⋊C311yescharacteristic
38C2×C31(C5⋊D5)⋊C911yescharacteristic, complemented
39D31—252no—
40C2×C3×D5—4652no—
41C2×C52D31⋊C911yescharacteristic, complemented
42C5⋊D5—312no—
43C22×C9—7751noHall
44C31C2×(C5⋊D5)⋊C911yescharacteristic, complemented, Sylow
45C2×C3×C5—32no—
46C3×D5—4654no—
47C52C2×D31⋊C911yescharacteristic, complemented, Sylow
48C2×D5—4652no—
49C2×C9—7752no—
50C2×C9—7751no—
51C3×C5—32no—
52C22×C3—7751no—
53C2×C5—32no—
54D5—4654no—
55C9—7751noSylow
56C2×C3—7752no—
57C2×C3#1798786911yescharacteristic
58C5—32no—
59C22—7751noSylow
60C3C2×#1798786911yescharacteristic
61C2—7752no—
62C2#2835842611yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C3#17987869
commutator, hypocenterC52×C31C22×C9
FrattiniC3C2×#17987869
Fitting, socleC2×C3×C52×C31C2×C3
prime radicalC2×C3×C5⋊D155C3
cosocleC3×C52×C31C22×C3
LCSG ▷ C52×C31
UCSC1 ◁ C2×C3

Complements

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

NH ≅ G/Ntype
1. C2×C52⋊(C31⋊C9)C2semidirect
2. #28358426C2direct (N × H)
4. C52⋊(C31⋊C9)C22semidirect
7. C2×C5⋊D155C9semidirect
10. C2×C52×C31C2×C9semidirect
11. C5⋊D155C2×C9semidirect
16. C52×C31C22×C9semidirect
38. C2×C31(C5⋊D5)⋊C9semidirect
41. C2×C52D31⋊C9semidirect
44. C31C2×(C5⋊D5)⋊C9semidirect
47. C52C2×D31⋊C9semidirect
62. C2#28358426direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C52⋊(C31⋊C9)2
#283584262
C2×C3×C5⋊D1553
C2×D31⋊C925
C2×(C5⋊D5)⋊C931