Finite Group Databasebeta

← C3×((C5⋊D5)⋊C3)⋊D31 #42124752

Subgroups — C3×((C5⋊D5)⋊C3)⋊D31 #42124752

Order 27900.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C31×(C5⋊D5)⋊C3C211yesmaximal, characteristic, complemented
2C3×C31⋊#3874C212yesmaximal, complemented
3C3×(C5⋊D5)⋊D31—31nomaximal
4((C5⋊D5)⋊C3)⋊D31C311yesmaximal, characteristic, direct product factor
5C3×C31×C52⋊C3C2211yescharacteristic, complemented, Hall
6C3×C31×C5⋊D5D311yescharacteristic, complemented
7C3×C5×D155—32no—
8C31×(C5⋊D5)⋊C3—21no—
9C31×(C5⋊D5)⋊C3C2×C311yescharacteristic, complemented
10C31⋊#3874C2×C312yescomplemented
11(C5⋊D5)⋊D31—31noHall
12C31×C52⋊C3—21no—
13C31×C52⋊C3C22×C311yescharacteristic, complemented
14C3×C52×C31C2×D311yescharacteristic, complemented
15C3×D5×D31—152no—
16C31×C5⋊D5C3×D311yescharacteristic, complemented
17C5×D155—32no—
18C2×C3×D93—251nomaximal, Hall
19C3×D155—32no—
20C3×D5×C31—152no—
21C3×C5×D31—152no—
22C3×#3874⋊C2—311nomaximal, Hall
23C52×C31C2×C3×D311yescharacteristic, complemented, Hall
24D5×D31—152no—
25C2×C32×C31—251no—
26C3×D93—252no—
27C3×C5×C31—32no—
28C3×(C5⋊D5)⋊C3D3111yescharacteristic, complemented
29C3×#3874—312no—
30C2×D93—251no—
31C2×C3×D31—751no—
32D155—32no—
33C5×D31—152no—
34D5×C31—152no—
35C3×D52—931no—
36#3874⋊C2—311no—
37C32×C31—251noHall
38C3×C52⋊C3C2×D3111yescharacteristic, complemented, Hall
39C2×C3×C31—251no—
40C2×C3×C31—251no—
41C2×C3×C31—501no—
42D93—252no—
43C3×D31—152no—
44C5×C31—32no—
45C3×C5⋊D5D9311yescharacteristic, complemented
46C3×C5×D5—932no—
47(C5⋊D5)⋊C3—21no—
48(C5⋊D5)⋊C3C3×D3111yescharacteristic, complemented
49#3874—312no—
50C2×D31—751noHall
51D52—931noHall
52C3×C31—251no—
53C3×C31—501no—
54C3×C31#3874⋊C211yescharacteristic, complemented
55C3×C52C2×D9311yescharacteristic, complemented
56C52⋊C3—21no—
57C52⋊C3C2×C3×D3111yescharacteristic, complemented
58C2×C31—251no—
59D31—152no—
60C2×C3×D5—4652no—
61C5⋊D5C3×D9311yescharacteristic, complemented
62C5×D5—932no—
63C2×C3×D3—7751noHall
64C31C3×#3874⋊C211yescharacteristic, complemented, Sylow
65C2×C3×C5—4652no—
66C3×D5—152no—
67C3×D5—932no—
68C52C2×C3×D9311yescharacteristic, complemented, Sylow
69C2×D5—4652no—
70C2×C32—251no—
71C3×D3—7752no—
72C3×C5—32no—
73C22×C3—23251no—
74C2×D3—7751no—
75C2×C5—4652no—
76D5—152no—
77D5—932no—
78C32—251noSylow
79C2×C3—251no—
80C2×C3—251no—
81C2×C3—501no—
82C2×C3—4652no—
83D3—7752no—
84C5—32no—
85C22—23251noSylow
86C3—251no—
87C3—501no—
88C3((C5⋊D5)⋊C3)⋊D3111yescharacteristic, direct product factor
89C2—251no—
90C2—4652no—
subgroupG/H
center, hypercenterC3((C5⋊D5)⋊C3)⋊D31
commutator, cosocle, hypocenterC31×C52⋊C3C22×C3
FrattiniC1G
Fitting, socleC3×C52×C31C2×D3
LCSG ▷ C31×C52⋊C3
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
1. C3×C31×(C5⋊D5)⋊C3C2semidirect
2. C3×C31⋊#3874C2semidirect
4. ((C5⋊D5)⋊C3)⋊D31C3direct (N × H)
5. C3×C31×C52⋊C3C22semidirect
6. C3×C31×C5⋊D5D3semidirect
9. C31×(C5⋊D5)⋊C3C2×C3semidirect
10. C31⋊#3874C2×C3semidirect
13. C31×C52⋊C3C22×C3semidirect
14. C3×C52×C31C2×D3semidirect
16. C31×C5⋊D5C3×D3semidirect
23. C52×C31C2×C3×D3semidirect
28. C3×(C5⋊D5)⋊C3D31semidirect
38. C3×C52⋊C3C2×D31semidirect
45. C3×C5⋊D5D93semidirect
48. (C5⋊D5)⋊C3C3×D31semidirect
54. C3×C31#3874⋊C2semidirect
55. C3×C52C2×D93semidirect
57. C52⋊C3C2×C3×D31semidirect
61. C5⋊D5C3×D93semidirect
64. C31C3×#3874⋊C2semidirect
68. C52C2×C3×D93semidirect
88. C3((C5⋊D5)⋊C3)⋊D31direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C31×(C5⋊D5)⋊C32
C3×C31⋊#38742
C3×(C5⋊D5)⋊D313
((C5⋊D5)⋊C3)⋊D313
C2×C3×D9325
C3×#3874⋊C231