Finite Group Databasebeta

← #13108560

Subgroups — #13108560

Order 1620.

448 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 448 conjugacy classes of subgroups — too many to draw. Only its 65 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C3⋊(C3⋊D15)C212yesmaximal, complemented
2C32×C5×C3⋊D3C211yesmaximal, characteristic, complemented
3C5⋊#1113—34nomaximal
4D3×C3⋊D15—32nomaximal
5C34×C5C2211yescharacteristic, complemented, Hall
6C3⋊#1113—51nomaximal, Hall
7C3⋊(C3⋊D15)D312yescomplemented
8C3×C3⋊D15—32no—
9C3×C3⋊D15—38no—
10C3×C3⋊D15—68no—
11C3×C5×C3⋊D3D314yescomplemented
12C32×C5×D3—32no—
13C32×C5×D3—61no—
14C2×C3⋊D15—91no—
15(C3⋊D3)⋊D5—91no—
16D3×D15—98no—
17C3×C3⋊(C3⋊D3)—52no—
18C32×C3⋊D3D511yescharacteristic, complemented
19C33×C5—21no—
20C33×C5—28no—
21C33×C5—44no—
22C33×C5C2×D312yescomplemented
23C33×C5C2×D314yescomplemented
24#1113—154no—
25D3×C3⋊D3—152no—
26C2×C32×C5—91no—
27C3⋊D15—32no—
28C3⋊D15—38no—
29C3⋊D15—68no—
30C5×C3⋊D3C3⋊D311yescharacteristic, complemented
31C3×D15—98no—
32C3×D15—92no—
33C3×D15—188no—
34C3×C5×D3—38no—
35C3×C5×D3—64no—
36C34C2×D511yescharacteristic, complemented, Sylow
37C2×D15—274no—
38D3×D5—272no—
39C3⋊(C3⋊D3)—52no—
40C3×C3⋊D3—152no—
41C3×C3⋊D3—158no—
42C3×C3⋊D3—308no—
43C3×C3⋊D3D1514yescomplemented
44C32×D3—32no—
45C32×D3—61no—
46C32×C5—28no—
47C32×C5—28no—
48C32×C5—24no—
49C32×C5—44no—
50C32×C5—412no—
51C32×C5—44no—
52C32×C5D3218yescomplemented
53C32×C5D3211yescharacteristic, complemented
54C32×C5C2×C3⋊D311yescharacteristic, complemented
55C2×C3⋊D3—451no—
56D32—458no—
57D32—451no—
58C2×C3×C5—94no—
59D15—92no—
60D15—98no—
61D15—188no—
62C3×D5—272no—
63C5×D3—32no—
64C5×D3—61no—
65C33—28no—
66C33—21no—
67C33—44no—
68C33D3×D512yescomplemented
69C33C2×D1514yescomplemented
70C2×D5—811noHall
71C2×C32—91no—
72C3⋊D3—152no—
73C3⋊D3—158no—
74C3⋊D3—308no—
75C3⋊D3C3⋊D1511yescharacteristic, complemented
76C3×D3—38no—
77C3×D3—64no—
78C3×D3—458no—
79C3×D3—452no—
80C3×D3—908no—
81C3×C5—21no—
82C3×C5—28no—
83C3×C5—44no—
84C3×C5D3×C3⋊D312yescomplemented
85C3×C5#111314yescomplemented
86C2×D3—1352no—
87C2×D3—1354no—
88C2×C5—91no—
89D5—272no—
90C32—28no—
91C32—28no—
92C32—24no—
93C32—44no—
94C32—412no—
95C32—44no—
96C32D3×D1518yescomplemented
97C32(C3⋊D3)⋊D511yescharacteristic, complemented
98C32C2×C3⋊D1511yescharacteristic, complemented
99C2×C3—94no—
100C2×C3—1352no—
101D3—32no—
102D3—61no—
103D3—452no—
104D3—458no—
105D3—908no—
106C5C3⋊#111311yescharacteristic, complemented, Sylow
107C22—4051noSylow
108C3—21no—
109C3—28no—
110C3—44no—
111C3D3×C3⋊D1512yescomplemented
112C3C5⋊#111314yescomplemented
113C2—91no—
114C2—1352no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC34×C5C22
LCSG ▷ C34×C5
UCSC1

Complements

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

NH ≅ G/Ntype
1. C3×C3⋊(C3⋊D15)C2semidirect
2. C32×C5×C3⋊D3C2semidirect
5. C34×C5C22semidirect
7. C3⋊(C3⋊D15)D3semidirect
11. C3×C5×C3⋊D3D3semidirect
18. C32×C3⋊D3D5semidirect
22. C33×C5C2×D3semidirect
23. C33×C5C2×D3semidirect
30. C5×C3⋊D3C3⋊D3semidirect
36. C34C2×D5semidirect
43. C3×C3⋊D3D15semidirect
52. C32×C5D32semidirect
53. C32×C5D32semidirect
54. C32×C5C2×C3⋊D3semidirect
68. C33D3×D5semidirect
69. C33C2×D15semidirect
75. C3⋊D3C3⋊D15semidirect
84. C3×C5D3×C3⋊D3semidirect
85. C3×C5#1113semidirect
96. C32D3×D15semidirect
97. C32(C3⋊D3)⋊D5semidirect
98. C32C2×C3⋊D15semidirect
106. C5C3⋊#1113semidirect
111. C3D3×C3⋊D15semidirect
112. C3C5⋊#1113semidirect

Maximal subgroups

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

subgroupindex
C3×C3⋊(C3⋊D15)2
C32×C5×C3⋊D32
C5⋊#11133
D3×C3⋊D153
C3⋊#11135