Finite Group Databasebeta

← C2×D3×Dic15 #10624209

Subgroups — C2×D3×Dic15 #10624209

Order 720.

232 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 232 conjugacy classes of subgroups — too many to draw. Only its 98 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
1C22×C3×C5×D3C211yesmaximal, characteristic
2C2×C3⋊Dic15C211yesmaximal, characteristic, complemented
3C2×C3×Dic15C211yesmaximal, characteristic, complemented
4D3×Dic15C214yesmaximal, direct product factor
5C22×Dic15—31nomaximal
6C2×D3×Dic5—31nomaximal
7C22×C32×C5C2211yescharacteristic
8C2×C3×C5×D3C414yescomplemented
9C2×C3×C5×D3C2212yes—
10C3⋊Dic15C2212yescomplemented
11C3×Dic15C2212yescomplemented
12C2×D3×Dic3—51nomaximal, Hall
13C23×C3×C5—31no—
14C22×C5×D3D311yescharacteristic
15C2×Dic15—31no—
16C2×Dic15—31no—
17C2×Dic15—34no—
18C2×Dic15—61no—
19C2×Dic15D311yescharacteristic, direct product factor
20C2×C3×Dic5—31no—
21D3×Dic5—34no—
22C2×C32×C5C2×C412yescomplemented
23C2×C32×C5C2311yescharacteristic
24C3×C5×D3C2×C414yescomplemented
25C22×Dic5—91noHall
26C22×C3×D3D511yescharacteristic
27C2×C3⋊Dic3—51no—
28C2×C3×Dic3—51no—
29D3×Dic3—54no—
30C22×C3×C5—21no—
31C22×C3×C5—34no—
32C22×C3×C5—32no—
33C22×C3×C5C2×D311yescharacteristic
34C22×C3×C5C2×D311yescharacteristic
35C2×C5×D3Dic314yescomplemented
36C2×C5×D3C2×D312yes—
37Dic15—32no—
38Dic15—32no—
39Dic15—62no—
40Dic15C2×D312yesdirect product factor
41C3×Dic5—32no—
42C22×Dic3—151no—
43C2×C4×D3—151no—
44C32×C5C22×C411yescharacteristic, complemented, Hall
45C23×C5—31no—
46C2×Dic5—31no—
47C2×Dic5—94no—
48C2×Dic5—91no—
49C22×C32C2×D511yescharacteristic
50C2×C3×D3Dic514yescomplemented
51C2×C3×D3C2×D512yes—
52C3⋊Dic3—52no—
53C3×Dic3—52no—
54C2×C3×C5—22no—
55C2×C3×C5—21no—
56C2×C3×C5—34no—
57C2×C3×C5C4×D312yescomplemented
58C2×C3×C5C2×Dic312yescomplemented
59C2×C3×C5C22×D311yescharacteristic
60C2×C3×C5C22×D311yescharacteristic
61C5×D3C2×Dic314yescomplemented
62C23×C3—31no—
63C22×D3D1511yescharacteristic
64C2×C3×C4—151no—
65C2×Dic3—51no—
66C2×Dic3—154no—
67C2×Dic3—151no—
68C2×Dic3—151no—
69C2×Dic3—301no—
70C4×D3—154no—
71C22×C5—34no—
72C22×C5—32no—
73C22×C5D3211yescharacteristic
74Dic5—32no—
75Dic5—92no—
76C2×C32C2×Dic512yescomplemented
77C2×C32C22×D511yescharacteristic
78C3×D3C2×Dic514yescomplemented
79C22×C4—451noSylow
80C3×C5—21no—
81C3×C5C2×C4×D311yescharacteristic, complemented
82C3×C5C22×Dic311yescharacteristic, complemented
83C22×C3—21no—
84C22×C3—34no—
85C22×C3—32no—
86C22×C3D3×D511yescharacteristic
87C22×C3C2×D1511yescharacteristic
88C2×D3Dic1514yesdirect product factor
89C2×D3C2×D1512yes—
90C3×C4—152no—
91Dic3—52no—
92Dic3—152no—
93Dic3—152no—
94Dic3—302no—
95C2×C5—34no—
96C2×C5D3×Dic312yescomplemented
97C2×C5C2×D3211yescharacteristic
98C32C22×Dic511yescharacteristic, complemented, Sylow
99C23—31no—
100C2×C4—151no—
101C2×C4—454no—
102C2×C4—451no—
103C2×C3—22no—
104C2×C3—21no—
105C2×C3—34no—
106C2×C3D3×Dic512yescomplemented
107C2×C3C2×Dic1512yescomplemented
108C2×C3C2×D3×D511yescharacteristic
109C2×C3C22×D1511yescharacteristic
110D3C2×Dic1514yesdirect product factor
111C5C2×D3×Dic311yescharacteristic, complemented, Sylow
112C22—34no—
113C22—32no—
114C22D3×D1511yescharacteristic
115C4—152no—
116C4—452no—
117C3—21no—
118C3C2×D3×Dic511yescharacteristic, complemented
119C3C22×Dic1511yescharacteristic, complemented
120C2—34no—
121C2D3×Dic1512yesdirect product factor
122C2C2×D3×D1511yescharacteristic
subgroupG/H
center, hypercenterC22D3×D15
commutator, hypocenterC32×C5C22×C4
FrattiniC2C2×D3×D15
Fitting, socleC22×C32×C5C22
prime radicalC22×C3×C5×D3C2
cosocleC2×C32×C5C23
LCSG ▷ C32×C5
UCSC1 ◁ C22

Complements

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

NH ≅ G/Ntype
2. C2×C3⋊Dic15C2semidirect
3. C2×C3×Dic15C2semidirect
4. D3×Dic15C2direct (N × H)
8. C2×C3×C5×D3C4semidirect
10. C3⋊Dic15C22semidirect
11. C3×Dic15C22semidirect
19. C2×Dic15D3direct (N × H)
22. C2×C32×C5C2×C4semidirect
24. C3×C5×D3C2×C4semidirect
35. C2×C5×D3Dic3semidirect
40. Dic15C2×D3direct (N × H)
44. C32×C5C22×C4semidirect
50. C2×C3×D3Dic5semidirect
57. C2×C3×C5C4×D3semidirect
58. C2×C3×C5C2×Dic3semidirect
61. C5×D3C2×Dic3semidirect
76. C2×C32C2×Dic5semidirect
78. C3×D3C2×Dic5semidirect
81. C3×C5C2×C4×D3semidirect
82. C3×C5C22×Dic3semidirect
88. C2×D3Dic15direct (N × H)
96. C2×C5D3×Dic3semidirect
98. C32C22×Dic5semidirect
106. C2×C3D3×Dic5semidirect
107. C2×C3C2×Dic15semidirect
110. D3C2×Dic15direct (N × H)
111. C5C2×D3×Dic3semidirect
118. C3C2×D3×Dic5semidirect
119. C3C22×Dic15semidirect
121. C2D3×Dic15direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×C5×D32
C2×C3⋊Dic152
C2×C3×Dic152
D3×Dic152
C22×Dic153
C2×D3×Dic53
C2×D3×Dic35