Finite Group Databasebeta

← D3×Dic60 #13087275

Subgroups — D3×Dic60 #13087275

Order 1440.

258 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 74 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
1D3×Dic30C212yesmaximal
2#10623902C211yesmaximal, characteristic, complemented
3C3×Dic60C211yesmaximal, characteristic, complemented
4C3×C5×D3×C8C211yesmaximal, characteristic
5#10623808C212yesmaximal, complemented
6C2×Dic60—31nomaximal
7D3×Dic20—31nomaximal
8#67180C2212yes—
9C3×Dic30C2212yes—
10C3×C4×C5×D3C2211yescharacteristic
11#67153—22no—
12D3×Dic15—22no—
13C32×C5×C8C2211yescharacteristic
14C3×C5×C3⋊C8C2211yescharacteristic
15D3×Dic12—51nomaximal, Hall
16C2×Dic30—32no—
17D3×Dic10—32no—
18C2×C3×C5×C8—31no—
19Dic60—32no—
20Dic60—31no—
21Dic60—31no—
22Dic60—61no—
23Dic60D311yescharacteristic, direct product factor
24C5×D3×C8D311yescharacteristic
25C3×Dic20—31no—
26#6662—32no—
27C2×C3×C5×D3D411yescharacteristic
28C32×C4×C5C2311yescharacteristic
29C3⋊Dic15—22no—
30C3×Dic15—22no—
31C3×C5×Dic3D411yescharacteristic
32C2×Dic20—91noHall
33D3×Dic6—52no—
34#3746—51no—
35C3×Dic12—51no—
36C3×D3×C8D511yescharacteristic
37#3719—52no—
38C2×C3×C4×C5—31no—
39C2×Dic15—62no—
40Dic30—32no—
41Dic30—32no—
42Dic30—62no—
43Dic30—62no—
44Dic30C2×D312yes—
45C4×C5×D3C2×D311yescharacteristic
46C3×Dic10—32no—
47#1204—62no—
48D3×Dic5—62no—
49C3×C5×C8—21no—
50C3×C5×C8—31no—
51C3×C5×C8C2×D311yescharacteristic
52C3×C5×C8C2×D311yescharacteristic
53C5×C3⋊C8C2×D311yescharacteristic
54D3×Q16—151no—
55C2×Dic12—151no—
56C2×C32×C5C2×D411yescharacteristic
57C3×C5×D3Q1612yescomplemented
58C2×Dic10—92no—
59C2×C5×C8—31no—
60Dic20—31no—
61Dic20—92no—
62Dic20—91no—
63#634—52no—
64C3×C4×D3C2×D511yescharacteristic
65C3×Dic6—52no—
66#627—102no—
67D3×Dic3—102no—
68C32×C8C2×D511yescharacteristic
69C3×C3⋊C8C2×D511yescharacteristic
70C22×C3×C5—31no—
71C2×C5×D3D1211yescharacteristic
72C3×C4×C5—21no—
73C3×C4×C5—31no—
74C3×C4×C5C22×D311yescharacteristic
75C3×C4×C5C22×D311yescharacteristic
76Dic15—22no—
77Dic15—62no—
78Dic15—62no—
79Dic15—122no—
80C3×Dic5—62no—
81C5×Dic3D1211yescharacteristic
82D3×Q8—152no—
83C2×Dic6—152no—
84C3×Q16—151no—
85C2×C3×C8—31no—
86#216—152no—
87Dic12—51no—
88Dic12—152no—
89Dic12—151no—
90Dic12—151no—
91Dic12—301no—
92D3×C8D1511yescharacteristic
93C32×C5C2×Q1611yescharacteristic, complemented, Hall
94C2×C4×C5—31no—
95C2×Dic5—182no—
96Dic10—32no—
97Dic10—92no—
98Dic10—182no—
99C5×C8—31no—
100C5×C8D3211yescharacteristic
101C2×C3×D3D2011yescharacteristic
102C32×C4C22×D511yescharacteristic
103C3⋊Dic3—102no—
104C3×Dic3—102no—
105C3×Dic3D2011yescharacteristic
106C2×Q16—451noSylow
107C2×C3×C5—21no—
108C2×C3×C5—32no—
109C2×C3×C5C2×D1211yescharacteristic
110C2×C3×C5D3×D411yescharacteristic
111C5×D3Dic1212yescomplemented
112C3×Q8—152no—
113C2×C3×C4—31no—
114C2×Dic3—302no—
115C4×D3—302no—
116C4×D3C2×D1511yescharacteristic
117Dic6—52no—
118Dic6—152no—
119Dic6—152no—
120Dic6—302no—
121Dic6—302no—
122Dic6—302no—
123C3×C8—21no—
124C3×C8—31no—
125C3×C8D3×D511yescharacteristic
126C3×C8C2×D1511yescharacteristic
127C3⋊C8C2×D1511yescharacteristic
128C22×C5—31no—
129C4×C5—31no—
130C4×C5C2×D3211yescharacteristic
131Dic5—62no—
132Dic5—182no—
133C2×C32C2×D2011yescharacteristic
134C3×D3Dic2012yescomplemented
135C2×Q8—452no—
136Q16—151no—
137Q16—452no—
138Q16—451no—
139C2×C8—31no—
140C3×C5—21no—
141C3×C5C2×Dic1211yescharacteristic, complemented
142C3×C5D3×Q1611yescharacteristic, complemented
143C22×C3—31no—
144C2×D3D6011yescharacteristic
145C3×C4—21no—
146C3×C4—31no—
147C3×C4—302no—
148C3×C4C2×D3×D511yescharacteristic
149C3×C4C22×D1511yescharacteristic
150Dic3—102no—
151Dic3—302no—
152Dic3—302no—
153Dic3—602no—
154Dic3D6011yescharacteristic
155C2×C5—32no—
156C2×C5D3×D1211yescharacteristic
157C32C2×Dic2011yescharacteristic, complemented, Sylow
158Q8—152no—
159Q8—452no—
160Q8—902no—
161C2×C4—31no—
162C2×C4—902no—
163C8—31no—
164C8D3×D1511yescharacteristic
165C2×C3—21no—
166C2×C3—32no—
167C2×C3D3×D2011yescharacteristic
168C2×C3C2×D6011yescharacteristic
169D3Dic6012yesdirect product factor
170C5D3×Dic1211yescharacteristic, complemented, Sylow
171C22—31no—
172C4—31no—
173C4—302no—
174C4—902no—
175C4C2×D3×D1511yescharacteristic
176C3—21no—
177C3D3×Dic2011yescharacteristic, complemented
178C3C2×Dic6011yescharacteristic, complemented
179C2—32no—
180C2D3×D6011yescharacteristic
subgroupG/H
centerC2D3×D60
commutator, cosocleC32×C4×C5C23
FrattiniC4C2×D3×D15
FittingC32×C5×C8C22
socleC2×C32×C5C2×D4
prime radicalC2×C3×C5×D3D4
hypercenterC8D3×D15
hypocenterC32×C5C2×Q16
LCSG ▷ C32×C4×C5 ▷ C2×C32×C5 ▷ C32×C5
UCSC1 ◁ C2 ◁ C4 ◁ C8

Complements

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

NH ≅ G/Ntype
2. #10623902C2semidirect
3. C3×Dic60C2semidirect
5. #10623808C2semidirect
23. Dic60D3direct (N × H)
57. C3×C5×D3Q16semidirect
93. C32×C5C2×Q16semidirect
111. C5×D3Dic12semidirect
134. C3×D3Dic20semidirect
141. C3×C5C2×Dic12semidirect
142. C3×C5D3×Q16semidirect
157. C32C2×Dic20semidirect
169. D3Dic60direct (N × H)
170. C5D3×Dic12semidirect
177. C3D3×Dic20semidirect
178. C3C2×Dic60semidirect

Maximal subgroups

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

subgroupindex
D3×Dic302
#106239022
C3×Dic602
C3×C5×D3×C82
#106238082
C2×Dic603
D3×Dic203
D3×Dic125