Finite Group Databasebeta

← D15×Dic12 #13087272

Subgroups — D15×Dic12 #13087272

Order 1440.

258 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 66 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
1Dic6×D15C212yesmaximal
2#10623902C211yesmaximal, characteristic, complemented
3C3×C8×D15C211yesmaximal, characteristic
4C3×C5×Dic12C211yesmaximal, characteristic, complemented
5#10623809C212yesmaximal, complemented
6Q16×D15—31nomaximal
7D5×Dic12—31nomaximal
8#67180C2212yes—
9C3×C4×D15C2211yescharacteristic
10C3×C5×Dic6C2212yes—
11#67153—22no—
12Dic3×D15—22no—
13C32×C5×C8C2211yescharacteristic
14C3×C3⋊#168C2211yescharacteristic
15D3×Dic12—51nomaximal, Hall
16Q8×D15—32no—
17D5×Dic6—32no—
18C3×C5×Q16—31no—
19#6718—32no—
20Dic60—31no—
21Dic60—31no—
22Dic60—61no—
23C8×D15D311yescharacteristic
24C5×Dic12D311yescharacteristic, complemented
25C3×C8×D5—31no—
26#6663—32no—
27C2×C3×D15D411yescharacteristic
28C32×C4×C5C2311yescharacteristic
29C3⋊Dic15—22no—
30C3×Dic15D411yescharacteristic
31C3×C5×Dic3—22no—
32D5×Q16—91noHall
33D3×Dic6—52no—
34#3746—51no—
35C3×Dic12D511yescharacteristic, complemented
36C3×D3×C8—51no—
37#3719—52no—
38C3×C5×Q8—32no—
39C4×D15—62no—
40C4×D15C2×D311yescharacteristic
41Dic30—32no—
42Dic30—32no—
43Dic30—62no—
44Dic30—62no—
45C5×Dic6C2×D312yes—
46C3×C4×D5—31no—
47#1204—62no—
48D5×Dic3—62no—
49C3×C5×C8—21no—
50C3×C5×C8C2×D311yescharacteristic
51C3×C5×C8C2×D311yescharacteristic
52C3⋊#168C2×D311yescharacteristic
53C3×#168—31no—
54D3×Q16—151no—
55C2×Dic12—151no—
56C2×C32×C5C2×D411yescharacteristic
57C3×D15Q1612yescomplemented
58Q8×D5—92no—
59C5×Q16—31no—
60#689—92no—
61Dic20—91no—
62C8×D5—31no—
63#634—52no—
64C3×C4×D3—51no—
65C3×Dic6C2×D512yes—
66#627—102no—
67D3×Dic3—102no—
68C32×C8C2×D511yescharacteristic
69C3×C3⋊C8—51no—
70C2×D15D1211yescharacteristic
71C2×C3×D5—31no—
72C3×C4×C5—21no—
73C3×C4×C5—62no—
74C3×C4×C5C22×D311yescharacteristic
75C3×C4×C5C22×D311yescharacteristic
76Dic15—62no—
77Dic15—62no—
78Dic15—122no—
79Dic15D1211yescharacteristic
80C3×Dic5—31no—
81C5×Dic3—22no—
82D3×Q8—152no—
83C2×Dic6—152no—
84C3×Q16—31no—
85C2×C3×C8—151no—
86#216—152no—
87Dic12—152no—
88Dic12—151no—
89Dic12—151no—
90Dic12—301no—
91Dic12D1511yescharacteristic, direct product factor
92D3×C8—51no—
93C32×C5C2×Q1611yescharacteristic, complemented, Hall
94C5×Q8—32no—
95C4×D5—31no—
96C4×D5—182no—
97Dic10—92no—
98Dic10—182no—
99C5×C8D3211yescharacteristic
100#168—31no—
101C2×C3×D3—51no—
102C32×C4C22×D511yescharacteristic
103C3⋊Dic3—102no—
104C3×Dic3—22no—
105C3×Dic3—51no—
106C2×Q16—451noSylow
107C2×C3×C5—21no—
108C2×C3×C5C2×D1211yescharacteristic
109C2×C3×C5D3×D411yescharacteristic
110D15Dic1212yesdirect product factor
111C3×D5—32no—
112C3×Q8—32no—
113C2×C3×C4—151no—
114C2×Dic3—302no—
115C4×D3—51no—
116C4×D3—302no—
117Dic6—152no—
118Dic6—152no—
119Dic6—302no—
120Dic6—302no—
121Dic6—302no—
122Dic6C2×D1512yes—
123C3×C8—21no—
124C3×C8—151no—
125C3×C8D3×D511yescharacteristic
126C3×C8C2×D1511yescharacteristic
127C3⋊C8—51no—
128C2×D5—31no—
129C4×C5—62no—
130C4×C5C2×D3211yescharacteristic
131Dic5—31no—
132Dic5—182no—
133C2×C32D4×D511yescharacteristic
134C3×D3—52no—
135C2×Q8—452no—
136Q16—31no—
137Q16—452no—
138Q16—451no—
139C2×C8—151no—
140C3×C5—21no—
141C3×C5C2×Dic1211yescharacteristic, complemented
142C3×C5D3×Q1611yescharacteristic, complemented
143C22×C3—151no—
144C2×D3—51no—
145C3×C4—21no—
146C3×C4—62no—
147C3×C4—151no—
148C3×C4C2×D3×D511yescharacteristic
149C3×C4C22×D1511yescharacteristic
150Dic3—22no—
151Dic3—51no—
152Dic3—302no—
153Dic3—302no—
154Dic3—602no—
155C2×C5D3×D1211yescharacteristic
156D5—32no—
157C32D5×Q1611yescharacteristic, complemented, Sylow
158Q8—32no—
159Q8—452no—
160Q8—902no—
161C2×C4—151no—
162C2×C4—902no—
163C8—151no—
164C8D3×D1511yescharacteristic
165C2×C3—21no—
166C2×C3—152no—
167C2×C3D5×D1211yescharacteristic
168C2×C3D4×D1511yescharacteristic
169D3—52no—
170C5D3×Dic1211yescharacteristic, complemented, Sylow
171C22—151no—
172C4—62no—
173C4—151no—
174C4—902no—
175C4C2×D3×D1511yescharacteristic
176C3—21no—
177C3D5×Dic1211yescharacteristic, complemented
178C3Q16×D1511yescharacteristic, complemented
179C2—152no—
180C2D12×D1511yescharacteristic
subgroupG/H
centerC2D12×D15
commutator, cosocleC32×C4×C5C23
FrattiniC4C2×D3×D15
FittingC32×C5×C8C22
socleC2×C32×C5C2×D4
prime radicalC2×C3×D15D4
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
4. C3×C5×Dic12C2semidirect
5. #10623809C2semidirect
24. C5×Dic12D3semidirect
35. C3×Dic12D5semidirect
57. C3×D15Q16semidirect
91. Dic12D15direct (N × H)
93. C32×C5C2×Q16semidirect
110. D15Dic12direct (N × H)
141. C3×C5C2×Dic12semidirect
142. C3×C5D3×Q16semidirect
157. C32D5×Q16semidirect
170. C5D3×Dic12semidirect
177. C3D5×Dic12semidirect
178. C3Q16×D15semidirect

Maximal subgroups

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

subgroupindex
Dic6×D152
#106239022
C3×C8×D152
C3×C5×Dic122
#106238092
Q16×D153
D5×Dic123
D3×Dic125