Finite Group Databasebeta

← D3×#6719 #13087563

Subgroups — D3×#6719 #13087563

Order 1440.

562 conjugacy classes of subgroups; only the 154 normal subgroups are shown.

normal subgroups only

This group has 562 conjugacy classes of subgroups — too many to draw. Only its 154 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
1C23×C3×C5×D3C211yesmaximal, characteristic
2C2×D3×Dic15C212yesmaximal, complemented
3#10623913C211yesmaximal, characteristic, complemented
4C3×#6719C211yesmaximal, characteristic, complemented
5(C2×D3)⋊Dic15C212yesmaximal, complemented
6C2×#6719—31nomaximal
7D3×C22⋊Dic5—31nomaximal
8C23×C32×C5C2211yescharacteristic
9C22×C3×C5×D3—24no—
10C22×C3×C5×D3C414yescomplemented
11C22×C3×C5×D3C2211yescharacteristic
12C22×C3×C5×D3C2211yescharacteristic
13C2×C3⋊Dic15C2212yescomplemented
14C2×C3×Dic15C2212yescomplemented
15D3×Dic15—24no—
16D3×#217—51nomaximal, Hall
17C24×C3×C5—31no—
18C23×C5×D3D311yescharacteristic
19C22×Dic15—32no—
20C2×D3×Dic5—32no—
21#6719—31no—
22#6719—31no—
23#6719—32no—
24#6719—61no—
25#6719D311yescharacteristic, direct product factor
26C3×C22⋊Dic5—31no—
27(C2×D3)⋊Dic5—32no—
28C22×C32×C5—22no—
29C22×C32×C5C2×C412yescomplemented
30C22×C32×C5C2311yescharacteristic
31C2×C3×C5×D3—22no—
32C2×C3×C5×D3—28no—
33C2×C3×C5×D3C2×C412yes—
34C2×C3×C5×D3C2×C412yescomplemented
35C2×C3×C5×D3D414yes—
36C3⋊Dic15—22no—
37C3×Dic15—22no—
38C2×C22⋊Dic5—91noHall
39C23×C3×D3D511yescharacteristic
40C2×D3×Dic3—52no—
41#3757—51no—
42C3×#217—51no—
43(C2×D3)⋊Dic3—52no—
44C23×C3×C5—21no—
45C23×C3×C5—31no—
46C23×C3×C5—34no—
47C23×C3×C5—31no—
48C23×C3×C5—64no—
49C23×C3×C5C2×D311yescharacteristic
50C23×C3×C5C2×D311yescharacteristic
51C22×C5×D3—24no—
52C22×C5×D3Dic314yescomplemented
53C22×C5×D3C2×D311yescharacteristic
54C22×C5×D3C2×D311yescharacteristic
55C2×Dic15—32no—
56C2×Dic15—32no—
57C2×Dic15—64no—
58C2×Dic15—62no—
59C2×Dic15C2×D312yescomplemented
60C2×C3×Dic5—32no—
61D3×Dic5—64no—
62C2×#217—151no—
63D3×C22⋊C4—151no—
64C2×C32×C5—22no—
65C2×C32×C5C22×C411yescharacteristic
66C2×C32×C5C2×D412yes—
67C3×C5×D3—22no—
68C3×C5×D3C22⋊C414yescomplemented
69C24×C5—31no—
70C22×Dic5—92no—
71C22⋊Dic5—31no—
72C22⋊Dic5—92no—
73C22⋊Dic5—91no—
74C23×C32C2×D511yescharacteristic
75C22×C3×D3—24no—
76C22×C3×D3Dic514yescomplemented
77C22×C3×D3C2×D511yescharacteristic
78C22×C3×D3C2×D511yescharacteristic
79C2×C3⋊Dic3—52no—
80C2×C3×Dic3—52no—
81D3×Dic3—104no—
82C22×C3×C5—22no—
83C22×C3×C5—22no—
84C22×C3×C5—22no—
85C22×C3×C5—21no—
86C22×C3×C5—32no—
87C22×C3×C5—34no—
88C22×C3×C5—32no—
89C22×C3×C5—42no—
90C22×C3×C5—68no—
91C22×C3×C5—62no—
92C22×C3×C5C4×D312yescomplemented
93C22×C3×C5C2×Dic312yescomplemented
94C22×C3×C5C22×D311yescharacteristic
95C22×C3×C5C22×D311yescharacteristic
96C2×C5×D3—22no—
97C2×C5×D3—28no—
98C2×C5×D3C2×Dic312yes—
99C2×C5×D3C2×Dic312yescomplemented
100C2×C5×D3#6714yes—
101Dic15—22no—
102Dic15—62no—
103Dic15—62no—
104Dic15—122no—
105C3×Dic5—62no—
106C24×C3—31no—
107C23×D3D1511yescharacteristic
108C22×Dic3—152no—
109C2×C4×D3—152no—
110C3×C22⋊C4—151no—
111#217—51no—
112#217—152no—
113#217—151no—
114#217—151no—
115#217—301no—
116(C2×D3)⋊C4—152no—
117C32×C5C2×C22⋊C411yescharacteristic, complemented, Hall
118C23×C5—31no—
119C23×C5—34no—
120C23×C5—31no—
121C23×C5—64no—
122C23×C5D3211yescharacteristic
123C2×Dic5—32no—
124C2×Dic5—92no—
125C2×Dic5—184no—
126C22×C32—22no—
127C22×C32C2×Dic512yescomplemented
128C22×C32C22×D511yescharacteristic
129C2×C3×D3—22no—
130C2×C3×D3—28no—
131C2×C3×D3C2×Dic512yes—
132C2×C3×D3C2×Dic512yescomplemented
133C2×C3×D3C22⋊D514yes—
134C3⋊Dic3—102no—
135C3×Dic3—102no—
136C2×C22⋊C4—451noSylow
137C2×C3×C5—22no—
138C2×C3×C5—22no—
139C2×C3×C5—21no—
140C2×C3×C5—22no—
141C2×C3×C5—34no—
142C2×C3×C5—42no—
143C2×C3×C5—62no—
144C2×C3×C5C2×C4×D311yescharacteristic
145C2×C3×C5D3×D412yes—
146C2×C3×C5C22×Dic311yescharacteristic
147C2×C3×C5C2×#6712yes—
148C5×D3—22no—
149C5×D3#21714yescomplemented
150C23×C3—21no—
151C23×C3—31no—
152C23×C3—34no—
153C23×C3—31no—
154C23×C3—64no—
155C23×C3D3×D511yescharacteristic
156C23×C3C2×D1511yescharacteristic
157C22×D3—24no—
158C22×D3Dic1514yescomplemented
159C22×D3C2×D1511yescharacteristic
160C22×D3C2×D1511yescharacteristic
161C2×C3×C4—152no—
162C2×Dic3—52no—
163C2×Dic3—152no—
164C2×Dic3—152no—
165C2×Dic3—302no—
166C2×Dic3—304no—
167C4×D3—304no—
168C22×C5—22no—
169C22×C5—32no—
170C22×C5—34no—
171C22×C5—32no—
172C22×C5—68no—
173C22×C5—62no—
174C22×C5D3×Dic312yescomplemented
175C22×C5C2×D3211yescharacteristic
176Dic5—62no—
177Dic5—182no—
178C2×C32—22no—
179C2×C32C22×Dic511yescharacteristic
180C2×C32C2×C22⋊D512yes—
181C3×D3—22no—
182C3×D3C22⋊Dic514yescomplemented
183C24—31no—
184C22×C4—452no—
185C22⋊C4—151no—
186C22⋊C4—452no—
187C22⋊C4—451no—
188C3×C5—21no—
189C3×C5D3×C22⋊C411yescharacteristic, complemented
190C3×C5C2×#21711yescharacteristic, complemented
191C22×C3—22no—
192C22×C3—22no—
193C22×C3—22no—
194C22×C3—21no—
195C22×C3—32no—
196C22×C3—34no—
197C22×C3—32no—
198C22×C3—42no—
199C22×C3—68no—
200C22×C3—62no—
201C22×C3D3×Dic512yescomplemented
202C22×C3C2×Dic1512yescomplemented
203C22×C3C2×D3×D511yescharacteristic
204C22×C3C22×D1511yescharacteristic
205C2×D3—22no—
206C2×D3—28no—
207C2×D3C2×Dic1512yes—
208C2×D3C2×Dic1512yescomplemented
209C2×D3#122014yes—
210C3×C4—302no—
211Dic3—102no—
212Dic3—302no—
213Dic3—302no—
214Dic3—602no—
215C2×C5—22no—
216C2×C5—34no—
217C2×C5—62no—
218C2×C5C2×D3×Dic311yescharacteristic
219C2×C5D3×#6712yes—
220C32C2×C22⋊Dic511yescharacteristic, complemented, Sylow
221C23—31no—
222C23—34no—
223C23—31no—
224C23—64no—
225C23D3×D1511yescharacteristic
226C2×C4—152no—
227C2×C4—452no—
228C2×C4—904no—
229C2×C3—22no—
230C2×C3—22no—
231C2×C3—21no—
232C2×C3—22no—
233C2×C3—34no—
234C2×C3—42no—
235C2×C3—62no—
236C2×C3C2×D3×Dic511yescharacteristic
237C2×C3D3×C22⋊D512yes—
238C2×C3C22×Dic1511yescharacteristic
239C2×C3C2×#122012yes—
240D3—22no—
241D3#671914yesdirect product factor
242C5D3×#21711yescharacteristic, complemented, Sylow
243C22—22no—
244C22—32no—
245C22—34no—
246C22—32no—
247C22—68no—
248C22—62no—
249C22D3×Dic1512yescomplemented
250C22C2×D3×D1511yescharacteristic
251C4—302no—
252C4—902no—
253C3—21no—
254C3D3×C22⋊Dic511yescharacteristic, complemented
255C3C2×#671911yescharacteristic, complemented
256C2—22no—
257C2—34no—
258C2—62no—
259C2C2×D3×Dic1511yescharacteristic
260C2D3×#122012yes—
subgroupG/H
center, FrattiniC22C2×D3×D15
commutatorC2×C32×C5C22×C4
FittingC23×C32×C5C22
socle, cosocleC22×C32×C5C23
prime radicalC23×C3×C5×D3C2
hypercenterC23D3×D15
hypocenterC32×C5C2×C22⋊C4
LCSG ▷ C2×C32×C5 ▷ C32×C5
UCSC1 ◁ C22 ◁ C23

Complements

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

NH ≅ G/Ntype
2. C2×D3×Dic15C2semidirect
3. #10623913C2semidirect
4. C3×#6719C2semidirect
5. (C2×D3)⋊Dic15C2semidirect
10. C22×C3×C5×D3C4semidirect
13. C2×C3⋊Dic15C22semidirect
14. C2×C3×Dic15C22semidirect
25. #6719D3direct (N × H)
29. C22×C32×C5C2×C4semidirect
34. C2×C3×C5×D3C2×C4semidirect
52. C22×C5×D3Dic3semidirect
59. C2×Dic15C2×D3semidirect
68. C3×C5×D3C22⋊C4semidirect
76. C22×C3×D3Dic5semidirect
92. C22×C3×C5C4×D3semidirect
93. C22×C3×C5C2×Dic3semidirect
99. C2×C5×D3C2×Dic3semidirect
117. C32×C5C2×C22⋊C4semidirect
127. C22×C32C2×Dic5semidirect
132. C2×C3×D3C2×Dic5semidirect
149. C5×D3#217semidirect
158. C22×D3Dic15semidirect
174. C22×C5D3×Dic3semidirect
182. C3×D3C22⋊Dic5semidirect
189. C3×C5D3×C22⋊C4semidirect
190. C3×C5C2×#217semidirect
201. C22×C3D3×Dic5semidirect
202. C22×C3C2×Dic15semidirect
208. C2×D3C2×Dic15semidirect
220. C32C2×C22⋊Dic5semidirect
241. D3#6719direct (N × H)
242. C5D3×#217semidirect
249. C22D3×Dic15semidirect
254. C3D3×C22⋊Dic5semidirect
255. C3C2×#6719semidirect

Maximal subgroups

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

subgroupindex
C23×C3×C5×D32
C2×D3×Dic152
#106239132
C3×#67192
(C2×D3)⋊Dic152
C2×#67193
D3×C22⋊Dic53
D3×#2175