Finite Group Databasebeta

← C3×C22⋊C4×D15 #13087978

Subgroups — C3×C22⋊C4×D15 #13087978

Order 1440.

562 conjugacy classes of subgroups; only the 142 normal subgroups are shown.

normal subgroups only

This group has 562 conjugacy classes of subgroups — too many to draw. Only its 142 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×D15C211yesmaximal, characteristic
2C2×C3×C4×D15C212yesmaximal, complemented
3C32×C5×C22⋊C4C211yesmaximal, characteristic, complemented
4C3×#6719C211yesmaximal, characteristic, complemented
5C3×#6714C212yesmaximal, complemented
6C22⋊C4×D15C311yesmaximal, characteristic, direct product factor
7C3×D5×C22⋊C4—31nomaximal
8C23×C32×C5C2211yescharacteristic
9C22×C3×D15—24no—
10C22×C3×D15C414yescomplemented
11C22×C3×D15C2211yescharacteristic
12C22×C3×D15C2211yescharacteristic
13C2×C32×C4×C5C2212yescomplemented
14C2×C3×Dic15C2212yescomplemented
15C3×C4×D15—24no—
16C3×D3×C22⋊C4—51nomaximal, Hall
17C23×D15C2×C311yescharacteristic
18C23×C3×D5—31no—
19C2×C4×D15C2×C312yescomplemented
20C2×C3×C4×D5—32no—
21C3×C5×C22⋊C4—21no—
22C3×C5×C22⋊C4D311yescharacteristic, complemented
23C3×C5×C22⋊C4C2×C311yescharacteristic, complemented
24#6719C2×C311yescharacteristic, complemented
25#6714C2×C312yescomplemented
26C3×C22⋊Dic5—31no—
27C3×#685—32no—
28C22×C32×C5—22no—
29C22×C32×C5C2×C412yescomplemented
30C22×C32×C5C2311yescharacteristic
31C2×C3×D15—22no—
32C2×C3×D15—28no—
33C2×C3×D15C2×C412yes—
34C2×C3×D15C2×C412yescomplemented
35C2×C3×D15D414yes—
36C32×C4×C5—22no—
37C3×Dic15—22no—
38D5×C22⋊C4—31noHall
39C23×C3×D3—51no—
40C2×C3×C4×D3—52no—
41C32×C22⋊C4D511yescharacteristic, complemented
42C3×#217—51no—
43C3×(C2×D3)⋊C4—52no—
44C23×C3×C5—21no—
45C23×C3×C5C2×D311yescharacteristic
46C23×C3×C5C22×C311yescharacteristic
47C22×D15—24no—
48C22×D15C3×C414yescomplemented
49C22×D15C22×C311yescharacteristic
50C22×D15C22×C311yescharacteristic
51C22×C3×D5—31no—
52C22×C3×D5—34no—
53C22×C3×D5—31no—
54C22×C3×D5—64no—
55C2×C3×C4×C5—22no—
56C2×C3×C4×C5C2×D312yescomplemented
57C2×C3×C4×C5C22×C312yescomplemented
58C2×Dic15C22×C312yescomplemented
59C4×D15—24no—
60C2×C3×Dic5—32no—
61C3×C4×D5—64no—
62C2×C3×C22⋊C4—151no—
63D3×C22⋊C4—51no—
64C2×C32×C5—22no—
65C2×C32×C5C22×C411yescharacteristic
66C2×C32×C5C2×D412yes—
67C3×D15—22no—
68C3×D15C22⋊C414yesdirect product factor
69C23×D5—31no—
70C2×C4×D5—32no—
71C5×C22⋊C4C3×D311yescharacteristic, complemented
72C22⋊Dic5—31no—
73#685—32no—
74C23×C32C2×D511yescharacteristic
75C22×C3×D3—51no—
76C22×C3×D3—54no—
77C22×C3×D3—51no—
78C22×C3×D3—104no—
79C2×C32×C4C2×D512yescomplemented
80C2×C3×Dic3—52no—
81C3×C4×D3—104no—
82C22×C3×C5—22no—
83C22×C3×C5—22no—
84C22×C3×C5—22no—
85C22×C3×C5—21no—
86C22×C3×C5—42no—
87C22×C3×C5C4×D312yescomplemented
88C22×C3×C5C2×C3×C412yescomplemented
89C22×C3×C5C22×D311yescharacteristic
90C22×C3×C5C23×C311yescharacteristic
91C2×D15—22no—
92C2×D15—28no—
93C2×D15C2×C3×C412yes—
94C2×D15C2×C3×C412yescomplemented
95C2×D15C3×D414yes—
96C2×C3×D5—32no—
97C2×C3×D5—34no—
98C2×C3×D5—32no—
99C2×C3×D5—68no—
100C2×C3×D5—62no—
101C3×C4×C5—22no—
102C3×C4×C5—22no—
103C3×C4×C5—42no—
104Dic15—22no—
105C3×Dic5—62no—
106C24×C3—151no—
107C23×D3—51no—
108C22×C3×C4—152no—
109C2×C4×D3—52no—
110C3×C22⋊C4—21no—
111C3×C22⋊C4—151no—
112C3×C22⋊C4—152no—
113C3×C22⋊C4C3×D511yescharacteristic, complemented
114C3×C22⋊C4D1511yescharacteristic, direct product factor
115#217—51no—
116(C2×D3)⋊C4—52no—
117C32×C5C2×C22⋊C411yescharacteristic, complemented, Hall
118C23×C5C2×C3×D311yescharacteristic
119C22×D5—31no—
120C22×D5—34no—
121C22×D5—31no—
122C22×D5—64no—
123C2×C4×C5C2×C3×D312yescomplemented
124C2×Dic5—32no—
125C4×D5—64no—
126C22×C32—22no—
127C22×C32C4×D512yescomplemented
128C22×C32C22×D511yescharacteristic
129C2×C3×D3—52no—
130C2×C3×D3—54no—
131C2×C3×D3—52no—
132C2×C3×D3—108no—
133C2×C3×D3—102no—
134C32×C4—22no—
135C3×Dic3—102no—
136C2×C22⋊C4—151noSylow
137C2×C3×C5—22no—
138C2×C3×C5—22no—
139C2×C3×C5—21no—
140C2×C3×C5—22no—
141C2×C3×C5—42no—
142C2×C3×C5C2×C4×D311yescharacteristic
143C2×C3×C5D3×D412yes—
144C2×C3×C5C22×C3×C411yescharacteristic
145C2×C3×C5C2×C3×D412yes—
146D15—22no—
147D15C3×C22⋊C414yesdirect product factor
148C3×D5—34no—
149C3×D5—62no—
150C23×C3—21no—
151C23×C3—151no—
152C23×C3—154no—
153C23×C3—151no—
154C23×C3—304no—
155C23×C3C2×C3×D511yescharacteristic
156C23×C3C2×D1511yescharacteristic
157C22×D3—51no—
158C22×D3—54no—
159C22×D3—51no—
160C22×D3—104no—
161C2×C3×C4—22no—
162C2×C3×C4—152no—
163C2×C3×C4—304no—
164C2×C3×C4C2×C3×D512yescomplemented
165C2×C3×C4C2×D1512yescomplemented
166C2×Dic3—52no—
167C4×D3—104no—
168C22×C5—22no—
169C22×C5C3×C4×D312yescomplemented
170C22×C5C22×C3×D311yescharacteristic
171C2×D5—32no—
172C2×D5—34no—
173C2×D5—32no—
174C2×D5—68no—
175C2×D5—62no—
176C4×C5—22no—
177Dic5—62no—
178C2×C32—22no—
179C2×C32C2×C4×D511yescharacteristic
180C2×C32D4×D512yes—
181C3×D3—54no—
182C3×D3—102no—
183C24—151no—
184C22×C4—152no—
185C22⋊C4—151no—
186C22⋊C4—152no—
187C22⋊C4C3×D1511yescharacteristic, direct product factor
188C3×C5—21no—
189C3×C5D3×C22⋊C411yescharacteristic, complemented
190C3×C5C2×C3×C22⋊C411yescharacteristic, complemented
191C22×C3—22no—
192C22×C3—22no—
193C22×C3—22no—
194C22×C3—21no—
195C22×C3—42no—
196C22×C3—152no—
197C22×C3—154no—
198C22×C3—152no—
199C22×C3—308no—
200C22×C3—302no—
201C22×C3C3×C4×D512yescomplemented
202C22×C3C4×D1512yescomplemented
203C22×C3C22×C3×D511yescharacteristic
204C22×C3C22×D1511yescharacteristic
205C2×D3—52no—
206C2×D3—54no—
207C2×D3—52no—
208C2×D3—108no—
209C2×D3—102no—
210C3×C4—22no—
211C3×C4—22no—
212C3×C4—42no—
213C3×C4—302no—
214Dic3—102no—
215C2×C5—22no—
216C2×C5C2×C3×C4×D311yescharacteristic
217C2×C5C3×D3×D412yes—
218D5—34no—
219D5—62no—
220C32D5×C22⋊C411yescharacteristic, complemented, Sylow
221C23—151no—
222C23—154no—
223C23—151no—
224C23—304no—
225C23C2×C3×D1511yescharacteristic
226C2×C4—152no—
227C2×C4—304no—
228C2×C4C2×C3×D1512yescomplemented
229C2×C3—22no—
230C2×C3—22no—
231C2×C3—21no—
232C2×C3—22no—
233C2×C3—42no—
234C2×C3—154no—
235C2×C3—302no—
236C2×C3C2×C3×C4×D511yescharacteristic
237C2×C3C3×D4×D512yes—
238C2×C3C2×C4×D1511yescharacteristic
239C2×C3D4×D1512yes—
240D3—54no—
241D3—102no—
242C5C3×D3×C22⋊C411yescharacteristic, complemented, Sylow
243C22—22no—
244C22—152no—
245C22—154no—
246C22—152no—
247C22—308no—
248C22—302no—
249C22C3×C4×D1512yescomplemented
250C22C22×C3×D1511yescharacteristic
251C4—22no—
252C4—302no—
253C3—21no—
254C3C3×D5×C22⋊C411yescharacteristic, complemented
255C3C22⋊C4×D1511yescharacteristic, direct product factor
256C2—22no—
257C2—154no—
258C2—302no—
259C2C2×C3×C4×D1511yescharacteristic
260C2C3×D4×D1512yes—
subgroupG/H
centerC22×C3C22×D15
commutatorC2×C3×C5C22×C3×C4
FrattiniC22C22×C3×D15
FittingC32×C5×C22⋊C4C2
socleC22×C32×C5C23
prime radicalC23×C3×D15C2
cosocleC22×C3×C5C23×C3
hypercenterC3×C22⋊C4D15
hypocenterC3×C5C2×C3×C22⋊C4
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22×C3 ◁ C3×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C3×C4×D15C2semidirect
3. C32×C5×C22⋊C4C2semidirect
4. C3×#6719C2semidirect
5. C3×#6714C2semidirect
6. C22⋊C4×D15C3direct (N × H)
10. C22×C3×D15C4semidirect
13. C2×C32×C4×C5C22semidirect
14. C2×C3×Dic15C22semidirect
19. C2×C4×D15C2×C3semidirect
22. C3×C5×C22⋊C4D3semidirect
23. C3×C5×C22⋊C4C2×C3semidirect
24. #6719C2×C3semidirect
25. #6714C2×C3semidirect
29. C22×C32×C5C2×C4semidirect
34. C2×C3×D15C2×C4semidirect
41. C32×C22⋊C4D5semidirect
48. C22×D15C3×C4semidirect
56. C2×C3×C4×C5C2×D3semidirect
57. C2×C3×C4×C5C22×C3semidirect
58. C2×Dic15C22×C3semidirect
68. C3×D15C22⋊C4direct (N × H)
71. C5×C22⋊C4C3×D3semidirect
79. C2×C32×C4C2×D5semidirect
87. C22×C3×C5C4×D3semidirect
88. C22×C3×C5C2×C3×C4semidirect
94. C2×D15C2×C3×C4semidirect
113. C3×C22⋊C4C3×D5semidirect
114. C3×C22⋊C4D15direct (N × H)
117. C32×C5C2×C22⋊C4semidirect
123. C2×C4×C5C2×C3×D3semidirect
127. C22×C32C4×D5semidirect
147. D15C3×C22⋊C4direct (N × H)
164. C2×C3×C4C2×C3×D5semidirect
165. C2×C3×C4C2×D15semidirect
169. C22×C5C3×C4×D3semidirect
187. C22⋊C4C3×D15direct (N × H)
189. C3×C5D3×C22⋊C4semidirect
190. C3×C5C2×C3×C22⋊C4semidirect
201. C22×C3C3×C4×D5semidirect
202. C22×C3C4×D15semidirect
220. C32D5×C22⋊C4semidirect
228. C2×C4C2×C3×D15semidirect
242. C5C3×D3×C22⋊C4semidirect
249. C22C3×C4×D15semidirect
254. C3C3×D5×C22⋊C4semidirect
255. C3C22⋊C4×D15direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C3×D152
C2×C3×C4×D152
C32×C5×C22⋊C42
C3×#67192
C3×#67142
C22⋊C4×D153
C3×D5×C22⋊C43
C3×D3×C22⋊C45