Finite Group Databasebeta

← C3×D5×Dic3⋊C4 #13086523

Subgroups — C3×D5×Dic3⋊C4 #13086523

Order 1440.

422 conjugacy classes of subgroups.

The subgroup lattice has 296 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×C4×D5C211yesmaximal, characteristic
2C2×C3×D5×Dic3C211yesmaximal, characteristic
3C2×C3×D5×Dic3C211yesmaximal, characteristic
4C3×#6712C211yesmaximal, characteristic, complemented
5C3×C5×Dic3⋊C4C211yesmaximal, characteristic, complemented
6C3×Dic3⋊Dic5C211yesmaximal, characteristic, complemented
7C3×#6669C211yesmaximal, characteristic, complemented
8C3×D5×C4⋊C4—31nomaximal
9D5×Dic3⋊C4C311yesmaximal, characteristic, direct product factor
10C22×C32×D5C2211yescharacteristic
11C2×C32×C4×C5C2211yescharacteristic
12C2×C3×Dic15C2211yescharacteristic
13C2×C3×Dic15C2211yescharacteristic
14C2×C3×C5×Dic3C2211yescharacteristic
15C2×C3×C5×Dic3C2211yescharacteristic
16C2×C32×Dic5C2211yescharacteristic
17C32×C4×D5—22no—
18C3×D5×Dic3—22no—
19C3×D5×Dic3C414yescomplemented
20C2×C3×Dic3⋊C4—51nomaximal, Hall
21C2×C3×C4×D5—21no—
22C2×C3×C4×D5—31no—
23C2×C3×C4×D5—31no—
24C2×C3×C4×D5D311yescharacteristic
25C2×C3×C4×D5C2×C311yescharacteristic
26C2×D5×Dic3C2×C311yescharacteristic
27C2×D5×Dic3C2×C311yescharacteristic
28C3×C5×C4⋊C4—31no—
29#6712C2×C311yescharacteristic, complemented
30C5×Dic3⋊C4C2×C311yescharacteristic, complemented
31C3×C4⋊Dic5—31no—
32C3×#683—31no—
33C3×#683—31no—
34Dic3⋊Dic5C2×C311yescharacteristic, complemented
35#6669C2×C311yescharacteristic, complemented
36C22×C32×C5C2311yescharacteristic
37C2×C32×D5C2×C412yes—
38C2×C32×D5D412yes—
39C2×C32×D5Q812yes—
40C32×C4×C5—21no—
41C3×Dic15—21no—
42C3×Dic15C2×C412yescomplemented
43C3×C5×Dic3—21no—
44C3×C5×Dic3C2×C412yescomplemented
45C32×Dic5—21no—
46D5×C4⋊C4—31noHall
47C22×C32×C4—51no—
48C22×C3×Dic3—51no—
49C22×C3×Dic3—51no—
50C3×Dic3⋊C4—51no—
51C3×Dic3⋊C4—51no—
52C3×Dic3⋊C4—51no—
53C3×Dic3⋊C4D511yescharacteristic, direct product factor
54C22×C3×D5—21no—
55C22×C3×D5C2×D311yescharacteristic
56C22×C3×D5C22×C311yescharacteristic
57C2×C3×C4×C5—21no—
58C2×C3×C4×C5—31no—
59C2×C3×C4×C5—31no—
60C2×C3×C4×C5C2×D311yescharacteristic
61C2×C3×C4×C5C22×C311yescharacteristic
62C2×Dic15C22×C311yescharacteristic
63C2×Dic15C22×C311yescharacteristic
64C2×C5×Dic3C22×C311yescharacteristic
65C2×C5×Dic3C22×C311yescharacteristic
66C2×C3×Dic5—21no—
67C2×C3×Dic5—31no—
68C2×C3×Dic5—31no—
69C2×C3×Dic5C2×D311yescharacteristic
70C2×C3×Dic5C22×C311yescharacteristic
71C3×C4×D5—24no—
72C3×C4×D5—22no—
73C3×C4×D5—22no—
74C3×C4×D5—34no—
75C3×C4×D5—62no—
76D5×Dic3—22no—
77D5×Dic3C3×C414yescomplemented
78C2×C3×C4⋊C4—151no—
79C2×Dic3⋊C4—51no—
80C2×C32×C5C22×C411yescharacteristic
81C2×C32×C5C2×D411yescharacteristic
82C2×C32×C5C2×Q811yescharacteristic
83C32×D5C4⋊C414yescomplemented
84C2×C4×D5—31no—
85C2×C4×D5—31no—
86C2×C4×D5C3×D311yescharacteristic
87C5×C4⋊C4—31no—
88C4⋊Dic5—31no—
89#683—31no—
90#683—31no—
91C23×C32—51no—
92C2×C32×C4—51no—
93C2×C32×C4—102no—
94C2×C32×C4C2×D511yescharacteristic
95C2×C3×Dic3—51no—
96C2×C3×Dic3—54no—
97C2×C3×Dic3—51no—
98C2×C3×Dic3—102no—
99C2×C3×Dic3C2×D511yescharacteristic
100C2×C3×Dic3C2×D511yescharacteristic
101C22×C3×C5—21no—
102C22×C3×C5C22×D311yescharacteristic
103C22×C3×C5C23×C311yescharacteristic
104C2×C3×D5—22no—
105C2×C3×D5—22no—
106C2×C3×D5—22no—
107C2×C3×D5Dic612yes—
108C2×C3×D5C4×D312yes—
109C2×C3×D5#6712yes—
110C2×C3×D5C2×C3×C412yes—
111C2×C3×D5C3×D412yes—
112C2×C3×D5C3×Q812yes—
113C3×C4×C5—22no—
114C3×C4×C5—21no—
115C3×C4×C5—21no—
116C3×C4×C5—32no—
117C3×C4×C5—61no—
118Dic15—21no—
119Dic15C2×C3×C412yescomplemented
120C3×Dic5—22no—
121C3×Dic5—21no—
122C3×Dic5—21no—
123C3×Dic5—32no—
124C3×Dic5—61no—
125C5×Dic3—21no—
126C5×Dic3C2×C3×C412yescomplemented
127C22×C3×C4—51no—
128C22×C3×C4—51no—
129C22×C3×C4—101no—
130C22×C3×C4—151no—
131C22×C3×C4—151no—
132C22×Dic3—51no—
133C22×Dic3—51no—
134C3×C4⋊C4—31no—
135C3×C4⋊C4—151no—
136C3×C4⋊C4—151no—
137C3×C4⋊C4—151no—
138Dic3⋊C4—51no—
139Dic3⋊C4—51no—
140Dic3⋊C4—51no—
141Dic3⋊C4C3×D511yescharacteristic, direct product factor
142C32×C5C2×C4⋊C411yescharacteristic, complemented, Hall
143C22×D5C2×C3×D311yescharacteristic
144C2×C4×C5—31no—
145C2×C4×C5—31no—
146C2×C4×C5C2×C3×D311yescharacteristic
147C2×Dic5—31no—
148C2×Dic5—31no—
149C2×Dic5C2×C3×D311yescharacteristic
150C4×D5—22no—
151C4×D5—34no—
152C4×D5—62no—
153C22×C32—52no—
154C22×C32—52no—
155C22×C32—52no—
156C22×C32C22×D511yescharacteristic
157C32×C4—21no—
158C32×C4—101no—
159C3×Dic3—21no—
160C3×Dic3—52no—
161C3×Dic3—101no—
162C3×Dic3C4×D512yescomplemented
163C2×C4⋊C4—151noSylow
164C2×C3×C5—21no—
165C2×C3×C5—21no—
166C2×C3×C5—21no—
167C2×C3×C5C2×Dic611yescharacteristic
168C2×C3×C5C2×C4×D311yescharacteristic
169C2×C3×C5C2×#6711yescharacteristic
170C2×C3×C5C22×C3×C411yescharacteristic
171C2×C3×C5C2×C3×D411yescharacteristic
172C2×C3×C5C2×C3×Q811yescharacteristic
173C3×D5—24no—
174C3×D5Dic3⋊C414yesdirect product factor
175C3×D5C3×C4⋊C414yescomplemented
176C23×C3—51no—
177C23×C3—51no—
178C23×C3—101no—
179C2×C3×C4—21no—
180C2×C3×C4—31no—
181C2×C3×C4—31no—
182C2×C3×C4—51no—
183C2×C3×C4—51no—
184C2×C3×C4—101no—
185C2×C3×C4—102no—
186C2×C3×C4—102no—
187C2×C3×C4—104no—
188C2×C3×C4—154no—
189C2×C3×C4—151no—
190C2×C3×C4—151no—
191C2×C3×C4—302no—
192C2×C3×C4D3×D511yescharacteristic
193C2×C3×C4C2×C3×D511yescharacteristic
194C2×Dic3—51no—
195C2×Dic3—54no—
196C2×Dic3—51no—
197C2×Dic3—102no—
198C2×Dic3C2×C3×D511yescharacteristic
199C2×Dic3C2×C3×D511yescharacteristic
200C22×C5C22×C3×D311yescharacteristic
201C2×D5C3×Dic612yes—
202C2×D5C3×C4×D312yes—
203C2×D5C3×#6712yes—
204C4×C5—21no—
205C4×C5—32no—
206C4×C5—61no—
207Dic5—21no—
208Dic5—32no—
209Dic5—61no—
210C2×C32—54no—
211C2×C32C2×C4×D511yescharacteristic
212C2×C32D4×D511yescharacteristic
213C2×C32Q8×D511yescharacteristic
214C22×C4—51no—
215C22×C4—151no—
216C22×C4—151no—
217C4⋊C4—31no—
218C4⋊C4—151no—
219C4⋊C4—151no—
220C4⋊C4—151no—
221C3×C5—21no—
222C3×C5C2×Dic3⋊C411yescharacteristic, complemented
223C3×C5C2×C3×C4⋊C411yescharacteristic, complemented
224C22×C3—21no—
225C22×C3—52no—
226C22×C3—52no—
227C22×C3—52no—
228C22×C3—52no—
229C22×C3—52no—
230C22×C3—52no—
231C22×C3—102no—
232C22×C3—102no—
233C22×C3—102no—
234C22×C3C2×D3×D511yescharacteristic
235C22×C3C22×C3×D511yescharacteristic
236C3×C4—22no—
237C3×C4—21no—
238C3×C4—21no—
239C3×C4—32no—
240C3×C4—61no—
241C3×C4—102no—
242C3×C4—101no—
243C3×C4—101no—
244C3×C4—152no—
245C3×C4—301no—
246Dic3—21no—
247Dic3—52no—
248Dic3—101no—
249Dic3C3×C4×D512yescomplemented
250C2×C5C2×C3×Dic611yescharacteristic
251C2×C5C2×C3×C4×D311yescharacteristic
252C2×C5C2×C3×#6711yescharacteristic
253D5C3×Dic3⋊C414yesdirect product factor
254C32D5×C4⋊C411yescharacteristic, complemented, Sylow
255C23—51no—
256C2×C4—31no—
257C2×C4—31no—
258C2×C4—51no—
259C2×C4—102no—
260C2×C4—154no—
261C2×C4—151no—
262C2×C4—151no—
263C2×C4—302no—
264C2×C4C3×D3×D511yescharacteristic
265C2×C3—21no—
266C2×C3—21no—
267C2×C3—21no—
268C2×C3—54no—
269C2×C3—54no—
270C2×C3—104no—
271C2×C3D5×Dic611yescharacteristic
272C2×C3C4×D3×D511yescharacteristic
273C2×C3D5×#6711yescharacteristic
274C2×C3C2×C3×C4×D511yescharacteristic
275C2×C3C3×D4×D511yescharacteristic
276C2×C3C3×Q8×D511yescharacteristic
277C5C2×C3×Dic3⋊C411yescharacteristic, complemented, Sylow
278C22—52no—
279C22—52no—
280C22—52no—
281C22C2×C3×D3×D511yescharacteristic
282C4—21no—
283C4—32no—
284C4—61no—
285C4—101no—
286C4—152no—
287C4—301no—
288C3—21no—
289C3D5×Dic3⋊C411yescharacteristic, direct product factor
290C3C3×D5×C4⋊C411yescharacteristic, complemented
291C2—54no—
292C2C3×D5×Dic611yescharacteristic
293C2C3×C4×D3×D511yescharacteristic
294C2C3×D5×#6711yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D5
commutatorC2×C3×C5C22×C3×C4
FrattiniC22C2×C3×D3×D5
FittingC2×C32×C4×C5C22
socleC22×C32×C5C23
prime radicalC22×C32×D5C22
cosocleC22×C3×C5C23×C3
hypercenterC2×C3×C4D3×D5
hypocenterC3×C5C2×C3×C4⋊C4
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22×C3 ◁ C2×C3×C4

Complements

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

NH ≅ G/Ntype
4. C3×#6712C2semidirect
5. C3×C5×Dic3⋊C4C2semidirect
6. C3×Dic3⋊Dic5C2semidirect
7. C3×#6669C2semidirect
9. D5×Dic3⋊C4C3direct (N × H)
19. C3×D5×Dic3C4semidirect
29. #6712C2×C3semidirect
30. C5×Dic3⋊C4C2×C3semidirect
34. Dic3⋊Dic5C2×C3semidirect
35. #6669C2×C3semidirect
42. C3×Dic15C2×C4semidirect
44. C3×C5×Dic3C2×C4semidirect
53. C3×Dic3⋊C4D5direct (N × H)
77. D5×Dic3C3×C4semidirect
83. C32×D5C4⋊C4semidirect
119. Dic15C2×C3×C4semidirect
126. C5×Dic3C2×C3×C4semidirect
141. Dic3⋊C4C3×D5direct (N × H)
142. C32×C5C2×C4⋊C4semidirect
162. C3×Dic3C4×D5semidirect
174. C3×D5Dic3⋊C4direct (N × H)
175. C3×D5C3×C4⋊C4semidirect
222. C3×C5C2×Dic3⋊C4semidirect
223. C3×C5C2×C3×C4⋊C4semidirect
249. Dic3C3×C4×D5semidirect
253. D5C3×Dic3⋊C4direct (N × H)
254. C32D5×C4⋊C4semidirect
277. C5C2×C3×Dic3⋊C4semidirect
289. C3D5×Dic3⋊C4direct (N × H)
290. C3C3×D5×C4⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×C32×C4×D52
C2×C3×D5×Dic32
C3×#67122
C3×C5×Dic3⋊C42
C3×Dic3⋊Dic52
C3×#66692
C3×D5×C4⋊C43
D5×Dic3⋊C43
C2×C3×Dic3⋊C45