Finite Group Databasebeta

← C2×D12×D15 #13089358

Subgroups — C2×D12×D15 #13089358

Order 1440.

998 conjugacy classes of subgroups; only the 186 normal subgroups are shown.

normal subgroups only

This group has 998 conjugacy classes of subgroups — too many to draw. Only its 186 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
1C22×D3×D15C212yesmaximal, complemented
2C2×C4⋊(C3⋊D15)C211yesmaximal, characteristic, complemented
3C2×C3×C4×D15C211yesmaximal, characteristic, complemented
4C2×C3×C5×D12C211yesmaximal, characteristic, complemented
5C2×#67152C212yesmaximal, complemented
6D12×D15C218yesmaximal, direct product factor
7C2×D4×D15—31nomaximal
8C2×D5×D12—31nomaximal
9C22×C3⋊D15C2212yescomplemented
10C22×C3×D15C2211yescharacteristic
11C22×C3×C5×D3C2212yescomplemented
12C2×D3×D15—28no—
13C2×D3×D15C2218yescomplemented
14C2×C32×C4×C5C2211yescharacteristic, complemented
15C4⋊(C3⋊D15)C2214yescomplemented
16C2×C3×Dic15C2211yescharacteristic, complemented
17C3×C4×D15C2214yescomplemented
18C3×C5×D12C2214yescomplemented
19#67152C2218yescomplemented
20C2×D3×D12—51nomaximal, Hall
21C23×D15—32no—
22C22×D3×D5—32no—
23C2×C3×C5×D4—31no—
24C2×#1220—32no—
25D4×D15—38no—
26C2×D60—31no—
27C2×D60—31no—
28C2×D60—61no—
29C2×C4×D15D311yescharacteristic, complemented
30C2×C5×D12D311yescharacteristic, complemented
31C2×C3×C4×D5—31no—
32C2×#1203—32no—
33D5×D12—38no—
34C22×C32×C5C2311yescharacteristic
35C2×C3⋊D15—24no—
36C2×C3⋊D15C2314yescomplemented
37C2×C3×D15D414yescomplemented
38C2×C3×D15C2312yes—
39C2×C3×C5×D3—24no—
40C2×C3×C5×D3C2314yescomplemented
41D3×D15—216no—
42C32×C4×C5C2312yescomplemented
43C3×Dic15C2312yescomplemented
44C2×D4×D5—91noHall
45C22×D32—52no—
46C2×C4⋊(C3⋊D3)—51no—
47C2×C3×D12D511yescharacteristic, complemented
48C2×C3×C4×D3—51no—
49C2×#626—52no—
50D3×D12—58no—
51C23×C3×C5—32no—
52C22×D15—32no—
53C22×D15—32no—
54C22×D15—38no—
55C22×D15—68no—
56C22×D15—62no—
57C22×D15C2×D311yescharacteristic
58C22×C5×D3C2×D312yescomplemented
59C22×C3×D5—31no—
60C2×D3×D5—38no—
61C2×D3×D5—68no—
62C3×C5×D4—34no—
63C2×C3×C4×C5—21no—
64C2×C3×C4×C5C2×D311yescharacteristic, complemented
65C2×C3×C4×C5C2×D311yescharacteristic, complemented
66#1220—38no—
67C2×Dic15C2×D311yescharacteristic, complemented
68D60—34no—
69D60—34no—
70D60—64no—
71C4×D15C2×D314yescomplemented
72C5×D12C2×D314yescomplemented
73C2×C3×Dic5—31no—
74C3×C4×D5—34no—
75#1203—38no—
76C2×D3×D4—151no—
77C22×D12—151no—
78C2×C32×C5C2×D412yescomplemented
79C2×C32×C5C2411yescharacteristic
80C3⋊D15—24no—
81C3×D15C2×D414yescomplemented
82C3×C5×D3—24no—
83C23×D5—92no—
84C2×C5×D4—31no—
85C2×C22⋊D5—92no—
86D4×D5—98no—
87C2×D20—91no—
88C2×C4×D5—31no—
89C22×C3⋊D3—52no—
90C22×C3×D3—51no—
91C22×C3×D3C2×D512yescomplemented
92C2×D32—58no—
93C2×D32—108no—
94C2×C32×C4C2×D511yescharacteristic, complemented
95C4⋊(C3⋊D3)—54no—
96C2×C3×Dic3—51no—
97C3×D12C2×D514yescomplemented
98C3×C4×D3—54no—
99#626—58no—
100C22×C3×C5—21no—
101C22×C3×C5—34no—
102C22×C3×C5—64no—
103C22×C3×C5C22×D311yescharacteristic
104C22×C3×C5C22×D311yescharacteristic
105C2×D15—34no—
106C2×D15—34no—
107C2×D15—64no—
108C2×D15—64no—
109C2×D15—64no—
110C2×D15—616no—
111C2×D15—124no—
112C2×D15D1214yesdirect product factor
113C2×D15C22×D312yes—
114C2×C5×D3—24no—
115C2×C5×D3C22×D314yescomplemented
116C2×C3×D5—34no—
117C2×C3×D5—32no—
118D3×D5—616no—
119C3×C4×C5—22no—
120C3×C4×C5C22×D312yescomplemented
121C3×C4×C5C22×D312yescomplemented
122Dic15C22×D312yescomplemented
123C3×Dic5—32no—
124C23×D3—152no—
125C23×D3—152no—
126C2×C3×D4—31no—
127C22×C3×C4—151no—
128C2×#67—152no—
129D3×D4—158no—
130C2×D12—152no—
131C2×D12—151no—
132C2×D12—151no—
133C2×D12—158no—
134C2×D12—301no—
135C2×D12D1511yescharacteristic, direct product factor
136C2×C4×D3—51no—
137C32×C5C22×D411yescharacteristic, complemented, Hall
138C23×C5—32no—
139C22×D5—31no—
140C22×D5—98no—
141C22×D5—92no—
142C22×D5—188no—
143C5×D4—34no—
144C2×C4×C5D3211yescharacteristic, complemented
145C22⋊D5—98no—
146C2×Dic5—31no—
147D20—94no—
148C4×D5—34no—
149C22×C32C22×D511yescharacteristic
150C2×C3⋊D3—54no—
151C2×C3⋊D3—104no—
152C2×C3×D3—24no—
153C2×C3×D3—54no—
154C2×C3×D3—52no—
155C2×C3×D3C22×D514yescomplemented
156D32—1016no—
157C32×C4C22×D512yescomplemented
158C3×Dic3—52no—
159C22×D4—451noSylow
160C2×C3×C5—21no—
161C2×C3×C5—22no—
162C2×C3×C5—64no—
163C2×C3×C5C2×D1212yescomplemented
164C2×C3×C5D3×D412yescomplemented
165C2×C3×C5C23×D311yescharacteristic
166C2×C3×C5C23×D311yescharacteristic
167D15—64no—
168D15—64no—
169D15—124no—
170D15C2×D1214yesdirect product factor
171C3×D5—34no—
172C5×D3—24no—
173C23×C3—32no—
174C23×C3—151no—
175C22×D3—51no—
176C22×D3—158no—
177C22×D3—152no—
178C22×D3—152no—
179C22×D3—158no—
180C22×D3—302no—
181C22×D3—308no—
182C22×D3—308no—
183C22×D3C2×D1512yescomplemented
184C3×D4—34no—
185C2×C3×C4—21no—
186C2×C3×C4—151no—
187C2×C3×C4—154no—
188C2×C3×C4D3×D511yescharacteristic, complemented
189C2×C3×C4C2×D1511yescharacteristic, complemented
190#67—158no—
191C2×Dic3—51no—
192D12—158no—
193D12—154no—
194D12—154no—
195D12—304no—
196D12C2×D1514yesdirect product factor
197C4×D3—54no—
198C22×C5—34no—
199C22×C5—64no—
200C22×C5C2×D3211yescharacteristic
201C2×D5—32no—
202C2×D5—34no—
203C2×D5—94no—
204C2×D5—1816no—
205C2×D5—184no—
206C4×C5C2×D3212yescomplemented
207Dic5—32no—
208C2×C32D4×D512yescomplemented
209C2×C32C23×D511yescharacteristic
210C3⋊D3—104no—
211C3×D3—24no—
212C3×D3—54no—
213C24—452no—
214C2×D4—31no—
215C2×D4—458no—
216C2×D4—452no—
217C2×D4—451no—
218C22×C4—151no—
219C3×C5—21no—
220C3×C5C22×D1211yescharacteristic, complemented
221C3×C5C2×D3×D411yescharacteristic, complemented
222C22×C3—21no—
223C22×C3—34no—
224C22×C3—64no—
225C22×C3—154no—
226C22×C3—152no—
227C22×C3C2×D3×D511yescharacteristic
228C22×C3C22×D1511yescharacteristic
229C2×D3—24no—
230C2×D3—54no—
231C2×D3—52no—
232C2×D3—154no—
233C2×D3—154no—
234C2×D3—304no—
235C2×D3—3016no—
236C2×D3—3016no—
237C2×D3—304no—
238C2×D3—304no—
239C2×D3—604no—
240C2×D3C22×D1514yescomplemented
241C3×C4—22no—
242C3×C4—152no—
243C3×C4C2×D3×D512yescomplemented
244C3×C4C22×D1512yescomplemented
245Dic3—52no—
246C2×C5—64no—
247C2×C5D3×D1212yescomplemented
248C2×C5C22×D3211yescharacteristic
249D5—34no—
250D5—184no—
251C32C2×D4×D511yescharacteristic, complemented, Sylow
252C23—32no—
253C23—151no—
254C23—458no—
255C23—452no—
256C23—908no—
257D4—34no—
258D4—458no—
259D4—454no—
260C2×C4—151no—
261C2×C4—154no—
262C2×C4D3×D1511yescharacteristic, complemented
263C2×C3—21no—
264C2×C3—22no—
265C2×C3—64no—
266C2×C3—154no—
267C2×C3D5×D1212yescomplemented
268C2×C3D4×D1512yescomplemented
269C2×C3C22×D3×D511yescharacteristic
270C2×C3C23×D1511yescharacteristic
271D3—24no—
272D3—54no—
273D3—304no—
274D3—304no—
275D3—604no—
276C5C2×D3×D1211yescharacteristic, complemented, Sylow
277C22—34no—
278C22—64no—
279C22—152no—
280C22—154no—
281C22—454no—
282C22—9016no—
283C22—904no—
284C22C2×D3×D1511yescharacteristic
285C4—152no—
286C4C2×D3×D1512yescomplemented
287C3—21no—
288C3C2×D5×D1211yescharacteristic, complemented
289C3C2×D4×D1511yescharacteristic, complemented
290C2—64no—
291C2—154no—
292C2—904no—
293C2D12×D1512yesdirect product factor
294C2C22×D3×D1511yescharacteristic
subgroupG/H
centerC22C2×D3×D15
commutator, cosocleC2×C32×C5C24
FrattiniC2C22×D3×D15
FittingC2×C32×C4×C5C22
socleC22×C32×C5C23
hypercenterC2×C4D3×D15
hypocenterC32×C5C22×D4
LCSG ▷ C2×C32×C5 ▷ C32×C5
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. C22×D3×D15C2semidirect
2. C2×C4⋊(C3⋊D15)C2semidirect
3. C2×C3×C4×D15C2semidirect
4. C2×C3×C5×D12C2semidirect
5. C2×#67152C2semidirect
6. D12×D15C2direct (N × H)
9. C22×C3⋊D15C22semidirect
11. C22×C3×C5×D3C22semidirect
13. C2×D3×D15C22semidirect
14. C2×C32×C4×C5C22semidirect
15. C4⋊(C3⋊D15)C22semidirect
16. C2×C3×Dic15C22semidirect
17. C3×C4×D15C22semidirect
18. C3×C5×D12C22semidirect
19. #67152C22semidirect
29. C2×C4×D15D3semidirect
30. C2×C5×D12D3semidirect
36. C2×C3⋊D15C23semidirect
37. C2×C3×D15D4semidirect
40. C2×C3×C5×D3C23semidirect
42. C32×C4×C5C23semidirect
43. C3×Dic15C23semidirect
47. C2×C3×D12D5semidirect
58. C22×C5×D3C2×D3semidirect
64. C2×C3×C4×C5C2×D3semidirect
65. C2×C3×C4×C5C2×D3semidirect
67. C2×Dic15C2×D3semidirect
71. C4×D15C2×D3semidirect
72. C5×D12C2×D3semidirect
78. C2×C32×C5C2×D4semidirect
81. C3×D15C2×D4semidirect
91. C22×C3×D3C2×D5semidirect
94. C2×C32×C4C2×D5semidirect
97. C3×D12C2×D5semidirect
112. C2×D15D12direct (N × H)
115. C2×C5×D3C22×D3semidirect
120. C3×C4×C5C22×D3semidirect
121. C3×C4×C5C22×D3semidirect
122. Dic15C22×D3semidirect
135. C2×D12D15direct (N × H)
137. C32×C5C22×D4semidirect
144. C2×C4×C5D32semidirect
155. C2×C3×D3C22×D5semidirect
157. C32×C4C22×D5semidirect
163. C2×C3×C5C2×D12semidirect
164. C2×C3×C5D3×D4semidirect
170. D15C2×D12direct (N × H)
183. C22×D3C2×D15semidirect
188. C2×C3×C4D3×D5semidirect
189. C2×C3×C4C2×D15semidirect
196. D12C2×D15direct (N × H)
206. C4×C5C2×D32semidirect
208. C2×C32D4×D5semidirect
220. C3×C5C22×D12semidirect
221. C3×C5C2×D3×D4semidirect
240. C2×D3C22×D15semidirect
243. C3×C4C2×D3×D5semidirect
244. C3×C4C22×D15semidirect
247. C2×C5D3×D12semidirect
251. C32C2×D4×D5semidirect
262. C2×C4D3×D15semidirect
267. C2×C3D5×D12semidirect
268. C2×C3D4×D15semidirect
276. C5C2×D3×D12semidirect
286. C4C2×D3×D15semidirect
288. C3C2×D5×D12semidirect
289. C3C2×D4×D15semidirect
293. C2D12×D15direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D3×D152
C2×C4⋊(C3⋊D15)2
C2×C3×C4×D152
C2×C3×C5×D122
C2×#671522
D12×D152
C2×D4×D153
C2×D5×D123
C2×D3×D125