Finite Group Databasebeta

← C2×#10624205 #13089360

Subgroups — C2×#10624205 #13089360

Order 1440.

998 conjugacy classes of subgroups; only the 178 normal subgroups are shown.

normal subgroups only

This group has 998 conjugacy classes of subgroups — too many to draw. Only its 178 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⋊D15C211yesmaximal, characteristic, complemented
3C2×C3×D60C211yesmaximal, characteristic, complemented
4C2×C3×C5×D12C211yesmaximal, characteristic, complemented
5C2×#67150C212yesmaximal, complemented
6#10624205C218yesmaximal, direct product factor
7C2×D4×D15—31nomaximal
8C2×#6777—31nomaximal
9C22×C3⋊D15C2211yescharacteristic
10C22×C3×D15C2212yescomplemented
11C22×C3×C5×D3C2212yescomplemented
12C2×D3×D15—28no—
13C2×D3×D15C2218yescomplemented
14C2×C32×C4×C5C2211yescharacteristic, complemented
15C2×C3⋊Dic15C2211yescharacteristic, complemented
16C4×C3⋊D15C2214yescomplemented
17C3×D60C2214yescomplemented
18C3×C5×D12C2214yescomplemented
19#67150C2218yescomplemented
20C2×#3802—51nomaximal, Hall
21C23×D15—32no—
22C22×D3×D5—32no—
23C2×C3×C5×D4—31no—
24C2×#1220—32no—
25D4×D15—38no—
26C2×D60D311yescharacteristic, complemented
27C2×C4×D15—31no—
28C2×C4×D15—31no—
29C2×C4×D15—61no—
30C2×C5×D12D311yescharacteristic, complemented
31C2×C3×D20—31no—
32C2×#1201—32no—
33#6777—38no—
34C22×C32×C5C2311yescharacteristic
35C2×C3⋊D15D414yescomplemented
36C2×C3⋊D15C2312yes—
37C2×C3×D15—24no—
38C2×C3×D15C2314yescomplemented
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×D12—51no—
48C2×C3×D12D511yescharacteristic, complemented
49C2×#625—52no—
50#3802—58no—
51C23×C3×C5—32no—
52C22×D15—31no—
53C22×D15—31no—
54C22×D15—38no—
55C22×D15—68no—
56C22×D15—61no—
57C22×D15C2×D312yescomplemented
58C22×C5×D3C2×D312yescomplemented
59C22×C3×D5—32no—
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×Dic15—31no—
68C2×Dic15—31no—
69C2×Dic15—61no—
70D60C2×D314yescomplemented
71C4×D15—34no—
72C4×D15—34no—
73C4×D15—64no—
74C5×D12C2×D314yescomplemented
75C3×D20—34no—
76#1201—38no—
77C2×D3×D4—151no—
78C2×D3×D4—151no—
79C2×C32×C5C2×D412yescomplemented
80C2×C32×C5C2411yescharacteristic
81C3⋊D15C2×D414yescomplemented
82C3×D15—24no—
83C3×C5×D3—24no—
84C23×D5—92no—
85C2×C5×D4—31no—
86C2×C22⋊D5—92no—
87D4×D5—98no—
88C2×D20—31no—
89C2×C4×D5—91no—
90C22×C3⋊D3—51no—
91C22×C3×D3—52no—
92C22×C3×D3C2×D512yescomplemented
93C2×D32—58no—
94C2×D32—108no—
95C2×C32×C4C2×D511yescharacteristic, complemented
96C2×C3⋊Dic3—51no—
97C4×C3⋊D3—54no—
98C3×D12—54no—
99C3×D12C2×D514yescomplemented
100#625—58no—
101C22×C3×C5—21no—
102C22×C3×C5—34no—
103C22×C3×C5—64no—
104C22×C3×C5C22×D311yescharacteristic
105C22×C3×C5C22×D311yescharacteristic
106C2×D15—24no—
107C2×D15—34no—
108C2×D15—34no—
109C2×D15—32no—
110C2×D15—32no—
111C2×D15—64no—
112C2×D15—62no—
113C2×D15—616no—
114C2×D15C22×D314yescomplemented
115C2×C5×D3—24no—
116C2×C5×D3C22×D314yescomplemented
117C2×C3×D5—34no—
118C2×C3×D5—64no—
119D3×D5—616no—
120C3×C4×C5—22no—
121C3×C4×C5C22×D312yescomplemented
122C3×C4×C5C22×D312yescomplemented
123Dic15—32no—
124Dic15—32no—
125Dic15—62no—
126C23×D3—152no—
127C23×D3—152no—
128C2×C3×D4—31no—
129C2×C3×D4—151no—
130C2×#67—152no—
131C2×#67—152no—
132D3×D4—158no—
133D3×D4—158no—
134C2×D12—51no—
135C2×D12D1511yescharacteristic, complemented
136C2×C4×D3—151no—
137C2×C4×D3—151no—
138C2×C4×D3—301no—
139C32×C5C22×D411yescharacteristic, complemented, Hall
140C23×C5—32no—
141C22×D5—32no—
142C22×D5—98no—
143C22×D5—91no—
144C22×D5—188no—
145C5×D4—34no—
146C2×C4×C5D3211yescharacteristic, complemented
147C22⋊D5—98no—
148C2×Dic5—91no—
149D20—34no—
150C4×D5—94no—
151C22×C32C22×D511yescharacteristic
152C2×C3⋊D3—54no—
153C2×C3⋊D3—52no—
154C2×C3×D3—24no—
155C2×C3×D3—54no—
156C2×C3×D3—104no—
157C2×C3×D3C22×D514yescomplemented
158D32—1016no—
159C32×C4C22×D512yescomplemented
160C3⋊Dic3—52no—
161C22×D4—451noSylow
162C2×C3×C5—21no—
163C2×C3×C5—22no—
164C2×C3×C5—64no—
165C2×C3×C5D3×D412yescomplemented
166C2×C3×C5D3×D412yescomplemented
167C2×C3×C5C23×D311yescharacteristic
168C2×C3×C5C23×D311yescharacteristic
169D15—24no—
170D15—34no—
171D15—34no—
172D15—64no—
173C3×D5—64no—
174C5×D3—24no—
175C23×C3—32no—
176C23×C3—152no—
177C22×D3—52no—
178C22×D3—158no—
179C22×D3—151no—
180C22×D3—151no—
181C22×D3—158no—
182C22×D3—301no—
183C22×D3—308no—
184C22×D3—308no—
185C22×D3C2×D1512yescomplemented
186C3×D4—34no—
187C3×D4—154no—
188C2×C3×C4—21no—
189C2×C3×C4D3×D511yescharacteristic, complemented
190C2×C3×C4C2×D1511yescharacteristic, complemented
191#67—158no—
192#67—158no—
193C2×Dic3—151no—
194C2×Dic3—151no—
195C2×Dic3—301no—
196D12—54no—
197D12C2×D1514yescomplemented
198C4×D3—154no—
199C4×D3—154no—
200C4×D3—304no—
201C22×C5—34no—
202C22×C5—64no—
203C22×C5C2×D3211yescharacteristic
204C2×D5—34no—
205C2×D5—64no—
206C2×D5—92no—
207C2×D5—94no—
208C2×D5—1816no—
209C4×C5C2×D3212yescomplemented
210Dic5—92no—
211C2×C32D4×D512yescomplemented
212C2×C32C23×D511yescharacteristic
213C3⋊D3—54no—
214C3×D3—24no—
215C3×D3—104no—
216C24—452no—
217C2×D4—31no—
218C2×D4—151no—
219C2×D4—458no—
220C2×D4—452no—
221C22×C4—451no—
222C3×C5—21no—
223C3×C5C2×D3×D411yescharacteristic, complemented
224C3×C5C2×D3×D411yescharacteristic, complemented
225C22×C3—21no—
226C22×C3—34no—
227C22×C3—64no—
228C22×C3—154no—
229C22×C3—304no—
230C22×C3C2×D3×D511yescharacteristic
231C22×C3C22×D1511yescharacteristic
232C2×D3—24no—
233C2×D3—54no—
234C2×D3—104no—
235C2×D3—154no—
236C2×D3—154no—
237C2×D3—152no—
238C2×D3—152no—
239C2×D3—302no—
240C2×D3—304no—
241C2×D3—3016no—
242C2×D3—3016no—
243C2×D3C22×D1514yescomplemented
244C3×C4—22no—
245C3×C4C2×D3×D512yescomplemented
246C3×C4C22×D1512yescomplemented
247Dic3—152no—
248Dic3—152no—
249Dic3—302no—
250C2×C5—64no—
251C2×C5#380212yescomplemented
252C2×C5C22×D3211yescharacteristic
253D5—64no—
254D5—94no—
255C32C2×D4×D511yescharacteristic, complemented, Sylow
256C23—32no—
257C23—152no—
258C23—458no—
259C23—451no—
260C23—908no—
261D4—34no—
262D4—154no—
263D4—458no—
264C2×C4—451no—
265C2×C4—454no—
266C2×C4D3×D1511yescharacteristic, complemented
267C2×C3—21no—
268C2×C3—22no—
269C2×C3—64no—
270C2×C3—304no—
271C2×C3#677712yescomplemented
272C2×C3D4×D1512yescomplemented
273C2×C3C22×D3×D511yescharacteristic
274C2×C3C23×D1511yescharacteristic
275D3—24no—
276D3—104no—
277D3—154no—
278D3—154no—
279D3—304no—
280C5C2×#380211yescharacteristic, complemented, Sylow
281C22—34no—
282C22—64no—
283C22—154no—
284C22—304no—
285C22—452no—
286C22—454no—
287C22—9016no—
288C22C2×D3×D1511yescharacteristic
289C4—452no—
290C4C2×D3×D1512yescomplemented
291C3—21no—
292C3C2×#677711yescharacteristic, complemented
293C3C2×D4×D1511yescharacteristic, complemented
294C2—64no—
295C2—304no—
296C2—454no—
297C2#1062420512yesdirect product factor
298C2C22×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⋊D15C2semidirect
3. C2×C3×D60C2semidirect
4. C2×C3×C5×D12C2semidirect
5. C2×#67150C2semidirect
6. #10624205C2direct (N × H)
10. C22×C3×D15C22semidirect
11. C22×C3×C5×D3C22semidirect
13. C2×D3×D15C22semidirect
14. C2×C32×C4×C5C22semidirect
15. C2×C3⋊Dic15C22semidirect
16. C4×C3⋊D15C22semidirect
17. C3×D60C22semidirect
18. C3×C5×D12C22semidirect
19. #67150C22semidirect
26. C2×D60D3semidirect
30. C2×C5×D12D3semidirect
35. C2×C3⋊D15D4semidirect
38. C2×C3×D15C23semidirect
40. C2×C3×C5×D3C23semidirect
42. C32×C4×C5C23semidirect
43. C3⋊Dic15C23semidirect
48. C2×C3×D12D5semidirect
57. C22×D15C2×D3semidirect
58. C22×C5×D3C2×D3semidirect
64. C2×C3×C4×C5C2×D3semidirect
65. C2×C3×C4×C5C2×D3semidirect
70. D60C2×D3semidirect
74. C5×D12C2×D3semidirect
79. C2×C32×C5C2×D4semidirect
81. C3⋊D15C2×D4semidirect
92. C22×C3×D3C2×D5semidirect
95. C2×C32×C4C2×D5semidirect
99. C3×D12C2×D5semidirect
114. C2×D15C22×D3semidirect
116. C2×C5×D3C22×D3semidirect
121. C3×C4×C5C22×D3semidirect
122. C3×C4×C5C22×D3semidirect
135. C2×D12D15semidirect
139. C32×C5C22×D4semidirect
146. C2×C4×C5D32semidirect
157. C2×C3×D3C22×D5semidirect
159. C32×C4C22×D5semidirect
165. C2×C3×C5D3×D4semidirect
166. C2×C3×C5D3×D4semidirect
185. C22×D3C2×D15semidirect
189. C2×C3×C4D3×D5semidirect
190. C2×C3×C4C2×D15semidirect
197. D12C2×D15semidirect
209. C4×C5C2×D32semidirect
211. C2×C32D4×D5semidirect
223. C3×C5C2×D3×D4semidirect
224. C3×C5C2×D3×D4semidirect
243. C2×D3C22×D15semidirect
245. C3×C4C2×D3×D5semidirect
246. C3×C4C22×D15semidirect
251. C2×C5#3802semidirect
255. C32C2×D4×D5semidirect
266. C2×C4D3×D15semidirect
271. C2×C3#6777semidirect
272. C2×C3D4×D15semidirect
280. C5C2×#3802semidirect
290. C4C2×D3×D15semidirect
292. C3C2×#6777semidirect
293. C3C2×D4×D15semidirect
297. C2#10624205direct (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⋊D152
C2×C3×D602
C2×C3×C5×D122
C2×#671502
#106242052
C2×D4×D153
C2×#67773
C2×#38025