Finite Group Databasebeta

← C2×D15×D16 #14478196

Subgroups — C2×D15×D16 #14478196

Order 1920.

880 conjugacy classes of subgroups; only the 175 normal subgroups are shown.

normal subgroups only

This group has 880 conjugacy classes of subgroups — too many to draw. Only its 175 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
1C2×D8×D15C212yesmaximal, complemented
2C2×C3×C5×D16C211yesmaximal, characteristic, complemented
3C2×#91110C212yesmaximal, complemented
4D15×D16C218yesmaximal, direct product factor
5C2×D240C211yesmaximal, characteristic, complemented
6C2×C16×D15C211yesmaximal, characteristic, complemented
7C2×D5×D16—31nomaximal, Hall
8C2×D4×D15—22no—
9C2×C3×C5×D8C2212yescomplemented
10C2×#6715—22no—
11D8×D15—24no—
12D8×D15C2218yescomplemented
13C2×D120C2212yescomplemented
14C2×C8×D15C2211yescharacteristic
15C3×C5×D16C2214yescomplemented
16C2×C3×C5×C16C2211yescharacteristic, complemented
17#91110C2218yescomplemented
18C2×C3⋊#672C2211yescharacteristic, complemented
19D240C2214yescomplemented
20C16×D15C2214yescomplemented
21C2×D3×D16—51nomaximal, Hall
22C2×D5×D8—32no—
23C2×C5×D16D311yescharacteristic, complemented
24C2×#3958—32no—
25D5×D16—38no—
26C2×D80—31no—
27C2×D5×C16—31no—
28C23×D15—42no—
29C2×C3×C5×D4—22no—
30C2×#1220—42no—
31D4×D15—28no—
32D4×D15—44no—
33C2×D60—22no—
34C2×C4×D15D411yescharacteristic
35C3×C5×D8—22no—
36C3×C5×D8C2314yescomplemented
37C2×C3×C5×C8C2311yescharacteristic
38#6715—28no—
39C2×C3⋊#168D411yescharacteristic
40D120—22no—
41D120C2314yescomplemented
42C8×D15D412yes—
43C8×D15C2312yes—
44C3×C5×C16C2312yescomplemented
45C3⋊#672C2312yescomplemented
46C2×D3×D8—52no—
47C2×C3×D16D511yescharacteristic, complemented
48C2×#826—52no—
49D3×D16—58no—
50C2×D48—51no—
51C2×D3×C16—51no—
52C2×D4×D5—62no—
53C2×C5×D8C2×D312yescomplemented
54C2×#686—62no—
55D5×D8—38no—
56D5×D8—64no—
57C2×D40—32no—
58C2×C8×D5—31no—
59C5×D16C2×D314yescomplemented
60C2×C5×C16C2×D311yescharacteristic, complemented
61#3958—38no—
62C2×#672—31no—
63D80—34no—
64D5×C16—34no—
65C22×D16—151noSylow
66C23×C3×C5—42no—
67C22×D15—42no—
68C22×D15—48no—
69C22×D15—88no—
70C22×D15D811yescharacteristic
71C3×C5×D4—24no—
72C3×C5×D4—42no—
73C2×C3×C4×C5C2×D411yescharacteristic
74#1220—48no—
75C2×Dic15D811yescharacteristic
76D60—24no—
77D60—42no—
78C4×D15D812yes—
79C4×D15C2×D412yes—
80C3×C5×C8C2×D411yescharacteristic
81C3×C5×C8C2411yescharacteristic
82C3⋊#168C2×D412yes—
83C2×D3×D4—102no—
84C2×C3×D8C2×D512yescomplemented
85C2×#213—102no—
86D3×D8—58no—
87D3×D8—104no—
88C2×D24—52no—
89C2×D3×C8—51no—
90C3×D16C2×D514yescomplemented
91C2×C3×C16C2×D511yescharacteristic, complemented
92#826—58no—
93C2×C3⋊C16—51no—
94D48—54no—
95D3×C16—54no—
96C23×D5—122no—
97C2×C5×D4—22no—
98C2×C22⋊D5—122no—
99D4×D5—68no—
100D4×D5—124no—
101C2×D20—62no—
102C2×C4×D5—31no—
103C5×D8—22no—
104C5×D8C22×D314yescomplemented
105C2×C5×C8C22×D311yescharacteristic
106#686—68no—
107C2×#168—31no—
108D40—34no—
109D40—62no—
110C8×D5—32no—
111C8×D5—32no—
112C5×C16C22×D312yescomplemented
113#672—32no—
114C22×D8—152no—
115C2×D16—152no—
116C2×D16—158no—
117C2×D16—151no—
118C2×D16D1511yescharacteristic, direct product factor
119C22×C16—151no—
120C22×C3×C5—44no—
121C22×C3×C5—84no—
122C22×C3×C5C2×D811yescharacteristic
123C2×D15—44no—
124C2×D15—84no—
125C2×D15—816no—
126C2×D15D1614yesdirect product factor
127C2×D15C2×D812yes—
128C3×C4×C5C2×D811yescharacteristic
129C3×C4×C5C22×D411yescharacteristic
130Dic15C2×D812yes—
131C23×D3—202no—
132C2×C3×D4—22no—
133C2×#67—202no—
134D3×D4—108no—
135D3×D4—204no—
136C2×D12—102no—
137C2×C4×D3—51no—
138C3×D8—22no—
139C3×D8C22×D514yescomplemented
140C2×C3×C8C22×D511yescharacteristic
141#213—108no—
142C2×C3⋊C8—51no—
143D24—54no—
144D24—102no—
145D3×C8—52no—
146D3×C8—52no—
147C3×C16C22×D512yescomplemented
148C3⋊C16—52no—
149C23×C5—42no—
150C22×D5—31no—
151C22×D5—128no—
152C22×D5—122no—
153C22×D5—248no—
154C5×D4—24no—
155C5×D4—42no—
156C2×C4×C5D3×D411yescharacteristic
157C22⋊D5—128no—
158C2×Dic5—31no—
159D20—64no—
160D20—122no—
161C4×D5—32no—
162C4×D5—32no—
163C5×C8D3×D411yescharacteristic
164C5×C8C23×D311yescharacteristic
165#168—32no—
166C22×D4—302no—
167C2×D8—158no—
168C2×D8—152no—
169C2×D8—304no—
170C2×D8—302no—
171C2×D8C2×D1512yescomplemented
172C22×C8—151no—
173D16—158no—
174D16—154no—
175D16C2×D1514yesdirect product factor
176C2×C16—151no—
177C2×C16—154no—
178C2×C16C2×D1511yescharacteristic, complemented
179C2×C3×C5—84no—
180C2×C3×C5C2×D1612yescomplemented
181C2×C3×C5C22×D811yescharacteristic
182D15—84no—
183D15C2×D1614yesdirect product factor
184C23×C3—42no—
185C22×D3—51no—
186C22×D3—208no—
187C22×D3—202no—
188C22×D3—408no—
189C3×D4—24no—
190C3×D4—42no—
191C2×C3×C4D4×D511yescharacteristic
192#67—208no—
193C2×Dic3—51no—
194D12—104no—
195D12—202no—
196C4×D3—52no—
197C4×D3—52no—
198C3×C8D4×D511yescharacteristic
199C3×C8C23×D511yescharacteristic
200C3⋊C8—52no—
201C22×C5—44no—
202C22×C5—84no—
203C22×C5D3×D811yescharacteristic
204C2×D5—34no—
205C2×D5—32no—
206C2×D5—124no—
207C2×D5—2416no—
208C2×D5—244no—
209C4×C5D3×D811yescharacteristic
210C4×C5C2×D3×D411yescharacteristic
211Dic5—32no—
212C24—602no—
213C2×D4—22no—
214C2×D4—308no—
215C2×D4—302no—
216C2×D4—604no—
217C2×D4—602no—
218C22×C4—151no—
219D8—22no—
220D8—154no—
221D8—308no—
222D8—302no—
223D8C22×D1514yescomplemented
224C2×C8—151no—
225C2×C8—152no—
226C2×C8—152no—
227C2×C8C22×D1511yescharacteristic
228C16—152no—
229C16C22×D1512yescomplemented
230C3×C5C22×D1611yescharacteristic, complemented, Hall
231C22×C3—44no—
232C22×C3—84no—
233C22×C3D5×D811yescharacteristic
234C2×D3—52no—
235C2×D3—54no—
236C2×D3—204no—
237C2×D3—4016no—
238C2×D3—404no—
239C3×C4D5×D811yescharacteristic
240C3×C4C2×D4×D511yescharacteristic
241Dic3—52no—
242C2×C5—84no—
243C2×C5D3×D1612yescomplemented
244C2×C5C2×D3×D811yescharacteristic
245D5—34no—
246D5—244no—
247C23—42no—
248C23—151no—
249C23—608no—
250C23—602no—
251C23—1208no—
252D4—24no—
253D4—42no—
254D4—304no—
255D4—608no—
256D4—602no—
257C2×C4—151no—
258C2×C4—152no—
259C2×C4—152no—
260C2×C4D4×D1511yescharacteristic
261C8—152no—
262C8D4×D1511yescharacteristic
263C8C23×D1511yescharacteristic
264C2×C3—84no—
265C2×C3D5×D1612yescomplemented
266C2×C3C2×D5×D811yescharacteristic
267D3—54no—
268D3—404no—
269C5C2×D3×D1611yescharacteristic, complemented, Sylow
270C22—44no—
271C22—84no—
272C22—154no—
273C22—152no—
274C22—604no—
275C22—12016no—
276C22—1204no—
277C22D8×D1511yescharacteristic
278C4—152no—
279C4D8×D1511yescharacteristic
280C4C2×D4×D1511yescharacteristic
281C3C2×D5×D1611yescharacteristic, complemented, Sylow
282C2—84no—
283C2—154no—
284C2—1204no—
285C2D15×D1612yesdirect product factor
286C2C2×D8×D1511yescharacteristic
subgroupG/H
centerC22D8×D15
commutator, cosocleC3×C5×C8C24
FrattiniC8C23×D15
FittingC2×C3×C5×D16C2
socleC22×C3×C5C2×D8
hypercenterC2×D16D15
hypocenterC3×C5C22×D16
LCSG ▷ C3×C5×C8 ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×D16

Complements

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

NH ≅ G/Ntype
1. C2×D8×D15C2semidirect
2. C2×C3×C5×D16C2semidirect
3. C2×#91110C2semidirect
4. D15×D16C2direct (N × H)
5. C2×D240C2semidirect
6. C2×C16×D15C2semidirect
9. C2×C3×C5×D8C22semidirect
12. D8×D15C22semidirect
13. C2×D120C22semidirect
15. C3×C5×D16C22semidirect
16. C2×C3×C5×C16C22semidirect
17. #91110C22semidirect
18. C2×C3⋊#672C22semidirect
19. D240C22semidirect
20. C16×D15C22semidirect
23. C2×C5×D16D3semidirect
36. C3×C5×D8C23semidirect
41. D120C23semidirect
44. C3×C5×C16C23semidirect
45. C3⋊#672C23semidirect
47. C2×C3×D16D5semidirect
53. C2×C5×D8C2×D3semidirect
59. C5×D16C2×D3semidirect
60. C2×C5×C16C2×D3semidirect
84. C2×C3×D8C2×D5semidirect
90. C3×D16C2×D5semidirect
91. C2×C3×C16C2×D5semidirect
104. C5×D8C22×D3semidirect
112. C5×C16C22×D3semidirect
118. C2×D16D15direct (N × H)
126. C2×D15D16direct (N × H)
139. C3×D8C22×D5semidirect
147. C3×C16C22×D5semidirect
171. C2×D8C2×D15semidirect
175. D16C2×D15direct (N × H)
178. C2×C16C2×D15semidirect
180. C2×C3×C5C2×D16semidirect
183. D15C2×D16direct (N × H)
223. D8C22×D15semidirect
229. C16C22×D15semidirect
230. C3×C5C22×D16semidirect
243. C2×C5D3×D16semidirect
265. C2×C3D5×D16semidirect
269. C5C2×D3×D16semidirect
281. C3C2×D5×D16semidirect
285. C2D15×D16direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D8×D152
C2×C3×C5×D162
C2×#911102
D15×D162
C2×D2402
C2×C16×D152
C2×D5×D163
C2×D3×D165