Finite Group Databasebeta

← #14438782

Subgroups — #14438782

Order 1920.

1520 conjugacy classes of subgroups; only the 220 normal subgroups are shown.

normal subgroups only

This group has 1520 conjugacy classes of subgroups — too many to draw. Only its 220 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×#91256C214yesmaximal, complemented
2#11752750C212yesmaximal, complemented
3C4×C8×D15C211yesmaximal, characteristic, complemented
4C5×#4695C211yesmaximal, characteristic, complemented
5C3×#64984C211yesmaximal, characteristic, complemented
6#11748012C214yesmaximal, complemented
7#11747039C212yesmaximal, complemented
8D5×#493—31nomaximal, Hall
9C2×#6777—24no—
10C2×#6777C2214yes—
11C2×C8×D15C2212yes—
12C42×D15C2211yescharacteristic
13C2×C5×D24C2214yescomplemented
14C5×#874C2212yescomplemented
15C2×C3×D40C2214yescomplemented
16C3×#4020C2212yescomplemented
17#91463—24no—
18#91463C2214yescomplemented
19C2×#6652C2218yescomplemented
20#91256—216no—
21C3×C4×C5×C8C2211yescharacteristic, complemented
22C8×Dic15C2212yescomplemented
23C4×C3⋊#168C2211yescharacteristic, complemented
24D3×#493—51nomaximal, Hall
25C2×D5×D8—34no—
26D5×#127—32no—
27C5×#493—31no—
28#65440—34no—
29#65362—32no—
30#64984D311yescharacteristic, complemented
31C4×C8×D5—31no—
32C22×D3×D5—24no—
33C2×C4×D15D412yes—
34C2×C4×D15C2311yescharacteristic
35C2×C5×D12—24no—
36C2×C5×D12C2314yes—
37C2×C3×D20—24no—
38C2×C3×D20C2314yes—
39C2×#1201—24no—
40C2×#1201—28no—
41#6777—216no—
42#6777—416no—
43C2×C3×C5×C8C2312yes—
44C3×C42×C5C2311yescharacteristic
45C4×Dic15D412yes—
46C4×Dic15C2311yescharacteristic
47C2×C3⋊#168C2312yes—
48C8×D15D418yescomplemented
49C5×D24—28no—
50C3×D40—28no—
51#6652—216no—
52C2×D3×D8—54no—
53D3×#127—52no—
54C3×#493—51no—
55#5151—54no—
56#5073—52no—
57#4695D511yescharacteristic, complemented
58C4×D3×C8—51no—
59C2×D4×D5—34no—
60C2×D4×D5—64no—
61C2×C5×D8—34no—
62C5×#127—32no—
63#4086—34no—
64#4086—64no—
65C2×#686—38no—
66D5×D8—616no—
67C2×D40C2×D314yescomplemented
68C2×C8×D5—32no—
69#4020C2×D312yescomplemented
70C42×D5—31no—
71C4×C5×C8C2×D311yescharacteristic, complemented
72C8×Dic5—32no—
73C4×#168—31no—
74C2×#493—151noSylow
75C22×D15C2×D411yescharacteristic
76C22×C5×D3—24no—
77C22×C3×D5—24no—
78C2×D3×D5—48no—
79C2×D3×D5—416no—
80C2×C3×C4×C5C2×D412yes—
81C2×C3×C4×C5C2411yescharacteristic
82C2×Dic15C2×D411yescharacteristic
83C2×Dic15C2×D412yes—
84C4×D15D818yescomplemented
85C4×D15C2×D414yes—
86C5×D12—28no—
87C5×D12—48no—
88C3×D20—28no—
89C3×D20—48no—
90#1201—48no—
91#1201—416no—
92C3×C5×C8C2×D414yescomplemented
93C3⋊#168C2×D414yescomplemented
94C2×D3×D4—54no—
95C2×D3×D4—104no—
96C2×C3×D8—54no—
97C3×#127—52no—
98#940—54no—
99#940—104no—
100C2×#213—58no—
101D3×D8—1016no—
102C2×D24C2×D514yescomplemented
103C2×D3×C8—52no—
104#874C2×D512yescomplemented
105C42×D3—51no—
106C3×C4×C8C2×D511yescharacteristic, complemented
107C8×Dic3—52no—
108C4×C3⋊C8—51no—
109C23×D5—64no—
110C2×C5×D4—34no—
111C2×C5×D4—64no—
112C2×C22⋊D5—64no—
113C2×C22⋊D5—68no—
114D4×D5—616no—
115D4×D5—1216no—
116C2×D20—24no—
117C2×D20C22×D314yes—
118C2×C4×D5—32no—
119C2×C4×D5—31no—
120C5×D8—68no—
121C2×C5×C8C22×D312yes—
122C42×C5C22×D311yescharacteristic
123#686—616no—
124C4×Dic5—32no—
125C4×Dic5—31no—
126C2×#168—32no—
127D40—28no—
128C8×D5—38no—
129C22×D8—154no—
130C2×#127—152no—
131#493—31no—
132#493—51no—
133#493—152no—
134#493—154no—
135C2×C4×C8—151no—
136C22×C3×C5C22×D411yescharacteristic
137C2×D15#12712yes—
138C2×D15C2×D814yes—
139C2×C5×D3—44no—
140C2×C5×D3—48no—
141C2×C3×D5—44no—
142C2×C3×D5—48no—
143D3×D5—816no—
144C3×C4×C5C2×D814yescomplemented
145C3×C4×C5C22×D412yes—
146Dic15#12712yes—
147Dic15C2×D814yescomplemented
148C23×D3—104no—
149C2×C3×D4—54no—
150C2×C3×D4—104no—
151C2×#67—108no—
152C2×#67—104no—
153D3×D4—1016no—
154D3×D4—2016no—
155C2×D12—24no—
156C2×D12C22×D514yes—
157C2×C4×D3—52no—
158C2×C4×D3—51no—
159C3×D8—108no—
160C2×C3×C8C22×D512yes—
161C3×C42C22×D511yescharacteristic
162#213—1016no—
163C4×Dic3—52no—
164C4×Dic3—51no—
165C2×C3⋊C8—52no—
166D24—28no—
167D3×C8—58no—
168C23×C5—64no—
169C22×D5—24no—
170C22×D5—31no—
171C22×D5—128no—
172C22×D5—1216no—
173C5×D4—68no—
174C5×D4—128no—
175C2×C4×C5D3×D412yes—
176C2×C4×C5C23×D311yescharacteristic
177C22⋊D5—128no—
178C22⋊D5—1216no—
179C2×Dic5—31no—
180C2×Dic5—32no—
181D20—28no—
182D20—48no—
183C4×D5—38no—
184C4×D5—34no—
185C5×C8D3×D414yescomplemented
186#168—34no—
187C22×D4—154no—
188C22×D4—304no—
189C2×D8—34no—
190C2×D8—54no—
191C2×D8—158no—
192C2×D8—3016no—
193C22×C8—152no—
194#127—32no—
195#127—52no—
196#127—154no—
197#127—304no—
198C2×C42—151no—
199C4×C8—152no—
200C4×C8—151no—
201C4×C8D3×D511yescharacteristic, complemented
202C2×C3×C5C2×#12711yescharacteristic
203C2×C3×C5C22×D812yes—
204D15#49314yescomplemented
205C3×D5—84no—
206C5×D3—84no—
207C23×C3—104no—
208C22×D3—24no—
209C22×D3—51no—
210C22×D3—208no—
211C22×D3—2016no—
212C3×D4—108no—
213C3×D4—208no—
214C2×C3×C4D4×D512yes—
215C2×C3×C4C23×D511yescharacteristic
216#67—208no—
217#67—2016no—
218C2×Dic3—51no—
219C2×Dic3—52no—
220D12—28no—
221D12—48no—
222C4×D3—54no—
223C4×D3—58no—
224C3×C8D4×D514yescomplemented
225C3⋊C8—54no—
226C22×C5—124no—
227C22×C5—128no—
228C22×C5C2×D3×D411yescharacteristic
229C2×D5—32no—
230C2×D5—34no—
231C2×D5—44no—
232C2×D5—48no—
233C2×D5—2416no—
234C4×C5D3×D814yescomplemented
235C4×C5C2×D3×D412yes—
236Dic5—32no—
237Dic5—34no—
238C24—304no—
239C2×D4—34no—
240C2×D4—54no—
241C2×D4—64no—
242C2×D4—104no—
243C2×D4—3016no—
244C2×D4—308no—
245C2×D4—304no—
246C2×D4—6016no—
247C22×C4—152no—
248C22×C4—151no—
249D8—68no—
250D8—108no—
251D8—3016no—
252C2×C8—152no—
253C2×C8—158no—
254C2×C8C2×D3×D512yes—
255C42—152no—
256C42—151no—
257C42C2×D3×D511yescharacteristic
258C3×C5C2×#49311yescharacteristic, complemented, Hall
259C22×C3—204no—
260C22×C3—208no—
261C22×C3C2×D4×D511yescharacteristic
262C2×D3—44no—
263C2×D3—48no—
264C2×D3—52no—
265C2×D3—54no—
266C2×D3—4016no—
267C3×C4D5×D814yescomplemented
268C3×C4C2×D4×D512yes—
269Dic3—52no—
270Dic3—54no—
271C2×C5—244no—
272C2×C5D3×#12711yescharacteristic
273C2×C5C2×D3×D812yes—
274D5—34no—
275D5—84no—
276C23—64no—
277C23—104no—
278C23—151no—
279C23—608no—
280C23—6016no—
281D4—68no—
282D4—108no—
283D4—128no—
284D4—208no—
285D4—608no—
286D4—6016no—
287C2×C4—151no—
288C2×C4—152no—
289C2×C4—154no—
290C2×C4—158no—
291C2×C4#677712yes—
292C2×C4C22×D3×D511yescharacteristic
293C8—154no—
294C8#677714yescomplemented
295C2×C3—404no—
296C2×C3D5×#12711yescharacteristic
297C2×C3C2×D5×D812yes—
298D3—54no—
299D3—84no—
300C5D3×#49311yescharacteristic, complemented, Sylow
301C22—124no—
302C22—128no—
303C22—152no—
304C22—154no—
305C22—204no—
306C22—208no—
307C22—12016no—
308C22C2×#677711yescharacteristic
309C4—152no—
310C4—154no—
311C4#9125614yescomplemented
312C4C2×#677712yes—
313C3D5×#49311yescharacteristic, complemented, Sylow
314C2—154no—
315C2—244no—
316C2—404no—
317C2#1175275011yescharacteristic
318C2C2×#9125612yes—
subgroupG/H
centerC22C2×#6777
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×C8C22
socleC22×C3×C5C22×D4
hypercenterC4×C8D3×D5
hypocenterC3×C5C2×#493
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
1. C2×#91256C2semidirect
2. #11752750C2semidirect
3. C4×C8×D15C2semidirect
4. C5×#4695C2semidirect
5. C3×#64984C2semidirect
6. #11748012C2semidirect
7. #11747039C2semidirect
13. C2×C5×D24C22semidirect
14. C5×#874C22semidirect
15. C2×C3×D40C22semidirect
16. C3×#4020C22semidirect
18. #91463C22semidirect
19. C2×#6652C22semidirect
21. C3×C4×C5×C8C22semidirect
22. C8×Dic15C22semidirect
23. C4×C3⋊#168C22semidirect
30. #64984D3semidirect
48. C8×D15D4semidirect
57. #4695D5semidirect
67. C2×D40C2×D3semidirect
69. #4020C2×D3semidirect
71. C4×C5×C8C2×D3semidirect
84. C4×D15D8semidirect
92. C3×C5×C8C2×D4semidirect
93. C3⋊#168C2×D4semidirect
102. C2×D24C2×D5semidirect
104. #874C2×D5semidirect
106. C3×C4×C8C2×D5semidirect
144. C3×C4×C5C2×D8semidirect
147. Dic15C2×D8semidirect
185. C5×C8D3×D4semidirect
201. C4×C8D3×D5semidirect
204. D15#493semidirect
224. C3×C8D4×D5semidirect
234. C4×C5D3×D8semidirect
258. C3×C5C2×#493semidirect
267. C3×C4D5×D8semidirect
294. C8#6777semidirect
300. C5D3×#493semidirect
311. C4#91256semidirect
313. C3D5×#493semidirect

Maximal subgroups

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

subgroupindex
C2×#912562
#117527502
C4×C8×D152
C5×#46952
C3×#649842
#117480122
#117470392
D5×#4933
D3×#4935