Finite Group Databasebeta

← #12097548

Subgroups — #12097548

Order 1280.

990 conjugacy classes of subgroups.

The subgroup lattice has 322 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C5×C8C211yesmaximal, characteristic
2#10613791C211yesmaximal, characteristic
3C2×#65215C211yesmaximal, characteristic
4#10602760C212yesmaximal
5C8×C22⋊Dic5C212yesmaximal
6#10600550C212yesmaximal, complemented
7C8×C4⋊Dic5C212yesmaximal, complemented
8#10600544C212yesmaximal, complemented
9#10600542C212yesmaximal, complemented
10C23×C5×C8C2211yescharacteristic
11C23×C5×C8C2211yescharacteristic
12C22×C42×C5C2211yescharacteristic
13C2×C4×C5×C8C418yescomplemented
14C2×C4×C5×C8C2211yescharacteristic
15C2×C4×C5×C8C2211yescharacteristic
16C2×C4×C5×C8C2211yescharacteristic
17C2×C4×C5×C8C2211yescharacteristic
18#65501C412yes—
19#65500C412yes—
20C4×C22⋊Dic5C2212yes—
21C2×C22⋊#168C2212yes—
22C2×#3947C2214yes—
23C2×C8×Dic5C2214yes—
24#65226C412yes—
25#65225C412yes—
26C4×C4⋊Dic5C2212yes—
27#65221C2212yes—
28#65215C418yescomplemented
29C2×C4⋊#168C2212yes—
30C2×#3935C2212yes—
31#64770C2214yes—
32#64770C2214yes—
33#20476—51nomaximal, Sylow
34C23×C4×C5C2×C411yescharacteristic
35C23×C4×C5C2×C411yescharacteristic
36C23×C4×C5C2311yescharacteristic
37C22×C5×C8—24no—
38C22×C5×C8—24no—
39C22×C5×C8C2×C414yes—
40C22×C5×C8C2×C414yes—
41C22×C5×C8C2311yescharacteristic
42C22×C5×C8C2311yescharacteristic
43C22×C5×C8C2311yescharacteristic
44C22×C5×C8C2311yescharacteristic
45C2×C42×C5C2×C411yescharacteristic
46C2×C42×C5C2×C411yescharacteristic
47C2×C42×C5C2×C414yes—
48C2×C42×C5C2×C414yes—
49C2×C42×C5C2311yescharacteristic
50C2×C42×C5C2311yescharacteristic
51C2×C22⋊Dic5C2×C414yes—
52C2×C4⋊Dic5C2×C414yes—
53C2×C4×Dic5C2314yes—
54C22×#168C2314yes—
55C4×C5×C8C2×C414yes—
56C4×C5×C8C2×C414yes—
57C4×C5×C8C2×C414yes—
58C4×C5×C8C2×C414yes—
59#3963C2×C414yes—
60#3963C2×C414yes—
61#3963C2×C414yes—
62#3963C2×C414yes—
63C22⋊#168C2×C418yes—
64#3947—28no—
65C8×Dic5—28no—
66C4⋊#168C2×C418yes—
67#3935C2×C418yes—
68C2×#432—51no—
69C22×C4×C8D511yescharacteristic
70#2283—51no—
71#1770—52no—
72C8×C4⋊C4—52no—
73#1752—52no—
74C8×C22⋊C4—52no—
75#1746—52no—
76#1726—52no—
77C24×C5C22×C411yescharacteristic
78C22×C4×C5—24no—
79C22×C4×C5—24no—
80C22×C4×C5—22no—
81C22×C4×C5—22no—
82C22×C4×C5C4214yes—
83C22×C4×C5C4214yes—
84C22×C4×C5C22×C411yescharacteristic
85C22×C4×C5C22×C411yescharacteristic
86C22×C4×C5C22×C411yescharacteristic
87C22×C4×C5C22×C411yescharacteristic
88C22×C4×C5C22×C412yes—
89C22×C4×C5C22×C411yescharacteristic
90C22×C4×C5C22×C412yes—
91C22×C4×C5C2411yescharacteristic
92C22×Dic5C22×C418yes—
93C2×C5×C8—22no—
94C2×C5×C8—22no—
95C2×C5×C8—28no—
96C2×C5×C8—28no—
97C2×C5×C8C22×C412yes—
98C2×C5×C8C22×C412yes—
99C2×C5×C8C22×C412yes—
100C2×C5×C8C22×C412yes—
101C2×C5×C8#4114yes—
102C2×C5×C8#4114yes—
103C42×C5C4214yes—
104C42×C5C4214yes—
105C42×C5C22×C412yes—
106C42×C5C22×C412yes—
107C42×C5C22×C412yes—
108C42×C5C22×C412yes—
109C22⋊Dic5—28no—
110C4⋊Dic5—28no—
111C4×Dic5—24no—
112C4×Dic5—24no—
113C2×#168—24no—
114C2×#168—24no—
115C2×#168C22×C418yes—
116C23×C8C2×D511yescharacteristic
117C23×C8C2×D511yescharacteristic
118C22×C42C2×D511yescharacteristic
119#432—58no—
120C2×C4⋊C8—52no—
121C2×C22⋊C8—52no—
122C2×#97—52no—
123C2×#97—54no—
124C2×C4×C8—54no—
125C2×C4×C8Dic518yescomplemented
126C2×C4×C8C2×D511yescharacteristic
127C2×C4×C8C2×D511yescharacteristic
128C2×C4×C8C2×D511yescharacteristic
129C2×C4×C8C2×D511yescharacteristic
130#383—52no—
131#382—52no—
132#381—52no—
133#380—52no—
134C4×C4⋊C4—52no—
135C4×C22⋊C4—52no—
136#376—52no—
137#336—54no—
138#336—54no—
139C23×C5—22no—
140C23×C5—22no—
141C23×C5C2×C4212yes—
142C23×C5#13114yes—
143C23×C5C23×C411yescharacteristic
144C2×C4×C5—22no—
145C2×C4×C5—22no—
146C2×C4×C5—22no—
147C2×C4×C5—22no—
148C2×C4×C5—28no—
149C2×C4×C5—22no—
150C2×C4×C5—22no—
151C2×C4×C5—24no—
152C2×C4×C5—28no—
153C2×C4×C5C2×C4212yes—
154C2×C4×C5C2×C4212yes—
155C2×C4×C5C2×C4212yes—
156C2×C4×C5C2×C4212yes—
157C2×C4×C5C2×C4212yes—
158C2×C4×C5#13114yes—
159C2×C4×C5C23×C411yescharacteristic
160C2×C4×C5C23×C411yescharacteristic
161C2×C4×C5C2×#4112yes—
162C2×C4×C5C2×#4112yes—
163C2×Dic5—28no—
164C2×Dic5—28no—
165C2×Dic5—28no—
166C5×C8—22no—
167C5×C8—22no—
168C5×C8#11714yes—
169C5×C8#11714yes—
170#168—28no—
171C23×C4C4×D511yescharacteristic
172C23×C4C4×D511yescharacteristic
173C23×C4C22×D511yescharacteristic
174C22×C8—24no—
175C22×C8—24no—
176C22×C8—54no—
177C22×C8C2×Dic514yes—
178C22×C8C2×Dic514yes—
179C22×C8C22×D511yescharacteristic
180C22×C8C22×D511yescharacteristic
181C22×C8C22×D511yescharacteristic
182C22×C8C22×D511yescharacteristic
183C2×C4⋊C4—54no—
184C2×C22⋊C4—54no—
185C2×C42—54no—
186C2×C42C4×D511yescharacteristic
187C2×C42C4×D511yescharacteristic
188C2×C42C4×D514yes—
189C2×C42C2×Dic514yes—
190C2×C42C22×D511yescharacteristic
191C2×C42C22×D511yescharacteristic
192C4⋊C8—58no—
193C22⋊C8—58no—
194#97—58no—
195#97—108no—
196C4×C8—108no—
197C4×C8C2×Dic514yes—
198C4×C8C2×Dic514yes—
199C4×C8C2×Dic514yes—
200C4×C8C2×Dic514yes—
201#95—54no—
202#95—54no—
203#95—54no—
204#95—54no—
205C22×C5—22no—
206C22×C5—28no—
207C22×C5—22no—
208C22×C5#40514yes—
209C22×C5C22×C4211yescharacteristic
210C22×C5C4×#4112yes—
211C22×C5C2×#13112yes—
212C22×C5C2×#13112yes—
213C4×C5—22no—
214C4×C5—22no—
215C4×C5—22no—
216C4×C5—22no—
217C4×C5#40514yes—
218C4×C5C2×#11711yescharacteristic
219C4×C5C2×#11711yescharacteristic
220C4×C5C4×#4112yes—
221Dic5—48no—
222C24C2×C4×D511yescharacteristic
223C22×C4—24no—
224C22×C4—22no—
225C22×C4—22no—
226C22×C4—24no—
227C22×C4—58no—
228C22×C4C4×Dic514yes—
229C22×C4C4×Dic514yes—
230C22×C4C2×C4×D512yes—
231C22×C4C2×C4×D511yescharacteristic
232C22×C4C2×C4×D511yescharacteristic
233C22×C4C2×C4×D511yescharacteristic
234C22×C4C2×C4×D511yescharacteristic
235C22×C4C2×C4×D511yescharacteristic
236C22×C4C22×Dic512yes—
237C22×C4C23×D511yescharacteristic
238C2×C8—22no—
239C2×C8—22no—
240C2×C8—28no—
241C2×C8—28no—
242C2×C8—58no—
243C2×C8—104no—
244C2×C8—104no—
245C2×C8#70914yes—
246C2×C8#70914yes—
247C2×C8C22×Dic512yes—
248C2×C8C22×Dic512yes—
249C2×C8C22×Dic512yes—
250C2×C8C22×Dic512yes—
251C4⋊C4—108no—
252C22⋊C4—108no—
253C42—104no—
254C42—104no—
255C42C4×Dic514yes—
256C42C4×Dic514yes—
257C42C2×C4×D512yes—
258C42C2×C4×D512yes—
259C42C22×Dic512yes—
260C42C22×Dic512yes—
261C2×C5—24no—
262C2×C5C4×#11711yescharacteristic
263C2×C5C2×#40511yescharacteristic
264C2×C5C2×#40511yescharacteristic
265C2×C5#296614yes—
266C23—22no—
267C23—22no—
268C23#404714yes—
269C23C2×C4×Dic512yes—
270C23C22×C4×D511yescharacteristic
271C2×C4—22no—
272C2×C4—22no—
273C2×C4—22no—
274C2×C4—22no—
275C2×C4—28no—
276C2×C4—24no—
277C2×C4—22no—
278C2×C4—22no—
279C2×C4—28no—
280C2×C4—108no—
281C2×C4—108no—
282C2×C4—108no—
283C2×C4#404714yes—
284C2×C4C2×C4×Dic512yes—
285C2×C4C2×C4×Dic512yes—
286C2×C4C2×C4×Dic512yes—
287C2×C4C2×C4×Dic512yes—
288C2×C4C2×C4×Dic512yes—
289C2×C4C22×C4×D511yescharacteristic
290C2×C4C2×#70912yes—
291C2×C4C2×#70912yes—
292C2×C4C23×Dic511yescharacteristic
293C8—22no—
294C8—22no—
295C8—108no—
296C8#407214yes—
297C8#407214yes—
298C5#2047611yescharacteristic, complemented, Sylow
299C22—28no—
300C22—22no—
301C22—22no—
302C22#6539014yes—
303C22C4×#70912yes—
304C22C2×#404712yes—
305C22C2×#404712yes—
306C22C22×C4×Dic511yescharacteristic
307C4—22no—
308C4—22no—
309C4—22no—
310C4—22no—
311C4—208no—
312C4#6539014yes—
313C4C4×#70912yes—
314C4C2×#407211yescharacteristic
315C4C2×#407211yescharacteristic
316C2—24no—
317C2#1061017914yes—
318C2C4×#407211yescharacteristic
319C2C2×#6539011yescharacteristic
320C2C2×#6539011yescharacteristic
subgroupG/H
centerC22×C8C22×D5
commutatorC22×C5C22×C42
FrattiniC22×C4C23×D5
FittingC22×C4×C5×C8C2
socleC23×C5C23×C4
prime radicalC24×C5C22×C4
cosocleC22×C4×C5C24
hypercenterC22×C4×C8D5
hypocenterC5#20476
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C8 ◁ C22×C4×C8

Complements

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

NH ≅ G/Ntype
6. #10600550C2semidirect
7. C8×C4⋊Dic5C2semidirect
8. #10600544C2semidirect
9. #10600542C2semidirect
13. C2×C4×C5×C8C4semidirect
28. #65215C4semidirect
125. C2×C4×C8Dic5semidirect
298. C5#20476semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C5×C82
#106137912
C2×#652152
#106027602
C8×C22⋊Dic52
#106005502
C8×C4⋊Dic52
#106005442
#106005422
#204765