Finite Group Databasebeta

← #11987557

Subgroups — #11987557

Order 1280.

556 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#4070C211yesmaximal, characteristic
2C5×#1728C211yesmaximal, characteristic
3#10602322C211yesmaximal, characteristic
4#10597971C212yesmaximal, complemented
5#10597969C212yesmaximal, complemented
6C22×C5×M16—21no—
7C22×C42×C5C2211yescharacteristic
8C2×#4070C411yescharacteristic
9C2×C4×Dic10C411yescharacteristic
10#65501C411yescharacteristic
11#65499—21no—
12C4×C22⋊Dic5—21no—
13C2×C22⋊#168—21no—
14C4×C4⋊Dic5C411yescharacteristic
15#65222—21no—
16C4×#683—21no—
17#65218C2211yescharacteristic
18#65217C2211yescharacteristic
19C2×#3935—21no—
20C5×#336—21no—
21C5×#336C2212yes—
22#64744C2212yes—
23#7634—51nomaximal, Sylow
24C23×C4×C5C2×C411yescharacteristic
25C23×C4×C5D411yescharacteristic
26C23×C4×C5D411yescharacteristic
27C22×Dic10C2×C411yescharacteristic
28C2×C5×M16—24no—
29C2×C5×M16—42no—
30C2×C5×M16—42no—
31C22×C5×C8—22no—
32C2×C42×C5—42no—
33C2×C42×C5C2×C411yescharacteristic
34C2×C42×C5D411yescharacteristic
35C2×C42×C5D411yescharacteristic
36C2×C42×C5C2311yescharacteristic
37C2×C22⋊Dic5—21no—
38C2×C22⋊Dic5—21no—
39C2×C4⋊Dic5C2×C411yescharacteristic
40C2×C4⋊Dic5C2×C411yescharacteristic
41C2×C4⋊Dic5C2×C411yescharacteristic
42#4070—22no—
43#4070—22no—
44C2×#683—21no—
45C2×#683—21no—
46C2×#683—21no—
47C2×C4×Dic5—21no—
48C2×C4×Dic5—21no—
49C22×#168—22no—
50C4×Dic10—42no—
51#3963—21no—
52#3963—21no—
53#3963—21no—
54#3963—21no—
55#3963—21no—
56C22⋊#168—24no—
57#3935—42no—
58C4×C22⋊Q8—51no—
59#1749—51no—
60#1728D511yescharacteristic
61#1272—52no—
62#1271—52no—
63C24×C5C22⋊C411yescharacteristic
64C22×C4×C5—22no—
65C22×C4×C5—22no—
66C22×C4×C5—21no—
67C22×C4×C5—21no—
68C22×C4×C5—22no—
69C22×C4×C5—21no—
70C22×C4×C5—21no—
71C22×C4×C5—22no—
72C22×C4×C5—41no—
73C22×C4×C5—41no—
74C22×C4×C5—41no—
75C22×C4×C5C22⋊C411yescharacteristic
76C22×C4×C5C22⋊C411yescharacteristic
77C22×C4×C5C22⋊C411yescharacteristic
78C22×C4×C5C22×C411yescharacteristic
79C22×C4×C5C2×D411yescharacteristic
80C22×C4×C5C2×D411yescharacteristic
81C22×Dic5—21no—
82C22×Dic5—21no—
83C22×Dic5—21no—
84C22×Dic5—21no—
85C2×Dic10—21no—
86C2×Dic10—41no—
87C2×Dic10—41no—
88C2×Dic10M1612yescomplemented
89C5×M16—48no—
90C2×C5×C8—24no—
91C2×C5×C8—42no—
92C2×C5×C8—42no—
93C42×C5—22no—
94C42×C5—22no—
95C42×C5—41no—
96C42×C5—41no—
97C22⋊Dic5—24no—
98C22⋊Dic5—42no—
99C4⋊Dic5—21no—
100C4⋊Dic5—41no—
101C4⋊Dic5—41no—
102C4⋊Dic5M1612yescomplemented
103#683—24no—
104#683—42no—
105#683—41no—
106#683—41no—
107C4×Dic5—42no—
108C4×Dic5—42no—
109C2×#168—24no—
110C2×#168—42no—
111C2×#168—42no—
112C22×M16—21no—
113C2×C22⋊Q8—51no—
114C2×C4×Q8—51no—
115C22×C42C2×D511yescharacteristic
116C2×C22⋊C8—101no—
117C2×#97—101no—
118#391—51no—
119#389—51no—
120#387—101no—
121#385—101no—
122#380—51no—
123C4×C4⋊C4—51no—
124C4×C4⋊C4—101no—
125C4×C22⋊C4—101no—
126#336—21no—
127#336—52no—
128#336C2×D512yes—
129C23×C5—21no—
130C23×C5—21no—
131C23×C5—21no—
132C23×C5—21no—
133C23×C5—21no—
134C23×C5—21no—
135C23×C5#10412yes—
136C23×C5C2×C22⋊C411yescharacteristic
137C2×C4×C5—24no—
138C2×C4×C5—24no—
139C2×C4×C5—21no—
140C2×C4×C5—21no—
141C2×C4×C5—21no—
142C2×C4×C5—21no—
143C2×C4×C5—21no—
144C2×C4×C5—21no—
145C2×C4×C5—21no—
146C2×C4×C5—21no—
147C2×C4×C5—21no—
148C2×C4×C5—21no—
149C2×C4×C5—21no—
150C2×C4×C5—21no—
151C2×C4×C5—21no—
152C2×C4×C5—44no—
153C2×C4×C5—42no—
154C2×C4×C5—42no—
155C2×C4×C5#9912yes—
156C2×C4×C5#10412yes—
157C2×C4×C5C2×M1611yescharacteristic
158C2×C4×C5C2×M1611yescharacteristic
159C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
160C2×C4×C5#13712yes—
161C2×C4×C5#13711yescharacteristic
162C2×Dic5—22no—
163C2×Dic5—22no—
164C2×Dic5—41no—
165C2×Dic5—41no—
166C2×Dic5—41no—
167C2×Dic5—41no—
168C2×Dic5—41no—
169C2×Dic5—41no—
170C2×Dic5—41no—
171C2×Dic5—41no—
172C2×Dic5—41no—
173C2×Dic5—41no—
174Dic10—42no—
175Dic10—42no—
176C5×C8—44no—
177#168—44no—
178C22×Q8—51no—
179C23×C4C4×D511yescharacteristic
180C23×C4D2011yescharacteristic
181C23×C4C22⋊D511yescharacteristic
182C2×M16—24no—
183C2×M16—42no—
184C2×M16—42no—
185C22×C8—22no—
186C22×C8—102no—
187C22⋊Q8—102no—
188C22⋊Q8—102no—
189C4×Q8—202no—
190C2×C4⋊C4—51no—
191C2×C4⋊C4—51no—
192C2×C4⋊C4—51no—
193C2×C4⋊C4—101no—
194C2×C4⋊C4—101no—
195C2×C4⋊C4—101no—
196C2×C22⋊C4—101no—
197C2×C22⋊C4—101no—
198C2×C42—42no—
199C2×C42—101no—
200C2×C42—101no—
201C2×C42C4×D511yescharacteristic
202C2×C42D2011yescharacteristic
203C2×C42C22⋊D511yescharacteristic
204C2×C42C22×D511yescharacteristic
205C22⋊C8—104no—
206#97—202no—
207#95—101no—
208#95—101no—
209#95—101no—
210#95—101no—
211#95—101no—
212C22×C5—22no—
213C22×C5—22no—
214C22×C5—22no—
215C22×C5—41no—
216C22×C5—41no—
217C22×C5—41no—
218C22×C5—41no—
219C22×C5#40711yescharacteristic
220C22×C5C2×#9911yescharacteristic
221C22×C5#41311yescharacteristic
222C22×C5#41711yescharacteristic
223C22×C5#41911yescharacteristic
224C22×C5C2×#10411yescharacteristic
225C22×C5C2×#10411yescharacteristic
226C4×C5—21no—
227C4×C5—21no—
228C4×C5—21no—
229C4×C5—22no—
230C4×C5—21no—
231C4×C5—22no—
232C4×C5—22no—
233C4×C5—41no—
234Dic5—42no—
235Dic5—42no—
236Dic5—81no—
237Dic5—81no—
238C24#68511yescharacteristic
239C2×Q8—52no—
240C2×Q8—101no—
241C2×Q8—201no—
242C2×Q8—201no—
243C22×C4—22no—
244C22×C4—22no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—22no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—22no—
251C22×C4—41no—
252C22×C4—41no—
253C22×C4—41no—
254C22×C4—101no—
255C22×C4—101no—
256C22×C4—101no—
257C22×C4—101no—
258C22×C4#68511yescharacteristic
259C22×C4#68511yescharacteristic
260C22×C4#68511yescharacteristic
261C22×C4C2×C4×D511yescharacteristic
262C22×C4C2×D2011yescharacteristic
263C22×C4C2×C22⋊D511yescharacteristic
264M16—48no—
265C2×C8—24no—
266C2×C8—42no—
267C2×C8—42no—
268C2×C8—104no—
269C2×C8—202no—
270C2×C8—202no—
271C4⋊C4—52no—
272C4⋊C4—104no—
273C4⋊C4—101no—
274C4⋊C4—201no—
275C4⋊C4—201no—
276C4⋊C4—202no—
277C4⋊C4—201no—
278C4⋊C4—201no—
279C22⋊C4—104no—
280C22⋊C4—202no—
281C42—22no—
282C42—22no—
283C42—41no—
284C42—41no—
285C42—202no—
286C42—202no—
287C2×C5—42no—
288C2×C5#146511yescharacteristic
289C2×C5#148911yescharacteristic
290C2×C5#149111yescharacteristic
291C2×C5#150411yescharacteristic
292C2×C5#150811yescharacteristic
293C2×C5#152411yescharacteristic
294C2×C5#155911yescharacteristic
295C23—21no—
296C23—21no—
297C23—21no—
298C23—21no—
299C23—21no—
300C23—21no—
301C23#393712yes—
302C23C2×#68511yescharacteristic
303Q8—202no—
304Q8—202no—
305C2×C4—24no—
306C2×C4—24no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—44no—
321C2×C4—42no—
322C2×C4—42no—
323C2×C4—102no—
324C2×C4—102no—
325C2×C4—201no—
326C2×C4—201no—
327C2×C4—201no—
328C2×C4—201no—
329C2×C4—201no—
330C2×C4—201no—
331C2×C4—201no—
332C2×C4—201no—
333C2×C4—201no—
334C2×C4—201no—
335C2×C4#393812yes—
336C2×C4#395712yes—
337C2×C4D5×M1611yescharacteristic
338C2×C4D5×M1611yescharacteristic
339C2×C4#405512yes—
340C2×C4#407811yescharacteristic
341C2×C4#408811yescharacteristic
342C8—44no—
343C8—204no—
344C5#763411yescharacteristic, complemented, Sylow
345C22—22no—
346C22—22no—
347C22—22no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22C2×#393711yescharacteristic
353C22C2×#393811yescharacteristic
354C22#6525511yescharacteristic
355C22#6540911yescharacteristic
356C22#6541511yescharacteristic
357C22#6542111yescharacteristic
358C22C2×#395711yescharacteristic
359C4—21no—
360C4—21no—
361C4—22no—
362C4—22no—
363C4—21no—
364C4—22no—
365C4—21no—
366C4—41no—
367C4—202no—
368C4—202no—
369C4—401no—
370C4—401no—
371C2—42no—
372C2#1060019111yescharacteristic
373C2#1060065011yescharacteristic
374C2#1060065111yescharacteristic
375C2#1060076111yescharacteristic
376C2#1060077311yescharacteristic
377C2#1060129011yescharacteristic
378C2#1060130311yescharacteristic
subgroupG/H
centerC23C2×#685
commutatorC22×C4×C5C22×C4
FrattiniC2×C42C22×D5
FittingC5×#1728C2
socleC23×C5C2×C22⋊C4
prime radicalC24×C5C22⋊C4
cosocleC2×C42×C5C23
hypercenter#1728D5
hypocenterC5#7634
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1728

Complements

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

NH ≅ G/Ntype
4. #10597971C2semidirect
5. #10597969C2semidirect
88. C2×Dic10M16semidirect
102. C4⋊Dic5M16semidirect
344. C5#7634semidirect

Maximal subgroups

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

subgroupindex
C4×#40702
C5×#17282
#106023222
#105979712
#105979692
#76345