Finite Group Databasebeta

← #11994906

Subgroups — #11994906

Order 1280.

626 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2851C211yesmaximal, characteristic
2C22×#3935C211yesmaximal, characteristic
3C2×#64763C212yesmaximal, complemented
4#10602322C211yesmaximal, characteristic
5#10598121C212yesmaximal, complemented
6C2×C5×#125C2211yescharacteristic
7C22×C42×C5C2211yescharacteristic
8C23×#168—21no—
9C5×#389C411yescharacteristic
10C5×#389C411yescharacteristic
11C5×#387—21no—
12C5×#387—21no—
13C5×#385—21no—
14C5×#385—21no—
15C5×#382C2211yescharacteristic
16C5×#380C411yescharacteristic
17C5×#380C411yescharacteristic
18C2×C22⋊#168—21no—
19C2×#3935—24no—
20C2×#3935—21no—
21C2×#3935C2212yes—
22C2×#3935C2212yes—
23#64763—24no—
24#64744—21no—
25#9121—51nomaximal, Sylow
26C23×C4×C5C2×C411yescharacteristic
27C23×C4×C5D411yescharacteristic
28C23×C4×C5D411yescharacteristic
29C5×#125—22no—
30C5×#125—22no—
31C2×C5×C4⋊C4—21no—
32C2×C5×C4⋊C4—21no—
33C2×C5×C4⋊C4—21no—
34C2×C5×C4⋊C4—21no—
35C2×C5×C4⋊C4C2×C411yescharacteristic
36C2×C5×C4⋊C4C2×C411yescharacteristic
37C2×C5×C4⋊C4C2×C411yescharacteristic
38C2×C5×C4⋊C4C2×C411yescharacteristic
39C2×C5×C22⋊C4—21no—
40C2×C5×C22⋊C4—21no—
41C2×C42×C5—22no—
42C2×C42×C5—22no—
43C2×C42×C5C2×C411yescharacteristic
44C2×C42×C5D411yescharacteristic
45C2×C42×C5D411yescharacteristic
46C2×C42×C5C2311yescharacteristic
47C22×#168—24no—
48C22×#168—24no—
49C22×#168—24no—
50C22×#168—22no—
51C22×#168—22no—
52C5×#95—21no—
53C5×#95—21no—
54C5×#95—21no—
55C5×#95—21no—
56C5×#95—21no—
57C5×#95—21no—
58C22⋊#168—24no—
59#3935—24no—
60#3935—22no—
61#3935—22no—
62#3935—22no—
63#3935D414yes—
64C22×#97—51no—
65#2851D511yescharacteristic
66#1749—51no—
67C2×#330—52no—
68#1295—52no—
69C24×C5C22⋊C411yescharacteristic
70C22×C4×C5—22no—
71C22×C4×C5—22no—
72C22×C4×C5—21no—
73C22×C4×C5—21no—
74C22×C4×C5—22no—
75C22×C4×C5—22no—
76C22×C4×C5—22no—
77C22×C4×C5—22no—
78C22×C4×C5—21no—
79C22×C4×C5—21no—
80C22×C4×C5—21no—
81C22×C4×C5—21no—
82C22×C4×C5—41no—
83C22×C4×C5—41no—
84C22×C4×C5C22⋊C411yescharacteristic
85C22×C4×C5C22⋊C411yescharacteristic
86C22×C4×C5C22⋊C411yescharacteristic
87C22×C4×C5C22×C411yescharacteristic
88C22×C4×C5C2×D411yescharacteristic
89C22×C4×C5C2×D411yescharacteristic
90C5×C4⋊C4—22no—
91C5×C4⋊C4—22no—
92C5×C4⋊C4—41no—
93C5×C4⋊C4—41no—
94C5×C4⋊C4—42no—
95C5×C4⋊C4—42no—
96C5×C4⋊C4—41no—
97C5×C4⋊C4—42no—
98C5×C4⋊C4—41no—
99C5×C22⋊C4—42no—
100C5×C22⋊C4—42no—
101C42×C5—22no—
102C42×C5—21no—
103C42×C5—22no—
104C42×C5—21no—
105C42×C5C2×D412yes—
106C42×C5#4112yes—
107C2×#168—216no—
108C2×#168—24no—
109C2×#168—24no—
110C2×#168—24no—
111C2×#168—24no—
112C2×#168—42no—
113C2×#168—42no—
114C23×C8—101no—
115C2×#125C2×D511yescharacteristic
116C22×C42C2×D511yescharacteristic
117C2×C22⋊C8—101no—
118C2×#97—52no—
119C2×#97—52no—
120C2×#97—104no—
121C2×#97—101no—
122#389Dic511yescharacteristic
123#389Dic511yescharacteristic
124#387—21no—
125#387—21no—
126#385—21no—
127#385—21no—
128#382C2×D511yescharacteristic
129#380Dic511yescharacteristic
130#380Dic511yescharacteristic
131#336—101no—
132#330—104no—
133C23×C5—21no—
134C23×C5—21no—
135C23×C5—21no—
136C23×C5—21no—
137C23×C5#10112yes—
138C23×C5#10412yes—
139C23×C5#10412yes—
140C23×C5C2×C22⋊C411yescharacteristic
141C2×C4×C5—24no—
142C2×C4×C5—24no—
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—21no—
153C2×C4×C5—21no—
154C2×C4×C5—21no—
155C2×C4×C5—21no—
156C2×C4×C5—21no—
157C2×C4×C5—44no—
158C2×C4×C5—44no—
159C2×C4×C5—41no—
160C2×C4×C5—41no—
161C2×C4×C5—41no—
162C2×C4×C5—41no—
163C2×C4×C5—41no—
164C2×C4×C5—41no—
165C2×C4×C5—41no—
166C2×C4×C5—41no—
167C2×C4×C5—41no—
168C2×C4×C5—41no—
169C2×C4×C5—41no—
170C2×C4×C5—41no—
171C2×C4×C5#10412yes—
172C2×C4×C5C4×D412yes—
173C2×C4×C5#12011yescharacteristic
174C2×C4×C5#12112yes—
175C2×C4×C5#12311yescharacteristic
176#168—28no—
177#168—44no—
178C23×C4C2×Dic511yescharacteristic
179C23×C4C22⋊D511yescharacteristic
180C23×C4C22⋊D511yescharacteristic
181C22×C8—104no—
182C22×C8—104no—
183C22×C8—104no—
184C22×C8—102no—
185C22×C8—102no—
186#125—22no—
187#125—22no—
188C2×C4⋊C4—21no—
189C2×C4⋊C4—21no—
190C2×C4⋊C4—21no—
191C2×C4⋊C4—21no—
192C2×C4⋊C4C2×Dic511yescharacteristic
193C2×C4⋊C4C2×Dic511yescharacteristic
194C2×C4⋊C4C2×Dic511yescharacteristic
195C2×C4⋊C4C2×Dic511yescharacteristic
196C2×C22⋊C4—21no—
197C2×C22⋊C4—21no—
198C2×C42—22no—
199C2×C42—22no—
200C2×C42C2×Dic511yescharacteristic
201C2×C42C22⋊D511yescharacteristic
202C2×C42C22⋊D511yescharacteristic
203C2×C42C22×D511yescharacteristic
204C22⋊C8—104no—
205#97—54no—
206#97—104no—
207#97—102no—
208#97—102no—
209#97—102no—
210#95—21no—
211#95—21no—
212#95—21no—
213#95—21no—
214#95—21no—
215#95—21no—
216C22×C5—22no—
217C22×C5—22no—
218C22×C5—22no—
219C22×C5—22no—
220C22×C5—22no—
221C22×C5—22no—
222C22×C5#33014yescomplemented
223C22×C5#38611yescharacteristic
224C22×C5C2×#10111yescharacteristic
225C22×C5#41311yescharacteristic
226C22×C5C2×#10411yescharacteristic
227C22×C5C2×#10411yescharacteristic
228C22×C5C2×#10411yescharacteristic
229C22×C5#42111yescharacteristic
230C4×C5—22no—
231C4×C5—21no—
232C4×C5—22no—
233C4×C5—21no—
234C4×C5—22no—
235C4×C5—41no—
236C4×C5—41no—
237C4×C5—81no—
238C4×C5—81no—
239C4×C5—81no—
240C4×C5—81no—
241C24C22⋊Dic511yescharacteristic
242C22×C4—22no—
243C22×C4—22no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—22no—
247C22×C4—22no—
248C22×C4—22no—
249C22×C4—22no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—41no—
255C22×C4—41no—
256C22×C4C22⋊Dic511yescharacteristic
257C22×C4C22⋊Dic511yescharacteristic
258C22×C4C22⋊Dic511yescharacteristic
259C22×C4C22×Dic511yescharacteristic
260C22×C4C2×C22⋊D511yescharacteristic
261C22×C4C2×C22⋊D511yescharacteristic
262C2×C8—1016no—
263C2×C8—104no—
264C2×C8—104no—
265C2×C8—104no—
266C2×C8—104no—
267C2×C8—202no—
268C2×C8—202no—
269C4⋊C4—22no—
270C4⋊C4—22no—
271C4⋊C4—41no—
272C4⋊C4—41no—
273C4⋊C4—42no—
274C4⋊C4—42no—
275C4⋊C4—41no—
276C4⋊C4—41no—
277C4⋊C4—42no—
278C22⋊C4—42no—
279C22⋊C4—42no—
280C42—22no—
281C42—21no—
282C42—21no—
283C42—22no—
284C42D4×D512yes—
285C42#71112yes—
286C2×C5—24no—
287C2×C5C2×#33011yescharacteristic
288C2×C5#152411yescharacteristic
289C2×C5#153111yescharacteristic
290C2×C5#153211yescharacteristic
291C2×C5#187111yescharacteristic
292C2×C5#189611yescharacteristic
293C2×C5#190111yescharacteristic
294C23—21no—
295C23—21no—
296C23—21no—
297C23—21no—
298C23#396812yes—
299C23#396912yes—
300C23#396912yes—
301C23C2×C22⋊Dic511yescharacteristic
302C2×C4—24no—
303C2×C4—24no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
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—44no—
319C2×C4—44no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4#396912yes—
333C2×C4D4×Dic512yes—
334C2×C4#408111yescharacteristic
335C2×C4#408311yescharacteristic
336C2×C4#408512yes—
337C8—108no—
338C8—204no—
339C5#912111yescharacteristic, complemented, Sylow
340C22—22no—
341C22—22no—
342C22—22no—
343C22—22no—
344C22—22no—
345C22—22no—
346C22#6476314yescomplemented
347C22#6550911yescharacteristic
348C22C2×#396811yescharacteristic
349C22C2×#396911yescharacteristic
350C22C2×#396911yescharacteristic
351C22C2×#396911yescharacteristic
352C22#6552511yescharacteristic
353C22#6552611yescharacteristic
354C4—21no—
355C4—22no—
356C4—21no—
357C4—22no—
358C4—22no—
359C4—41no—
360C4—41no—
361C4—81no—
362C4—81no—
363C4—81no—
364C4—81no—
365C2—24no—
366C2#1060249111yescharacteristic
367C2#1060250411yescharacteristic
368C2#1060250611yescharacteristic
369C2C2×#6476311yescharacteristic
370C2#1060253911yescharacteristic
371C2#1060254111yescharacteristic
372C2#1060261511yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic5
commutatorC22×C4×C5C22×C4
FrattiniC2×C42C22×D5
FittingC5×#2851C2
socleC23×C5C2×C22⋊C4
prime radicalC24×C5C22⋊C4
cosocleC2×C42×C5C23
hypercenter#2851D5
hypocenterC5#9121
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C22×C42 ◁ #2851

Complements

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

NH ≅ G/Ntype
3. C2×#64763C2semidirect
5. #10598121C2semidirect
222. C22×C5#330semidirect
339. C5#9121semidirect
346. C22#64763semidirect

Maximal subgroups

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

subgroupindex
C5×#28512
C22×#39352
C2×#647632
#106023222
#105981212
#91215