Finite Group Databasebeta

← #12065639

Subgroups — #12065639

Order 1280.

884 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65901C211yesmaximal, characteristic
2#10611046C212yesmaximal
3C5×#1467C211yesmaximal, characteristic
4#10602417C211yesmaximal, characteristic
5#10601624C212yesmaximal
6#10598921C214yesmaximal
7#10598920C212yesmaximal
8#10598918C212yesmaximal
9C2×C4×C5×Q8C2211yescharacteristic
10C2×#4090C412yes—
11#65901—22no—
12#65901—22no—
13#65901—24no—
14C2×#4035C412yes—
15C2×#4035C2212yes—
16C2×#4033C2212yes—
17C2×#4016C411yescharacteristic
18C2×#4016C2211yescharacteristic
19C2×#4015C411yescharacteristic
20C2×C4×Dic10C411yescharacteristic
21C2×C4×Dic10C411yescharacteristic
22C2×C4×Dic10C2211yescharacteristic
23C5×#432C2212yes—
24#65214C2212yes—
25#65120—22no—
26#65119—22no—
27#65008C2214yes—
28#65007C2214yes—
29#64990—24no—
30C5×#324C2212yes—
31C5×#324C2212yes—
32#64748C2211yescharacteristic
33#64748C2211yescharacteristic
34#64748C2212yes—
35#64689C2214yes—
36#64689C2214yes—
37#17430—51nomaximal, Sylow
38C22×C5×Q8C2×C411yescharacteristic
39C22×Dic10C2×C412yes—
40C22×Dic10C2×C411yescharacteristic
41C4×C5×Q8—22no—
42C4×C5×Q8—22no—
43C2×C5×C4⋊C4C2×C411yescharacteristic
44C2×C5×C4⋊C4C2311yescharacteristic
45C2×C5×C4⋊C4C2311yescharacteristic
46C2×C42×C5C2×C411yescharacteristic
47C2×C42×C5C2×C411yescharacteristic
48C2×C42×C5C2311yescharacteristic
49#4090—24no—
50#4090—24no—
51C2×C4⋊Dic5C2×C411yescharacteristic
52C2×C4⋊Dic5C2×C411yescharacteristic
53C2×C4⋊Dic5C2×C412yes—
54C2×C4⋊Dic5C2×C411yescharacteristic
55C2×#683C2×C412yes—
56C2×#683C2×C412yes—
57C2×#683C2×C412yes—
58C2×#683C2×C412yes—
59C2×#683C2×C412yes—
60C2×#683C2×C412yes—
61C2×#683C2312yes—
62C2×C4×Dic5C2×C412yes—
63C2×C4×Dic5C2×C412yes—
64C2×C4×Dic5C2312yes—
65#4035—24no—
66#4035—24no—
67#4035—24no—
68#4035—24no—
69#4033—24no—
70#4033—24no—
71#4016—22no—
72#4016—22no—
73#4016—22no—
74#4016—22no—
75#4015—22no—
76#4015—22no—
77C4×Dic10—21no—
78C4×Dic10—22no—
79C4×Dic10—21no—
80C4×Dic10—21no—
81C4×Dic10—22no—
82C4×Dic10—21no—
83C4×Dic10D412yes—
84C4×Dic10D412yes—
85C4×Dic10D414yes—
86C5×C4⋊C8—22no—
87C5×C22⋊C8C2314yes—
88C5×#97—22no—
89C22⋊#168C2312yes—
90C22⋊#168C2312yes—
91#3947—24no—
92#3946—24no—
93#3946—24no—
94C8×Dic5—24no—
95C4⋊#168—22no—
96C4×#168—22no—
97C2×#557—51no—
98#2984—52no—
99#1470—52no—
100#1470—54no—
101#1467—52no—
102#1467D511yescharacteristic
103#1461—52no—
104#1461—51no—
105C2×C5×Q8—22no—
106C2×C5×Q8—22no—
107C2×C5×Q8—41no—
108C22×C4×C5C22×C411yescharacteristic
109C22×C4×C5C22×C411yescharacteristic
110C22×C4×C5C22×C411yescharacteristic
111C22×C4×C5C22×C411yescharacteristic
112C22×C4×C5C22×C411yescharacteristic
113C22×C4×C5C22×C411yescharacteristic
114C22×C4×C5C2411yescharacteristic
115C22×Dic5C22×C412yes—
116C22×Dic5C22×C412yes—
117C22×Dic5C22×C412yes—
118C22×Dic5C22×C412yes—
119C2×Dic10—24no—
120C2×Dic10—24no—
121C2×Dic10—24no—
122C2×Dic10—42no—
123C2×Dic10C22⋊C411yescharacteristic
124C2×Dic10C22⋊C412yes—
125C2×Dic10C22⋊C411yescharacteristic
126C2×C5×C8—24no—
127C5×C4⋊C4—22no—
128C5×C4⋊C4—22no—
129C5×C4⋊C4—22no—
130C42×C5—21no—
131C42×C5—21no—
132C42×C5—21no—
133C42×C5—21no—
134C42×C5C2×D412yes—
135C42×C5C2×D412yes—
136C4⋊Dic5—21no—
137C4⋊Dic5—21no—
138C4⋊Dic5—21no—
139C4⋊Dic5—21no—
140C4⋊Dic5—24no—
141C4⋊Dic5C22⋊C412yes—
142C4⋊Dic5C22⋊C412yes—
143#683—24no—
144#683—24no—
145#683—22no—
146#683—22no—
147#683—22no—
148#683—22no—
149#683—24no—
150#683—24no—
151#683C22⋊C414yes—
152#683C22⋊C414yes—
153C4×Dic5—22no—
154C4×Dic5—22no—
155C4×Dic5—22no—
156C4×Dic5—22no—
157C4×Dic5C2×D414yes—
158C4×Dic5C2×D414yes—
159C2×#168—22no—
160C2×#168—22no—
161#557—102no—
162#557—102no—
163#557—104no—
164C2×C4⋊Q8—52no—
165C2×C4⋊Q8—51no—
166C2×#125—52no—
167C2×#125—52no—
168C2×#125—51no—
169C2×#125—51no—
170C2×C4×Q8—52no—
171C2×C4×Q8—51no—
172C2×C4×Q8—51no—
173C2×C4×Q8—51no—
174C2×C4×Q8C2×D511yescharacteristic
175#446—104no—
176#446—102no—
177C8×Q8—102no—
178#432—54no—
179#432C2×D512yes—
180#431—52no—
181#431—54no—
182#324—51no—
183#324—51no—
184#324—52no—
185#324—54no—
186#324—54no—
187#324C2×D512yes—
188#324C2×D512yes—
189C23×C5C23×C411yescharacteristic
190C5×Q8—44no—
191C2×C4×C5—21no—
192C2×C4×C5—21no—
193C2×C4×C5—21no—
194C2×C4×C5—21no—
195C2×C4×C5—22no—
196C2×C4×C5—21no—
197C2×C4×C5—21no—
198C2×C4×C5—21no—
199C2×C4×C5—21no—
200C2×C4×C5—21no—
201C2×C4×C5—41no—
202C2×C4×C5—41no—
203C2×C4×C5—41no—
204C2×C4×C5C2×C22⋊C412yes—
205C2×C4×C5C2×C22⋊C411yescharacteristic
206C2×C4×C5C2×C22⋊C411yescharacteristic
207C2×C4×C5#13112yes—
208C2×C4×C5C22×D412yes—
209C2×Dic5—22no—
210C2×Dic5—22no—
211C2×Dic5—24no—
212C2×Dic5—22no—
213C2×Dic5—22no—
214C2×Dic5—22no—
215C2×Dic5—22no—
216C2×Dic5—42no—
217C2×Dic5C2×C22⋊C412yes—
218C2×Dic5C2×C22⋊C414yes—
219C2×Dic5C2×C22⋊C412yes—
220Dic10—22no—
221Dic10—24no—
222Dic10—48no—
223Dic10#10114yes—
224C5×C8—44no—
225#168—42no—
226#168—42no—
227C22×Q8—51no—
228C22×Q8—52no—
229C22×Q8C4×D511yescharacteristic
230C4⋊Q8—102no—
231C4⋊Q8—102no—
232C4⋊Q8—104no—
233C4⋊Q8—104no—
234#125—102no—
235#125—102no—
236#125—104no—
237#125—104no—
238#125—104no—
239#125—104no—
240#125—102no—
241#125—102no—
242C4×Q8—22no—
243C4×Q8—22no—
244C4×Q8—52no—
245C4×Q8—54no—
246C4×Q8—52no—
247C4×Q8—101no—
248C4×Q8—102no—
249C4×Q8—101no—
250C4×Q8—101no—
251C4×Q8—102no—
252C4×Q8—101no—
253C4×Q8—104no—
254C4×Q8—104no—
255C2×C4⋊C4—52no—
256C2×C4⋊C4—51no—
257C2×C4⋊C4—52no—
258C2×C4⋊C4—52no—
259C2×C4⋊C4—51no—
260C2×C4⋊C4—52no—
261C2×C4⋊C4—51no—
262C2×C4⋊C4—52no—
263C2×C4⋊C4—52no—
264C2×C4⋊C4—52no—
265C2×C4⋊C4—52no—
266C2×C4⋊C4C4×D511yescharacteristic
267C2×C4⋊C4C22×D511yescharacteristic
268C2×C4⋊C4C22×D511yescharacteristic
269C2×C42—52no—
270C2×C42—52no—
271C2×C42—52no—
272C2×C42C4×D511yescharacteristic
273C2×C42C4×D511yescharacteristic
274C2×C42C22×D511yescharacteristic
275C4⋊C8—22no—
276C4⋊C8—104no—
277C4⋊C8—104no—
278C4⋊C8—102no—
279C22⋊C8—52no—
280C22⋊C8—52no—
281C22⋊C8C22×D514yes—
282#97—22no—
283#97—104no—
284C4×C8—104no—
285C4×C8—102no—
286C22×C5—21no—
287C22×C5—21no—
288C22×C5C22×C22⋊C411yescharacteristic
289C22×C5C2×#13111yescharacteristic
290C22×C5#56811yescharacteristic
291C4×C5—22no—
292C4×C5—22no—
293C4×C5—22no—
294C4×C5—21no—
295C4×C5—41no—
296C4×C5—41no—
297C4×C5—41no—
298C4×C5C2×#10112yes—
299Dic5—24no—
300Dic5—22no—
301Dic5—42no—
302Dic5—42no—
303Dic5C2×#10114yes—
304C2×Q8—22no—
305C2×Q8—22no—
306C2×Q8—41no—
307C2×Q8—51no—
308C2×Q8—52no—
309C2×Q8—51no—
310C2×Q8—104no—
311C2×Q8—104no—
312C2×Q8—104no—
313C2×Q8—202no—
314C22×C4—52no—
315C22×C4—52no—
316C22×C4—52no—
317C22×C4—52no—
318C22×C4C2×C4×D511yescharacteristic
319C22×C4C2×C4×D511yescharacteristic
320C22×C4C2×C4×D511yescharacteristic
321C22×C4C2×C4×D511yescharacteristic
322C22×C4C2×C4×D511yescharacteristic
323C22×C4C2×C4×D511yescharacteristic
324C22×C4C23×D511yescharacteristic
325C2×C8—24no—
326C2×C8—102no—
327C2×C8—102no—
328C4⋊C4—22no—
329C4⋊C4—22no—
330C4⋊C4—22no—
331C4⋊C4—54no—
332C4⋊C4—54no—
333C4⋊C4—52no—
334C4⋊C4—52no—
335C4⋊C4—104no—
336C4⋊C4—102no—
337C4⋊C4—102no—
338C4⋊C4—102no—
339C4⋊C4—102no—
340C4⋊C4—104no—
341C4⋊C4—104no—
342C4⋊C4—104no—
343C4⋊C4—101no—
344C4⋊C4—101no—
345C4⋊C4—101no—
346C4⋊C4—101no—
347C4⋊C4—104no—
348C42—21no—
349C42—21no—
350C42—21no—
351C42—21no—
352C42—54no—
353C42—54no—
354C42—102no—
355C42—102no—
356C42—102no—
357C42—102no—
358C42D4×D512yes—
359C42D4×D512yes—
360C2×C5—21no—
361C2×C5—21no—
362C2×C5#288011yescharacteristic
363C2×C5#288411yescharacteristic
364C2×C5C22×#10111yescharacteristic
365C23C22×C4×D511yescharacteristic
366Q8—44no—
367Q8—54no—
368Q8—104no—
369Q8—102no—
370Q8—208no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—22no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—52no—
385C2×C4—52no—
386C2×C4—54no—
387C2×C4—104no—
388C2×C4—102no—
389C2×C4—102no—
390C2×C4—102no—
391C2×C4—102no—
392C2×C4—102no—
393C2×C4—102no—
394C2×C4—202no—
395C2×C4D5×C22⋊C411yescharacteristic
396C2×C4D5×C22⋊C412yes—
397C2×C4D5×C22⋊C411yescharacteristic
398C2×C4#405312yes—
399C2×C4C2×D4×D512yes—
400C8—44no—
401C8—202no—
402C8—202no—
403C5#1743011yescharacteristic, complemented, Sylow
404C22—21no—
405C22—21no—
406C22C2×D5×C22⋊C411yescharacteristic
407C22C2×#405311yescharacteristic
408C22#6607911yescharacteristic
409C4—21no—
410C4—22no—
411C4—22no—
412C4—22no—
413C4—41no—
414C4—41no—
415C4—41no—
416C4—54no—
417C4—102no—
418C4—104no—
419C4—202no—
420C4—202no—
421C4D5×#10112yes—
422C2—21no—
423C2—21no—
424C2#1061036211yescharacteristic
425C2#1061042011yescharacteristic
426C2C2×D5×#10111yescharacteristic
subgroupG/H
centerC22C2×D5×C22⋊C4
commutator, prime radicalC23×C5C23×C4
FrattiniC22×C4C23×D5
FittingC5×#1467C2
socleC22×C5C22×C22⋊C4
cosocleC22×C4×C5C24
hypercenter#1467D5
hypocenterC5#17430
LCSG ▷ C23×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1467

Complements

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

NH ≅ G/Ntype
403. C5#17430semidirect

Maximal subgroups

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

subgroupindex
C2×#659012
#106110462
C5×#14672
#106024172
#106016242
#105989212
#105989202
#105989182
#174305