Finite Group Databasebeta

← #11989090

Subgroups — #11989090

Order 1280.

634 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10611013C211yesmaximal, characteristic
2#10610769C211yesmaximal, characteristic
3D5×#382C211yesmaximal, characteristic
4C5×#1286C211yesmaximal, characteristic, complemented
5#10598229C211yesmaximal, characteristic, complemented
6#10598204C211yesmaximal, characteristic, complemented
7#10598122C211yesmaximal, characteristic, complemented
8C2×D5×C4⋊C4—21no—
9C2×C42×D5C2211yescharacteristic
10C5×#431C2211yescharacteristic
11C5×#423C2211yescharacteristic
12C5×#382C2211yescharacteristic
13#65415—21no—
14M16×Dic5—21no—
15#65266—21no—
16#65225C2211yescharacteristic
17#65214C2211yescharacteristic
18#65213C2211yescharacteristic
19#65126—21no—
20#65124—21no—
21#65124—21no—
22#65124C412yescomplemented
23#65122—21no—
24#65122C412yescomplemented
25#65015—21no—
26#65008—21no—
27C4×#676C412yescomplemented
28#64974C412yescomplemented
29D5×#95—21no—
30D5×#95C412yes—
31#64939—21no—
32#64939C412yes—
33#7959—51nomaximal, Sylow
34C22×C4×D5—22no—
35C22×C4×D5C2×C411yescharacteristic
36C22×C4×D5D411yescharacteristic
37C22×C4×D5D411yescharacteristic
38C2×C5×M16—21no—
39C2×C5×C4⋊C4—21no—
40C2×C42×C5C2311yescharacteristic
41C2×C4⋊Dic5—21no—
42C2×#683—22no—
43C2×C4×Dic5C2×C411yescharacteristic
44C2×C4×Dic5D411yescharacteristic
45C2×C4×Dic5D411yescharacteristic
46C2×#681—21no—
47C2×#676—22no—
48D5×C4⋊C4—42no—
49D5×C4⋊C4—42no—
50C42×D5C2×C411yescharacteristic
51C42×D5C2×C411yescharacteristic
52C42×D5C2×C411yescharacteristic
53C42×D5C2×C411yescharacteristic
54C42×D5D411yescharacteristic
55C42×D5D411yescharacteristic
56C42×D5Q811yescharacteristic
57C42×D5Q811yescharacteristic
58C5×C4⋊C8—21no—
59C5×C4⋊C8—21no—
60C5×C4⋊C8C2×C412yescomplemented
61C5×C22⋊C8—21no—
62C4×C5×C8C2×C412yescomplemented
63C5×#95—21no—
64C5×#95C2×C412yes—
65#3963—21no—
66#3963—22no—
67#3963—22no—
68#3963C2×C412yes—
69C22⋊#168—21no—
70#3952—22no—
71#3952—22no—
72#3952—22no—
73#3947—22no—
74#3947—22no—
75#3946—22no—
76C8×Dic5—22no—
77C4⋊#168—21no—
78C4⋊#168—21no—
79C4⋊#168C2×C412yescomplemented
80C4×#168C2×C412yescomplemented
81#2920—51no—
82#2920—51no—
83C2×#382—51no—
84#1286—51no—
85#1286—51no—
86#1286—51no—
87#1286D511yescharacteristic, complemented
88C23×D5C22⋊C411yescharacteristic
89C22×C4×C5—22no—
90C22×C4×C5C22×C411yescharacteristic
91C22×C4×C5C2×D411yescharacteristic
92C22×C4×C5C2×D411yescharacteristic
93C22×Dic5—22no—
94C22×Dic5C22⋊C411yescharacteristic
95C22×Dic5C22⋊C411yescharacteristic
96C22×Dic5C22⋊C411yescharacteristic
97C2×C4×D5—21no—
98C2×C4×D5—21no—
99C2×C4×D5—21no—
100C2×C4×D5—21no—
101C2×C4×D5—42no—
102C2×C4×D5—42no—
103C2×C4×D5—44no—
104C2×C4×D5—44no—
105C2×C4×D5—44no—
106C2×C4×D5C4211yescharacteristic
107C2×C4×D5C4211yescharacteristic
108C2×C4×D5C22⋊C411yescharacteristic
109C2×C4×D5C22⋊C411yescharacteristic
110C2×C4×D5C22⋊C411yescharacteristic
111C2×C4×D5C22⋊C411yescharacteristic
112C2×C4×D5C4⋊C411yescharacteristic
113C2×C4×D5C4⋊C411yescharacteristic
114C2×C4×D5C4⋊C411yescharacteristic
115C2×C4×D5C4⋊C411yescharacteristic
116C2×C4×D5C4⋊C411yescharacteristic
117C2×C4×D5C4⋊C411yescharacteristic
118C5×M16—41no—
119C5×M16—41no—
120C2×C5×C8—22no—
121C2×C5×C8—22no—
122C5×C4⋊C4—41no—
123C5×C4⋊C4—41no—
124C42×C5C22×C411yescharacteristic
125C42×C5C22×C411yescharacteristic
126C42×C5C2×D411yescharacteristic
127C42×C5C2×Q811yescharacteristic
128C4⋊Dic5—41no—
129C4⋊Dic5—41no—
130#683—44no—
131C4×Dic5C4211yescharacteristic
132C4×Dic5C4211yescharacteristic
133C4×Dic5C22⋊C411yescharacteristic
134C4×Dic5C22⋊C411yescharacteristic
135C4×Dic5C22⋊C411yescharacteristic
136C4×Dic5C22⋊C411yescharacteristic
137C4×Dic5C4⋊C411yescharacteristic
138C4×Dic5C4⋊C411yescharacteristic
139C4×Dic5C4⋊C411yescharacteristic
140C4×Dic5C4⋊C411yescharacteristic
141C4×Dic5C4⋊C411yescharacteristic
142C4×Dic5C4⋊C411yescharacteristic
143#681—41no—
144#681—41no—
145C2×#168—22no—
146C2×#168—22no—
147#676—44no—
148C22×C4⋊C4—101no—
149C22×C42—51no—
150#432—52no—
151#432—101no—
152#432—101no—
153#432—101no—
154#431—51no—
155#431—52no—
156#431—52no—
157#431—101no—
158#431C2×D511yescharacteristic
159#423—51no—
160#423—101no—
161#423C2×D511yescharacteristic
162#407—101no—
163#407—101no—
164C4×M16—52no—
165C4×M16—101no—
166#382—51no—
167#382—52no—
168#382—101no—
169#382—101no—
170#382C2×D511yescharacteristic
171C2×#95—52no—
172C2×#95—101no—
173C23×C5C2×C22⋊C411yescharacteristic
174C22×D5—21no—
175C22×D5—21no—
176C22×D5—22no—
177C22×D5—22no—
178C22×D5#9511yescharacteristic
179C22×D5#9511yescharacteristic
180C2×C4×C5—41no—
181C2×C4×C5—41no—
182C2×C4×C5—42no—
183C2×C4×C5—42no—
184C2×C4×C5—42no—
185C2×C4×C5C2×C4211yescharacteristic
186C2×C4×C5C2×C22⋊C411yescharacteristic
187C2×C4×C5C2×C22⋊C411yescharacteristic
188C2×C4×C5C2×C4⋊C411yescharacteristic
189C2×C4×C5C2×C4⋊C411yescharacteristic
190C2×C4×C5C2×C4⋊C411yescharacteristic
191C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
192C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
193C2×C4×C5#13711yescharacteristic
194C2×C4×C5#13711yescharacteristic
195C2×Dic5—21no—
196C2×Dic5—21no—
197C2×Dic5—41no—
198C2×Dic5—41no—
199C2×Dic5—42no—
200C2×Dic5—42no—
201C2×Dic5—42no—
202C2×Dic5#9511yescharacteristic
203C2×Dic5#9511yescharacteristic
204C2×Dic5#9511yescharacteristic
205C2×Dic5#9511yescharacteristic
206C2×Dic5#9511yescharacteristic
207C2×Dic5#9511yescharacteristic
208C4×D5—22no—
209C4×D5—22no—
210C4×D5—22no—
211C4×D5—22no—
212C4×D5—21no—
213C4×D5—21no—
214C4×D5—21no—
215C4×D5—21no—
216C4×D5—21no—
217C4×D5—21no—
218C4×D5—21no—
219C4×D5—21no—
220C4×D5—41no—
221C4×D5—41no—
222C4×D5—41no—
223C4×D5—41no—
224C4×D5—88no—
225C5×C8—42no—
226C5×C8—42no—
227#168—42no—
228#168—42no—
229C23×C4—51no—
230C23×C4—51no—
231C23×C4—51no—
232C23×C4—102no—
233C2×M16—21no—
234C2×M16—102no—
235C2×M16—101no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—102no—
238C2×C4⋊C4—101no—
239C2×C4⋊C4—202no—
240C2×C4⋊C4—202no—
241C2×C42—51no—
242C2×C42—51no—
243C2×C42—51no—
244C2×C42—51no—
245C2×C42—51no—
246C2×C42—51no—
247C2×C42—51no—
248C2×C42—51no—
249C2×C42—51no—
250C2×C42—51no—
251C2×C42—51no—
252C2×C42C22×D511yescharacteristic
253C4⋊C8—21no—
254C4⋊C8—21no—
255C4⋊C8—52no—
256C4⋊C8—102no—
257C4⋊C8—101no—
258C4⋊C8—101no—
259C4⋊C8C4×D512yescomplemented
260C22⋊C8—21no—
261C22⋊C8—102no—
262C22⋊C8—102no—
263C22⋊C8—102no—
264C22⋊C8—101no—
265#97—102no—
266#97—102no—
267C4×C8—52no—
268C4×C8—102no—
269C4×C8C4×D512yescomplemented
270#95—21no—
271#95—52no—
272#95—102no—
273#95—102no—
274#95—101no—
275#95C4×D512yes—
276C22×C5—21no—
277C22×C5—21no—
278C22×C5C2×#9511yescharacteristic
279C22×C5#41811yescharacteristic
280C22×C5#41911yescharacteristic
281C2×D5—24no—
282C2×D5—24no—
283C2×D5—21no—
284C2×D5—21no—
285C2×D5—21no—
286C2×D5—21no—
287C2×D5H(3,ℤ/4)12yes—
288C2×D5#34412yes—
289C4×C5—21no—
290C4×C5—21no—
291C4×C5—21no—
292C4×C5—21no—
293C4×C5—82no—
294C4×C5#41711yescharacteristic
295C4×C5#41711yescharacteristic
296C4×C5#42811yescharacteristic
297C4×C5#42811yescharacteristic
298Dic5—21no—
299Dic5—21no—
300Dic5—21no—
301Dic5—21no—
302Dic5—21no—
303Dic5—21no—
304Dic5—82no—
305C24—51no—
306C22×C4—22no—
307C22×C4—51no—
308C22×C4—51no—
309C22×C4—51no—
310C22×C4—51no—
311C22×C4—51no—
312C22×C4—51no—
313C22×C4—51no—
314C22×C4—51no—
315C22×C4—51no—
316C22×C4—51no—
317C22×C4—51no—
318C22×C4—51no—
319C22×C4—51no—
320C22×C4—51no—
321C22×C4—51no—
322C22×C4—101no—
323C22×C4—101no—
324C22×C4—101no—
325C22×C4—101no—
326C22×C4—102no—
327C22×C4—202no—
328C22×C4—202no—
329C22×C4—204no—
330C22×C4—204no—
331C22×C4—204no—
332C22×C4C2×C4×D511yescharacteristic
333C22×C4D4×D511yescharacteristic
334C22×C4D4×D511yescharacteristic
335M16—41no—
336M16—41no—
337M16—204no—
338M16—201no—
339M16—201no—
340C2×C8—22no—
341C2×C8—22no—
342C2×C8—102no—
343C2×C8—102no—
344C4⋊C4—41no—
345C4⋊C4—41no—
346C4⋊C4—204no—
347C4⋊C4—201no—
348C4⋊C4—201no—
349C42—51no—
350C42—51no—
351C42—51no—
352C42—51no—
353C42—51no—
354C42—51no—
355C42—51no—
356C42—51no—
357C42—51no—
358C42—51no—
359C42—51no—
360C42—51no—
361C42C2×C4×D511yescharacteristic
362C42C2×C4×D511yescharacteristic
363C42D4×D511yescharacteristic
364C42Q8×D511yescharacteristic
365C2×C5—21no—
366C2×C5—21no—
367C2×C5C2×H(3,ℤ/4)11yescharacteristic
368C2×C5#173611yescharacteristic
369C2×C5C2×#34411yescharacteristic
370D5—22no—
371D5—22no—
372C23—51no—
373C23—51no—
374C23—102no—
375C23—102no—
376C23—101no—
377C23—101no—
378C23D5×C22⋊C411yescharacteristic
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—42no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—51no—
385C2×C4—51no—
386C2×C4—51no—
387C2×C4—51no—
388C2×C4—51no—
389C2×C4—51no—
390C2×C4—102no—
391C2×C4—102no—
392C2×C4—102no—
393C2×C4—102no—
394C2×C4—101no—
395C2×C4—101no—
396C2×C4—101no—
397C2×C4—101no—
398C2×C4—101no—
399C2×C4—101no—
400C2×C4—101no—
401C2×C4—101no—
402C2×C4—101no—
403C2×C4—101no—
404C2×C4—201no—
405C2×C4—201no—
406C2×C4—201no—
407C2×C4—201no—
408C2×C4—201no—
409C2×C4—201no—
410C2×C4—202no—
411C2×C4—202no—
412C2×C4—202no—
413C2×C4—408no—
414C2×C4C42×D511yescharacteristic
415C2×C4D5×C22⋊C411yescharacteristic
416C2×C4D5×C22⋊C411yescharacteristic
417C2×C4D5×C4⋊C411yescharacteristic
418C2×C4D5×C4⋊C411yescharacteristic
419C2×C4D5×C4⋊C411yescharacteristic
420C2×C4#405711yescharacteristic
421C2×C4#406011yescharacteristic
422C2×C4#406111yescharacteristic
423C2×C4#406411yescharacteristic
424C8—42no—
425C8—42no—
426C8—202no—
427C8—202no—
428C5#795911yescharacteristic, complemented, Sylow
429C22—21no—
430C22—21no—
431C22—52no—
432C22—52no—
433C22—104no—
434C22—104no—
435C22—101no—
436C22—101no—
437C22—101no—
438C22—101no—
439C22D5×#9511yescharacteristic
440C22#6505911yescharacteristic
441C22#6509111yescharacteristic
442C4—21no—
443C4—21no—
444C4—21no—
445C4—21no—
446C4—82no—
447C4—101no—
448C4—101no—
449C4—101no—
450C4—101no—
451C4—101no—
452C4—101no—
453C4—402no—
454C4#6506011yescharacteristic
455C4#6509211yescharacteristic
456C4#6515011yescharacteristic
457C4#6517011yescharacteristic
458C2—21no—
459C2—21no—
460C2—102no—
461C2—102no—
462C2D5×H(3,ℤ/4)11yescharacteristic
463C2#1059966011yescharacteristic
464C2D5×#34411yescharacteristic
subgroupG/H
centerC22D5×#95
commutatorC2×C4×C5C2×C42
FrattiniC2×C42C22×D5
FittingC5×#1286C2
socleC22×C5C2×#95
prime radicalC23×D5C22⋊C4
cosocleC2×C42×C5C23
hypercenter#1286D5
hypocenterC5#7959
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1286

Complements

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

NH ≅ G/Ntype
4. C5×#1286C2semidirect
5. #10598229C2semidirect
6. #10598204C2semidirect
7. #10598122C2semidirect
22. #65124C4semidirect
24. #65122C4semidirect
27. C4×#676C4semidirect
28. #64974C4semidirect
60. C5×C4⋊C8C2×C4semidirect
62. C4×C5×C8C2×C4semidirect
79. C4⋊#168C2×C4semidirect
80. C4×#168C2×C4semidirect
87. #1286D5semidirect
259. C4⋊C8C4×D5semidirect
269. C4×C8C4×D5semidirect
428. C5#7959semidirect

Maximal subgroups

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

subgroupindex
#106110132
#106107692
D5×#3822
C5×#12862
#105982292
#105982042
#105981222
#79595