Finite Group Databasebeta

← #11989098

Subgroups — #11989098

Order 1280.

606 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10611013C211yesmaximal, characteristic
2#10610769C211yesmaximal, characteristic
3#10605879C211yesmaximal, characteristic
4C5×#1286C211yesmaximal, characteristic, complemented
5#10598229C211yesmaximal, characteristic, complemented
6#10598204C211yesmaximal, characteristic, complemented
7#10598122C211yesmaximal, characteristic, complemented
8C2×#4038—21no—
9C2×C42×D5C2211yescharacteristic
10C5×#431C2211yescharacteristic
11C5×#423C2211yescharacteristic
12C5×#382C2211yescharacteristic
13#65415—21no—
14M16×Dic5—21no—
15#65265—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
29#64956—21no—
30#64956C412yes—
31#64938—21no—
32#64938C412yes—
33#7961—51nomaximal, Sylow
34C22×C4×D5C2×C411yescharacteristic
35C22×C4×D5D411yescharacteristic
36C22×C4×D5D411yescharacteristic
37C2×C5×M16—21no—
38C2×C5×C4⋊C4—21no—
39C2×C42×C5C2311yescharacteristic
40C2×#685—22no—
41C2×C4⋊Dic5—21no—
42C2×#683—22no—
43C2×#683—22no—
44C2×C4×Dic5—22no—
45C2×C4×Dic5C2×C411yescharacteristic
46C2×C4×Dic5D411yescharacteristic
47C2×C4×Dic5D411yescharacteristic
48C2×#681—21no—
49C2×#676—22no—
50#4038—42no—
51#4038—42no—
52C42×D5C2×C411yescharacteristic
53C42×D5C2×C411yescharacteristic
54C42×D5C2×C411yescharacteristic
55C42×D5C2×C411yescharacteristic
56C42×D5D411yescharacteristic
57C42×D5D411yescharacteristic
58C42×D5Q811yescharacteristic
59C42×D5Q811yescharacteristic
60C5×C4⋊C8—21no—
61C5×C4⋊C8—21no—
62C5×C4⋊C8C2×C412yes—
63C5×C22⋊C8—21no—
64C4×C5×C8C2×C412yes—
65C5×#95—21no—
66C5×#95C2×C412yes—
67#3963—21no—
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×C412yes—
80C4×#168C2×C412yes—
81#2920—51no—
82#2920—51no—
83#2285—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×D5C4211yescharacteristic
104C2×C4×D5C4211yescharacteristic
105C2×C4×D5C22⋊C411yescharacteristic
106C2×C4×D5C22⋊C411yescharacteristic
107C2×C4×D5C22⋊C411yescharacteristic
108C2×C4×D5C22⋊C411yescharacteristic
109C2×C4×D5C4⋊C411yescharacteristic
110C2×C4×D5C4⋊C411yescharacteristic
111C2×C4×D5C4⋊C411yescharacteristic
112C2×C4×D5C4⋊C411yescharacteristic
113C2×C4×D5C4⋊C411yescharacteristic
114C2×C4×D5C4⋊C411yescharacteristic
115C5×M16—41no—
116C5×M16—41no—
117C2×C5×C8—22no—
118C2×C5×C8—22no—
119C5×C4⋊C4—41no—
120C5×C4⋊C4—41no—
121C42×C5C22×C411yescharacteristic
122C42×C5C22×C411yescharacteristic
123C42×C5C2×D411yescharacteristic
124C42×C5C2×Q811yescharacteristic
125#685—44no—
126C4⋊Dic5—41no—
127C4⋊Dic5—41no—
128#683—44no—
129#683—44no—
130C4×Dic5—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—
148C2×#117—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#384—101no—
167#382—51no—
168#382C2×D511yescharacteristic
169#380—52no—
170#380—101no—
171C4×C4⋊C4—52no—
172C4×C4⋊C4—101no—
173C23×C5C2×C22⋊C411yescharacteristic
174C22×D5—21no—
175C22×D5—21no—
176C22×D5—41no—
177C22×D5—41no—
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—22no—
198C2×Dic5—22no—
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—21no—
209C4×D5—21no—
210C4×D5—21no—
211C4×D5—21no—
212C4×D5—21no—
213C4×D5—21no—
214C4×D5—21no—
215C4×D5—21no—
216C4×D5—22no—
217C4×D5—22no—
218C4×D5—22no—
219C4×D5—22no—
220C4×D5—41no—
221C4×D5—41no—
222C4×D5—41no—
223C4×D5—41no—
224C5×C8—42no—
225C5×C8—42no—
226#168—42no—
227#168—42no—
228C23×C4—51no—
229C23×C4—51no—
230C23×C4—51no—
231C2×M16—21no—
232C2×M16—102no—
233C2×M16—101no—
234#117—202no—
235#117—202no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—102no—
238C2×C4⋊C4—102no—
239C2×C4⋊C4—101no—
240C2×C22⋊C4—102no—
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×C42—102no—
253C2×C42C22×D511yescharacteristic
254C4⋊C8—21no—
255C4⋊C8—21no—
256C4⋊C8—52no—
257C4⋊C8—102no—
258C4⋊C8—101no—
259C4⋊C8—101no—
260C4⋊C8C4×D512yes—
261C22⋊C8—21no—
262C22⋊C8—102no—
263C22⋊C8—102no—
264C22⋊C8—102no—
265C22⋊C8—101no—
266#97—102no—
267#97—102no—
268C4×C8—52no—
269C4×C8—102no—
270C4×C8C4×D512yes—
271#95—21no—
272#95—52no—
273#95—101no—
274#95C4×D512yes—
275C22×C5—21no—
276C22×C5—21no—
277C22×C5C2×#9511yescharacteristic
278C22×C5#41811yescharacteristic
279C22×C5#41911yescharacteristic
280C2×D5—21no—
281C2×D5—21no—
282C2×D5—21no—
283C2×D5—21no—
284C2×D5—21no—
285C2×D5—21no—
286C2×D5—42no—
287C2×D5—42no—
288C4×C5—21no—
289C4×C5—21no—
290C4×C5—21no—
291C4×C5—21no—
292C4×C5—82no—
293C4×C5#41711yescharacteristic
294C4×C5#41711yescharacteristic
295C4×C5#42811yescharacteristic
296C4×C5#42811yescharacteristic
297Dic5—21no—
298Dic5—21no—
299Dic5—21no—
300Dic5—21no—
301Dic5—82no—
302Dic5H(3,ℤ/4)12yes—
303Dic5#34412yes—
304C24—51no—
305C22×C4—22no—
306C22×C4—51no—
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—101no—
322C22×C4—101no—
323C22×C4—101no—
324C22×C4—101no—
325C22×C4—102no—
326C22×C4—202no—
327C22×C4—202no—
328C22×C4C2×C4×D511yescharacteristic
329C22×C4D4×D511yescharacteristic
330C22×C4D4×D511yescharacteristic
331M16—41no—
332M16—41no—
333M16—204no—
334M16—201no—
335M16—201no—
336C2×C8—22no—
337C2×C8—22no—
338C2×C8—102no—
339C2×C8—102no—
340C4⋊C4—41no—
341C4⋊C4—41no—
342C4⋊C4—204no—
343C4⋊C4—204no—
344C4⋊C4—201no—
345C4⋊C4—201no—
346C22⋊C4—204no—
347C42—51no—
348C42—51no—
349C42—51no—
350C42—51no—
351C42—51no—
352C42—51no—
353C42—51no—
354C42—51no—
355C42—51no—
356C42—51no—
357C42—51no—
358C42—51no—
359C42—204no—
360C42C2×C4×D511yescharacteristic
361C42C2×C4×D511yescharacteristic
362C42D4×D511yescharacteristic
363C42Q8×D511yescharacteristic
364C2×C5—21no—
365C2×C5—21no—
366C2×C5C2×H(3,ℤ/4)11yescharacteristic
367C2×C5#173611yescharacteristic
368C2×C5C2×#34411yescharacteristic
369D5—41no—
370D5—41no—
371C23—51no—
372C23—51no—
373C23—101no—
374C23—101no—
375C23—201no—
376C23—201no—
377C23D5×C22⋊C411yescharacteristic
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—42no—
381C2×C4—42no—
382C2×C4—42no—
383C2×C4—51no—
384C2×C4—51no—
385C2×C4—51no—
386C2×C4—51no—
387C2×C4—51no—
388C2×C4—51no—
389C2×C4—102no—
390C2×C4—102no—
391C2×C4—102no—
392C2×C4—102no—
393C2×C4—102no—
394C2×C4—102no—
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—101no—
405C2×C4—201no—
406C2×C4—201no—
407C2×C4—201no—
408C2×C4—201no—
409C2×C4—202no—
410C2×C4—202no—
411C2×C4—202no—
412C2×C4C42×D511yescharacteristic
413C2×C4D5×C22⋊C411yescharacteristic
414C2×C4D5×C22⋊C411yescharacteristic
415C2×C4D5×C4⋊C411yescharacteristic
416C2×C4D5×C4⋊C411yescharacteristic
417C2×C4D5×C4⋊C411yescharacteristic
418C2×C4#405711yescharacteristic
419C2×C4#406011yescharacteristic
420C2×C4#406111yescharacteristic
421C2×C4#406411yescharacteristic
422C8—42no—
423C8—42no—
424C8—202no—
425C8—202no—
426C5#796111yescharacteristic, complemented, Sylow
427C22—21no—
428C22—21no—
429C22—101no—
430C22—101no—
431C22—101no—
432C22—101no—
433C22—101no—
434C22—101no—
435C22—202no—
436C22—202no—
437C22D5×#9511yescharacteristic
438C22#6505911yescharacteristic
439C22#6509111yescharacteristic
440C4—21no—
441C4—21no—
442C4—21no—
443C4—21no—
444C4—52no—
445C4—52no—
446C4—82no—
447C4—101no—
448C4—101no—
449C4—101no—
450C4—101no—
451C4—402no—
452C4#6506011yescharacteristic
453C4#6509211yescharacteristic
454C4#6515011yescharacteristic
455C4#6517011yescharacteristic
456C2—21no—
457C2—21no—
458C2—201no—
459C2—201no—
460C2D5×H(3,ℤ/4)11yescharacteristic
461C2#1059966011yescharacteristic
462C2D5×#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#7961
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
87. #1286D5semidirect
426. C5#7961semidirect

Maximal subgroups

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

subgroupindex
#106110132
#106107692
#106058792
C5×#12862
#105982292
#105982042
#105981222
#79615