Finite Group Databasebeta

← #12068498

Subgroups — #12068498

Order 1280.

616 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10611062C211yesmaximal, characteristic
2#10610769C211yesmaximal, characteristic
3#10610248C211yesmaximal, characteristic
4C5×#1569C211yesmaximal, characteristic, complemented
5#10601588C211yesmaximal, characteristic, complemented
6#10601285C211yesmaximal, characteristic, complemented
7#10600644C211yesmaximal, characteristic, complemented
8#10599368C212yesmaximal, complemented
9#10599366C212yesmaximal, complemented
10#10599328C212yesmaximal, complemented
11#10599326C212yesmaximal, complemented
12C2×C42×D5C2211yescharacteristic
13C5×#432C2211yescharacteristic
14C5×#423C2211yescharacteristic
15C4×C5×M16C2211yescharacteristic
16#65415—21no—
17#65415C412yes—
18#65407C412yes—
19M16×Dic5—21no—
20#65215C2211yescharacteristic
21#65213C2211yescharacteristic
22C4×#681C2211yescharacteristic
23#65126C2211yescharacteristic
24#65126C2211yescharacteristic
25#65124—21no—
26#65124C2212yes—
27#65122—21no—
28#65122C2212yes—
29#65122C2211yescharacteristic
30#65122C2211yescharacteristic
31#65015—21no—
32#65007—21no—
33#64996—21no—
34#64994—21no—
35#64994C412yes—
36#64994C412yes—
37#64974C2212yes—
38#64974C2212yes—
39C5×#335C2212yescomplemented
40C5×#334C2212yescomplemented
41#64700C2212yescomplemented
42#64700C2212yescomplemented
43#64699C2212yescomplemented
44#64699C2212yescomplemented
45#64678C2212yescomplemented
46#64677C2212yescomplemented
47#17823—51nomaximal, Sylow
48C22×C4×D5C2×C411yescharacteristic
49C22×C4×D5D411yescharacteristic
50C22×C4×D5Q811yescharacteristic
51C2×C5×M16—21no—
52C2×C5×M16C2×C412yes—
53C2×C42×C5C2311yescharacteristic
54C2×C4×Dic5C2×C411yescharacteristic
55C2×C4×Dic5D411yescharacteristic
56C2×C4×Dic5Q811yescharacteristic
57C2×#681—21no—
58C2×#681C2×C412yes—
59C2×#676—21no—
60C2×#676—21no—
61C42×D5C2×C411yescharacteristic
62C42×D5C2×C411yescharacteristic
63C42×D5D411yescharacteristic
64C42×D5D411yescharacteristic
65C42×D5Q811yescharacteristic
66C42×D5Q811yescharacteristic
67C42×D5C2311yescharacteristic
68C42×D5C2311yescharacteristic
69C5×C4⋊C8—21no—
70C5×C4⋊C8C2311yescharacteristic
71C5×C4⋊C8C2312yes—
72C5×C4⋊C8C2311yescharacteristic
73C5×C22⋊C8—21no—
74C5×#97—21no—
75C5×#97C2×C412yes—
76C4×C5×C8C2312yes—
77C22⋊#168—21no—
78#3952—22no—
79#3952—22no—
80#3952—21no—
81#3952—21no—
82#3952C2×C414yes—
83#3952C2×C414yes—
84#3947—22no—
85#3946—21no—
86#3946—21no—
87#3946C2×C414yes—
88#3946C2×C414yes—
89C8×Dic5—22no—
90C8×Dic5—21no—
91C8×Dic5—21no—
92C4⋊#168—21no—
93C4⋊#168C2312yes—
94C4⋊#168C2311yescharacteristic
95C4⋊#168C2311yescharacteristic
96#3935—21no—
97#3935C2×C412yes—
98C4×#168C2312yes—
99#2920—51no—
100#2920—51no—
101#2920—51no—
102#1574—52no—
103#1574—52no—
104#1572—52no—
105#1572—52no—
106#1569—51no—
107#1569—51no—
108#1569—51no—
109#1569D511yescharacteristic, complemented
110C23×D5C4⋊C411yescharacteristic
111C22×C4×C5C22×C411yescharacteristic
112C22×C4×C5C2×D411yescharacteristic
113C22×C4×C5C2×Q811yescharacteristic
114C22×Dic5C4⋊C411yescharacteristic
115C22×Dic5C4⋊C411yescharacteristic
116C22×Dic5C4⋊C411yescharacteristic
117C2×C4×D5—42no—
118C2×C4×D5—42no—
119C2×C4×D5—41no—
120C2×C4×D5—41no—
121C2×C4×D5C4⋊C411yescharacteristic
122C2×C4×D5C4⋊C411yescharacteristic
123C2×C4×D5C4⋊C411yescharacteristic
124C2×C4×D5C4⋊C411yescharacteristic
125C2×C4×D5C4⋊C411yescharacteristic
126C2×C4×D5C4⋊C411yescharacteristic
127C2×C4×D5C22×C411yescharacteristic
128C2×C4×D5C22×C411yescharacteristic
129C2×C4×D5C2×D411yescharacteristic
130C2×C4×D5C2×D411yescharacteristic
131C2×C4×D5C2×Q811yescharacteristic
132C2×C4×D5C2×Q811yescharacteristic
133C5×M16—42no—
134C5×M16—42no—
135C2×C5×C8—22no—
136C2×C5×C8—21no—
137C2×C5×C8—21no—
138C2×C5×C8C22×C414yes—
139C42×C5C22×C411yescharacteristic
140C42×C5C2×D411yescharacteristic
141C42×C5C2×Q811yescharacteristic
142C42×C5C2411yescharacteristic
143C4×Dic5C4⋊C411yescharacteristic
144C4×Dic5C4⋊C411yescharacteristic
145C4×Dic5C4⋊C411yescharacteristic
146C4×Dic5C4⋊C411yescharacteristic
147C4×Dic5C4⋊C411yescharacteristic
148C4×Dic5C4⋊C411yescharacteristic
149C4×Dic5C22×C411yescharacteristic
150C4×Dic5C22×C411yescharacteristic
151C4×Dic5C2×D411yescharacteristic
152C4×Dic5C2×D411yescharacteristic
153C4×Dic5C2×Q811yescharacteristic
154C4×Dic5C2×Q811yescharacteristic
155#681—42no—
156#681—42no—
157C2×#168—21no—
158C2×#168—21no—
159C2×#168—22no—
160C2×#168C22×C414yes—
161#676—42no—
162#676—42no—
163C22×C42—51no—
164#432—52no—
165#432—52no—
166#432—51no—
167#432—52no—
168#432—101no—
169#432—101no—
170#432C2×D511yescharacteristic
171#431—52no—
172#431—52no—
173#431—51no—
174#431—51no—
175#431—52no—
176#431—101no—
177#431—101no—
178#423—52no—
179#423—51no—
180#423—51no—
181#423—51no—
182#423C2×D511yescharacteristic
183#407—52no—
184#407—101no—
185#407—101no—
186C4×M16—51no—
187C4×M16—101no—
188C4×M16—101no—
189C4×M16C2×D511yescharacteristic
190#335—52no—
191#335—52no—
192#335—52no—
193#335C2×D512yescomplemented
194#334—52no—
195#334—52no—
196#334—52no—
197#334C2×D512yescomplemented
198C23×C5C2×C4⋊C411yescharacteristic
199C22×D5—41no—
200C22×D5—41no—
201C22×D5—41no—
202C22×D5C2×C4⋊C411yescharacteristic
203C22×D5C2×C4⋊C411yescharacteristic
204C2×C4×C5—22no—
205C2×C4×C5—21no—
206C2×C4×C5—21no—
207C2×C4×C5—41no—
208C2×C4×C5C2×C4⋊C411yescharacteristic
209C2×C4×C5C2×C4⋊C411yescharacteristic
210C2×C4×C5C2×C4⋊C411yescharacteristic
211C2×C4×C5C23×C411yescharacteristic
212C2×C4×C5C22×D411yescharacteristic
213C2×C4×C5C22×Q811yescharacteristic
214C2×Dic5—22no—
215C2×Dic5—41no—
216C2×Dic5—41no—
217C2×Dic5C2×C4⋊C411yescharacteristic
218C2×Dic5C2×C4⋊C411yescharacteristic
219C2×Dic5C2×C4⋊C411yescharacteristic
220C2×Dic5C2×C4⋊C411yescharacteristic
221C2×Dic5C2×C4⋊C411yescharacteristic
222C2×Dic5C2×C4⋊C411yescharacteristic
223C4×D5—22no—
224C4×D5—22no—
225C4×D5—21no—
226C4×D5—21no—
227C4×D5—21no—
228C4×D5—21no—
229C4×D5—22no—
230C4×D5—22no—
231C4×D5—41no—
232C4×D5—41no—
233C4×D5—41no—
234C4×D5—41no—
235C4×D5—41no—
236C4×D5—41no—
237C5×C8—24no—
238C5×C8—41no—
239C5×C8—41no—
240C5×C8—42no—
241#168—24no—
242#168—41no—
243#168—41no—
244#168—42no—
245C23×C4—51no—
246C23×C4—51no—
247C23×C4—51no—
248C2×M16—21no—
249C2×M16—52no—
250C2×M16—101no—
251C2×M16—101no—
252C2×M16—101no—
253C2×M16C4×D512yes—
254C2×C42—51no—
255C2×C42—51no—
256C2×C42—51no—
257C2×C42—51no—
258C2×C42—51no—
259C2×C42—51no—
260C2×C42—51no—
261C2×C42—51no—
262C2×C42—51no—
263C2×C42—51no—
264C2×C42—51no—
265C2×C42C22×D511yescharacteristic
266C4⋊C8—21no—
267C4⋊C8—54no—
268C4⋊C8—54no—
269C4⋊C8—51no—
270C4⋊C8—52no—
271C4⋊C8—51no—
272C4⋊C8—101no—
273C4⋊C8—101no—
274C4⋊C8—101no—
275C4⋊C8C22×D511yescharacteristic
276C4⋊C8C22×D512yes—
277C4⋊C8C22×D511yescharacteristic
278C22⋊C8—21no—
279C22⋊C8—54no—
280C22⋊C8—54no—
281C22⋊C8—101no—
282C22⋊C8—101no—
283C22⋊C8—102no—
284C22⋊C8—102no—
285C22⋊C8—101no—
286#97—21no—
287#97—52no—
288#97—102no—
289#97—101no—
290#97C4×D512yes—
291C4×C8—52no—
292C4×C8—101no—
293C4×C8—101no—
294C4×C8—102no—
295C4×C8C22×D512yes—
296C22×C5—21no—
297C22×C5—21no—
298C22×C5—21no—
299C22×C5C22×C4⋊C411yescharacteristic
300C2×D5—21no—
301C2×D5—21no—
302C2×D5—21no—
303C2×D5—21no—
304C2×D5—21no—
305C2×D5—21no—
306C2×D5—44no—
307C4×C5—21no—
308C4×C5—21no—
309C4×C5—21no—
310C4×C5—21no—
311C4×C5#56812yes—
312C4×C5#57511yescharacteristic
313C4×C5#57511yescharacteristic
314Dic5—21no—
315Dic5—21no—
316Dic5—21no—
317Dic5—21no—
318Dic5—21no—
319Dic5#43012yes—
320C24—51no—
321C22×C4—51no—
322C22×C4—51no—
323C22×C4—51no—
324C22×C4—51no—
325C22×C4—51no—
326C22×C4—51no—
327C22×C4—51no—
328C22×C4—51no—
329C22×C4—51no—
330C22×C4—51no—
331C22×C4—51no—
332C22×C4—51no—
333C22×C4—51no—
334C22×C4—51no—
335C22×C4—51no—
336C22×C4—202no—
337C22×C4—201no—
338C22×C4—201no—
339C22×C4—202no—
340C22×C4C2×C4×D511yescharacteristic
341C22×C4D4×D511yescharacteristic
342C22×C4Q8×D511yescharacteristic
343M16—42no—
344M16—42no—
345M16—202no—
346M16—202no—
347M16—202no—
348M16—202no—
349C2×C8—21no—
350C2×C8—21no—
351C2×C8—22no—
352C2×C8—54no—
353C2×C8—101no—
354C2×C8—102no—
355C2×C8—101no—
356C2×C8C2×C4×D514yes—
357C42—51no—
358C42—51no—
359C42—51no—
360C42—51no—
361C42—51no—
362C42—51no—
363C42—51no—
364C42—51no—
365C42—51no—
366C42—51no—
367C42—51no—
368C42—51no—
369C42C2×C4×D511yescharacteristic
370C42D4×D511yescharacteristic
371C42Q8×D511yescharacteristic
372C42C23×D511yescharacteristic
373C2×C5—41no—
374C2×C5#290511yescharacteristic
375C2×C5#291111yescharacteristic
376C2×C5C2×#43011yescharacteristic
377D5—41no—
378D5—41no—
379C23—51no—
380C23—51no—
381C23—201no—
382C23—201no—
383C23—201no—
384C23D5×C4⋊C411yescharacteristic
385C2×C4—22no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—41no—
389C2×C4—51no—
390C2×C4—51no—
391C2×C4—51no—
392C2×C4—51no—
393C2×C4—51no—
394C2×C4—51no—
395C2×C4—102no—
396C2×C4—102no—
397C2×C4—102no—
398C2×C4—102no—
399C2×C4—102no—
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—201no—
411C2×C4—201no—
412C2×C4D5×C4⋊C411yescharacteristic
413C2×C4D5×C4⋊C411yescharacteristic
414C2×C4D5×C4⋊C411yescharacteristic
415C2×C4C22×C4×D511yescharacteristic
416C2×C4C2×D4×D511yescharacteristic
417C2×C4C2×Q8×D511yescharacteristic
418C8—24no—
419C8—42no—
420C8—41no—
421C8—41no—
422C8—104no—
423C8—201no—
424C8—201no—
425C8—202no—
426C5#1782311yescharacteristic, complemented, Sylow
427C22—21no—
428C22—21no—
429C22—21no—
430C22—101no—
431C22—101no—
432C22—101no—
433C22—101no—
434C22—101no—
435C22—101no—
436C22—204no—
437C22C2×D5×C4⋊C411yescharacteristic
438C4—21no—
439C4—21no—
440C4—21no—
441C4—21no—
442C4—52no—
443C4—101no—
444C4—101no—
445C4—101no—
446C4—101no—
447C4—101no—
448C4#6607912yes—
449C4#6610711yescharacteristic
450C4#6611111yescharacteristic
451C2—41no—
452C2—201no—
453C2—201no—
454C2#1061077911yescharacteristic
455C2#1061093911yescharacteristic
456C2D5×#43011yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D5
commutatorC2×C4×C5C23×C4
FrattiniC42C23×D5
FittingC5×#1569C2
socleC22×C5C22×C4⋊C4
prime radicalC23×D5C4⋊C4
cosocleC42×C5C24
hypercenter#1569D5
hypocenterC5#17823
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1569

Complements

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

NH ≅ G/Ntype
4. C5×#1569C2semidirect
5. #10601588C2semidirect
6. #10601285C2semidirect
7. #10600644C2semidirect
8. #10599368C2semidirect
9. #10599366C2semidirect
10. #10599328C2semidirect
11. #10599326C2semidirect
39. C5×#335C22semidirect
40. C5×#334C22semidirect
41. #64700C22semidirect
42. #64700C22semidirect
43. #64699C22semidirect
44. #64699C22semidirect
45. #64678C22semidirect
46. #64677C22semidirect
109. #1569D5semidirect
193. #335C2×D5semidirect
197. #334C2×D5semidirect
426. C5#17823semidirect

Maximal subgroups

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

subgroupindex
#106110622
#106107692
#106102482
C5×#15692
#106015882
#106012852
#106006442
#105993682
#105993662
#105993282
#105993262
#178235