Finite Group Databasebeta

← #11993180

Subgroups — #11993180

Order 1280.

466 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10611022C211yesmaximal, characteristic
2C5×#1565C211yesmaximal, characteristic, complemented
3#10601238C211yesmaximal, characteristic, complemented
4#10601218C211yesmaximal, characteristic
5C4×#3957C211yesmaximal, characteristic
6#10598227C211yesmaximal, characteristic, complemented
7#10598159C211yesmaximal, characteristic, complemented
8C4×#709C2211yescharacteristic
9C5×#431C2211yescharacteristic
10C2×C5×C4⋊C8C2211yescharacteristic
11C4×C5×M16C2211yescharacteristic
12C2×#3957C411yescharacteristic
13C2×#3957C411yescharacteristic
14C2×#3946—22no—
15C42×Dic5C2211yescharacteristic
16#65214C2211yescharacteristic
17C2×C4⋊#168C2211yescharacteristic
18#65122—21no—
19D5×C4⋊C8—21no—
20#65014—22no—
21C8×D20—21no—
22C8×Dic10—21no—
23C5×#335—21no—
24C5×#334—21no—
25#64775C411yescharacteristic
26#64775C411yescharacteristic
27#64704—21no—
28#64703—21no—
29#8839—51nomaximal, Sylow
30C2×#709C2×C411yescharacteristic
31C2×C5×M16C2×C411yescharacteristic
32C2×C5×M16C2×C411yescharacteristic
33C22×C5×C8—21no—
34C2×C42×C5C2311yescharacteristic
35C4×C22⋊D5—21no—
36C4×C22⋊D5—21no—
37#4072C2×C411yescharacteristic
38C2×C4×Dic5—21no—
39C2×C4×Dic5—21no—
40C2×C4×Dic5C2×C411yescharacteristic
41C2×C4×Dic5C2×C411yescharacteristic
42C22×#168D412yes—
43C2×C8×D5—22no—
44C4×D20D411yescharacteristic
45C4×D20Q811yescharacteristic
46#4018—21no—
47C42×D5—21no—
48C4×Dic10D411yescharacteristic
49C4×Dic10Q811yescharacteristic
50C5×C4⋊C8—21no—
51C5×C4⋊C8—21no—
52C5×C4⋊C8D411yescharacteristic
53C5×C4⋊C8D411yescharacteristic
54C5×C22⋊C8—21no—
55C5×#97—21no—
56C4×C5×C8—21no—
57C4×C5×C8—21no—
58C22⋊#168—21no—
59#3957—22no—
60#3957C814yescomplemented
61#3952—22no—
62#3946—22no—
63#3946—44no—
64C8×Dic5—22no—
65C4⋊#168—21no—
66C4⋊#168—21no—
67C4⋊#168—21no—
68C4×#168—21no—
69#2988—51no—
70#1842—51no—
71C4×#104—51no—
72#1565D511yescharacteristic, complemented
73#1477—51no—
74#1283—51no—
75#1276—51no—
76C22×C4×C5C22×C411yescharacteristic
77C22×C4×C5C2×D411yescharacteristic
78C22×C4×C5#4111yescharacteristic
79C2×C22⋊D5—21no—
80C22×Dic5—21no—
81C22×Dic5—21no—
82#709—21no—
83#709—21no—
84#709C2×C812yes—
85#709M1612yes—
86C2×D20C4⋊C411yescharacteristic
87C2×C4×D5—21no—
88C2×C4×D5—21no—
89C2×C4×D5—21no—
90C2×Dic10C4⋊C411yescharacteristic
91C5×M16—21no—
92C5×M16—21no—
93C5×M16—21no—
94C5×M16C2×C812yescomplemented
95C2×C5×C8—21no—
96C2×C5×C8—21no—
97C2×C5×C8—21no—
98C2×C5×C8—21no—
99C2×C5×C8—42no—
100C2×C5×C8—41no—
101C42×C5C2×D411yescharacteristic
102C42×C5C2×D411yescharacteristic
103C42×C5C2×Q811yescharacteristic
104C42×C5#4111yescharacteristic
105C22⋊Dic5—21no—
106#685—21no—
107#685—21no—
108C4⋊Dic5C4⋊C411yescharacteristic
109C4⋊Dic5C4⋊C411yescharacteristic
110#683—21no—
111#683—21no—
112C4×Dic5—22no—
113C4×Dic5—22no—
114C4×Dic5—21no—
115C4×Dic5—21no—
116C4×Dic5—21no—
117C4×Dic5—21no—
118C4×Dic5—21no—
119C4×Dic5—21no—
120C4×Dic5—42no—
121C4×Dic5C2×C812yescomplemented
122C2×#168—22no—
123C2×#168—42no—
124C2×#168—41no—
125C8×D5—82no—
126C4×#41—51no—
127C8×Q8—101no—
128C8×D4—101no—
129C8×D4—102no—
130#431—51no—
131#431—101no—
132#431C2×D511yescharacteristic
133C2×C4⋊C8—51no—
134C2×C4⋊C8—101no—
135C2×C4⋊C8—102no—
136C2×C4⋊C8C2×D511yescharacteristic
137C2×#104—51no—
138C2×#104—51no—
139C4×M16C2×D511yescharacteristic
140C43—51no—
141#339—51no—
142#339—51no—
143#335—21no—
144#334—21no—
145Q8⋊C8—101no—
146D4⋊C8—101no—
147C23×C5C4×D411yescharacteristic
148C22×D5—21no—
149C2×C4×C5—21no—
150C2×C4×C5—21no—
151C2×C4×C5—41no—
152C2×C4×C5C2×C4⋊C411yescharacteristic
153C2×C4×C5C4×D411yescharacteristic
154C2×C4×C5#12011yescharacteristic
155C2×C4×C5C22⋊Q811yescharacteristic
156C2×C4×C5C22⋊Q811yescharacteristic
157C2×C4×C5#12311yescharacteristic
158C2×C4×C5C22×C811yescharacteristic
159C2×C4×C5C2×M1611yescharacteristic
160C2×C4×C5#13111yescharacteristic
161C2×C4×C5#13111yescharacteristic
162C22⋊D5—22no—
163C22⋊D5—22no—
164C2×Dic5—22no—
165C2×Dic5—22no—
166C2×Dic5—21no—
167C2×Dic5—22no—
168C2×Dic5—22no—
169C2×Dic5—21no—
170C2×Dic5—21no—
171C2×Dic5—41no—
172C2×Dic5—41no—
173D20—21no—
174D20C4⋊C812yescomplemented
175C4×D5—22no—
176C4×D5—22no—
177C4×D5—41no—
178C4×D5—41no—
179C4×D5—81no—
180Dic10—21no—
181Dic10C4⋊C812yescomplemented
182C5×C8—22no—
183C5×C8—41no—
184C5×C8—41no—
185C5×C8—41no—
186C5×C8—81no—
187#168—42no—
188#168—81no—
189C2×#41—51no—
190C2×M16C4×D511yescharacteristic
191C2×M16C4×D511yescharacteristic
192C22×C8—21no—
193C22×C8—52no—
194C22×C8—102no—
195C4×Q8—51no—
196C4×Q8—51no—
197C4×D4—51no—
198C4×D4—51no—
199C4×D4—101no—
200C4×D4—101no—
201#117—51no—
202#117—101no—
203C2×C42—51no—
204C2×C42—51no—
205C2×C42—101no—
206C2×C42—101no—
207C2×C42—101no—
208C2×C42C22×D511yescharacteristic
209C4⋊C8—21no—
210C4⋊C8—21no—
211C4⋊C8—102no—
212C4⋊C8—101no—
213C4⋊C8—101no—
214C4⋊C8—101no—
215C4⋊C8—204no—
216C4⋊C8C22⋊D511yescharacteristic
217C4⋊C8C22⋊D511yescharacteristic
218#104—54no—
219#104—102no—
220C22⋊C8—21no—
221C22⋊C8—102no—
222C22⋊C8—101no—
223#97—21no—
224C4×C8—21no—
225C4×C8—21no—
226C4×C8—102no—
227C4×C8—101no—
228C22×C5—21no—
229C22×C5—21no—
230C22×C5#38511yescharacteristic
231C22×C5C8×D411yescharacteristic
232C22×C5#43511yescharacteristic
233C2×D5—22no—
234C2×D5—41no—
235C2×D5—41no—
236C4×C5—21no—
237C4×C5—21no—
238C4×C5—21no—
239C4×C5C2×C4⋊C811yescharacteristic
240C4×C5#42411yescharacteristic
241C4×C5C8×D411yescharacteristic
242C4×C5#43511yescharacteristic
243C4×C5#45311yescharacteristic
244C4×C5#45611yescharacteristic
245Dic5—24no—
246Dic5—22no—
247Dic5—42no—
248Dic5—41no—
249Dic5—41no—
250#41—52no—
251#41—52no—
252#41—101no—
253#41—101no—
254C2×Q8—51no—
255C2×D4—51no—
256C2×D4—101no—
257C22×C4—101no—
258C22×C4—101no—
259C22×C4—101no—
260C22×C4—101no—
261C22×C4—101no—
262C22×C4C2×C4×D511yescharacteristic
263C22×C4D4×D511yescharacteristic
264C22×C4#71311yescharacteristic
265M16—21no—
266M16—21no—
267M16—21no—
268M16C8×D512yescomplemented
269C2×C8—21no—
270C2×C8—21no—
271C2×C8—21no—
272C2×C8—21no—
273C2×C8—42no—
274C2×C8—41no—
275C2×C8—102no—
276C2×C8—202no—
277C2×C8—201no—
278C2×C8—402no—
279C4⋊C4—51no—
280C4⋊C4—51no—
281C4⋊C4—101no—
282C4⋊C4—101no—
283C22⋊C4—101no—
284C22⋊C4—101no—
285C22⋊C4—101no—
286C42—52no—
287C42—102no—
288C42—102no—
289C42—101no—
290C42—101no—
291C42—101no—
292C42—101no—
293C42—101no—
294C42—101no—
295C42—202no—
296C42#70911yescharacteristic
297C42D4×D511yescharacteristic
298C42Q8×D511yescharacteristic
299C42C2×C22⋊D511yescharacteristic
300C2×C5—21no—
301C2×C5—21no—
302C2×C5#185011yescharacteristic
303C2×C5#185911yescharacteristic
304C2×C5#186111yescharacteristic
305D5—42no—
306C23—101no—
307C23#403911yescharacteristic
308Q8—52no—
309Q8—101no—
310D4—52no—
311D4—102no—
312D4—102no—
313D4—101no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—41no—
317C2×C4—102no—
318C2×C4—102no—
319C2×C4—102no—
320C2×C4—101no—
321C2×C4—102no—
322C2×C4—102no—
323C2×C4—102no—
324C2×C4—101no—
325C2×C4—101no—
326C2×C4—201no—
327C2×C4—201no—
328C2×C4—201no—
329C2×C4—201no—
330C2×C4—401no—
331C2×C4D5×C4⋊C411yescharacteristic
332C2×C4#404011yescharacteristic
333C2×C4#404211yescharacteristic
334C2×C4C2×C8×D511yescharacteristic
335C2×C4#404711yescharacteristic
336C2×C4D5×M1611yescharacteristic
337C2×C4#405311yescharacteristic
338C2×C4C4×C22⋊D511yescharacteristic
339C2×C4#408311yescharacteristic
340C2×C4#409211yescharacteristic
341C8—22no—
342C8—41no—
343C8—41no—
344C8—41no—
345C8—81no—
346C8—202no—
347C8—401no—
348C5#883911yescharacteristic, complemented, Sylow
349C22—21no—
350C22—21no—
351C22—102no—
352C22—201no—
353C22—201no—
354C22#6512311yescharacteristic
355C22#6512511yescharacteristic
356C22#6527811yescharacteristic
357C4—21no—
358C4—21no—
359C4—21no—
360C4—104no—
361C4—102no—
362C4—202no—
363C4—201no—
364C4—201no—
365C4D5×C4⋊C811yescharacteristic
366C4#6512811yescharacteristic
367C4C8×C22⋊D511yescharacteristic
368C4#6541611yescharacteristic
369C4#6548711yescharacteristic
370C4#6549411yescharacteristic
371C2—21no—
372C2—21no—
373C2—202no—
374C2#1060127011yescharacteristic
375C2#1060147311yescharacteristic
376C2#1060152811yescharacteristic
subgroupG/H
centerC2×C4#4083
commutatorC2×C4×C5C22×C8
FrattiniC2×C42C22×D5
FittingC5×#1565C2
socleC22×C5#385
prime radicalC2×#709C2×C4
cosocleC2×C42×C5C23
hypercenter#1565D5
hypocenterC5#8839
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1565

Complements

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

NH ≅ G/Ntype
2. C5×#1565C2semidirect
3. #10601238C2semidirect
6. #10598227C2semidirect
7. #10598159C2semidirect
60. #3957C8semidirect
72. #1565D5semidirect
94. C5×M16C2×C8semidirect
121. C4×Dic5C2×C8semidirect
174. D20C4⋊C8semidirect
181. Dic10C4⋊C8semidirect
268. M16C8×D5semidirect
348. C5#8839semidirect

Maximal subgroups

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

subgroupindex
#106110222
C5×#15652
#106012382
#106012182
C4×#39572
#105982272
#105981592
#88395