Finite Group Databasebeta

← #11994530

Subgroups — #11994530

Order 1280.

470 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3167C211yesmaximal, characteristic
2#10615061C211yesmaximal, characteristic, complemented
3#10602628C211yesmaximal, characteristic, complemented
4#10602611C211yesmaximal, characteristic
5#10602593C211yesmaximal, characteristic
6#10598147C211yesmaximal, characteristic, complemented
7#10598146C211yesmaximal, characteristic, complemented
8C5×#533C2211yescharacteristic
9C5×#532C2211yescharacteristic
10C5×#498C411yescharacteristic, complemented
11C5×#492C411yescharacteristic, complemented
12C5×#487C411yescharacteristic, complemented
13C5×#486C411yescharacteristic, complemented
14C5×#465—22no—
15C4×C5×SD16—22no—
16C2×C4×C5×C8C2211yescharacteristic
17C2×#3969—21no—
18C2×#3969—21no—
19#65313—21no—
20#65313—22no—
21Q8×#168—21no—
22#65288—21no—
23#65286—21no—
24C4×C4⋊Dic5C2211yescharacteristic
25#65214C2211yescharacteristic
26C2×C4⋊#168C2211yescharacteristic
27C4×#681C2211yescharacteristic
28#64758—22no—
29D4⋊#168—21no—
30D4⋊#168—21no—
31#9054—51nomaximal, Sylow
32C2×C5×#41—21no—
33C2×C5×SD16—22no—
34C22×C5×C8—21no—
35C5×C4⋊Q8C2×C411yescharacteristic
36C5×C4⋊Q8C2×C411yescharacteristic
37C5×C4⋊Q8C2×C411yescharacteristic
38C5×#127C2×C411yescharacteristic
39C5×#125—21no—
40C5×#124—21no—
41C5×C22⋊Q8—21no—
42C5×C22⋊Q8D412yes—
43C5×#121—21no—
44C5×#121—21no—
45C4×C5×Q8—21no—
46C4×C5×Q8D412yes—
47C4×C5×D4—21no—
48C4×C5×D4—21no—
49C5×#117—21no—
50C2×C42×C5C2311yescharacteristic
51C2×C4⋊Dic5—21no—
52C2×C4×Dic5—21no—
53C2×#681D411yescharacteristic
54C2×#681D411yescharacteristic
55C22×#168—21no—
56C5×#106—22no—
57C5×#103—22no—
58C5×#102—22no—
59C4×C5×C8—21no—
60C4×C5×C8C2×C411yescharacteristic
61C4×C5×C8C2×C411yescharacteristic
62#3969—42no—
63#3969—42no—
64#3963—21no—
65C22⋊#168—21no—
66C4⋊#168—22no—
67C4⋊#168—22no—
68C4⋊#168—21no—
69C4⋊#168—21no—
70C4⋊#168D411yescharacteristic
71C4⋊#168D411yescharacteristic
72#3935—22no—
73#3935—21no—
74C4×#168—22no—
75C4×#168—21no—
76C4×#168—21no—
77#3167D511yescharacteristic
78#2962—51no—
79#1980—51no—
80#1503—51no—
81#1480—51no—
82#1279—51no—
83#1278—51no—
84C5×#41—41no—
85C5×#41—41no—
86C5×#41—41no—
87C5×#41—41no—
88C2×C5×Q8—21no—
89C2×C5×Q8—21no—
90C2×C5×Q8C22⋊C412yes—
91C2×C5×D4—21no—
92C2×C5×D4—21no—
93C2×C5×D4—21no—
94C2×C5×D4—41no—
95C22×C4×C5—41no—
96C22×C4×C5C2×D411yescharacteristic
97C22×C4×C5C2×D411yescharacteristic
98C22×C4×C5#4111yescharacteristic
99C22×Dic5—41no—
100C5×SD16—44no—
101C2×C5×C8—21no—
102C2×C5×C8—21no—
103C2×C5×C8—42no—
104C5×C4⋊C4—21no—
105C5×C4⋊C4—21no—
106C5×C4⋊C4—21no—
107C5×C4⋊C4—22no—
108C5×C4⋊C4—22no—
109C5×C4⋊C4—21no—
110C5×C4⋊C4—21no—
111C5×C4⋊C4C22⋊C412yes—
112C5×C22⋊C4—22no—
113C5×C22⋊C4—41no—
114C5×C22⋊C4—41no—
115C42×C5—22no—
116C42×C5C22×C411yescharacteristic
117C42×C5C2×D411yescharacteristic
118C42×C5C2×D411yescharacteristic
119C42×C5#4111yescharacteristic
120C4⋊Dic5—22no—
121C4⋊Dic5—41no—
122C4×Dic5—41no—
123C4×Dic5—41no—
124#681—21no—
125#681—21no—
126#681—21no—
127#681SD1612yescomplemented
128C2×#168—21no—
129C2×#168—21no—
130C2×#168—21no—
131C2×#168—21no—
132C2×#168—41no—
133C2×#168—41no—
134C2×#168—41no—
135#533C2×D511yescharacteristic
136#532C2×D511yescharacteristic
137#498Dic511yescharacteristic, complemented
138#492Dic511yescharacteristic, complemented
139#487Dic511yescharacteristic, complemented
140#486Dic511yescharacteristic, complemented
141#465—22no—
142#446—101no—
143#446—102no—
144C8×Q8—101no—
145C4×SD16—22no—
146#431—51no—
147#424—101no—
148C2×C4⋊C8—51no—
149C2×#104—101no—
150C2×#104—101no—
151#405—101no—
152C4×M16—51no—
153C2×C4×C8C2×D511yescharacteristic
154C4×C4⋊C4—51no—
155#328—102no—
156D4⋊C8—101no—
157D4⋊C8—101no—
158C23×C5—41no—
159C23×C5#12111yescharacteristic
160C5×Q8—42no—
161C5×Q8—41no—
162C5×Q8—41no—
163C5×Q8—41no—
164C5×Q8—41no—
165C5×D4—42no—
166C5×D4—41no—
167C5×D4—41no—
168C5×D4—41no—
169C5×D4—41no—
170C5×D4—81no—
171C5×D4—81no—
172C2×C4×C5—21no—
173C2×C4×C5—21no—
174C2×C4×C5—22no—
175C2×C4×C5—22no—
176C2×C4×C5—41no—
177C2×C4×C5—41no—
178C2×C4×C5—81no—
179C2×C4×C5—81no—
180C2×C4×C5C2×C22⋊C411yescharacteristic
181C2×C4×C5C4×D411yescharacteristic
182C2×C4×C5C4×D411yescharacteristic
183C2×C4×C5#12011yescharacteristic
184C2×C4×C5#12111yescharacteristic
185C2×C4×C5#12311yescharacteristic
186C2×C4×C5C2×SD1611yescharacteristic
187C2×C4×C5#13511yescharacteristic
188C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
189C2×C4×C5#13711yescharacteristic
190C2×Dic5—42no—
191C2×Dic5—81no—
192C2×Dic5—81no—
193C5×C8—22no—
194C5×C8—41no—
195#168—22no—
196#168—41no—
197#168—41no—
198#168—41no—
199#168—81no—
200C2×#41—21no—
201C2×SD16—22no—
202C2×M16—51no—
203C2×M16—51no—
204C22×C8—21no—
205C22×C8—101no—
206C4⋊Q8C2×Dic511yescharacteristic
207C4⋊Q8C2×Dic511yescharacteristic
208C4⋊Q8C2×Dic511yescharacteristic
209#127C2×Dic511yescharacteristic
210#125—21no—
211#124—21no—
212C22⋊Q8—21no—
213C22⋊Q8C22⋊D512yes—
214#121—21no—
215#121—21no—
216C4×Q8—21no—
217C4×Q8C22⋊D512yes—
218C4×D4—21no—
219C4×D4—21no—
220#117—21no—
221C2×C4⋊C4—101no—
222C2×C42—101no—
223C2×C42C22×D511yescharacteristic
224#106—22no—
225C4⋊C8—51no—
226C4⋊C8—51no—
227C4⋊C8—102no—
228C4⋊C8—102no—
229C4⋊C8—101no—
230C4⋊C8—101no—
231#104—202no—
232#104—202no—
233#103—22no—
234#102—22no—
235C22⋊C8—101no—
236#97—102no—
237#97—101no—
238C4×C8—21no—
239C4×C8—102no—
240C4×C8—101no—
241C4×C8—101no—
242C4×C8C2×Dic511yescharacteristic
243C4×C8C2×Dic511yescharacteristic
244#95—101no—
245C22×C5—21no—
246C22×C5—21no—
247C22×C5—81no—
248C22×C5—81no—
249C22×C5—81no—
250C22×C5#38611yescharacteristic
251C22×C5#46011yescharacteristic
252C22×C5#46411yescharacteristic
253C4×C5—21no—
254C4×C5—21no—
255C4×C5—21no—
256C4×C5—42no—
257C4×C5—42no—
258C4×C5—81no—
259C4×C5C4×SD1611yescharacteristic
260C4×C5#44011yescharacteristic
261C4×C5#44311yescharacteristic
262C4×C5#44411yescharacteristic
263C4×C5#44811yescharacteristic
264C4×C5#44911yescharacteristic
265Dic5—82no—
266#41—41no—
267#41—41no—
268#41—41no—
269#41—41no—
270C2×Q8—21no—
271C2×Q8—21no—
272C2×Q8C22⋊Dic512yes—
273C2×D4—21no—
274C2×D4—21no—
275C2×D4—21no—
276C2×D4—41no—
277C22×C4—41no—
278C22×C4—201no—
279C22×C4D4×D511yescharacteristic
280C22×C4#71111yescharacteristic
281C22×C4C2×C22⋊D511yescharacteristic
282SD16—44no—
283M16—52no—
284M16—101no—
285M16—101no—
286M16—101no—
287C2×C8—21no—
288C2×C8—21no—
289C2×C8—42no—
290C2×C8—101no—
291C2×C8—101no—
292C2×C8—101no—
293C2×C8—101no—
294C2×C8—201no—
295C2×C8—201no—
296C2×C8—201no—
297C4⋊C4—21no—
298C4⋊C4—21no—
299C4⋊C4—21no—
300C4⋊C4—22no—
301C4⋊C4—22no—
302C4⋊C4—21no—
303C4⋊C4—21no—
304C4⋊C4—102no—
305C4⋊C4—201no—
306C4⋊C4C22⋊Dic512yes—
307C22⋊C4—22no—
308C22⋊C4—41no—
309C22⋊C4—41no—
310C42—22no—
311C42—201no—
312C42—201no—
313C42D4×D511yescharacteristic
314C42#71111yescharacteristic
315C42C22×Dic511yescharacteristic
316C42C2×C22⋊D511yescharacteristic
317C2×C5—21no—
318C2×C5—21no—
319C2×C5—161no—
320C2×C5#187611yescharacteristic
321C2×C5#188011yescharacteristic
322C2×C5#188411yescharacteristic
323C23—41no—
324C23#408511yescharacteristic
325Q8—42no—
326Q8—41no—
327Q8—41no—
328Q8—41no—
329Q8—41no—
330D4—42no—
331D4—41no—
332D4—41no—
333D4—41no—
334D4—41no—
335D4—81no—
336D4—81no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—22no—
340C2×C4—22no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—81no—
344C2×C4—81no—
345C2×C4—202no—
346C2×C4—401no—
347C2×C4—401no—
348C2×C4D5×SD1611yescharacteristic
349C2×C4#406011yescharacteristic
350C2×C4#406111yescharacteristic
351C2×C4#406211yescharacteristic
352C2×C4D4×Dic511yescharacteristic
353C2×C4D4×Dic511yescharacteristic
354C2×C4#408111yescharacteristic
355C2×C4#408311yescharacteristic
356C2×C4#408511yescharacteristic
357C2×C4C2×C22⋊Dic511yescharacteristic
358C8—22no—
359C8—41no—
360C8—102no—
361C8—201no—
362C8—201no—
363C8—201no—
364C8—401no—
365C5#905411yescharacteristic, complemented, Sylow
366C22—21no—
367C22—21no—
368C22—81no—
369C22—81no—
370C22—81no—
371C22#6545211yescharacteristic
372C22#6545511yescharacteristic
373C22#6550911yescharacteristic
374C4—21no—
375C4—21no—
376C4—21no—
377C4—42no—
378C4—42no—
379C4—81no—
380C4—402no—
381C4SD16×Dic511yescharacteristic
382C4#6545311yescharacteristic
383C4#6545911yescharacteristic
384C4#6546111yescharacteristic
385C4#6548511yescharacteristic
386C4#6548611yescharacteristic
387C2—21no—
388C2—21no—
389C2—161no—
390C2#1060261011yescharacteristic
391C2#1060284111yescharacteristic
392C2#1060288011yescharacteristic
subgroupG/H
centerC2×C4#4083
commutatorC42×C5C22×C4
FrattiniC2×C42C22×D5
FittingC5×#3167C2
socleC22×C5#386
prime radicalC5×#532C22
cosocleC2×C42×C5C23
hypercenter#3167D5
hypocenterC5#9054
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3167

Complements

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

NH ≅ G/Ntype
2. #10615061C2semidirect
3. #10602628C2semidirect
6. #10598147C2semidirect
7. #10598146C2semidirect
10. C5×#498C4semidirect
11. C5×#492C4semidirect
12. C5×#487C4semidirect
13. C5×#486C4semidirect
127. #681SD16semidirect
137. #498Dic5semidirect
138. #492Dic5semidirect
139. #487Dic5semidirect
140. #486Dic5semidirect
365. C5#9054semidirect

Maximal subgroups

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

subgroupindex
C5×#31672
#106150612
#106026282
#106026112
#106025932
#105981472
#105981462
#90545