Finite Group Databasebeta

← #12003521

Subgroups — #12003521

Order 1280.

490 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65377C211yesmaximal, characteristic
2C2×C5×#333C211yesmaximal, characteristic, complemented
3#10602572C211yesmaximal, characteristic, complemented
4#10601261C211yesmaximal, characteristic, complemented
5#10601250C211yesmaximal, characteristic
6C2×#64705C211yesmaximal, characteristic
7#10598194C211yesmaximal, characteristic, complemented
8C2×C5×C4⋊Q8C2211yescharacteristic
9C2×#4020C2211yescharacteristic
10C2×C5×C4⋊C8C2211yescharacteristic
11C2×C5×C4⋊C8C2211yescharacteristic
12C2×#3953—21no—
13C2×#3953—21no—
14C2×#3946—21no—
15#65377—22no—
16#65377—22no—
17C2×#3941—21no—
18C2×#3941—21no—
19C4×C4⋊Dic5C2211yescharacteristic
20C2×C4⋊#168C2211yescharacteristic
21C2×C4×#168C2211yescharacteristic
22C5×#333—22no—
23#64770—21no—
24#64749—21no—
25#64749—21no—
26#64705—22no—
27#10539—51nomaximal, Sylow
28C22×C5×Q8—21no—
29C22×D20—21no—
30C22×D20—21no—
31C22×D20—21no—
32C22×C5×C8—21no—
33C22×C5×C8—21no—
34C5×C4⋊Q8—21no—
35C5×C4⋊Q8—21no—
36C5×C4⋊Q8—21no—
37C5×C4⋊Q8D412yes—
38C2×C5×C4⋊C4—21no—
39C2×C5×C4⋊C4—21no—
40C2×C42×C5C2311yescharacteristic
41C2×C4⋊Dic5D411yescharacteristic
42C2×C4⋊Dic5D411yescharacteristic
43C2×C4×Dic5—21no—
44C22×#168—21no—
45C22×#168D411yescharacteristic
46C22×#168D411yescharacteristic
47#4020—21no—
48#4020—21no—
49#4020—21no—
50#4020D412yes—
51C5×C4⋊C8—21no—
52C5×C4⋊C8—21no—
53C5×C4⋊C8—21no—
54C5×C4⋊C8—21no—
55#3963—21no—
56#3953—42no—
57#3953—42no—
58#3946—42no—
59#3941—24no—
60#3941—24no—
61C4⋊#168—21no—
62C4⋊#168—21no—
63C4×#168—21no—
64C4×#168—21no—
65C2×#486—51no—
66#1987—51no—
67#1982—51no—
68#1939—51no—
69C2×#333D511yescharacteristic, complemented
70C2×#331—51no—
71#1277—51no—
72C23×D5—41no—
73C2×C5×Q8—22no—
74C2×C5×Q8—41no—
75C2×C5×Q8—81no—
76C2×C5×Q8—81no—
77C22×C4×C5—41no—
78C22×C4×C5C2×D411yescharacteristic
79C22×C4×C5C2×D411yescharacteristic
80C22×C4×C5#4111yescharacteristic
81C22×Dic5—21no—
82C22×Dic5—21no—
83C2×D20—22no—
84C2×D20—22no—
85C2×D20—22no—
86C2×D20—41no—
87C2×D20—41no—
88C2×D20—41no—
89C2×D20—41no—
90C2×D20—41no—
91C2×D20—41no—
92C2×D20—41no—
93C2×D20—41no—
94C2×D20—41no—
95C2×D20—41no—
96C2×D20—41no—
97C2×D20—81no—
98C2×D20—81no—
99C2×C5×C8—41no—
100C2×C5×C8—41no—
101C2×C5×C8—41no—
102C2×C5×C8—41no—
103C2×C5×C8—41no—
104C2×C5×C8—41no—
105C5×C4⋊C4—22no—
106C5×C4⋊C4—22no—
107C5×C4⋊C4—41no—
108C5×C4⋊C4—41no—
109C42×C5C2×D411yescharacteristic
110C42×C5C2×D411yescharacteristic
111C42×C5#4111yescharacteristic
112C42×C5#4111yescharacteristic
113C4⋊Dic5—21no—
114C4⋊Dic5—21no—
115C4⋊Dic5—21no—
116C4⋊Dic5SD1612yes—
117C4×Dic5—41no—
118C4×Dic5—41no—
119C2×#168—21no—
120C2×#168—21no—
121C2×#168—21no—
122C2×#168—21no—
123C2×#168—21no—
124C2×#168—21no—
125C2×#168—41no—
126C2×#168—41no—
127C2×#168—41no—
128C2×C4⋊Q8C2×D511yescharacteristic
129C2×#127—51no—
130#486—102no—
131#486—102no—
132C2×C4⋊C8—51no—
133C2×C4⋊C8—101no—
134C2×C4⋊C8C2×D511yescharacteristic
135C2×C4⋊C8C2×D511yescharacteristic
136C2×#102—101no—
137C2×#102—101no—
138C2×#102—101no—
139C2×#102—101no—
140C2×C4×C8—51no—
141C4×C4⋊C4—51no—
142#340—101no—
143#340—101no—
144#336—101no—
145#333—22no—
146#331—102no—
147C23×C5#12111yescharacteristic
148C22×D5—42no—
149C22×D5—81no—
150C22×D5—81no—
151C22×D5—81no—
152C22×D5—81no—
153C22×D5—81no—
154C22×D5—81no—
155C5×Q8—82no—
156C5×Q8—82no—
157C2×C4×C5—21no—
158C2×C4×C5—21no—
159C2×C4×C5—42no—
160C2×C4×C5—81no—
161C2×C4×C5—81no—
162C2×C4×C5#12011yescharacteristic
163C2×C4×C5#12111yescharacteristic
164C2×C4×C5#12111yescharacteristic
165C2×C4×C5#12311yescharacteristic
166C2×C4×C5#12311yescharacteristic
167C2×C4×C5#12411yescharacteristic
168C2×C4×C5C2×SD1611yescharacteristic
169C2×C4×C5#13511yescharacteristic
170C2×C4×C5#13511yescharacteristic
171C2×C4×C5#13511yescharacteristic
172C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
173C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
174C2×C4×C5#13711yescharacteristic
175C2×C4×C5#13711yescharacteristic
176C2×Dic5—22no—
177C2×Dic5—41no—
178C2×Dic5—41no—
179C2×Dic5—41no—
180C2×Dic5—41no—
181C2×Dic5—41no—
182D20—42no—
183D20—42no—
184D20—42no—
185D20—42no—
186D20—82no—
187D20—82no—
188D20—81no—
189D20—81no—
190D20—81no—
191D20—81no—
192C5×C8—81no—
193C5×C8—81no—
194#168—41no—
195#168—41no—
196#168—81no—
197C22×Q8—21no—
198C22×D4—101no—
199C22×D4—101no—
200C22×D4—101no—
201C22×C8—21no—
202C22×C8—21no—
203C22×C8—51no—
204C22×C8—51no—
205C22×C8—101no—
206C4⋊Q8—21no—
207C4⋊Q8—21no—
208C4⋊Q8—21no—
209C4⋊Q8C22⋊D512yes—
210#127—52no—
211#127—101no—
212#127—101no—
213#127—101no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—21no—
216C2×C4⋊C4—51no—
217C2×C4⋊C4—51no—
218C2×C42—101no—
219C2×C42C22×D511yescharacteristic
220C4⋊C8—21no—
221C4⋊C8—21no—
222C4⋊C8—21no—
223C4⋊C8—21no—
224C4⋊C8—101no—
225C4⋊C8—101no—
226C4⋊C8—202no—
227#102—104no—
228#102—104no—
229#102—202no—
230#102—202no—
231C4×C8—101no—
232C4×C8—101no—
233#95—101no—
234C22×C5#39411yescharacteristic
235C22×C5#46311yescharacteristic
236C22×C5#46411yescharacteristic
237C22×C5#46511yescharacteristic
238C22×C5#46811yescharacteristic
239C22×C5#47211yescharacteristic
240C22×C5#47211yescharacteristic
241C2×D5—82no—
242C2×D5—82no—
243C2×D5—82no—
244C2×D5—161no—
245C2×D5—161no—
246C2×D5—161no—
247C2×D5—161no—
248C4×C5—21no—
249C4×C5—21no—
250C4×C5—82no—
251C4×C5#44911yescharacteristic
252C4×C5#45211yescharacteristic
253C4×C5#46011yescharacteristic
254C4×C5#46111yescharacteristic
255C4×C5#46311yescharacteristic
256C4×C5#46411yescharacteristic
257C4×C5#48811yescharacteristic
258C4×C5#48911yescharacteristic
259Dic5—42no—
260Dic5—81no—
261C24—201no—
262C2×Q8—22no—
263C2×Q8—41no—
264C2×Q8—81no—
265C2×Q8—81no—
266C2×D4—102no—
267C2×D4—102no—
268C2×D4—102no—
269C2×D4—201no—
270C2×D4—201no—
271C2×D4—201no—
272C2×D4—201no—
273C2×D4—201no—
274C2×D4—201no—
275C2×D4—201no—
276C2×D4—201no—
277C2×D4—201no—
278C2×D4—201no—
279C2×D4—201no—
280C2×D4—401no—
281C2×D4—401no—
282C22×C4—41no—
283C22×C4—101no—
284C22×C4—101no—
285C22×C4#70911yescharacteristic
286C22×C4D4×D511yescharacteristic
287C22×C4D4×D511yescharacteristic
288C2×C8—41no—
289C2×C8—41no—
290C2×C8—41no—
291C2×C8—41no—
292C2×C8—41no—
293C2×C8—41no—
294C2×C8—101no—
295C2×C8—101no—
296C2×C8—101no—
297C2×C8—101no—
298C2×C8—101no—
299C2×C8—101no—
300C2×C8—201no—
301C2×C8—201no—
302C2×C8—201no—
303C4⋊C4—22no—
304C4⋊C4—22no—
305C4⋊C4—41no—
306C4⋊C4—41no—
307C4⋊C4—52no—
308C4⋊C4—101no—
309C4⋊C4—101no—
310C4⋊C4—101no—
311C42—201no—
312C42—201no—
313C42#70911yescharacteristic
314C42D4×D511yescharacteristic
315C42#71111yescharacteristic
316C42C2×C22⋊D511yescharacteristic
317C2×C5#167711yescharacteristic
318C2×C5#167811yescharacteristic
319C2×C5#169711yescharacteristic
320C2×C5#169811yescharacteristic
321C2×C5#204211yescharacteristic
322C2×C5#204511yescharacteristic
323C2×C5#205511yescharacteristic
324D5—162no—
325C23—202no—
326C23—401no—
327C23—401no—
328C23—401no—
329C23—401no—
330C23—401no—
331C23—401no—
332C23#403011yescharacteristic
333Q8—82no—
334Q8—82no—
335D4—202no—
336D4—202no—
337D4—202no—
338D4—202no—
339D4—402no—
340D4—402no—
341D4—401no—
342D4—401no—
343D4—401no—
344D4—401no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—42no—
348C2×C4—81no—
349C2×C4—81no—
350C2×C4—102no—
351C2×C4—201no—
352C2×C4—201no—
353C2×C4—201no—
354C2×C4—201no—
355C2×C4—201no—
356C2×C4#402911yescharacteristic
357C2×C4#403011yescharacteristic
358C2×C4#403111yescharacteristic
359C2×C4D5×SD1611yescharacteristic
360C2×C4#406011yescharacteristic
361C2×C4#406011yescharacteristic
362C2×C4#406211yescharacteristic
363C2×C4#406411yescharacteristic
364C2×C4#406411yescharacteristic
365C2×C4#406511yescharacteristic
366C2×C4#406511yescharacteristic
367C2×C4#407511yescharacteristic
368C2×C4#408311yescharacteristic
369C2×C4#408511yescharacteristic
370C8—81no—
371C8—81no—
372C8—201no—
373C8—201no—
374C8—401no—
375C5#1053911yescharacteristic, complemented, Sylow
376C22—402no—
377C22—402no—
378C22—402no—
379C22—801no—
380C22—801no—
381C22—801no—
382C22—801no—
383C22#6503811yescharacteristic
384C22#6503811yescharacteristic
385C22#6508711yescharacteristic
386C22#6509611yescharacteristic
387C22#6510111yescharacteristic
388C22#6510811yescharacteristic
389C22#6524811yescharacteristic
390C4—21no—
391C4—21no—
392C4—82no—
393C4—202no—
394C4—401no—
395C4#6508411yescharacteristic
396C4#6508911yescharacteristic
397C4#6510711yescharacteristic
398C4#6510811yescharacteristic
399C4#6545211yescharacteristic
400C4#6546111yescharacteristic
401C4#6547411yescharacteristic
402C4#6547611yescharacteristic
403C2—802no—
404C2#1059929111yescharacteristic
405C2#1059929511yescharacteristic
406C2#1059930311yescharacteristic
407C2#1059930711yescharacteristic
408C2#1060087611yescharacteristic
409C2#1060107211yescharacteristic
410C2#1060107311yescharacteristic
subgroupG/H
centerC23#4030
commutator, cosocleC2×C42×C5C23
FrattiniC2×C42C22×D5
FittingC2×C5×#333C2
socleC23×C5#121
prime radicalC2×#4020C22
hypercenterC2×#333D5
hypocenterC5#10539
LCSG ▷ C2×C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#333

Complements

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

NH ≅ G/Ntype
2. C2×C5×#333C2semidirect
3. #10602572C2semidirect
4. #10601261C2semidirect
7. #10598194C2semidirect
69. C2×#333D5semidirect
375. C5#10539semidirect

Maximal subgroups

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

subgroupindex
C2×#653772
C2×C5×#3332
#106025722
#106012612
#106012502
C2×#647052
#105981942
#105395