Finite Group Databasebeta

← #11989238

Subgroups — #11989238

Order 1280.

522 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10611062C211yesmaximal, characteristic
2D5×#432C211yesmaximal, characteristic
3#10610248C211yesmaximal, characteristic
4C5×#1291C211yesmaximal, characteristic, complemented
5#10598245C211yesmaximal, characteristic, complemented
6#10598244C211yesmaximal, characteristic, complemented
7#10598161C211yesmaximal, characteristic, complemented
8C2×C42×D5C2211yescharacteristic
9C5×#432C2211yescharacteristic
10C5×#432C2211yescharacteristic
11C4×C5×M16C2211yescharacteristic
12#65415—21no—
13#65407—21no—
14#65215C2211yescharacteristic
15#65215C2211yescharacteristic
16C4×#681C2211yescharacteristic
17#65126C412yes—
18#65124—21no—
19#65122C412yes—
20D5×C4⋊C8—21no—
21#65015—21no—
22D5×C22⋊C8C412yes—
23#65008C412yes—
24#65007—21no—
25#64996—21no—
26#64994—21no—
27#64994—21no—
28#64994—21no—
29#64994—21no—
30D5×#97—21no—
31#64974C412yes—
32#64974C412yes—
33#7998—51nomaximal, Sylow
34C22×C4×D5C2×C411yescharacteristic
35C22×C4×D5D411yescharacteristic
36C22×C4×D5Q811yescharacteristic
37C2×C5×M16—21no—
38C2×C42×C5C2311yescharacteristic
39C2×C4×Dic5C2×C411yescharacteristic
40C2×C4×Dic5D411yescharacteristic
41C2×C4×Dic5Q811yescharacteristic
42C2×#681—21no—
43C2×#676—22no—
44C2×C8×D5—22no—
45C42×D5C2×C411yescharacteristic
46C42×D5C2×C411yescharacteristic
47C42×D5C2×C411yescharacteristic
48C42×D5C2×C411yescharacteristic
49C42×D5D411yescharacteristic
50C42×D5D411yescharacteristic
51C42×D5D411yescharacteristic
52C42×D5D411yescharacteristic
53C5×C4⋊C8—21no—
54C5×C4⋊C8C2×C412yes—
55C5×C22⋊C8—21no—
56C5×C22⋊C8C2×C412yes—
57C5×#97—21no—
58C5×#97—21no—
59C5×#97—21no—
60C4×C5×C8C2×C412yes—
61C22⋊#168—21no—
62C22⋊#168C2×C412yes—
63#3952—22no—
64#3952—22no—
65#3952—22no—
66#3952—22no—
67#3947—22no—
68#3946—22no—
69#3946—22no—
70#3946—22no—
71#3946—22no—
72C8×Dic5—22no—
73C4⋊#168—21no—
74C4⋊#168C2×C412yes—
75#3935—21no—
76#3935—21no—
77#3935—21no—
78C4×#168C2×C412yes—
79#2920—51no—
80#2920—51no—
81C2×#432—51no—
82#1291—51no—
83#1291—51no—
84#1291—51no—
85#1291D511yescharacteristic, complemented
86C23×D5C4⋊C411yescharacteristic
87C22×C4×C5C22×C411yescharacteristic
88C22×C4×C5C2×D411yescharacteristic
89C22×C4×C5C2×Q811yescharacteristic
90C22×Dic5C4⋊C411yescharacteristic
91C22×Dic5C4⋊C411yescharacteristic
92C22×Dic5C4⋊C411yescharacteristic
93C2×C4×D5—42no—
94C2×C4×D5—42no—
95C2×C4×D5—42no—
96C2×C4×D5C4211yescharacteristic
97C2×C4×D5C4211yescharacteristic
98C2×C4×D5C22⋊C411yescharacteristic
99C2×C4×D5C22⋊C411yescharacteristic
100C2×C4×D5C22⋊C411yescharacteristic
101C2×C4×D5C22⋊C411yescharacteristic
102C2×C4×D5C22⋊C411yescharacteristic
103C2×C4×D5C22⋊C411yescharacteristic
104C2×C4×D5C4⋊C411yescharacteristic
105C2×C4×D5C4⋊C411yescharacteristic
106C2×C4×D5C4⋊C411yescharacteristic
107C2×C4×D5C4⋊C411yescharacteristic
108C5×M16—42no—
109C2×C5×C8—22no—
110C2×C5×C8—22no—
111C2×C5×C8—22no—
112C42×C5C22×C411yescharacteristic
113C42×C5C22×C411yescharacteristic
114C42×C5C2×D411yescharacteristic
115C42×C5C2×D411yescharacteristic
116C4×Dic5C4211yescharacteristic
117C4×Dic5C4211yescharacteristic
118C4×Dic5C22⋊C411yescharacteristic
119C4×Dic5C22⋊C411yescharacteristic
120C4×Dic5C22⋊C411yescharacteristic
121C4×Dic5C22⋊C411yescharacteristic
122C4×Dic5C22⋊C411yescharacteristic
123C4×Dic5C22⋊C411yescharacteristic
124C4×Dic5C4⋊C411yescharacteristic
125C4×Dic5C4⋊C411yescharacteristic
126C4×Dic5C4⋊C411yescharacteristic
127C4×Dic5C4⋊C411yescharacteristic
128#681—42no—
129C2×#168—22no—
130C2×#168—22no—
131C2×#168—22no—
132#676—44no—
133C8×D5—44no—
134C22×C42—51no—
135#432—51no—
136#432—52no—
137#432—51no—
138#432—101no—
139#432—101no—
140#432—101no—
141#432—101no—
142#432—101no—
143#432C2×D511yescharacteristic
144#432C2×D511yescharacteristic
145#431—52no—
146#431—52no—
147#431—52no—
148#431—101no—
149#423—52no—
150#423—101no—
151C2×C4⋊C8—101no—
152#407—101no—
153#407—101no—
154C2×C22⋊C8—52no—
155C4×M16—51no—
156C4×M16—101no—
157C4×M16C2×D511yescharacteristic
158C2×#97—101no—
159C23×C5C2×C4⋊C411yescharacteristic
160C22×D5—22no—
161C22×D5—41no—
162C22×D5—41no—
163C22×D5#9511yescharacteristic
164C22×D5#9511yescharacteristic
165C2×C4×C5—22no—
166C2×C4×C5—41no—
167C2×C4×C5—41no—
168C2×C4×C5C2×C4211yescharacteristic
169C2×C4×C5C2×C22⋊C411yescharacteristic
170C2×C4×C5C2×C22⋊C411yescharacteristic
171C2×C4×C5C2×C22⋊C411yescharacteristic
172C2×C4×C5C2×C4⋊C411yescharacteristic
173C2×C4×C5C2×C4⋊C411yescharacteristic
174C2×Dic5—22no—
175C2×Dic5—41no—
176C2×Dic5—41no—
177C2×Dic5#9511yescharacteristic
178C2×Dic5#9511yescharacteristic
179C2×Dic5#9511yescharacteristic
180C2×Dic5#9511yescharacteristic
181C2×Dic5#9511yescharacteristic
182C2×Dic5#9511yescharacteristic
183C4×D5—22no—
184C4×D5—22no—
185C4×D5—22no—
186C4×D5—22no—
187C4×D5—22no—
188C4×D5—22no—
189C4×D5—41no—
190C4×D5—41no—
191C4×D5—41no—
192C4×D5—41no—
193C4×D5—41no—
194C4×D5—41no—
195C5×C8—42no—
196C5×C8—42no—
197C5×C8—42no—
198#168—42no—
199#168—42no—
200#168—42no—
201C23×C4—51no—
202C23×C4—51no—
203C23×C4—51no—
204C2×M16—21no—
205C2×M16—102no—
206C2×M16—101no—
207C22×C8—102no—
208C2×C42—51no—
209C2×C42—51no—
210C2×C42—51no—
211C2×C42—51no—
212C2×C42—51no—
213C2×C42—51no—
214C2×C42—51no—
215C2×C42—51no—
216C2×C42—51no—
217C2×C42—51no—
218C2×C42—51no—
219C2×C42C22×D511yescharacteristic
220C4⋊C8—21no—
221C4⋊C8—52no—
222C4⋊C8—102no—
223C4⋊C8—102no—
224C4⋊C8—102no—
225C4⋊C8—102no—
226C4⋊C8—101no—
227C4⋊C8C4×D512yes—
228C22⋊C8—21no—
229C22⋊C8—52no—
230C22⋊C8—102no—
231C22⋊C8—102no—
232C22⋊C8—102no—
233C22⋊C8—102no—
234C22⋊C8—101no—
235C22⋊C8C4×D512yes—
236#97—21no—
237#97—21no—
238#97—21no—
239#97—102no—
240#97—101no—
241#97—101no—
242#97—101no—
243C4×C8—52no—
244C4×C8—102no—
245C4×C8C4×D512yes—
246C22×C5—21no—
247C22×C5—21no—
248C22×C5—21no—
249C22×C5C2×#9511yescharacteristic
250C2×D5—21no—
251C2×D5—21no—
252C2×D5—21no—
253C2×D5—21no—
254C2×D5—21no—
255C2×D5—44no—
256C2×D5#33812yes—
257C4×C5—21no—
258C4×C5—21no—
259C4×C5—21no—
260C4×C5—21no—
261C4×C5—21no—
262C4×C5#42112yes—
263Dic5—21no—
264Dic5—21no—
265Dic5—21no—
266Dic5—21no—
267Dic5—21no—
268Dic5#34412yes—
269C24—51no—
270C22×C4—51no—
271C22×C4—51no—
272C22×C4—51no—
273C22×C4—51no—
274C22×C4—51no—
275C22×C4—51no—
276C22×C4—51no—
277C22×C4—51no—
278C22×C4—51no—
279C22×C4—51no—
280C22×C4—51no—
281C22×C4—51no—
282C22×C4—51no—
283C22×C4—51no—
284C22×C4—51no—
285C22×C4—202no—
286C22×C4—202no—
287C22×C4—202no—
288C22×C4C2×C4×D511yescharacteristic
289C22×C4D4×D511yescharacteristic
290C22×C4Q8×D511yescharacteristic
291M16—42no—
292M16—204no—
293M16—202no—
294C2×C8—22no—
295C2×C8—22no—
296C2×C8—22no—
297C2×C8—102no—
298C2×C8—102no—
299C2×C8—102no—
300C2×C8—204no—
301C42—51no—
302C42—51no—
303C42—51no—
304C42—51no—
305C42—51no—
306C42—51no—
307C42—51no—
308C42—51no—
309C42—51no—
310C42—51no—
311C42—51no—
312C42—51no—
313C42C2×C4×D511yescharacteristic
314C42C2×C4×D511yescharacteristic
315C42D4×D511yescharacteristic
316C42D4×D511yescharacteristic
317C2×C5—41no—
318C2×C5C2×#33811yescharacteristic
319C2×C5#173311yescharacteristic
320C2×C5C2×#34411yescharacteristic
321D5—22no—
322D5—41no—
323C23—51no—
324C23—51no—
325C23—102no—
326C23—201no—
327C23—201no—
328C23D5×C4⋊C411yescharacteristic
329C2×C4—22no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—51no—
333C2×C4—51no—
334C2×C4—51no—
335C2×C4—51no—
336C2×C4—51no—
337C2×C4—51no—
338C2×C4—102no—
339C2×C4—102no—
340C2×C4—102no—
341C2×C4—102no—
342C2×C4—102no—
343C2×C4—102no—
344C2×C4—102no—
345C2×C4—201no—
346C2×C4—201no—
347C2×C4—201no—
348C2×C4—201no—
349C2×C4—201no—
350C2×C4—201no—
351C2×C4—201no—
352C2×C4—201no—
353C2×C4C42×D511yescharacteristic
354C2×C4D5×C22⋊C411yescharacteristic
355C2×C4D5×C22⋊C411yescharacteristic
356C2×C4D5×C22⋊C411yescharacteristic
357C2×C4D5×C4⋊C411yescharacteristic
358C2×C4D5×C4⋊C411yescharacteristic
359C8—42no—
360C8—42no—
361C8—42no—
362C8—202no—
363C8—202no—
364C8—202no—
365C5#799811yescharacteristic, complemented, Sylow
366C22—21no—
367C22—21no—
368C22—21no—
369C22—52no—
370C22—101no—
371C22—101no—
372C22—101no—
373C22—101no—
374C22—101no—
375C22—204no—
376C22D5×#9511yescharacteristic
377C4—21no—
378C4—21no—
379C4—21no—
380C4—21no—
381C4—21no—
382C4—52no—
383C4—101no—
384C4—101no—
385C4—101no—
386C4—101no—
387C4—101no—
388C4#6511012yes—
389C2—41no—
390C2—102no—
391C2—201no—
392C2D5×#33811yescharacteristic
393C2#1059954611yescharacteristic
394C2D5×#34411yescharacteristic
subgroupG/H
centerC22D5×#95
commutatorC2×C4×C5C2×C42
FrattiniC2×C42C22×D5
FittingC5×#1291C2
socleC22×C5C2×#95
prime radicalC23×D5C4⋊C4
cosocleC2×C42×C5C23
hypercenter#1291D5
hypocenterC5#7998
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1291

Complements

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

NH ≅ G/Ntype
4. C5×#1291C2semidirect
5. #10598245C2semidirect
6. #10598244C2semidirect
7. #10598161C2semidirect
85. #1291D5semidirect
365. C5#7998semidirect

Maximal subgroups

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

subgroupindex
#106110622
D5×#4322
#106102482
C5×#12912
#105982452
#105982442
#105981612
#79985