Finite Group Databasebeta

← #11988998

Subgroups — #11988998

Order 1280.

550 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10611013C211yesmaximal, characteristic
2C2×#65122C211yesmaximal, characteristic
3#10610248C211yesmaximal, characteristic
4C5×#1283C211yesmaximal, characteristic, complemented
5#10598235C211yesmaximal, characteristic, complemented
6#10598197C211yesmaximal, characteristic, complemented
7#10598159C211yesmaximal, characteristic, complemented
8C2×C42×D5C2211yescharacteristic
9C5×#431C2211yescharacteristic
10C2×C5×C4⋊C8C2211yescharacteristic
11C4×C5×M16C2211yescharacteristic
12#65415C412yes—
13#65407C412yes—
14C2×#3952C412yes—
15C2×C8×Dic5C412yes—
16#65214C2211yescharacteristic
17C2×C4⋊#168C2211yescharacteristic
18C4×#681C2211yescharacteristic
19#65126—21no—
20#65124—21no—
21#65122—21no—
22#65122—21no—
23#65122—21no—
24#65122—21no—
25#65015C412yes—
26#65008C412yes—
27#64994—21no—
28#64994—21no—
29C4×#676—21no—
30#64974—21no—
31#64974—21no—
32#64974—21no—
33#7936—51nomaximal, Sylow
34C22×C4×D5C2×C411yescharacteristic
35C22×C4×D5C2×C411yescharacteristic
36C22×C4×D5C2×C411yescharacteristic
37C2×C5×M16C2×C412yes—
38C22×C5×C8C2×C412yes—
39C2×C42×C5C2311yescharacteristic
40C2×C4×Dic5C2×C411yescharacteristic
41C2×C4×Dic5C2×C411yescharacteristic
42C2×C4×Dic5C2×C411yescharacteristic
43C2×#681C2×C412yes—
44C22×#168C2×C412yes—
45C2×#676—22no—
46C42×D5D411yescharacteristic
47C42×D5D411yescharacteristic
48C42×D5D411yescharacteristic
49C42×D5D411yescharacteristic
50C42×D5D411yescharacteristic
51C42×D5D411yescharacteristic
52C42×D5Q811yescharacteristic
53C42×D5Q811yescharacteristic
54C5×C4⋊C8—21no—
55C5×C4⋊C8—21no—
56C5×C4⋊C8—21no—
57C5×C22⋊C8C2×C412yes—
58C5×#97—21no—
59C4×C5×C8—21no—
60C4×C5×C8—21no—
61C22⋊#168C2×C412yes—
62#3952—22no—
63#3952—22no—
64#3952—22no—
65#3952—22no—
66#3952—22no—
67#3947—22no—
68#3946—22no—
69#3946—22no—
70#3946—22no—
71C8×Dic5—22no—
72C8×Dic5—22no—
73C4⋊#168—21no—
74C4⋊#168—21no—
75C4⋊#168—21no—
76#3935—21no—
77C4×#168—21no—
78C4×#168—21no—
79#2920—51no—
80#2920—51no—
81C2×#431—51no—
82#1283—51no—
83#1283—51no—
84#1283—51no—
85#1283D511yescharacteristic, complemented
86C23×D5C4211yescharacteristic
87C22×C4×C5C22×C411yescharacteristic
88C22×C4×C5C22×C411yescharacteristic
89C22×C4×C5C22×C411yescharacteristic
90C22×Dic5C4211yescharacteristic
91C22×Dic5C4211yescharacteristic
92C22×Dic5C4211yescharacteristic
93C2×C4×D5—22no—
94C2×C4×D5—22no—
95C2×C4×D5—42no—
96C2×C4×D5—41no—
97C2×C4×D5—41no—
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
108C2×C4×D5C4⋊C411yescharacteristic
109C2×C4×D5C4⋊C411yescharacteristic
110C5×M16—22no—
111C5×M16—22no—
112C2×C5×C8—22no—
113C2×C5×C8—22no—
114C2×C5×C8—22no—
115C2×C5×C8—42no—
116C42×C5C2×D411yescharacteristic
117C42×C5C2×D411yescharacteristic
118C42×C5C2×D411yescharacteristic
119C42×C5C2×Q811yescharacteristic
120C4×Dic5C22⋊C411yescharacteristic
121C4×Dic5C22⋊C411yescharacteristic
122C4×Dic5C22⋊C411yescharacteristic
123C4×Dic5C22⋊C411yescharacteristic
124C4×Dic5C22⋊C411yescharacteristic
125C4×Dic5C22⋊C411yescharacteristic
126C4×Dic5C4⋊C411yescharacteristic
127C4×Dic5C4⋊C411yescharacteristic
128C4×Dic5C4⋊C411yescharacteristic
129C4×Dic5C4⋊C411yescharacteristic
130C4×Dic5C4⋊C411yescharacteristic
131C4×Dic5C4⋊C411yescharacteristic
132#681—22no—
133#681—22no—
134C2×#168—22no—
135C2×#168—22no—
136C2×#168—22no—
137C2×#168—42no—
138#676—44no—
139C22×C42—51no—
140#432—52no—
141#432—101no—
142#432—101no—
143#432—101no—
144#431—51no—
145#431—101no—
146#431—101no—
147#431—101no—
148#431—101no—
149#431—101no—
150#431—101no—
151#431—101no—
152#431C2×D511yescharacteristic
153#423—52no—
154#423—101no—
155C2×C4⋊C8—51no—
156C2×C4⋊C8C2×D511yescharacteristic
157#407—52no—
158#407—52no—
159C2×C22⋊C8—52no—
160C4×M16—51no—
161C4×M16—101no—
162C4×M16C2×D511yescharacteristic
163C2×C4×C8—52no—
164C23×C5C2×C4211yescharacteristic
165C22×D5—21no—
166C22×D5—21no—
167C22×D5—41no—
168C22×D5—41no—
169C22×D5#9511yescharacteristic
170C22×D5#9511yescharacteristic
171C2×C4×C5—21no—
172C2×C4×C5—21no—
173C2×C4×C5—41no—
174C2×C4×C5C2×C22⋊C411yescharacteristic
175C2×C4×C5C2×C22⋊C411yescharacteristic
176C2×C4×C5C2×C22⋊C411yescharacteristic
177C2×C4×C5C2×C4⋊C411yescharacteristic
178C2×C4×C5C2×C4⋊C411yescharacteristic
179C2×C4×C5C2×C4⋊C411yescharacteristic
180C2×C4×C5#13112yes—
181C2×C4×C5#13112yes—
182C2×Dic5—21no—
183C2×Dic5—21no—
184C2×Dic5—22no—
185C2×Dic5—41no—
186C2×Dic5#9511yescharacteristic
187C2×Dic5#9511yescharacteristic
188C2×Dic5#9511yescharacteristic
189C2×Dic5#9511yescharacteristic
190C2×Dic5#9511yescharacteristic
191C2×Dic5#9511yescharacteristic
192C4×D5—22no—
193C4×D5—22no—
194C4×D5—21no—
195C4×D5—21no—
196C4×D5—21no—
197C4×D5—21no—
198C4×D5—22no—
199C4×D5—22no—
200C4×D5—22no—
201C4×D5—22no—
202C4×D5—41no—
203C4×D5—41no—
204C4×D5—41no—
205C4×D5—41no—
206C5×C8—42no—
207C5×C8—42no—
208C5×C8—42no—
209#168—42no—
210#168—42no—
211#168—42no—
212C23×C4—51no—
213C23×C4—51no—
214C23×C4—51no—
215C2×M16—52no—
216C2×M16—102no—
217C2×M16C4×D512yes—
218C22×C8—52no—
219C22×C8C4×D512yes—
220C2×C42—51no—
221C2×C42—51no—
222C2×C42—51no—
223C2×C42—51no—
224C2×C42—51no—
225C2×C42—51no—
226C2×C42—51no—
227C2×C42—51no—
228C2×C42—51no—
229C2×C42—51no—
230C2×C42—51no—
231C2×C42C22×D511yescharacteristic
232C4⋊C8—21no—
233C4⋊C8—21no—
234C4⋊C8—21no—
235C4⋊C8—102no—
236C4⋊C8—102no—
237C4⋊C8—102no—
238C4⋊C8—101no—
239C4⋊C8—101no—
240C4⋊C8—101no—
241C22⋊C8—52no—
242C22⋊C8—102no—
243C22⋊C8—102no—
244C22⋊C8—102no—
245C22⋊C8—102no—
246C22⋊C8—102no—
247C22⋊C8C4×D512yes—
248#97—21no—
249#97—102no—
250#97—101no—
251C4×C8—21no—
252C4×C8—21no—
253C4×C8—102no—
254C4×C8—102no—
255C4×C8—101no—
256C4×C8—101no—
257C22×C5—21no—
258C22×C5—21no—
259C22×C5C2×#9511yescharacteristic
260C22×C5#40511yescharacteristic
261C22×C5#40511yescharacteristic
262C2×D5—21no—
263C2×D5—21no—
264C2×D5—21no—
265C2×D5—21no—
266C2×D5—21no—
267C2×D5—21no—
268C2×D5—42no—
269C2×D5—42no—
270C4×C5—21no—
271C4×C5—21no—
272C4×C5—21no—
273C4×C5#40812yes—
274C4×C5#41311yescharacteristic
275C4×C5#41311yescharacteristic
276C4×C5#42412yes—
277Dic5—21no—
278Dic5—21no—
279Dic5—21no—
280Dic5—21no—
281Dic5—21no—
282Dic5#34412yes—
283C24—51no—
284C22×C4—51no—
285C22×C4—51no—
286C22×C4—51no—
287C22×C4—51no—
288C22×C4—51no—
289C22×C4—51no—
290C22×C4—51no—
291C22×C4—51no—
292C22×C4—51no—
293C22×C4—51no—
294C22×C4—51no—
295C22×C4—51no—
296C22×C4—51no—
297C22×C4—51no—
298C22×C4—51no—
299C22×C4—102no—
300C22×C4—102no—
301C22×C4—201no—
302C22×C4—201no—
303C22×C4—202no—
304C22×C4C2×C4×D511yescharacteristic
305C22×C4C2×C4×D511yescharacteristic
306C22×C4C2×C4×D511yescharacteristic
307M16—22no—
308M16—22no—
309M16—102no—
310M16—102no—
311M16—204no—
312C2×C8—22no—
313C2×C8—22no—
314C2×C8—22no—
315C2×C8—42no—
316C2×C8—102no—
317C2×C8—102no—
318C2×C8—102no—
319C2×C8—202no—
320C42—51no—
321C42—51no—
322C42—51no—
323C42—51no—
324C42—51no—
325C42—51no—
326C42—51no—
327C42—51no—
328C42—51no—
329C42—51no—
330C42—51no—
331C42—51no—
332C42D4×D511yescharacteristic
333C42D4×D511yescharacteristic
334C42D4×D511yescharacteristic
335C42Q8×D511yescharacteristic
336C2×C5—21no—
337C2×C5—21no—
338C2×C5#172911yescharacteristic
339C2×C5#174211yescharacteristic
340C2×C5C2×#34411yescharacteristic
341D5—41no—
342D5—41no—
343C23—51no—
344C23—51no—
345C23—101no—
346C23—101no—
347C23—201no—
348C23—201no—
349C23C42×D511yescharacteristic
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—41no—
353C2×C4—51no—
354C2×C4—51no—
355C2×C4—51no—
356C2×C4—51no—
357C2×C4—51no—
358C2×C4—51no—
359C2×C4—102no—
360C2×C4—102no—
361C2×C4—102no—
362C2×C4—101no—
363C2×C4—101no—
364C2×C4—101no—
365C2×C4—101no—
366C2×C4—101no—
367C2×C4—101no—
368C2×C4—102no—
369C2×C4—102no—
370C2×C4—102no—
371C2×C4—102no—
372C2×C4—201no—
373C2×C4—201no—
374C2×C4—201no—
375C2×C4—201no—
376C2×C4—201no—
377C2×C4D5×C22⋊C411yescharacteristic
378C2×C4D5×C22⋊C411yescharacteristic
379C2×C4D5×C22⋊C411yescharacteristic
380C2×C4D5×C4⋊C411yescharacteristic
381C2×C4D5×C4⋊C411yescharacteristic
382C2×C4D5×C4⋊C411yescharacteristic
383C2×C4#404712yes—
384C2×C4#405312yes—
385C8—42no—
386C8—42no—
387C8—42no—
388C8—202no—
389C8—202no—
390C8—202no—
391C5#793611yescharacteristic, complemented, Sylow
392C22—21no—
393C22—21no—
394C22—101no—
395C22—101no—
396C22—101no—
397C22—101no—
398C22—101no—
399C22—101no—
400C22—202no—
401C22—202no—
402C22D5×#9511yescharacteristic
403C22#6497811yescharacteristic
404C22#6499711yescharacteristic
405C4—21no—
406C4—21no—
407C4—21no—
408C4—52no—
409C4—101no—
410C4—101no—
411C4—101no—
412C4—101no—
413C4—101no—
414C4#6501612yes—
415C4#6503411yescharacteristic
416C4#6504011yescharacteristic
417C4#6512812yes—
418C2—21no—
419C2—21no—
420C2—201no—
421C2—201no—
422C2#1059945411yescharacteristic
423C2#1059978211yescharacteristic
424C2D5×#34411yescharacteristic
subgroupG/H
centerC2×C4D5×C22⋊C4
commutatorC23×C5C2×C42
FrattiniC2×C42C22×D5
FittingC5×#1283C2
socleC22×C5C2×#95
prime radicalC23×D5C42
cosocleC2×C42×C5C23
hypercenter#1283D5
hypocenterC5#7936
LCSG ▷ C23×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1283

Complements

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

NH ≅ G/Ntype
4. C5×#1283C2semidirect
5. #10598235C2semidirect
6. #10598197C2semidirect
7. #10598159C2semidirect
85. #1283D5semidirect
391. C5#7936semidirect

Maximal subgroups

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

subgroupindex
#106110132
C2×#651222
#106102482
C5×#12832
#105982352
#105981972
#105981592
#79365