Finite Group Databasebeta

← #11990293

Subgroups — #11990293

Order 1280.

510 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10615465C211yesmaximal, characteristic
2C5×#1752C211yesmaximal, characteristic, complemented
3#10602760C211yesmaximal, characteristic, complemented
4#10600735C211yesmaximal, characteristic
5#10600236C211yesmaximal, characteristic
6#10598171C211yesmaximal, characteristic, complemented
7#10598109C211yesmaximal, characteristic, complemented
8C23×C5×C8C2211yescharacteristic
9#66125C2211yescharacteristic
10C2×#4047C411yescharacteristic, complemented
11C2×C5×C22⋊C8C2211yescharacteristic
12C2×C5×#97—21no—
13C4×C5×C22⋊C4C2211yescharacteristic
14C4×C22⋊Dic5C2211yescharacteristic
15#65496C2211yescharacteristic
16C2×C22⋊#168C2211yescharacteristic
17#65400—21no—
18#65400—21no—
19#65399C411yescharacteristic, complemented
20C8×C22⋊D5—21no—
21C8×C22⋊D5—21no—
22#65391C411yescharacteristic, complemented
23#65390C411yescharacteristic, complemented
24C2×#3947—21no—
25C5×#336—21no—
26#64770—21no—
27#64690C412yescomplemented
28#64687C412yescomplemented
29#64672C412yescomplemented
30#64671C412yescomplemented
31#8239—51nomaximal, Sylow
32C23×C4×C5C2311yescharacteristic
33C2×#709C2×C411yescharacteristic
34C22×C5×C8—21no—
35C22×C5×C8—42no—
36C22×C5×C8C2×C411yescharacteristic
37C22×C5×C8C2×C411yescharacteristic
38C22×C5×C8D411yescharacteristic
39C22×C5×C8D411yescharacteristic
40C22×C5×C8D411yescharacteristic
41C22×C5×C8D411yescharacteristic
42C2×C5×C22⋊C4—21no—
43C2×C42×C5—21no—
44#4099—21no—
45C2×C22⋊Dic5—21no—
46#4076C2×C411yescharacteristic
47#4076C2×C411yescharacteristic
48#4075—21no—
49C4×C22⋊D5—21no—
50C4×C22⋊D5—21no—
51#4072C2×C411yescharacteristic
52#4070C2×C411yescharacteristic
53#4070C2×C411yescharacteristic
54C2×C4×Dic5—21no—
55C2×#681C2×C411yescharacteristic
56C2×#681C2×C411yescharacteristic
57C22×#168—21no—
58#4047—42no—
59C2×#676—21no—
60C2×C8×D5—21no—
61C5×C22⋊C8—21no—
62C5×C22⋊C8C2×C412yes—
63C5×#97—42no—
64C5×#95C2×C412yes—
65#3963C2×C412yes—
66C22⋊#168—21no—
67C22⋊#168—21no—
68C22⋊#168—21no—
69C22⋊#168C2×C412yes—
70#3952—21no—
71#3952—21no—
72#3947—21no—
73#3947—42no—
74#3946—21no—
75#3946—21no—
76C8×Dic5—21no—
77#2929—51no—
78#1752—51no—
79#1752D511yescharacteristic, complemented
80#1501—51no—
81#1501—51no—
82#1298—51no—
83#1297—51no—
84C24×C5#4111yescharacteristic
85C22×C4×C5—22no—
86C22×C4×C5—41no—
87C22×C4×C5—41no—
88C22×C4×C5C22×C411yescharacteristic
89C22×C4×C5C22×C411yescharacteristic
90C22×C4×C5C22×C411yescharacteristic
91C22×C4×C5C2×D411yescharacteristic
92C22×C4×C5C2×D411yescharacteristic
93C22×C4×C5#4111yescharacteristic
94C2×C22⋊D5—21no—
95C2×C22⋊D5—21no—
96C2×C22⋊D5—21no—
97C22×Dic5—22no—
98#709—41no—
99#709—41no—
100C2×D20C4211yescharacteristic
101C2×C4×D5—21no—
102C2×Dic10C4211yescharacteristic
103C2×C5×C8—22no—
104C2×C5×C8—22no—
105C2×C5×C8—22no—
106C2×C5×C8—22no—
107C2×C5×C8—41no—
108C2×C5×C8—41no—
109C2×C5×C8—41no—
110C2×C5×C8—41no—
111C2×C5×C8—41no—
112C2×C5×C8C22⋊C411yescharacteristic
113C2×C5×C8C22⋊C411yescharacteristic
114C2×C5×C8C22⋊C411yescharacteristic
115C2×C5×C8C22⋊C411yescharacteristic
116C5×C22⋊C4—42no—
117C42×C5—41no—
118C42×C5—41no—
119C22⋊Dic5—21no—
120C22⋊Dic5—21no—
121C22⋊Dic5—21no—
122C22⋊Dic5—42no—
123#685—21no—
124#685—21no—
125C4⋊Dic5C4211yescharacteristic
126C4⋊Dic5C4211yescharacteristic
127#683—21no—
128#683—21no—
129C4×Dic5—21no—
130C4×Dic5—41no—
131C4×Dic5—41no—
132#681—41no—
133#681—41no—
134C2×#168—21no—
135C2×#168—21no—
136C2×#168—22no—
137C2×#168—41no—
138C2×#168—41no—
139#676—42no—
140C8×D5—42no—
141C2×#131—51no—
142C23×C8C2×D511yescharacteristic
143#525—51no—
144#435—101no—
145#435—101no—
146C8×D4—101no—
147C8×D4—101no—
148#424—51no—
149#408—51no—
150#407—51no—
151C2×C22⋊C8—51no—
152C2×C22⋊C8C2×D511yescharacteristic
153#405—51no—
154C2×#97—21no—
155C2×#97—101no—
156C4×C22⋊C4—51no—
157C4×C22⋊C4C2×D511yescharacteristic
158#336—21no—
159#336—101no—
160#328—52no—
161#328—52no—
162#327—52no—
163#327—52no—
164C23×C5—22no—
165C23×C5—22no—
166C23×C5—41no—
167C23×C5#11711yescharacteristic
168C23×C5C4×D411yescharacteristic
169C23×C5C4×D411yescharacteristic
170C22×D5—21no—
171C2×C4×C5—21no—
172C2×C4×C5—21no—
173C2×C4×C5—21no—
174C2×C4×C5—21no—
175C2×C4×C5—21no—
176C2×C4×C5—21no—
177C2×C4×C5—41no—
178C2×C4×C5—41no—
179C2×C4×C5—41no—
180C2×C4×C5—42no—
181C2×C4×C5—42no—
182C2×C4×C5—42no—
183C2×C4×C5C2×C4211yescharacteristic
184C2×C4×C5C2×C22⋊C411yescharacteristic
185C2×C4×C5C4×D411yescharacteristic
186C2×C4×C5C4×D411yescharacteristic
187C22⋊D5—42no—
188C22⋊D5—42no—
189C22⋊D5—42no—
190C2×Dic5—21no—
191C2×Dic5—21no—
192C2×Dic5—21no—
193C2×Dic5—42no—
194C2×Dic5—42no—
195C2×Dic5—42no—
196D20—41no—
197C4×D5—41no—
198C4×D5—41no—
199Dic10—41no—
200C5×C8—21no—
201C5×C8—21no—
202C5×C8—21no—
203C5×C8—42no—
204C5×C8#9912yes—
205#168—42no—
206#168—41no—
207#168—41no—
208C2×#41—51no—
209C23×C4C22×D511yescharacteristic
210#131—202no—
211C2×M16—51no—
212C2×M16—51no—
213C2×M16—101no—
214C22×C8—21no—
215C22×C8—42no—
216C22×C8—101no—
217C22×C8—101no—
218C22×C8C4×D511yescharacteristic
219C22×C8C4×D511yescharacteristic
220C22×C8D2011yescharacteristic
221C22×C8D2011yescharacteristic
222C22×C8C22⋊D511yescharacteristic
223C22×C8C22⋊D511yescharacteristic
224#123—101no—
225C22⋊Q8—51no—
226C22⋊Q8—51no—
227#121—51no—
228#121—51no—
229#120—101no—
230C4×D4—101no—
231C4×D4—101no—
232#117—51no—
233C2×C22⋊C4—21no—
234C2×C22⋊C4—101no—
235C2×C42—21no—
236C2×C42—101no—
237C4⋊C8—101no—
238C4⋊C8—101no—
239C22⋊C8—21no—
240C22⋊C8—52no—
241C22⋊C8—101no—
242C22⋊C8—101no—
243C22⋊C8—101no—
244C22⋊C8—101no—
245C22⋊C8—101no—
246C22⋊C8C4×D512yes—
247#97—42no—
248#97—101no—
249#97—202no—
250C4×C8—101no—
251#95—52no—
252#95C4×D512yes—
253C22×C5—21no—
254C22×C5—21no—
255C22×C5—21no—
256C22×C5—21no—
257C22×C5—21no—
258C22×C5—21no—
259C22×C5—21no—
260C22×C5—44no—
261C22×C5C4×C22⋊C411yescharacteristic
262C22×C5#44412yes—
263C22×C5#44412yes—
264C2×D5—41no—
265C2×D5—41no—
266C2×D5—41no—
267C4×C5—21no—
268C4×C5—21no—
269C4×C5—21no—
270C4×C5—82no—
271C4×C5C2×#9911yescharacteristic
272C4×C5#41011yescharacteristic
273Dic5—41no—
274Dic5—41no—
275Dic5—41no—
276Dic5—82no—
277C24#70911yescharacteristic
278#41—201no—
279#41—201no—
280C2×Q8—51no—
281C2×D4—51no—
282C2×D4—101no—
283C2×D4—101no—
284C2×D4—101no—
285C22×C4—22no—
286C22×C4—41no—
287C22×C4—41no—
288C22×C4—101no—
289C22×C4—102no—
290C22×C4C2×C4×D511yescharacteristic
291C22×C4C2×C4×D511yescharacteristic
292C22×C4C2×C4×D511yescharacteristic
293C22×C4C2×D2011yescharacteristic
294C22×C4#70911yescharacteristic
295C22×C4C2×C22⋊D511yescharacteristic
296M16—202no—
297M16—201no—
298M16—201no—
299C2×C8—22no—
300C2×C8—22no—
301C2×C8—22no—
302C2×C8—22no—
303C2×C8—41no—
304C2×C8—41no—
305C2×C8—41no—
306C2×C8—41no—
307C2×C8—41no—
308C2×C8—102no—
309C2×C8—101no—
310C2×C8—101no—
311C2×C8—201no—
312C2×C8—201no—
313C2×C8—202no—
314C2×C8#68511yescharacteristic
315C2×C8#68511yescharacteristic
316C2×C8#68511yescharacteristic
317C2×C8#68511yescharacteristic
318C4⋊C4—51no—
319C4⋊C4—51no—
320C4⋊C4—101no—
321C4⋊C4—101no—
322C22⋊C4—42no—
323C22⋊C4—101no—
324C22⋊C4—101no—
325C22⋊C4—101no—
326C22⋊C4—101no—
327C22⋊C4—101no—
328C22⋊C4—202no—
329C42—41no—
330C42—41no—
331C42—101no—
332C42—201no—
333C42—201no—
334C2×C5—22no—
335C2×C5—22no—
336C2×C5—41no—
337C2×C5C4×#9911yescharacteristic
338C2×C5#176511yescharacteristic
339C2×C5#176511yescharacteristic
340D5—81no—
341C23—22no—
342C23—22no—
343C23—41no—
344C23—101no—
345C23#401811yescharacteristic
346C23C4×D2011yescharacteristic
347C23C4×C22⋊D511yescharacteristic
348Q8—201no—
349D4—201no—
350D4—202no—
351D4—202no—
352D4—202no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—42no—
363C2×C4—42no—
364C2×C4—42no—
365C2×C4—101no—
366C2×C4—101no—
367C2×C4—101no—
368C2×C4—201no—
369C2×C4—201no—
370C2×C4—202no—
371C2×C4—202no—
372C2×C4—202no—
373C2×C4C42×D511yescharacteristic
374C2×C4C4×D2011yescharacteristic
375C2×C4C2×#68511yescharacteristic
376C2×C4C4×C22⋊D511yescharacteristic
377C8—21no—
378C8—21no—
379C8—21no—
380C8—42no—
381C8—202no—
382C8—201no—
383C8—201no—
384C8#393812yes—
385C5#823911yescharacteristic, complemented, Sylow
386C22—21no—
387C22—21no—
388C22—21no—
389C22—21no—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—44no—
394C22—201no—
395C22—201no—
396C22—201no—
397C22#6500612yes—
398C22C4×#68511yescharacteristic
399C22#6543412yes—
400C4—21no—
401C4—21no—
402C4—21no—
403C4—82no—
404C4—201no—
405C4—201no—
406C4—201no—
407C4—402no—
408C4C2×#393811yescharacteristic
409C4#6529511yescharacteristic
410C2—22no—
411C2—22no—
412C2—41no—
413C2—401no—
414C2C4×#393811yescharacteristic
415C2#1060063211yescharacteristic
416C2#1060068111yescharacteristic
subgroupG/H
centerC2×C4C2×#685
commutatorC2×C4×C5C2×C42
FrattiniC23×C4C22×D5
FittingC5×#1752C2
socleC22×C5C4×C22⋊C4
prime radical#66125C22
cosocleC23×C4×C5C23
hypercenter#1752D5
hypocenterC5#8239
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C23×C8 ◁ #1752

Complements

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

NH ≅ G/Ntype
2. C5×#1752C2semidirect
3. #10602760C2semidirect
6. #10598171C2semidirect
7. #10598109C2semidirect
10. C2×#4047C4semidirect
19. #65399C4semidirect
22. #65391C4semidirect
23. #65390C4semidirect
27. #64690C4semidirect
28. #64687C4semidirect
29. #64672C4semidirect
30. #64671C4semidirect
79. #1752D5semidirect
385. C5#8239semidirect

Maximal subgroups

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

subgroupindex
#106154652
C5×#17522
#106027602
#106007352
#106002362
#105981712
#105981092
#82395