Finite Group Databasebeta

← #11990888

Subgroups — #11990888

Order 1280.

846 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#555C211yesmaximal, characteristic
2#10602466C212yesmaximal, complemented
3C4×#3966C211yesmaximal, characteristic, complemented
4#10602395C211yesmaximal, characteristic, complemented
5#10602383C212yesmaximal, complemented
6C5×#555—24no—
7C5×#555—24no—
8C2×C5×C4⋊Q8C411yescharacteristic, complemented
9C2×C5×#124—21no—
10C2×C5×#124—21no—
11C2×C5×#121—21no—
12C2×C5×#121C411yescharacteristic, complemented
13C2×C5×#121C2211yescharacteristic
14C2×C4×C5×D4C411yescharacteristic, complemented
15C2×C4×C5×D4C2211yescharacteristic
16C2×C5×#117—21no—
17C2×C5×#117C411yescharacteristic, complemented
18C2×C5×#117C2211yescharacteristic
19C2×#3966—21no—
20C4×C22⋊Dic5C2212yes—
21#65496C2212yes—
22#64757—24no—
23#64752—24no—
24#64748—21no—
25#64746—21no—
26#64745—21no—
27#8360—51nomaximal, Sylow
28C22×C5×Q8—21no—
29C22×C5×D4—21no—
30C22×C5×D4—21no—
31C22×C5×D4C2×C411yescharacteristic
32C22×C5×D4D411yescharacteristic
33C23×C4×C5—21no—
34C23×C4×C5C2×C411yescharacteristic
35C23×C4×C5C2311yescharacteristic
36C5×C4⋊Q8—22no—
37C5×C4⋊Q8—22no—
38C5×#124—28no—
39C5×#124—28no—
40C5×#121—28no—
41C5×#121—22no—
42C5×#121—22no—
43C5×#121—22no—
44C5×#121D414yes—
45C4×C5×D4—22no—
46C4×C5×D4—22no—
47C4×C5×D4—22no—
48C4×C5×D4—22no—
49C5×#117—28no—
50C5×#117—22no—
51C5×#117—22no—
52C5×#117—22no—
53C5×#117D414yes—
54C2×C5×C4⋊C4—21no—
55C2×C5×C4⋊C4C2×C411yescharacteristic
56C2×C5×C4⋊C4C2×C411yescharacteristic
57C2×C5×C4⋊C4C2×C411yescharacteristic
58C2×C5×C4⋊C4D411yescharacteristic
59C2×C5×C22⋊C4—21no—
60C2×C5×C22⋊C4—21no—
61C2×C5×C22⋊C4—21no—
62C2×C5×C22⋊C4—21no—
63C2×C5×C22⋊C4—21no—
64C2×C5×C22⋊C4D411yescharacteristic
65C2×C5×C22⋊C4D411yescharacteristic
66C2×C42×C5—21no—
67C2×C42×C5—21no—
68C2×C42×C5C2×C411yescharacteristic
69C2×C22⋊Dic5—22no—
70C2×C4×Dic5—22no—
71C2×#681—22no—
72#3966—24no—
73#3963—22no—
74C22⋊#168—22no—
75C22⋊#168—22no—
76C2×#555D511yescharacteristic
77#1826—52no—
78C4×#99—51no—
79#1507—52no—
80#1465—51no—
81C24×C5—21no—
82C24×C5C22⋊C411yescharacteristic
83C24×C5C2×D411yescharacteristic
84C2×C5×Q8—24no—
85C2×C5×Q8—82no—
86C2×C5×D4—22no—
87C2×C5×D4—24no—
88C2×C5×D4—24no—
89C2×C5×D4—22no—
90C2×C5×D4—21no—
91C2×C5×D4—41no—
92C2×C5×D4—42no—
93C2×C5×D4—82no—
94C2×C5×D4—82no—
95C2×C5×D4C22⋊C412yes—
96C22×C4×C5—24no—
97C22×C4×C5—21no—
98C22×C4×C5—21no—
99C22×C4×C5—21no—
100C22×C4×C5—21no—
101C22×C4×C5—21no—
102C22×C4×C5—42no—
103C22×C4×C5—42no—
104C22×C4×C5—42no—
105C22×C4×C5—42no—
106C22×C4×C5C22⋊C411yescharacteristic
107C22×C4×C5C22⋊C411yescharacteristic
108C22×C4×C5C22⋊C411yescharacteristic
109C22×C4×C5C22×C411yescharacteristic
110C22×C4×C5C2×D412yes—
111C22×C4×C5C2×D412yes—
112C22×C4×C5C2×D411yescharacteristic
113C22×Dic5—42no—
114C5×C4⋊C4—24no—
115C5×C4⋊C4—21no—
116C5×C4⋊C4—21no—
117C5×C4⋊C4—21no—
118C5×C4⋊C4—22no—
119C5×C4⋊C4C22⋊C412yes—
120C5×C4⋊C4C22⋊C412yes—
121C5×C4⋊C4C22⋊C412yes—
122C5×C22⋊C4—24no—
123C5×C22⋊C4—24no—
124C5×C22⋊C4—24no—
125C5×C22⋊C4—24no—
126C5×C22⋊C4—22no—
127C5×C22⋊C4—24no—
128C5×C22⋊C4—22no—
129C42×C5—24no—
130C42×C5—21no—
131C42×C5—21no—
132C42×C5—24no—
133C22⋊Dic5—24no—
134C22⋊Dic5—42no—
135C4×Dic5—44no—
136#681—44no—
137C2×#168—42no—
138#555—24no—
139#555—24no—
140C2×C4⋊Q8Dic511yescharacteristic, complemented
141C2×#124—21no—
142C2×#124—21no—
143C2×#121—21no—
144C2×#121Dic511yescharacteristic, complemented
145C2×#121C2×D511yescharacteristic
146C2×C4×D4Dic511yescharacteristic, complemented
147C2×C4×D4C2×D511yescharacteristic
148C2×#117—21no—
149C2×#117Dic511yescharacteristic, complemented
150C2×#117C2×D511yescharacteristic
151C2×#99—101no—
152#407—52no—
153C4×C22⋊C4—52no—
154#342—101no—
155#339—104no—
156#327—104no—
157#324—101no—
158#323—101no—
159C23×C5—21no—
160C23×C5—21no—
161C23×C5—21no—
162C23×C5—22no—
163C23×C5—21no—
164C23×C5—21no—
165C23×C5—41no—
166C23×C5—41no—
167C23×C5—42no—
168C23×C5—42no—
169C23×C5—41no—
170C23×C5—41no—
171C23×C5—41no—
172C23×C5—41no—
173C23×C5C2×C22⋊C411yescharacteristic
174C23×C5#12012yes—
175C5×Q8—84no—
176C5×D4—44no—
177C5×D4—42no—
178C5×D4—42no—
179C5×D4—84no—
180C5×D4—84no—
181C2×C4×C5—21no—
182C2×C4×C5—21no—
183C2×C4×C5—24no—
184C2×C4×C5—22no—
185C2×C4×C5—21no—
186C2×C4×C5—22no—
187C2×C4×C5—21no—
188C2×C4×C5—22no—
189C2×C4×C5—22no—
190C2×C4×C5—41no—
191C2×C4×C5—42no—
192C2×C4×C5—42no—
193C2×C4×C5—48no—
194C2×C4×C5—42no—
195C2×C4×C5—42no—
196C2×C4×C5—41no—
197C2×C4×C5—41no—
198C2×C4×C5—42no—
199C2×C4×C5—41no—
200C2×C4×C5—41no—
201C2×C4×C5#10412yes—
202C2×C4×C5C2×C22⋊C411yescharacteristic
203C2×C4×C5C2×C22⋊C411yescharacteristic
204C2×C4×C5#12012yes—
205C2×Dic5—44no—
206C2×Dic5—82no—
207C2×Dic5—82no—
208#168—82no—
209C22×Q8—21no—
210C22×D4—21no—
211C22×D4—21no—
212C22×D4C2×Dic511yescharacteristic
213C22×D4C22⋊D511yescharacteristic
214C23×C4—21no—
215C23×C4C2×Dic511yescharacteristic
216C23×C4C22×D511yescharacteristic
217C2×M16—102no—
218C4⋊Q8—22no—
219C4⋊Q8—22no—
220#124—28no—
221#124—28no—
222#121—28no—
223#121—22no—
224#121—22no—
225#121—22no—
226#121C22⋊D514yes—
227C4×D4—22no—
228C4×D4—22no—
229C4×D4—22no—
230C4×D4—22no—
231#117—28no—
232#117—22no—
233#117—22no—
234#117—22no—
235#117C22⋊D514yes—
236C2×C4⋊C4—21no—
237C2×C4⋊C4C2×Dic511yescharacteristic
238C2×C4⋊C4C2×Dic511yescharacteristic
239C2×C4⋊C4C2×Dic511yescharacteristic
240C2×C4⋊C4C22⋊D511yescharacteristic
241C2×C22⋊C4—21no—
242C2×C22⋊C4—21no—
243C2×C22⋊C4—21no—
244C2×C22⋊C4—21no—
245C2×C22⋊C4—21no—
246C2×C22⋊C4—102no—
247C2×C22⋊C4C22⋊D511yescharacteristic
248C2×C22⋊C4C22⋊D511yescharacteristic
249C2×C42—21no—
250C2×C42—21no—
251C2×C42—102no—
252C2×C42C2×Dic511yescharacteristic
253#99—104no—
254C22⋊C8—102no—
255C22⋊C8—102no—
256#95—102no—
257C22×C5—21no—
258C22×C5—21no—
259C22×C5—22no—
260C22×C5—22no—
261C22×C5—22no—
262C22×C5—41no—
263C22×C5—42no—
264C22×C5—41no—
265C22×C5—42no—
266C22×C5—42no—
267C22×C5—41no—
268C22×C5—81no—
269C22×C5—81no—
270C22×C5—81no—
271C22×C5—81no—
272C22×C5—82no—
273C22×C5—82no—
274C22×C5#37911yescharacteristic
275C22×C5C2×#10411yescharacteristic
276C22×C5#42111yescharacteristic
277C4×C5—22no—
278C4×C5—21no—
279C4×C5—22no—
280C4×C5—42no—
281C4×C5—42no—
282C4×C5—41no—
283C4×C5—41no—
284C4×C5—42no—
285C4×C5#41012yes—
286Dic5—84no—
287C24—21no—
288C24C22⋊Dic511yescharacteristic
289C24C2×C22⋊D511yescharacteristic
290C2×Q8—24no—
291C2×Q8—82no—
292C2×D4—22no—
293C2×D4—24no—
294C2×D4—24no—
295C2×D4—21no—
296C2×D4—22no—
297C2×D4—41no—
298C2×D4—42no—
299C2×D4—82no—
300C2×D4—82no—
301C2×D4C22⋊Dic512yes—
302C22×C4—24no—
303C22×C4—21no—
304C22×C4—21no—
305C22×C4—21no—
306C22×C4—21no—
307C22×C4—21no—
308C22×C4—42no—
309C22×C4—42no—
310C22×C4—42no—
311C22×C4—42no—
312C22×C4—202no—
313C22×C4C22⋊Dic511yescharacteristic
314C22×C4C22⋊Dic511yescharacteristic
315C22×C4C22⋊Dic511yescharacteristic
316C22×C4C22×Dic511yescharacteristic
317C22×C4C2×C22⋊D512yes—
318C22×C4C2×C22⋊D512yes—
319C22×C4C2×C22⋊D511yescharacteristic
320M16—204no—
321C2×C8—202no—
322C4⋊C4—24no—
323C4⋊C4—21no—
324C4⋊C4—21no—
325C4⋊C4—21no—
326C4⋊C4—22no—
327C4⋊C4C22⋊Dic512yes—
328C4⋊C4C22⋊Dic512yes—
329C4⋊C4C22⋊Dic512yes—
330C22⋊C4—24no—
331C22⋊C4—24no—
332C22⋊C4—24no—
333C22⋊C4—24no—
334C22⋊C4—22no—
335C22⋊C4—24no—
336C22⋊C4—22no—
337C22⋊C4—104no—
338C22⋊C4—202no—
339C42—24no—
340C42—21no—
341C42—21no—
342C42—24no—
343C42—204no—
344C2×C5—21no—
345C2×C5—21no—
346C2×C5—42no—
347C2×C5—81no—
348C2×C5—82no—
349C2×C5#178211yescharacteristic
350C2×C5#178911yescharacteristic
351C2×C5#179511yescharacteristic
352C23—21no—
353C23—21no—
354C23—21no—
355C23—22no—
356C23—21no—
357C23—21no—
358C23—41no—
359C23—41no—
360C23—42no—
361C23—42no—
362C23—41no—
363C23—41no—
364C23—41no—
365C23—41no—
366C23C2×C22⋊Dic511yescharacteristic
367C23#409912yes—
368Q8—84no—
369D4—44no—
370D4—42no—
371D4—42no—
372D4—84no—
373D4—84no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—24no—
377C2×C4—22no—
378C2×C4—21no—
379C2×C4—22no—
380C2×C4—21no—
381C2×C4—22no—
382C2×C4—22no—
383C2×C4—41no—
384C2×C4—42no—
385C2×C4—48no—
386C2×C4—42no—
387C2×C4—42no—
388C2×C4—42no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—42no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—204no—
395C2×C4—402no—
396C2×C4—402no—
397C2×C4#396912yes—
398C2×C4C2×C22⋊Dic511yescharacteristic
399C2×C4C2×C22⋊Dic511yescharacteristic
400C2×C4#409912yes—
401C8—402no—
402C5#836011yescharacteristic, complemented, Sylow
403C22—21no—
404C22—21no—
405C22—22no—
406C22—22no—
407C22—22no—
408C22—42no—
409C22—41no—
410C22—41no—
411C22—42no—
412C22—42no—
413C22—41no—
414C22—81no—
415C22—81no—
416C22—81no—
417C22—81no—
418C22—82no—
419C22—82no—
420C22C2×#396911yescharacteristic
421C22#6552511yescharacteristic
422C22#6553611yescharacteristic
423C4—22no—
424C4—22no—
425C4—21no—
426C4—42no—
427C4—41no—
428C4—42no—
429C4—42no—
430C4—41no—
431C4—404no—
432C4#6552912yes—
433C2—21no—
434C2—21no—
435C2—42no—
436C2—82no—
437C2—81no—
438C2#1060293111yescharacteristic
439C2#1060293211yescharacteristic
440C2#1060293411yescharacteristic
subgroupG/H
centerC22#65536
commutatorC22×C4×C5C22×C4
FrattiniC23×C4C22×D5
Fitting, prime radicalC2×C5×#555C2
socleC22×C5#379
cosocleC23×C4×C5C23
hypercenterC2×#555D5
hypocenterC5#8360
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#555

Complements

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

NH ≅ G/Ntype
2. #10602466C2semidirect
3. C4×#3966C2semidirect
4. #10602395C2semidirect
5. #10602383C2semidirect
8. C2×C5×C4⋊Q8C4semidirect
12. C2×C5×#121C4semidirect
14. C2×C4×C5×D4C4semidirect
17. C2×C5×#117C4semidirect
140. C2×C4⋊Q8Dic5semidirect
144. C2×#121Dic5semidirect
146. C2×C4×D4Dic5semidirect
149. C2×#117Dic5semidirect
402. C5#8360semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#5552
#106024662
C4×#39662
#106023952
#106023832
#83605