Finite Group Databasebeta

← #11992050

Subgroups — #11992050

Order 1280.

742 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#4076C211yesmaximal, characteristic
2C5×C4⋊#95C211yesmaximal, characteristic, complemented
3#10602323C211yesmaximal, characteristic, complemented
4C2×#64671C212yesmaximal
5#10598103C212yesmaximal, complemented
6C22×C5×C4⋊C4—21no—
7C22×C42×C5C2211yescharacteristic
8C2×#4076C2211yescharacteristic
9C2×C4×C22⋊D5—21no—
10C2×C4×D20C411yescharacteristic, complemented
11C2×C5×#95—21no—
12C2×C5×#95C2212yes—
13#65502—21no—
14#65501C2211yescharacteristic
15C2×C22⋊#168C2212yes—
16#65229—21no—
17#65228C411yescharacteristic, complemented
18C4×#685—21no—
19C4×C4⋊Dic5C411yescharacteristic, complemented
20#65217C411yescharacteristic, complemented
21C2×C4⋊#168—21no—
22#64744—21no—
23#64671—24no—
24#8577—51nomaximal, Sylow
25C23×C4×C5—22no—
26C23×C4×C5D411yescharacteristic
27C23×C4×C5D411yescharacteristic
28C23×C4×C5C2311yescharacteristic
29C22×C22⋊D5—21no—
30C22×D20C2×C411yescharacteristic
31C22×C4×D5—21no—
32C2×C5×C4⋊C4—24no—
33C2×C5×C4⋊C4—42no—
34C2×C5×C4⋊C4—42no—
35C2×C42×C5—42no—
36C2×C42×C5C2×C411yescharacteristic
37C2×C42×C5C2×C411yescharacteristic
38C2×C42×C5D411yescharacteristic
39C2×C42×C5D411yescharacteristic
40C2×C22⋊Dic5—21no—
41#4076—21no—
42#4076—21no—
43#4076D412yes—
44#4076Q812yes—
45C4×C22⋊D5—42no—
46C4×C22⋊D5—42no—
47C2×#685—21no—
48C2×#685—21no—
49C2×#685—21no—
50C2×#685—21no—
51C2×C4⋊Dic5C2×C411yescharacteristic
52C2×C4⋊Dic5C2×C411yescharacteristic
53C2×C4⋊Dic5C2×C411yescharacteristic
54C2×#683—21no—
55C2×C4×Dic5—21no—
56C22×#168—22no—
57C4×D20—42no—
58C5×#95—22no—
59C5×#95—22no—
60C5×#95—42no—
61#3963—21no—
62#3963—21no—
63#3963—21no—
64C22⋊#168—22no—
65C22⋊#168—22no—
66C4⋊#168—42no—
67C4×#121—51no—
68#1797—51no—
69C2×#327—52no—
70C4⋊#95D511yescharacteristic, complemented
71#1294—52no—
72C24×C5C2×D411yescharacteristic
73C23×D5—21no—
74C22×C4×C5—21no—
75C22×C4×C5—21no—
76C22×C4×C5—22no—
77C22×C4×C5—22no—
78C22×C4×C5—24no—
79C22×C4×C5—41no—
80C22×C4×C5—41no—
81C22×C4×C5—41no—
82C22×C4×C5—41no—
83C22×C4×C5—42no—
84C22×C4×C5—42no—
85C22×C4×C5—42no—
86C22×C4×C5—42no—
87C22×C4×C5—42no—
88C22×C4×C5—42no—
89C22×C4×C5C22⋊C411yescharacteristic
90C22×C4×C5C22⋊C411yescharacteristic
91C22×C4×C5C22⋊C411yescharacteristic
92C22×C4×C5C22⋊C411yescharacteristic
93C22×C4×C5D812yes—
94C22×C4×C5SD1612yes—
95C22×C4×C5C22×C411yescharacteristic
96C22×C4×C5C2×D411yescharacteristic
97C22×C4×C5C2×D411yescharacteristic
98C22×C4×C5C2×Q811yescharacteristic
99C22×C4×C5#4111yescharacteristic
100C22×C4×C5#4111yescharacteristic
101C2×C22⋊D5—22no—
102C2×C22⋊D5—22no—
103C2×C22⋊D5—41no—
104C2×C22⋊D5—41no—
105C2×C22⋊D5—41no—
106C2×C22⋊D5—41no—
107C22×Dic5—21no—
108C22×Dic5—21no—
109C22×Dic5—21no—
110C2×D20—21no—
111C2×D20—41no—
112C2×D20—41no—
113C2×D20C4⋊C412yescomplemented
114C2×C4×D5—42no—
115C2×C4×D5—42no—
116C2×C4×D5—42no—
117C5×C4⋊C4—48no—
118C42×C5—22no—
119C42×C5—22no—
120C42×C5—41no—
121C42×C5—41no—
122C22⋊Dic5—41no—
123C22⋊Dic5—41no—
124#685—22no—
125#685—22no—
126#685—42no—
127#685—42no—
128#685—42no—
129C4⋊Dic5—21no—
130C4⋊Dic5—41no—
131C4⋊Dic5—41no—
132C4⋊Dic5C4⋊C412yescomplemented
133#683—42no—
134C4×Dic5—42no—
135C2×#168—42no—
136C2×#168—42no—
137C2×#168—42no—
138C2×#121—51no—
139C2×C4×D4—51no—
140C2×C4×D4—101no—
141C22×C4⋊C4—21no—
142C22×C42C2×D511yescharacteristic
143C2×C4⋊C8—101no—
144C2×C22⋊C8—52no—
145#390—51no—
146#389—51no—
147#388—101no—
148#386—101no—
149#380—51no—
150C4×C4⋊C4—51no—
151C4×C22⋊C4—101no—
152C2×#95—21no—
153C2×#95C2×D512yes—
154#336—101no—
155#327—104no—
156C23×C5—21no—
157C23×C5—21no—
158C23×C5—21no—
159C23×C5—21no—
160C23×C5C2×C22⋊C411yescharacteristic
161C23×C5#12111yescharacteristic
162C23×C5C22⋊Q811yescharacteristic
163C23×C5C2×D811yescharacteristic
164C23×C5C2×SD1611yescharacteristic
165C23×C5AGL(1,ℤ/8)11yescharacteristic
166C23×C5#13711yescharacteristic
167C22×D5—22no—
168C22×D5—41no—
169C22×D5—41no—
170C22×D5—41no—
171C22×D5—41no—
172C22×D5—41no—
173C22×D5—41no—
174C2×C4×C5—24no—
175C2×C4×C5—24no—
176C2×C4×C5—21no—
177C2×C4×C5—21no—
178C2×C4×C5—21no—
179C2×C4×C5—21no—
180C2×C4×C5—21no—
181C2×C4×C5—21no—
182C2×C4×C5—21no—
183C2×C4×C5—21no—
184C2×C4×C5—21no—
185C2×C4×C5—21no—
186C2×C4×C5—21no—
187C2×C4×C5—21no—
188C2×C4×C5—42no—
189C2×C4×C5—42no—
190C2×C4×C5—41no—
191C2×C4×C5—41no—
192C2×C4×C5—41no—
193C2×C4×C5—41no—
194C2×C4×C5—44no—
195C2×C4×C5—44no—
196C2×C4×C5—44no—
197C2×C4×C5—82no—
198C2×C4×C5—82no—
199C2×C4×C5—82no—
200C2×C4×C5—82no—
201C2×C4×C5#9912yes—
202C2×C4×C5#10212yes—
203C2×C4×C5#10212yes—
204C2×C4×C5#10412yes—
205C2×C4×C5C2×C4⋊C411yescharacteristic
206C2×C4×C5#11711yescharacteristic
207C2×C4×C5#12111yescharacteristic
208C2×C4×C5C22⋊Q811yescharacteristic
209C22⋊D5—42no—
210C22⋊D5—42no—
211C22⋊D5—42no—
212C22⋊D5—42no—
213C2×Dic5—22no—
214C2×Dic5—41no—
215C2×Dic5—41no—
216C2×Dic5—41no—
217C2×Dic5—41no—
218C2×Dic5—41no—
219C2×Dic5—41no—
220C2×Dic5—41no—
221C2×Dic5—41no—
222D20—42no—
223D20—42no—
224C4×D5—84no—
225#168—82no—
226C22×D4—51no—
227C22×D4—101no—
228C23×C4—22no—
229C23×C4—101no—
230C23×C4C22⋊D511yescharacteristic
231C23×C4C22⋊D511yescharacteristic
232C23×C4C22×D511yescharacteristic
233C22×C8—102no—
234#121—52no—
235#121—52no—
236#121—101no—
237#121—101no—
238C4×D4—202no—
239C4×D4—202no—
240C4×D4—202no—
241C2×C4⋊C4—24no—
242C2×C4⋊C4—42no—
243C2×C4⋊C4—42no—
244C2×C4⋊C4—51no—
245C2×C4⋊C4—51no—
246C2×C4⋊C4—51no—
247C2×C4⋊C4—101no—
248C2×C22⋊C4—101no—
249C2×C22⋊C4—101no—
250C2×C22⋊C4—101no—
251C2×C22⋊C4—101no—
252C2×C22⋊C4—101no—
253C2×C42—42no—
254C2×C42—101no—
255C2×C42C4×D511yescharacteristic
256C2×C42C4×D511yescharacteristic
257C2×C42D2011yescharacteristic
258C2×C42D2011yescharacteristic
259C4⋊C8—202no—
260C22⋊C8—102no—
261C22⋊C8—102no—
262#95—22no—
263#95—22no—
264#95—42no—
265#95—101no—
266#95—101no—
267#95—101no—
268C22×C5—21no—
269C22×C5—21no—
270C22×C5—21no—
271C22×C5—21no—
272C22×C5—21no—
273C22×C5—21no—
274C22×C5—21no—
275C22×C5—21no—
276C22×C5—21no—
277C22×C5—21no—
278C22×C5—21no—
279C22×C5—21no—
280C22×C5#38011yescharacteristic
281C22×C5C2×#9911yescharacteristic
282C22×C5#41011yescharacteristic
283C22×C5C2×#10211yescharacteristic
284C22×C5#41711yescharacteristic
285C22×C5C2×#10411yescharacteristic
286C22×C5#42111yescharacteristic
287C22×C5#45911yescharacteristic
288C22×C5#46111yescharacteristic
289C22×C5#47411yescharacteristic
290C22×C5#47611yescharacteristic
291C2×D5—42no—
292C2×D5—42no—
293C2×D5—42no—
294C2×D5—81no—
295C2×D5—81no—
296C2×D5—81no—
297C2×D5—81no—
298C4×C5—21no—
299C4×C5—21no—
300C4×C5—21no—
301C4×C5—21no—
302C4×C5—22no—
303C4×C5—22no—
304C4×C5—22no—
305C4×C5—22no—
306C4×C5—84no—
307Dic5—42no—
308Dic5—81no—
309Dic5—81no—
310C24—101no—
311C24C2×C22⋊D511yescharacteristic
312C2×D4—52no—
313C2×D4—102no—
314C2×D4—102no—
315C2×D4—101no—
316C2×D4—201no—
317C2×D4—201no—
318C2×D4—201no—
319C2×D4—201no—
320C2×D4—201no—
321C2×D4—201no—
322C22×C4—21no—
323C22×C4—21no—
324C22×C4—22no—
325C22×C4—22no—
326C22×C4—24no—
327C22×C4—41no—
328C22×C4—41no—
329C22×C4—41no—
330C22×C4—41no—
331C22×C4—42no—
332C22×C4—42no—
333C22×C4—42no—
334C22×C4—42no—
335C22×C4—42no—
336C22×C4—42no—
337C22×C4—101no—
338C22×C4—101no—
339C22×C4—101no—
340C22×C4—202no—
341C22×C4—202no—
342C22×C4—202no—
343C22×C4#68511yescharacteristic
344C22×C4#68511yescharacteristic
345C22×C4#68511yescharacteristic
346C22×C4#68511yescharacteristic
347C22×C4#68612yes—
348C22×C4#68812yes—
349C22×C4C2×C4×D511yescharacteristic
350C22×C4C2×D2011yescharacteristic
351C22×C4D4×D511yescharacteristic
352C22×C4#71111yescharacteristic
353C22×C4Q8×D511yescharacteristic
354C22×C4#71311yescharacteristic
355C2×C8—202no—
356C2×C8—202no—
357C2×C8—202no—
358C4⋊C4—48no—
359C4⋊C4—52no—
360C4⋊C4—101no—
361C4⋊C4—201no—
362C4⋊C4—201no—
363C4⋊C4—202no—
364C22⋊C4—102no—
365C22⋊C4—102no—
366C22⋊C4—201no—
367C22⋊C4—201no—
368C22⋊C4—202no—
369C22⋊C4—202no—
370C22⋊C4—202no—
371C42—22no—
372C42—22no—
373C42—41no—
374C42—41no—
375C42—202no—
376C2×C5—21no—
377C2×C5—21no—
378C2×C5—21no—
379C2×C5—21no—
380C2×C5#150211yescharacteristic
381C2×C5#150411yescharacteristic
382C2×C5#151211yescharacteristic
383C2×C5#151911yescharacteristic
384C2×C5#179911yescharacteristic
385C2×C5#180211yescharacteristic
386C2×C5#180611yescharacteristic
387D5—82no—
388C23—21no—
389C23—21no—
390C23—21no—
391C23—21no—
392C23—102no—
393C23—201no—
394C23—201no—
395C23—201no—
396C23—201no—
397C23—201no—
398C23—201no—
399C23C2×#68511yescharacteristic
400C23C2×#68611yescharacteristic
401C23#407811yescharacteristic
402C23#408411yescharacteristic
403C23C2×#68811yescharacteristic
404C23#408811yescharacteristic
405C23#409211yescharacteristic
406D4—202no—
407D4—202no—
408D4—202no—
409D4—202no—
410D4—202no—
411D4—202no—
412C2×C4—24no—
413C2×C4—24no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—42no—
427C2×C4—42no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—44no—
433C2×C4—44no—
434C2×C4—44no—
435C2×C4—82no—
436C2×C4—82no—
437C2×C4—82no—
438C2×C4—82no—
439C2×C4—102no—
440C2×C4—201no—
441C2×C4—201no—
442C2×C4—201no—
443C2×C4—201no—
444C2×C4—201no—
445C2×C4—201no—
446C2×C4—201no—
447C2×C4—201no—
448C2×C4—404no—
449C2×C4#393712yes—
450C2×C4#393812yes—
451C2×C4#394112yes—
452C2×C4#394112yes—
453C2×C4D5×C4⋊C411yescharacteristic
454C2×C4#403811yescharacteristic
455C2×C4#404111yescharacteristic
456C2×C4#404311yescharacteristic
457C8—402no—
458C5#857711yescharacteristic, complemented, Sylow
459C22—21no—
460C22—21no—
461C22—21no—
462C22—21no—
463C22—21no—
464C22—21no—
465C22—21no—
466C22—21no—
467C22—21no—
468C22—21no—
469C22—21no—
470C22—21no—
471C22—202no—
472C22—202no—
473C22—202no—
474C22—401no—
475C22—401no—
476C22—401no—
477C22—401no—
478C22C2×#393711yescharacteristic
479C22C2×#393811yescharacteristic
480C22C2×#394111yescharacteristic
481C22#6525511yescharacteristic
482C22#6527611yescharacteristic
483C22#6529411yescharacteristic
484C22#6529511yescharacteristic
485C22#6536111yescharacteristic
486C22#6537211yescharacteristic
487C22#6537311yescharacteristic
488C22#6537611yescharacteristic
489C4—22no—
490C4—22no—
491C4—21no—
492C4—21no—
493C4—21no—
494C4—21no—
495C4—22no—
496C4—22no—
497C4—84no—
498C4—202no—
499C4—401no—
500C4—401no—
501C2—21no—
502C2—21no—
503C2—21no—
504C2—21no—
505C2—402no—
506C2#1060019111yescharacteristic
507C2#1060026211yescharacteristic
508C2#1060028711yescharacteristic
509C2#1060030211yescharacteristic
510C2#1060032311yescharacteristic
511C2#1060033711yescharacteristic
512C2#1060037711yescharacteristic
subgroupG/H
centerC23C2×#685
commutatorC22×C4×C5C22×C4
FrattiniC23×C4C22×D5
FittingC5×C4⋊#95C2
socleC23×C5C2×C22⋊C4
prime radicalC2×#4076C22
cosocleC23×C4×C5C23
hypercenterC4⋊#95D5
hypocenterC5#8577
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C22×C42 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
2. C5×C4⋊#95C2semidirect
3. #10602323C2semidirect
5. #10598103C2semidirect
10. C2×C4×D20C4semidirect
17. #65228C4semidirect
19. C4×C4⋊Dic5C4semidirect
20. #65217C4semidirect
70. C4⋊#95D5semidirect
113. C2×D20C4⋊C4semidirect
132. C4⋊Dic5C4⋊C4semidirect
458. C5#8577semidirect

Maximal subgroups

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

subgroupindex
C4×#40762
C5×C4⋊#952
#106023232
C2×#646712
#105981032
#85775