Finite Group Databasebeta

← #11994702

Subgroups — #11994702

Order 1280.

928 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#385C211yesmaximal, characteristic
2C2×#65496C211yesmaximal, characteristic
3#10602919C211yesmaximal, characteristic
4C2×#64748C212yesmaximal, complemented
5#10598104C212yesmaximal, complemented
6C24×C4×C5C2211yescharacteristic
7C22×C5×C4⋊C4C411yescharacteristic
8C22×C5×C4⋊C4C2211yescharacteristic
9C22×C5×C22⋊C4C411yescharacteristic
10C22×C5×C22⋊C4C411yescharacteristic
11C22×#681—21no—
12C5×#385—21no—
13C5×#385—21no—
14C5×#385—21no—
15C5×#385—21no—
16C2×C5×#95C411yescharacteristic
17C2×C5×#95C2211yescharacteristic
18#65496—24no—
19C2×C22⋊#168—21no—
20C2×C22⋊#168—21no—
21C2×C22⋊#168—21no—
22C2×C22⋊#168C2212yes—
23C2×C22⋊#168C2212yes—
24#64748—24no—
25#9085—51nomaximal, Sylow
26C25×C5C2×C411yescharacteristic
27C23×C4×C5—22no—
28C23×C4×C5—22no—
29C23×C4×C5—42no—
30C23×C4×C5—42no—
31C23×C4×C5C2×C411yescharacteristic
32C23×C4×C5C2×C411yescharacteristic
33C23×C4×C5C2×C411yescharacteristic
34C23×C4×C5C2×C411yescharacteristic
35C23×C4×C5C2×C411yescharacteristic
36C23×C4×C5D411yescharacteristic
37C23×C4×C5D411yescharacteristic
38C23×C4×C5D411yescharacteristic
39C23×C4×C5D411yescharacteristic
40C23×C4×C5C2311yescharacteristic
41C2×C5×C4⋊C4—21no—
42C2×C5×C4⋊C4—21no—
43C2×C5×C4⋊C4—21no—
44C2×C5×C4⋊C4—21no—
45C2×C5×C4⋊C4—22no—
46C2×C5×C4⋊C4—22no—
47C2×C5×C4⋊C4—42no—
48C2×C5×C22⋊C4—21no—
49C2×C5×C22⋊C4—21no—
50C2×C5×C22⋊C4—22no—
51C2×C5×C22⋊C4—22no—
52C2×C5×C22⋊C4—21no—
53C2×C5×C22⋊C4—21no—
54C2×C5×C22⋊C4—42no—
55C2×#681—24no—
56C2×#681—42no—
57C2×#681—42no—
58C22×#168—22no—
59C22×#168—22no—
60C5×#95—21no—
61C5×#95—21no—
62C5×#95—21no—
63C5×#95—21no—
64C22⋊#168—24no—
65C22⋊#168—22no—
66C22⋊#168—22no—
67C22⋊#168—22no—
68C22⋊#168—42no—
69C22⋊#168—42no—
70C22⋊#168D414yes—
71C2×#407—51no—
72C2×#385D511yescharacteristic
73#1779—51no—
74C2×#324—52no—
75#1280—52no—
76C24×C5—22no—
77C24×C5—22no—
78C24×C5—21no—
79C24×C5—21no—
80C24×C5—22no—
81C24×C5—22no—
82C24×C5—41no—
83C24×C5—41no—
84C24×C5C22⋊C411yescharacteristic
85C24×C5C22⋊C411yescharacteristic
86C24×C5C22×C411yescharacteristic
87C22×C4×C5—22no—
88C22×C4×C5—22no—
89C22×C4×C5—21no—
90C22×C4×C5—21no—
91C22×C4×C5—22no—
92C22×C4×C5—21no—
93C22×C4×C5—21no—
94C22×C4×C5—22no—
95C22×C4×C5—22no—
96C22×C4×C5—21no—
97C22×C4×C5—21no—
98C22×C4×C5—22no—
99C22×C4×C5—22no—
100C22×C4×C5—22no—
101C22×C4×C5—21no—
102C22×C4×C5—22no—
103C22×C4×C5—22no—
104C22×C4×C5—21no—
105C22×C4×C5—21no—
106C22×C4×C5—21no—
107C22×C4×C5—22no—
108C22×C4×C5—22no—
109C22×C4×C5—41no—
110C22×C4×C5—41no—
111C22×C4×C5—41no—
112C22×C4×C5—41no—
113C22×C4×C5—41no—
114C22×C4×C5—41no—
115C22×C4×C5—41no—
116C22×C4×C5—48no—
117C22×C4×C5—48no—
118C22×C4×C5—41no—
119C22×C4×C5—41no—
120C22×C4×C5—41no—
121C22×C4×C5—41no—
122C22×C4×C5—41no—
123C22×C4×C5—41no—
124C22×C4×C5C22⋊C411yescharacteristic
125C22×C4×C5C22⋊C411yescharacteristic
126C22×C4×C5M1612yescomplemented
127C22×C4×C5M1612yescomplemented
128C22×C4×C5C2×D412yes—
129C22×C4×C5C2×D411yescharacteristic
130C22×C4×C5C2×D411yescharacteristic
131C22×C4×C5#4112yes—
132C5×C4⋊C4—42no—
133C5×C4⋊C4—42no—
134C5×C4⋊C4—41no—
135C5×C4⋊C4—42no—
136C5×C4⋊C4—41no—
137C5×C22⋊C4—24no—
138C5×C22⋊C4—24no—
139C5×C22⋊C4—42no—
140C5×C22⋊C4—42no—
141#681—48no—
142C2×#168—24no—
143C2×#168—42no—
144C2×#168—42no—
145C2×#168—42no—
146C2×#168—42no—
147C2×#168—42no—
148C24×C4C2×D511yescharacteristic
149C22×M16—101no—
150C22×C4⋊C4Dic511yescharacteristic
151C22×C4⋊C4C2×D511yescharacteristic
152C22×C22⋊C4Dic511yescharacteristic
153C22×C22⋊C4Dic511yescharacteristic
154#407—104no—
155C2×C22⋊C8—52no—
156C2×C22⋊C8—52no—
157C2×C22⋊C8—101no—
158C2×C22⋊C8—101no—
159C2×C22⋊C8—101no—
160#385—21no—
161#385—21no—
162#385—21no—
163#385—21no—
164C2×#95Dic511yescharacteristic
165C2×#95C2×D511yescharacteristic
166#324—104no—
167C23×C5—21no—
168C23×C5—21no—
169C23×C5—21no—
170C23×C5—21no—
171C23×C5—24no—
172C23×C5—24no—
173C23×C5—21no—
174C23×C5—21no—
175C23×C5—21no—
176C23×C5—21no—
177C23×C5—21no—
178C23×C5—21no—
179C23×C5—21no—
180C23×C5—21no—
181C23×C5—21no—
182C23×C5—21no—
183C23×C5—21no—
184C23×C5—21no—
185C23×C5—44no—
186C23×C5—44no—
187C23×C5—44no—
188C23×C5—44no—
189C23×C5—42no—
190C23×C5—42no—
191C23×C5—42no—
192C23×C5—42no—
193C23×C5#9912yes—
194C23×C5#10112yes—
195C23×C5C2×C22⋊C411yescharacteristic
196C23×C5C4×D412yes—
197C23×C5C2×M1611yescharacteristic
198C23×C5C2×M1611yescharacteristic
199C23×C5#13112yes—
200C2×C4×C5—24no—
201C2×C4×C5—24no—
202C2×C4×C5—21no—
203C2×C4×C5—21no—
204C2×C4×C5—21no—
205C2×C4×C5—21no—
206C2×C4×C5—21no—
207C2×C4×C5—21no—
208C2×C4×C5—21no—
209C2×C4×C5—22no—
210C2×C4×C5—22no—
211C2×C4×C5—21no—
212C2×C4×C5—21no—
213C2×C4×C5—24no—
214C2×C4×C5—42no—
215C2×C4×C5—42no—
216C2×C4×C5—44no—
217C2×C4×C5—44no—
218C2×C4×C5—44no—
219C2×C4×C5—42no—
220C2×C4×C5—42no—
221C2×C4×C5—42no—
222C2×C4×C5—41no—
223C2×C4×C5—41no—
224C2×C4×C5—41no—
225C2×C4×C5—41no—
226C2×C4×C5—42no—
227C2×C4×C5—42no—
228C2×C4×C5—41no—
229C2×C4×C5—41no—
230C2×C4×C5—41no—
231C2×C4×C5—41no—
232C2×C4×C5—41no—
233C2×C4×C5—41no—
234C2×C4×C5—82no—
235C2×C4×C5—82no—
236C2×C4×C5#9912yes—
237C2×C4×C5#12011yescharacteristic
238C2×C4×C5#12112yes—
239C2×C4×C5#12311yescharacteristic
240#168—44no—
241#168—82no—
242C25C2×Dic511yescharacteristic
243C23×C4—22no—
244C23×C4—22no—
245C23×C4—42no—
246C23×C4—42no—
247C23×C4C2×Dic511yescharacteristic
248C23×C4C2×Dic511yescharacteristic
249C23×C4C2×Dic511yescharacteristic
250C23×C4C2×Dic511yescharacteristic
251C23×C4C2×Dic511yescharacteristic
252C23×C4C22⋊D511yescharacteristic
253C23×C4C22⋊D511yescharacteristic
254C23×C4C22⋊D511yescharacteristic
255C23×C4C22⋊D511yescharacteristic
256C23×C4C22×D511yescharacteristic
257C2×M16—104no—
258C2×M16—202no—
259C2×M16—202no—
260C22×C8—102no—
261C22×C8—102no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—22no—
265C2×C4⋊C4—22no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—42no—
269C2×C22⋊C4—21no—
270C2×C22⋊C4—21no—
271C2×C22⋊C4—22no—
272C2×C22⋊C4—22no—
273C2×C22⋊C4—21no—
274C2×C22⋊C4—21no—
275C2×C22⋊C4—42no—
276C22⋊C8—54no—
277C22⋊C8—104no—
278C22⋊C8—102no—
279C22⋊C8—102no—
280C22⋊C8—102no—
281C22⋊C8—202no—
282C22⋊C8—202no—
283#95—21no—
284#95—21no—
285#95—21no—
286#95—21no—
287C22×C5—22no—
288C22×C5—22no—
289C22×C5—21no—
290C22×C5—21no—
291C22×C5—21no—
292C22×C5—21no—
293C22×C5—22no—
294C22×C5—22no—
295C22×C5—22no—
296C22×C5—22no—
297C22×C5—22no—
298C22×C5—22no—
299C22×C5—22no—
300C22×C5—22no—
301C22×C5—48no—
302C22×C5—48no—
303C22×C5—41no—
304C22×C5—41no—
305C22×C5—41no—
306C22×C5—41no—
307C22×C5—41no—
308C22×C5—41no—
309C22×C5—41no—
310C22×C5—41no—
311C22×C5#38611yescharacteristic
312C22×C5#40711yescharacteristic
313C22×C5#40811yescharacteristic
314C22×C5C2×#9911yescharacteristic
315C22×C5C2×#9911yescharacteristic
316C22×C5C2×#10111yescharacteristic
317C22×C5#41311yescharacteristic
318C22×C5#43512yes—
319C22×C5#43612yes—
320C4×C5—21no—
321C4×C5—22no—
322C4×C5—22no—
323C4×C5—21no—
324C4×C5—42no—
325C4×C5—41no—
326C4×C5—42no—
327C4×C5—81no—
328C4×C5—81no—
329C24—22no—
330C24—22no—
331C24—21no—
332C24—21no—
333C24—22no—
334C24—22no—
335C24—41no—
336C24—41no—
337C24C22⋊Dic511yescharacteristic
338C24C22⋊Dic511yescharacteristic
339C24C22×Dic511yescharacteristic
340C22×C4—22no—
341C22×C4—22no—
342C22×C4—21no—
343C22×C4—21no—
344C22×C4—21no—
345C22×C4—21no—
346C22×C4—22no—
347C22×C4—21no—
348C22×C4—21no—
349C22×C4—22no—
350C22×C4—22no—
351C22×C4—22no—
352C22×C4—22no—
353C22×C4—22no—
354C22×C4—21no—
355C22×C4—21no—
356C22×C4—22no—
357C22×C4—22no—
358C22×C4—21no—
359C22×C4—21no—
360C22×C4—22no—
361C22×C4—22no—
362C22×C4—41no—
363C22×C4—41no—
364C22×C4—41no—
365C22×C4—41no—
366C22×C4—41no—
367C22×C4—41no—
368C22×C4—41no—
369C22×C4—48no—
370C22×C4—48no—
371C22×C4—41no—
372C22×C4—41no—
373C22×C4—41no—
374C22×C4—41no—
375C22×C4—41no—
376C22×C4—41no—
377C22×C4#68112yescomplemented
378C22×C4#68112yescomplemented
379C22×C4C22⋊Dic511yescharacteristic
380C22×C4C22⋊Dic511yescharacteristic
381C22×C4D4×D512yes—
382C22×C4#71112yes—
383C22×C4C2×C22⋊D511yescharacteristic
384C22×C4C2×C22⋊D511yescharacteristic
385M16—208no—
386C2×C8—104no—
387C2×C8—202no—
388C2×C8—202no—
389C2×C8—202no—
390C2×C8—202no—
391C2×C8—202no—
392C4⋊C4—42no—
393C4⋊C4—42no—
394C4⋊C4—41no—
395C4⋊C4—41no—
396C4⋊C4—42no—
397C22⋊C4—24no—
398C22⋊C4—24no—
399C22⋊C4—42no—
400C22⋊C4—42no—
401C2×C5—22no—
402C2×C5—22no—
403C2×C5—42no—
404C2×C5—42no—
405C2×C5#146311yescharacteristic
406C2×C5#146511yescharacteristic
407C2×C5#146811yescharacteristic
408C2×C5#147211yescharacteristic
409C2×C5#187011yescharacteristic
410C2×C5#189811yescharacteristic
411C2×C5#190111yescharacteristic
412C23—21no—
413C23—21no—
414C23—21no—
415C23—21no—
416C23—24no—
417C23—24no—
418C23—21no—
419C23—21no—
420C23—21no—
421C23—21no—
422C23—21no—
423C23—21no—
424C23—21no—
425C23—21no—
426C23—21no—
427C23—21no—
428C23—21no—
429C23—21no—
430C23—44no—
431C23—44no—
432C23—44no—
433C23—44no—
434C23—42no—
435C23—42no—
436C23—42no—
437C23—42no—
438C23#396612yes—
439C23#396812yes—
440C23C2×#68111yescharacteristic
441C23C2×#68111yescharacteristic
442C23D4×Dic512yes—
443C23#409412yes—
444C23C2×C22⋊Dic511yescharacteristic
445C2×C4—24no—
446C2×C4—24no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—24no—
454C2×C4—22no—
455C2×C4—22no—
456C2×C4—21no—
457C2×C4—21no—
458C2×C4—21no—
459C2×C4—42no—
460C2×C4—42no—
461C2×C4—44no—
462C2×C4—44no—
463C2×C4—44no—
464C2×C4—42no—
465C2×C4—42no—
466C2×C4—42no—
467C2×C4—42no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—42no—
473C2×C4—41no—
474C2×C4—41no—
475C2×C4—41no—
476C2×C4—41no—
477C2×C4—41no—
478C2×C4—41no—
479C2×C4—82no—
480C2×C4—82no—
481C2×C4#396612yes—
482C2×C4#408111yescharacteristic
483C2×C4#408311yescharacteristic
484C2×C4#408512yes—
485C8—204no—
486C8—402no—
487C5#908511yescharacteristic, complemented, Sylow
488C22—21no—
489C22—21no—
490C22—21no—
491C22—21no—
492C22—22no—
493C22—22no—
494C22—22no—
495C22—22no—
496C22—22no—
497C22—22no—
498C22—22no—
499C22—22no—
500C22—22no—
501C22—22no—
502C22—48no—
503C22—48no—
504C22—41no—
505C22—41no—
506C22—41no—
507C22—41no—
508C22—41no—
509C22—41no—
510C22—41no—
511C22—41no—
512C22#6530012yes—
513C22#6530112yes—
514C22#6549611yescharacteristic
515C22C2×#396611yescharacteristic
516C22C2×#396611yescharacteristic
517C22#6550911yescharacteristic
518C22C2×#396811yescharacteristic
519C22#6552311yescharacteristic
520C22#6552611yescharacteristic
521C4—21no—
522C4—22no—
523C4—22no—
524C4—21no—
525C4—42no—
526C4—42no—
527C4—41no—
528C4—81no—
529C4—81no—
530C2—22no—
531C2—22no—
532C2—42no—
533C2—42no—
534C2#1060234511yescharacteristic
535C2#1060239511yescharacteristic
536C2#1060240411yescharacteristic
537C2#1060246311yescharacteristic
538C2#1060248411yescharacteristic
539C2#1060249111yescharacteristic
540C2#1060249511yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic5
commutatorC24×C5C22×C4
FrattiniC23×C4C22×D5
FittingC2×C5×#385C2
socleC23×C5C2×C22⋊C4
prime radicalC25×C5C2×C4
cosocleC23×C4×C5C23
hypercenterC2×#385D5
hypocenterC5#9085
LCSG ▷ C24×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C24×C4 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
4. C2×#64748C2semidirect
5. #10598104C2semidirect
126. C22×C4×C5M16semidirect
127. C22×C4×C5M16semidirect
377. C22×C4#681semidirect
378. C22×C4#681semidirect
487. C5#9085semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#3852
C2×#654962
#106029192
C2×#647482
#105981042
#90855