Finite Group Databasebeta

← #12007164

Subgroups — #12007164

Order 1280.

1042 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#407C211yesmaximal, characteristic
2C2×#65501C211yesmaximal, characteristic
3C2×#65496C211yesmaximal, characteristic
4C2×#64774C212yesmaximal, complemented
5C2×#64774C212yesmaximal, complemented
6C24×C4×C5C2211yescharacteristic
7C22×C5×M16C2212yes—
8C22×C22⋊Dic5C412yes—
9C22×C4⋊Dic5C2211yescharacteristic
10C22×C4⋊Dic5C2211yescharacteristic
11C22×#681C2212yes—
12C5×#407—24no—
13C2×C5×C22⋊C8—21no—
14C2×C5×C22⋊C8—21no—
15#65501—21no—
16#65501—21no—
17#65501—21no—
18#65501—21no—
19C2×#3963C412yes—
20#65496—24no—
21C2×C22⋊#168—21no—
22C2×C22⋊#168—21no—
23#64774—24no—
24#64774—24no—
25#11198—51nomaximal, Sylow
26C25×C5C2×C411yescharacteristic
27C23×C4×C5—22no—
28C23×C4×C5—22no—
29C23×C4×C5—22no—
30C23×C4×C5—22no—
31C23×C4×C5—22no—
32C23×C4×C5—22no—
33C23×C4×C5C2×C411yescharacteristic
34C23×C4×C5D411yescharacteristic
35C23×C4×C5D411yescharacteristic
36C23×C4×C5D411yescharacteristic
37C23×C4×C5D411yescharacteristic
38C23×C4×C5C2311yescharacteristic
39C23×Dic5C2×C412yes—
40C23×Dic5C2×C412yes—
41C2×C5×M16—22no—
42C2×C5×M16—22no—
43C2×C5×M16—22no—
44C2×C5×M16—22no—
45C2×C5×M16—22no—
46C2×C5×M16D414yes—
47C22×C5×C8—22no—
48C2×C22⋊Dic5—22no—
49C2×C22⋊Dic5—22no—
50C2×C22⋊Dic5—44no—
51C2×C4⋊Dic5—22no—
52C2×C4⋊Dic5—22no—
53C2×C4⋊Dic5—21no—
54C2×C4⋊Dic5—21no—
55C2×C4⋊Dic5—21no—
56C2×C4⋊Dic5—21no—
57C2×C4⋊Dic5—22no—
58C2×C4⋊Dic5—22no—
59C2×#681—22no—
60C2×#681—22no—
61C2×#681—22no—
62C2×#681—22no—
63C2×#681—22no—
64C2×#681D414yes—
65C22×#168—22no—
66C5×C22⋊C8—24no—
67C5×C22⋊C8—24no—
68#3963—22no—
69#3963—22no—
70C22⋊#168—24no—
71C22⋊#168—24no—
72C2×#407—51no—
73C2×#407D511yescharacteristic
74C2×#380—51no—
75C2×#343—52no—
76C2×#343—52no—
77C24×C5—22no—
78C24×C5—22no—
79C24×C5—21no—
80C24×C5—21no—
81C24×C5—22no—
82C24×C5—22no—
83C24×C5—41no—
84C24×C5—41no—
85C24×C5C22⋊C411yescharacteristic
86C24×C5C22⋊C411yescharacteristic
87C24×C5C22×C411yescharacteristic
88C22×C4×C5—21no—
89C22×C4×C5—21no—
90C22×C4×C5—22no—
91C22×C4×C5—22no—
92C22×C4×C5—21no—
93C22×C4×C5—21no—
94C22×C4×C5—21no—
95C22×C4×C5—21no—
96C22×C4×C5—22no—
97C22×C4×C5—22no—
98C22×C4×C5—22no—
99C22×C4×C5—22no—
100C22×C4×C5—22no—
101C22×C4×C5—22no—
102C22×C4×C5—21no—
103C22×C4×C5—21no—
104C22×C4×C5—21no—
105C22×C4×C5—21no—
106C22×C4×C5—22no—
107C22×C4×C5—22no—
108C22×C4×C5—42no—
109C22×C4×C5—42no—
110C22×C4×C5—42no—
111C22×C4×C5—42no—
112C22×C4×C5—42no—
113C22×C4×C5—42no—
114C22×C4×C5—42no—
115C22×C4×C5—42no—
116C22×C4×C5C22⋊C411yescharacteristic
117C22×C4×C5C22⋊C411yescharacteristic
118C22×C4×C5C2×D411yescharacteristic
119C22×C4×C5C2×D412yes—
120C22×C4×C5C2×D412yes—
121C22×C4×C5C2×D411yescharacteristic
122C22×C4×C5#4112yes—
123C22×C4×C5#4112yes—
124C22×C4×C5#4112yes—
125C22×C4×C5#4112yes—
126C22×Dic5—22no—
127C22×Dic5—22no—
128C22×Dic5—24no—
129C22×Dic5—24no—
130C22×Dic5—42no—
131C22×Dic5—42no—
132C22×Dic5—42no—
133C22×Dic5—42no—
134C5×M16—24no—
135C5×M16—24no—
136C5×M16—42no—
137C5×M16—42no—
138C2×C5×C8—24no—
139C2×C5×C8—42no—
140C2×C5×C8—42no—
141C22⋊Dic5—44no—
142C22⋊Dic5—44no—
143C4⋊Dic5—41no—
144C4⋊Dic5—41no—
145C4⋊Dic5—42no—
146C4⋊Dic5—42no—
147C4⋊Dic5—41no—
148C4⋊Dic5—41no—
149#681—24no—
150#681—24no—
151#681—42no—
152#681—42no—
153C2×#168—24no—
154C2×#168—42no—
155C2×#168—42no—
156C24×C4C2×D511yescharacteristic
157C22×M16—52no—
158C22×M16C2×D512yes—
159C22×C4⋊C4—51no—
160C22×C4⋊C4—51no—
161C22×C22⋊C4—52no—
162#407—24no—
163#407—104no—
164C2×C22⋊C8—21no—
165C2×C22⋊C8—21no—
166C2×C22⋊C8—101no—
167C2×C22⋊C8—101no—
168#380—101no—
169#380—101no—
170#380—101no—
171#380—101no—
172C2×#95—52no—
173#343—104no—
174#343—104no—
175C23×C5—21no—
176C23×C5—21no—
177C23×C5—21no—
178C23×C5—21no—
179C23×C5—24no—
180C23×C5—24no—
181C23×C5—21no—
182C23×C5—21no—
183C23×C5—21no—
184C23×C5—21no—
185C23×C5—21no—
186C23×C5—21no—
187C23×C5—21no—
188C23×C5—21no—
189C23×C5—21no—
190C23×C5—21no—
191C23×C5—21no—
192C23×C5—21no—
193C23×C5—44no—
194C23×C5—44no—
195C23×C5—44no—
196C23×C5—44no—
197C23×C5—42no—
198C23×C5—42no—
199C23×C5—42no—
200C23×C5—42no—
201C23×C5#10012yes—
202C23×C5#10112yes—
203C23×C5C2×C22⋊C411yescharacteristic
204C23×C5#11711yescharacteristic
205C23×C5#11711yescharacteristic
206C23×C5C4×D412yes—
207C23×C5C4×D412yes—
208C2×C4×C5—21no—
209C2×C4×C5—21no—
210C2×C4×C5—21no—
211C2×C4×C5—21no—
212C2×C4×C5—21no—
213C2×C4×C5—21no—
214C2×C4×C5—42no—
215C2×C4×C5—42no—
216C2×C4×C5—42no—
217C2×C4×C5—42no—
218C2×C4×C5—42no—
219C2×C4×C5—42no—
220C2×C4×C5—42no—
221C2×C4×C5—42no—
222C2×C4×C5—42no—
223C2×C4×C5—42no—
224C2×C4×C5#12011yescharacteristic
225C2×C4×C5#12011yescharacteristic
226C2×C4×C5#12112yes—
227C2×C4×C5#12112yes—
228C2×C4×C5#12112yes—
229C2×C4×C5#12112yes—
230C2×C4×C5#12312yes—
231C2×C4×C5#12312yes—
232C2×C4×C5#12311yescharacteristic
233C2×C4×C5#12311yescharacteristic
234C2×C4×C5#12312yes—
235C2×C4×C5#12312yes—
236C2×C4×C5#12412yes—
237C2×C4×C5#12412yes—
238C2×C4×C5#12612yes—
239C2×C4×C5#12612yes—
240C2×Dic5—42no—
241C2×Dic5—42no—
242C2×Dic5—42no—
243C2×Dic5—42no—
244C2×Dic5—42no—
245C2×Dic5—42no—
246C2×Dic5—84no—
247C2×Dic5—84no—
248C5×C8—44no—
249#168—44no—
250C25C4×D511yescharacteristic
251C23×C4—22no—
252C23×C4—22no—
253C23×C4—22no—
254C23×C4—22no—
255C23×C4—22no—
256C23×C4—22no—
257C23×C4—52no—
258C23×C4—52no—
259C23×C4C4×D511yescharacteristic
260C23×C4D2011yescharacteristic
261C23×C4D2011yescharacteristic
262C23×C4C22⋊D511yescharacteristic
263C23×C4C22⋊D511yescharacteristic
264C23×C4C22×D511yescharacteristic
265C2×M16—22no—
266C2×M16—22no—
267C2×M16—22no—
268C2×M16—22no—
269C2×M16—22no—
270C2×M16—54no—
271C2×M16—102no—
272C2×M16—102no—
273C2×M16—102no—
274C2×M16—102no—
275C2×M16—102no—
276C2×M16C22⋊D514yes—
277C22×C8—22no—
278C22×C8—102no—
279C2×C4⋊C4—101no—
280C2×C4⋊C4—101no—
281C2×C4⋊C4—102no—
282C2×C4⋊C4—102no—
283C2×C4⋊C4—102no—
284C2×C4⋊C4—102no—
285C2×C4⋊C4—101no—
286C2×C4⋊C4—101no—
287C2×C22⋊C4—102no—
288C2×C22⋊C4—102no—
289C2×C22⋊C4—204no—
290C22⋊C8—24no—
291C22⋊C8—24no—
292C22⋊C8—104no—
293C22⋊C8—104no—
294#95—102no—
295#95—102no—
296C22×C5—21no—
297C22×C5—21no—
298C22×C5—21no—
299C22×C5—21no—
300C22×C5—22no—
301C22×C5—22no—
302C22×C5—22no—
303C22×C5—22no—
304C22×C5—22no—
305C22×C5—22no—
306C22×C5—22no—
307C22×C5—22no—
308C22×C5—22no—
309C22×C5—22no—
310C22×C5—48no—
311C22×C5—48no—
312C22×C5—41no—
313C22×C5—41no—
314C22×C5—41no—
315C22×C5—41no—
316C22×C5—41no—
317C22×C5—41no—
318C22×C5—41no—
319C22×C5—41no—
320C22×C5#38111yescharacteristic
321C22×C5#38611yescharacteristic
322C22×C5#38611yescharacteristic
323C22×C5#38812yes—
324C22×C5#38812yes—
325C22×C5C2×#10011yescharacteristic
326C22×C5C2×#10111yescharacteristic
327C22×C5#41311yescharacteristic
328C22×C5#41311yescharacteristic
329C4×C5—41no—
330C4×C5—41no—
331C4×C5#39412yes—
332C4×C5#39412yes—
333C4×C5#39712yes—
334C4×C5#39712yes—
335Dic5—82no—
336Dic5—82no—
337C24—22no—
338C24—22no—
339C24—21no—
340C24—21no—
341C24—22no—
342C24—22no—
343C24—41no—
344C24—41no—
345C24#68511yescharacteristic
346C24#68511yescharacteristic
347C24C2×C4×D511yescharacteristic
348C22×C4—21no—
349C22×C4—21no—
350C22×C4—22no—
351C22×C4—22no—
352C22×C4—21no—
353C22×C4—21no—
354C22×C4—21no—
355C22×C4—21no—
356C22×C4—22no—
357C22×C4—22no—
358C22×C4—21no—
359C22×C4—21no—
360C22×C4—21no—
361C22×C4—21no—
362C22×C4—22no—
363C22×C4—22no—
364C22×C4—22no—
365C22×C4—22no—
366C22×C4—22no—
367C22×C4—22no—
368C22×C4—42no—
369C22×C4—42no—
370C22×C4—42no—
371C22×C4—42no—
372C22×C4—42no—
373C22×C4—42no—
374C22×C4—42no—
375C22×C4—42no—
376C22×C4—102no—
377C22×C4—102no—
378C22×C4—104no—
379C22×C4—104no—
380C22×C4—202no—
381C22×C4—202no—
382C22×C4—202no—
383C22×C4—202no—
384C22×C4#68511yescharacteristic
385C22×C4#68511yescharacteristic
386C22×C4C2×D2011yescharacteristic
387C22×C4#70912yes—
388C22×C4D4×D512yes—
389C22×C4#71112yes—
390C22×C4#71112yes—
391C22×C4#71112yes—
392C22×C4C2×C22⋊D511yescharacteristic
393C22×C4C2×C22⋊D512yes—
394M16—24no—
395M16—24no—
396M16—42no—
397M16—42no—
398M16—104no—
399M16—104no—
400M16—202no—
401M16—202no—
402C2×C8—24no—
403C2×C8—42no—
404C2×C8—42no—
405C2×C8—104no—
406C2×C8—202no—
407C2×C8—202no—
408C4⋊C4—201no—
409C4⋊C4—201no—
410C4⋊C4—201no—
411C4⋊C4—201no—
412C4⋊C4—202no—
413C4⋊C4—202no—
414C22⋊C4—204no—
415C22⋊C4—204no—
416C2×C5—22no—
417C2×C5—22no—
418C2×C5—42no—
419C2×C5—42no—
420C2×C5#144011yescharacteristic
421C2×C5#182111yescharacteristic
422C2×C5#182211yescharacteristic
423C2×C5#190011yescharacteristic
424C2×C5#190011yescharacteristic
425C2×C5#190111yescharacteristic
426C2×C5#190111yescharacteristic
427C23—21no—
428C23—21no—
429C23—21no—
430C23—21no—
431C23—24no—
432C23—24no—
433C23—21no—
434C23—21no—
435C23—21no—
436C23—21no—
437C23—21no—
438C23—21no—
439C23—21no—
440C23—21no—
441C23—21no—
442C23—21no—
443C23—21no—
444C23—21no—
445C23—44no—
446C23—44no—
447C23—44no—
448C23—44no—
449C23—42no—
450C23—42no—
451C23—42no—
452C23—42no—
453C23#395512yes—
454C23#395612yes—
455C23#402311yescharacteristic
456C23#402311yescharacteristic
457C23#402712yes—
458C23C2×#68511yescharacteristic
459C23C4×C22⋊D512yes—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—21no—
463C2×C4—21no—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—42no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—42no—
470C2×C4—42no—
471C2×C4—42no—
472C2×C4—42no—
473C2×C4—42no—
474C2×C4—42no—
475C2×C4—42no—
476C2×C4—202no—
477C2×C4—202no—
478C2×C4—202no—
479C2×C4—202no—
480C2×C4—202no—
481C2×C4—202no—
482C2×C4—404no—
483C2×C4—404no—
484C2×C4#402512yes—
485C2×C4#402512yes—
486C2×C4#402811yescharacteristic
487C2×C4#402912yes—
488C2×C4#403112yes—
489C2×C4#403211yescharacteristic
490C2×C4#403212yes—
491C2×C4#407511yescharacteristic
492C2×C4#407612yes—
493C2×C4#408112yes—
494C2×C4#408112yes—
495C2×C4#408212yes—
496C2×C4#408412yes—
497C2×C4#408512yes—
498C2×C4#408512yes—
499C2×C4#409911yescharacteristic
500C8—44no—
501C8—204no—
502C5#1119811yescharacteristic, complemented, Sylow
503C22—22no—
504C22—22no—
505C22—21no—
506C22—21no—
507C22—21no—
508C22—21no—
509C22—22no—
510C22—22no—
511C22—22no—
512C22—22no—
513C22—22no—
514C22—22no—
515C22—22no—
516C22—22no—
517C22—48no—
518C22—48no—
519C22—41no—
520C22—41no—
521C22—41no—
522C22—41no—
523C22—41no—
524C22—41no—
525C22—41no—
526C22—41no—
527C22#6523211yescharacteristic
528C22#6523312yes—
529C22#6523412yes—
530C22#6524711yescharacteristic
531C22C2×#395511yescharacteristic
532C22#6542111yescharacteristic
533C22#6542111yescharacteristic
534C22C2×#395611yescharacteristic
535C22#6550211yescharacteristic
536C4—41no—
537C4—41no—
538C4—402no—
539C4—402no—
540C4#6524112yes—
541C4#6524212yes—
542C4#6525012yes—
543C4#6551112yes—
544C2—22no—
545C2—22no—
546C2—42no—
547C2—42no—
548C2#1060076611yescharacteristic
549C2#1060076711yescharacteristic
550C2#1060077811yescharacteristic
551C2#1060077911yescharacteristic
552C2#1060234211yescharacteristic
553C2#1060279511yescharacteristic
554C2#1060279611yescharacteristic
subgroupG/H
centerC23C2×#685
commutatorC24×C5C22×C4
FrattiniC23×C4C22×D5
FittingC2×C5×#407C2
socleC23×C5C2×C22⋊C4
prime radicalC25×C5C2×C4
cosocleC23×C4×C5C23
hypercenterC2×#407D5
hypocenterC5#11198
LCSG ▷ C24×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C24×C4 ◁ C2×#407

Complements

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

NH ≅ G/Ntype
4. C2×#64774C2semidirect
5. C2×#64774C2semidirect
502. C5#11198semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#4072
C2×#655012
C2×#654962
C2×#647742
#111985