Finite Group Databasebeta

← #12109911

Subgroups — #12109911

Order 1280.

762 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#433C211yesmaximal, characteristic
2#10613964C211yesmaximal, characteristic
3#10613962C211yesmaximal, characteristic
4#10601248C211yesmaximal, characteristic, complemented
5#10601248C211yesmaximal, characteristic, complemented
6#10601247C211yesmaximal, characteristic, complemented
7#10601246C211yesmaximal, characteristic, complemented
8#10600722C211yesmaximal, characteristic
9#10600722C211yesmaximal, characteristic
10#10600721C211yesmaximal, characteristic
11#10600720C211yesmaximal, characteristic
12#10600609C211yesmaximal, characteristic, complemented
13#10600608C211yesmaximal, characteristic, complemented
14#10600559C211yesmaximal, characteristic, complemented
15#10600555C211yesmaximal, characteristic, complemented
16C2×C5×#117C2211yescharacteristic
17C2×#4072C2211yescharacteristic
18C22×C4⋊Dic5C2211yescharacteristic
19C5×#433C418yescomplemented
20C2×C5×C4⋊C8C2211yescharacteristic
21C2×C5×C4⋊C8C2211yescharacteristic
22C2×C5×C22⋊C8C2211yescharacteristic
23C2×C5×C22⋊C8C2211yescharacteristic
24C2×C5×#97C2211yescharacteristic
25C2×C4×C5×C8C2211yescharacteristic
26#65501C2211yescharacteristic
27#65501C2211yescharacteristic
28C2×#3950C2211yescharacteristic
29C2×#3950C2211yescharacteristic
30C2×#3950C2211yescharacteristic
31C2×#3950C2211yescharacteristic
32C2×#3949C2211yescharacteristic
33C2×#3949C2211yescharacteristic
34C2×#3949C2211yescharacteristic
35C2×#3949C2211yescharacteristic
36#65274—21no—
37#65274—21no—
38#65270—21no—
39#65270—21no—
40#65240—21no—
41#65240—21no—
42#65239—21no—
43#65239—21no—
44#65225C2211yescharacteristic
45#65225C2211yescharacteristic
46#65225C2211yescharacteristic
47#65224C2211yescharacteristic
48#65224C2211yescharacteristic
49#65224C2211yescharacteristic
50C4×C4⋊Dic5C2211yescharacteristic
51C4×C4⋊Dic5C2211yescharacteristic
52#64771C2211yescharacteristic
53#64771C2211yescharacteristic
54#64771C2211yescharacteristic
55#64771C2211yescharacteristic
56#64771C2211yescharacteristic
57#64771C2211yescharacteristic
58#64771C2211yescharacteristic
59#64771C2211yescharacteristic
60#21992—51nomaximal, Sylow
61C23×C4×C5C2311yescharacteristic
62C23×Dic5—21no—
63C22×C5×C8C2311yescharacteristic
64C22×C5×C8C2311yescharacteristic
65C22×C5×C8C2311yescharacteristic
66C22×C5×C8C2311yescharacteristic
67C5×#117C2×C414yes—
68C5×#117Q814yes—
69C2×C5×C4⋊C4D411yescharacteristic
70C2×C5×C4⋊C4D411yescharacteristic
71C2×C5×C22⋊C4D411yescharacteristic
72C2×C5×C22⋊C4D411yescharacteristic
73C2×C42×C5C2311yescharacteristic
74C2×C42×C5C2311yescharacteristic
75C2×C22⋊Dic5—21no—
76C2×C22⋊Dic5—21no—
77C2×C22⋊Dic5—21no—
78#4072—41no—
79#4072—41no—
80C2×C4⋊Dic5—21no—
81C2×C4⋊Dic5—21no—
82C2×C4⋊Dic5—21no—
83C2×C4⋊Dic5—21no—
84C2×C4⋊Dic5—21no—
85C2×C4⋊Dic5—21no—
86C2×C4⋊Dic5—21no—
87C2×C4⋊Dic5—41no—
88C2×C4⋊Dic5—41no—
89C2×C4⋊Dic5C2311yescharacteristic
90C2×C4⋊Dic5C2311yescharacteristic
91C2×C4⋊Dic5C2311yescharacteristic
92C2×C4⋊Dic5C2311yescharacteristic
93C2×C4⋊Dic5C2311yescharacteristic
94C2×C4⋊Dic5C2311yescharacteristic
95C2×C4⋊Dic5C2311yescharacteristic
96C2×C4⋊Dic5C2311yescharacteristic
97C2×C4×Dic5—21no—
98C2×C4×Dic5—21no—
99C2×C4×Dic5—21no—
100C5×C4⋊C8C2×C414yescomplemented
101C5×C4⋊C8C2×C414yescomplemented
102C5×C22⋊C8C2×C414yes—
103C5×C22⋊C8C2×C414yes—
104C5×#97C2×C414yescomplemented
105C4×C5×C8C2×C414yescomplemented
106#3963—21no—
107#3963—21no—
108#3963—21no—
109#3963—21no—
110#3963—21no—
111#3963—21no—
112#3963—21no—
113#3963—21no—
114#3963—21no—
115#3963—21no—
116#3950—41no—
117#3950—41no—
118#3950—41no—
119#3950—41no—
120#3949—41no—
121#3949—41no—
122#3949—41no—
123#3949—41no—
124C2×#433D511yescharacteristic
125#2317—51no—
126#2314—51no—
127#1949—51no—
128#1949—51no—
129#1948—51no—
130#1947—51no—
131#1854—51no—
132#1854—51no—
133#1853—51no—
134#1852—51no—
135#1847—51no—
136#1846—51no—
137#1836—51no—
138#1834—51no—
139C24×C5C2×D411yescharacteristic
140C22×C4×C5—21no—
141C22×C4×C5—21no—
142C22×C4×C5—21no—
143C22×C4×C5—21no—
144C22×C4×C5C22×C412yes—
145C22×C4×C5C2×D411yescharacteristic
146C22×C4×C5C2×D411yescharacteristic
147C22×C4×C5C2×D411yescharacteristic
148C22×C4×C5C2×D411yescharacteristic
149C22×C4×C5C2×D411yescharacteristic
150C22×C4×C5C2×Q812yes—
151C22×C4×C5C2411yescharacteristic
152C22×Dic5—21no—
153C22×Dic5—21no—
154C22×Dic5—21no—
155C22×Dic5—21no—
156C22×Dic5—21no—
157C22×Dic5—21no—
158C22×Dic5—21no—
159C22×Dic5—21no—
160C22×Dic5—42no—
161C22×Dic5—81no—
162C22×Dic5—81no—
163C2×C5×C8—21no—
164C2×C5×C8—21no—
165C2×C5×C8—21no—
166C2×C5×C8—21no—
167C2×C5×C8—21no—
168C2×C5×C8—21no—
169C2×C5×C8—21no—
170C2×C5×C8—21no—
171C2×C5×C8C22×C412yes—
172C2×C5×C8C22×C412yes—
173C2×C5×C8C22×C412yes—
174C2×C5×C8C22×C412yes—
175C5×C4⋊C4C4⋊C414yes—
176C5×C4⋊C4C4⋊C414yes—
177C5×C22⋊C4C4⋊C414yes—
178C5×C22⋊C4C4⋊C414yes—
179C42×C5C22×C412yes—
180C42×C5C22×C412yes—
181C42×C5C2×Q812yes—
182C42×C5C2×Q812yes—
183C22⋊Dic5—42no—
184C22⋊Dic5—81no—
185C22⋊Dic5—81no—
186C4⋊Dic5—21no—
187C4⋊Dic5—21no—
188C4⋊Dic5—21no—
189C4⋊Dic5—21no—
190C4⋊Dic5—21no—
191C4⋊Dic5—21no—
192C4⋊Dic5—21no—
193C4⋊Dic5—21no—
194C4⋊Dic5—21no—
195C4⋊Dic5—21no—
196C4⋊Dic5—21no—
197C4⋊Dic5—21no—
198C4⋊Dic5—21no—
199C4⋊Dic5—21no—
200C4⋊Dic5—21no—
201C4⋊Dic5—21no—
202C4⋊Dic5—42no—
203C4⋊Dic5—81no—
204C4⋊Dic5—81no—
205C4⋊Dic5—81no—
206C4⋊Dic5—81no—
207C4⋊Dic5—81no—
208C4⋊Dic5—81no—
209C4×Dic5—42no—
210C4×Dic5—81no—
211C4×Dic5—81no—
212C2×#117—51no—
213C2×#117C2×D511yescharacteristic
214C22×C4⋊C4—51no—
215#433Dic518yescomplemented
216C2×#107—51no—
217C2×#107—51no—
218C2×#107—51no—
219C2×#107—51no—
220C2×#106—51no—
221C2×#106—51no—
222C2×#106—51no—
223C2×#106—51no—
224C2×C4⋊C8C2×D511yescharacteristic
225C2×C4⋊C8C2×D511yescharacteristic
226C2×C22⋊C8C2×D511yescharacteristic
227C2×C22⋊C8C2×D511yescharacteristic
228C2×#97C2×D511yescharacteristic
229C2×C4×C8C2×D511yescharacteristic
230#389—101no—
231#389—101no—
232#388—101no—
233#388—101no—
234#387—101no—
235#387—101no—
236#385—101no—
237#385—101no—
238#384—51no—
239#384—51no—
240#384—51no—
241#382—51no—
242#382—51no—
243#382—51no—
244#380—51no—
245#380—51no—
246C4×C4⋊C4—51no—
247C4×C4⋊C4—51no—
248#340—51no—
249#340—51no—
250#340—51no—
251#340—51no—
252#340—51no—
253#340—51no—
254#340—51no—
255#340—51no—
256C23×C5—21no—
257C23×C5—21no—
258C23×C5—21no—
259C23×C5—21no—
260C23×C5—21no—
261C23×C5—21no—
262C23×C5C2×C4⋊C412yes—
263C23×C5C22×D411yescharacteristic
264C2×C4×C5—21no—
265C2×C4×C5—21no—
266C2×C4×C5—21no—
267C2×C4×C5—21no—
268C2×C4×C5—21no—
269C2×C4×C5—21no—
270C2×C4×C5—21no—
271C2×C4×C5—21no—
272C2×C4×C5—21no—
273C2×C4×C5—21no—
274C2×C4×C5—22no—
275C2×C4×C5—22no—
276C2×C4×C5—22no—
277C2×C4×C5—22no—
278C2×C4×C5C2×C4⋊C412yes—
279C2×C4×C5C2×C4⋊C412yes—
280C2×C4×C5C2×C4⋊C412yes—
281C2×C4×C5C2×C4⋊C412yes—
282C2×C4×C5C2×C4⋊C412yes—
283C2×C4×C5C23×C411yescharacteristic
284C2×C4×C5C22×Q811yescharacteristic
285C2×C4×C5H(5,𝔽2)11yescharacteristic
286C2×C4×C5H(5,𝔽2)11yescharacteristic
287C2×C4×C52−1+411yescharacteristic
288C2×C4×C52−1+411yescharacteristic
289C2×Dic5—41no—
290C2×Dic5—41no—
291C2×Dic5—41no—
292C2×Dic5—41no—
293C2×Dic5—41no—
294C2×Dic5—41no—
295C2×Dic5—41no—
296C2×Dic5—41no—
297C2×Dic5—41no—
298C2×Dic5—41no—
299C2×Dic5—41no—
300C2×Dic5—41no—
301C2×Dic5—41no—
302C2×Dic5—41no—
303C2×Dic5—41no—
304C2×Dic5—41no—
305C2×Dic5—41no—
306C2×Dic5—41no—
307C2×Dic5—41no—
308C2×Dic5—41no—
309C2×Dic5—41no—
310C2×Dic5—41no—
311C2×Dic5—41no—
312C2×Dic5—41no—
313C2×Dic5—84no—
314C5×C8—22no—
315C5×C8—22no—
316C5×C8—22no—
317C5×C8—22no—
318C23×C4—101no—
319C23×C4C22×D511yescharacteristic
320C22×C8C22×D511yescharacteristic
321C22×C8C22×D511yescharacteristic
322C22×C8C22×D511yescharacteristic
323C22×C8C22×D511yescharacteristic
324#117—201no—
325#117—201no—
326#117Dic1014yes—
327#117C2×Dic514yes—
328C2×C4⋊C4—51no—
329C2×C4⋊C4—51no—
330C2×C4⋊C4—51no—
331C2×C4⋊C4—51no—
332C2×C4⋊C4—51no—
333C2×C4⋊C4—51no—
334C2×C4⋊C4—51no—
335C2×C4⋊C4—51no—
336C2×C4⋊C4—101no—
337C2×C4⋊C4—101no—
338C2×C4⋊C4—101no—
339C2×C4⋊C4—101no—
340C2×C4⋊C4—101no—
341C2×C4⋊C4—101no—
342C2×C4⋊C4—101no—
343C2×C4⋊C4—201no—
344C2×C4⋊C4—201no—
345C2×C4⋊C4D2011yescharacteristic
346C2×C4⋊C4D2011yescharacteristic
347C2×C22⋊C4—101no—
348C2×C22⋊C4—101no—
349C2×C22⋊C4—101no—
350C2×C22⋊C4D2011yescharacteristic
351C2×C22⋊C4D2011yescharacteristic
352C2×C42—101no—
353C2×C42—101no—
354C2×C42—101no—
355C2×C42C22×D511yescharacteristic
356C2×C42C22×D511yescharacteristic
357#107—201no—
358#107—201no—
359#107—201no—
360#107—201no—
361#106—201no—
362#106—201no—
363#106—201no—
364#106—201no—
365C4⋊C8C2×Dic514yescomplemented
366C4⋊C8C2×Dic514yescomplemented
367C22⋊C8C2×Dic514yes—
368C22⋊C8C2×Dic514yes—
369#97C2×Dic514yescomplemented
370C4×C8C2×Dic514yescomplemented
371#95—101no—
372#95—101no—
373#95—101no—
374#95—101no—
375#95—101no—
376#95—101no—
377#95—101no—
378#95—101no—
379#95—101no—
380#95—101no—
381C22×C5—22no—
382C22×C5—22no—
383C22×C5—22no—
384C22×C5—41no—
385C22×C5—41no—
386C22×C5—41no—
387C22×C5—41no—
388C22×C5C22×C4⋊C411yescharacteristic
389C22×C5#53511yescharacteristic
390C22×C5#53611yescharacteristic
391C22×C5#57611yescharacteristic
392C22×C5#57711yescharacteristic
393C22×C5#57711yescharacteristic
394C22×C5#57811yescharacteristic
395C4×C5—22no—
396C4×C5—22no—
397C4×C5—22no—
398C4×C5—22no—
399C4×C5—22no—
400C4×C5#52011yescharacteristic
401C4×C5#52011yescharacteristic
402C4×C5#54411yescharacteristic
403C4×C5#54411yescharacteristic
404Dic5—81no—
405Dic5—81no—
406Dic5—81no—
407Dic5—81no—
408Dic5—81no—
409Dic5—81no—
410Dic5—81no—
411Dic5—81no—
412C24C2×D2011yescharacteristic
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—101no—
418C22×C4—101no—
419C22×C4—101no—
420C22×C4—101no—
421C22×C4—101no—
422C22×C4—101no—
423C22×C4—101no—
424C22×C4—101no—
425C22×C4—202no—
426C22×C4—401no—
427C22×C4—401no—
428C22×C4C2×Dic1012yes—
429C22×C4C2×D2011yescharacteristic
430C22×C4C2×D2011yescharacteristic
431C22×C4C2×D2011yescharacteristic
432C22×C4C2×D2011yescharacteristic
433C22×C4C2×D2011yescharacteristic
434C22×C4C22×Dic512yes—
435C22×C4C23×D511yescharacteristic
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8C22×Dic512yes—
445C2×C8C22×Dic512yes—
446C2×C8C22×Dic512yes—
447C2×C8C22×Dic512yes—
448C4⋊C4—101no—
449C4⋊C4—101no—
450C4⋊C4—101no—
451C4⋊C4—101no—
452C4⋊C4—101no—
453C4⋊C4—101no—
454C4⋊C4—101no—
455C4⋊C4—101no—
456C4⋊C4—101no—
457C4⋊C4—101no—
458C4⋊C4—101no—
459C4⋊C4—101no—
460C4⋊C4—101no—
461C4⋊C4—101no—
462C4⋊C4—101no—
463C4⋊C4—101no—
464C4⋊C4—202no—
465C4⋊C4—401no—
466C4⋊C4—401no—
467C4⋊C4—401no—
468C4⋊C4—401no—
469C4⋊C4—401no—
470C4⋊C4—401no—
471C4⋊C4C4⋊Dic514yes—
472C4⋊C4C4⋊Dic514yes—
473C22⋊C4—202no—
474C22⋊C4—401no—
475C22⋊C4—401no—
476C22⋊C4C4⋊Dic514yes—
477C22⋊C4C4⋊Dic514yes—
478C42—202no—
479C42—401no—
480C42—401no—
481C42C2×Dic1012yes—
482C42C2×Dic1012yes—
483C42C22×Dic512yes—
484C42C22×Dic512yes—
485C2×C5—42no—
486C2×C5#231711yescharacteristic
487C2×C5#291211yescharacteristic
488C2×C5#291311yescharacteristic
489C2×C5#322411yescharacteristic
490C2×C5#322511yescharacteristic
491C2×C5#324111yescharacteristic
492C2×C5#324211yescharacteristic
493C23—21no—
494C23—21no—
495C23—21no—
496C23—21no—
497C23—21no—
498C23—21no—
499C23C2×C4⋊Dic512yes—
500C23C22×D2011yescharacteristic
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—201no—
516C2×C4—201no—
517C2×C4—201no—
518C2×C4—201no—
519C2×C4—201no—
520C2×C4—201no—
521C2×C4—201no—
522C2×C4—201no—
523C2×C4—201no—
524C2×C4—201no—
525C2×C4—201no—
526C2×C4—201no—
527C2×C4—201no—
528C2×C4—201no—
529C2×C4—201no—
530C2×C4—201no—
531C2×C4—201no—
532C2×C4—201no—
533C2×C4—201no—
534C2×C4—201no—
535C2×C4—201no—
536C2×C4—201no—
537C2×C4—201no—
538C2×C4—201no—
539C2×C4—404no—
540C2×C4C2×C4⋊Dic512yes—
541C2×C4C2×C4⋊Dic512yes—
542C2×C4C2×C4⋊Dic512yes—
543C2×C4C2×C4⋊Dic512yes—
544C2×C4C2×C4⋊Dic512yes—
545C2×C4C22×Dic1011yescharacteristic
546C2×C4#414911yescharacteristic
547C2×C4#414911yescharacteristic
548C2×C4#415011yescharacteristic
549C2×C4#415011yescharacteristic
550C2×C4C23×Dic511yescharacteristic
551C8—22no—
552C8—22no—
553C8—22no—
554C8—22no—
555C5#2199211yescharacteristic, complemented, Sylow
556C22—22no—
557C22—22no—
558C22—22no—
559C22—41no—
560C22—41no—
561C22—41no—
562C22—41no—
563C22#6585911yescharacteristic
564C22#6586011yescharacteristic
565C22#6608511yescharacteristic
566C22#6608511yescharacteristic
567C22#6608611yescharacteristic
568C22#6608711yescharacteristic
569C22C22×C4⋊Dic511yescharacteristic
570C4—22no—
571C4—22no—
572C4—22no—
573C4—22no—
574C4—22no—
575C4—401no—
576C4—401no—
577C4—401no—
578C4—401no—
579C4—401no—
580C4—401no—
581C4—401no—
582C4—401no—
583C4#6585311yescharacteristic
584C4#6585311yescharacteristic
585C4#6616111yescharacteristic
586C4#6616111yescharacteristic
587C2—42no—
588C2#1061109311yescharacteristic
589C2#1061109411yescharacteristic
590C2#1061112311yescharacteristic
591C2#1061112411yescharacteristic
592C2#1061396411yescharacteristic
593C2#1061551511yescharacteristic
594C2#1061551611yescharacteristic
subgroupG/H
centerC23C22×D20
commutatorC2×C4×C5C23×C4
FrattiniC22×C4C23×D5
FittingC2×C5×#433C2
socleC23×C5C22×D4
prime radicalC24×C5C2×D4
cosocleC22×C4×C5C24
hypercenterC2×#433D5
hypocenterC5#21992
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#433

Complements

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

NH ≅ G/Ntype
4. #10601248C2semidirect
5. #10601248C2semidirect
6. #10601247C2semidirect
7. #10601246C2semidirect
12. #10600609C2semidirect
13. #10600608C2semidirect
14. #10600559C2semidirect
15. #10600555C2semidirect
19. C5×#433C4semidirect
100. C5×C4⋊C8C2×C4semidirect
101. C5×C4⋊C8C2×C4semidirect
104. C5×#97C2×C4semidirect
105. C4×C5×C8C2×C4semidirect
215. #433Dic5semidirect
365. C4⋊C8C2×Dic5semidirect
366. C4⋊C8C2×Dic5semidirect
369. #97C2×Dic5semidirect
370. C4×C8C2×Dic5semidirect
555. C5#21992semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#4332
#106139642
#106139622
#106012482
#106012472
#106012462
#106007222
#106007212
#106007202
#106006092
#106006082
#106005592
#106005552
#219925