Finite Group Databasebeta

← #12106974

Subgroups — #12106974

Order 1280.

936 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C5×#125C211yesmaximal, characteristic, complemented
2C2×#65355C211yesmaximal, characteristic
3C42×D20C211yesmaximal, characteristic
4#10602531C211yesmaximal, characteristic, complemented
5#10600419C211yesmaximal, characteristic
6#10600418C211yesmaximal, characteristic
7#10600395C211yesmaximal, characteristic, complemented
8#10600393C211yesmaximal, characteristic, complemented
9#10600349C211yesmaximal, characteristic
10#10600333C211yesmaximal, characteristic, complemented
11#10600274C211yesmaximal, characteristic, complemented
12#10600274C211yesmaximal, characteristic, complemented
13#10600267C211yesmaximal, characteristic
14#10600267C211yesmaximal, characteristic
15#10600184C211yesmaximal, characteristic, complemented
16C2×C5×#125C2211yescharacteristic
17C2×C4×D20C2211yescharacteristic
18C2×C4×D20C2211yescharacteristic
19C2×C4×D20C2211yescharacteristic
20C2×C42×D5—21no—
21C5×#389C2211yescharacteristic
22C5×#389C2211yescharacteristic
23C5×#387—21no—
24C5×#387—21no—
25C5×#382C2211yescharacteristic
26C4×C5×C4⋊C4—21no—
27C4×C5×C4⋊C4—21no—
28C4×C5×C4⋊C4C2211yescharacteristic
29C4×C5×C4⋊C4C2211yescharacteristic
30C43×C5C2211yescharacteristic
31#65355C418yescomplemented
32C2×#3941C2211yescharacteristic
33C2×#3941C2211yescharacteristic
34C2×#3941C2211yescharacteristic
35C2×#3941C2211yescharacteristic
36C2×#3940C2211yescharacteristic
37C2×#3940C2211yescharacteristic
38C2×#3939C2211yescharacteristic
39C2×#3939C2211yescharacteristic
40C4×#685—21no—
41C4×#685—21no—
42C4×#685—21no—
43C4×C4⋊Dic5C2211yescharacteristic
44C4×C4⋊Dic5C2211yescharacteristic
45C4×C4⋊Dic5C2211yescharacteristic
46C2×C4⋊#168C2211yescharacteristic
47C2×C4⋊#168C2211yescharacteristic
48C2×#3935C2211yescharacteristic
49C2×#3935C2211yescharacteristic
50#64749C2211yescharacteristic
51#64749C2211yescharacteristic
52#64749C2211yescharacteristic
53#64749C2211yescharacteristic
54#64749C2211yescharacteristic
55#64749C2211yescharacteristic
56#64749C2211yescharacteristic
57#64749C2211yescharacteristic
58#64744C2211yescharacteristic
59#64744C2211yescharacteristic
60#21617—51nomaximal, Sylow
61C22×D20C2311yescharacteristic
62C22×C4×D5—21no—
63C22×C4×D5—21no—
64C22×C4×D5—21no—
65C5×#125—22no—
66C5×#125C2×C414yescomplemented
67C2×C5×C4⋊C4—21no—
68C2×C5×C4⋊C4—21no—
69C2×C5×C4⋊C4—21no—
70C2×C5×C4⋊C4—21no—
71C2×C5×C4⋊C4C2311yescharacteristic
72C2×C5×C4⋊C4C2311yescharacteristic
73C2×C5×C4⋊C4C2311yescharacteristic
74C2×C5×C4⋊C4C2311yescharacteristic
75C2×C42×C5—21no—
76C2×C42×C5—21no—
77C2×C42×C5D411yescharacteristic
78C2×C42×C5D411yescharacteristic
79C2×C42×C5D411yescharacteristic
80C2×C42×C5D411yescharacteristic
81C2×C42×C5C2311yescharacteristic
82C2×C42×C5C2311yescharacteristic
83C2×C42×C5C2311yescharacteristic
84C2×#685—21no—
85C2×#685—21no—
86C2×#685—21no—
87C2×C4⋊Dic5C2311yescharacteristic
88C2×C4⋊Dic5C2311yescharacteristic
89C2×C4⋊Dic5C2311yescharacteristic
90C2×C4×Dic5—21no—
91C2×C4×Dic5—21no—
92C2×C4×Dic5—21no—
93C22×#168C2311yescharacteristic
94C22×#168C2311yescharacteristic
95C22×#168C2311yescharacteristic
96C22×#168C2311yescharacteristic
97C4×D20—22no—
98C4×D20—22no—
99C4×D20—22no—
100C4×D20—22no—
101C4×D20C2×C414yes—
102C4×D20Q814yes—
103C42×D5—44no—
104C5×#95—21no—
105C5×#95—21no—
106C5×#95—21no—
107C5×#95—21no—
108C5×#95—21no—
109C5×#95—21no—
110#3963—21no—
111#3963—21no—
112#3963—21no—
113#3941—22no—
114#3941—22no—
115#3941C2×C414yes—
116#3941C2×C414yes—
117#3940—22no—
118#3940C2×C414yescomplemented
119#3939—22no—
120#3939C2×C414yescomplemented
121C4⋊#168—22no—
122C4⋊#168C2×C414yescomplemented
123#3935—22no—
124#3935—22no—
125C2×#478—51no—
126C4×#125D511yescharacteristic, complemented
127C42×D4—51no—
128#1989—51no—
129#1949—51no—
130#1920—51no—
131#1918—51no—
132#1864—51no—
133#1862—51no—
134#1804—51no—
135#1776—51no—
136#1776—51no—
137#1767—51no—
138#1762—51no—
139#1762—51no—
140C23×D5—21no—
141C22×C4×C5—21no—
142C22×C4×C5—21no—
143C22×C4×C5—21no—
144C22×C4×C5—21no—
145C22×C4×C5C2×D411yescharacteristic
146C22×C4×C5C2×D411yescharacteristic
147C22×C4×C5C2×D411yescharacteristic
148C22×C4×C5C2×D411yescharacteristic
149C22×C4×C5C2×D411yescharacteristic
150C22×C4×C5C2×D411yescharacteristic
151C22×C4×C5C2411yescharacteristic
152C22×Dic5—21no—
153C22×Dic5—21no—
154C22×Dic5—21no—
155C2×D20—21no—
156C2×D20—21no—
157C2×D20—21no—
158C2×D20C22×C412yes—
159C2×D20C2×Q812yes—
160C2×D20#4112yes—
161C2×C4×D5—24no—
162C2×C4×D5—24no—
163C2×C4×D5—24no—
164C2×C4×D5—42no—
165C2×C4×D5—42no—
166C2×C4×D5—42no—
167C2×C4×D5—42no—
168C2×C4×D5—42no—
169C2×C4×D5—42no—
170C5×C4⋊C4—24no—
171C5×C4⋊C4—24no—
172C5×C4⋊C4—21no—
173C5×C4⋊C4—21no—
174C5×C4⋊C4—21no—
175C5×C4⋊C4—21no—
176C5×C4⋊C4—21no—
177C5×C4⋊C4—21no—
178C5×C4⋊C4—42no—
179C5×C4⋊C4—42no—
180C5×C4⋊C4C22×C412yes—
181C5×C4⋊C4C22×C412yes—
182C42×C5—22no—
183C42×C5—21no—
184C42×C5—21no—
185C42×C5—41no—
186C42×C5—41no—
187C42×C5—41no—
188C42×C5—42no—
189C42×C5—42no—
190C42×C5C22×C412yes—
191C42×C5C2×Q812yes—
192C42×C5#4112yes—
193C42×C5#4112yes—
194#685—24no—
195#685—24no—
196#685—24no—
197C4⋊Dic5—21no—
198C4⋊Dic5—21no—
199C4⋊Dic5—21no—
200C4⋊Dic5C22×C412yes—
201C4⋊Dic5C2×Q812yes—
202C4⋊Dic5#4112yes—
203C4×Dic5—42no—
204C4×Dic5—42no—
205C4×Dic5—42no—
206C2×#168—21no—
207C2×#168—21no—
208C2×#168—21no—
209C2×#168—21no—
210C2×#168—21no—
211C2×#168—21no—
212C2×#168—21no—
213C2×#168—21no—
214C2×#168—21no—
215C2×#168—21no—
216C2×#168C22×C412yes—
217C2×#168C22×C412yes—
218C2×#125C2×D511yescharacteristic
219C2×C4×D4—51no—
220C2×C4×D4—51no—
221C2×C4×D4—51no—
222C22×C42—101no—
223#478—58no—
224C2×#107—51no—
225C2×#107—51no—
226C2×#106—51no—
227C2×#106—51no—
228C2×C4⋊C8—51no—
229C2×C4⋊C8—51no—
230C2×#102—51no—
231C2×#102—51no—
232C2×#102—51no—
233C2×#102—51no—
234C2×#97—51no—
235C2×#97—51no—
236#389C2×D511yescharacteristic
237#389C2×D511yescharacteristic
238#387—21no—
239#387—21no—
240#382C2×D511yescharacteristic
241C4×C4⋊C4—21no—
242C4×C4⋊C4—21no—
243C4×C4⋊C4—51no—
244C4×C4⋊C4—51no—
245C4×C4⋊C4—51no—
246C4×C4⋊C4C2×D511yescharacteristic
247C4×C4⋊C4C2×D511yescharacteristic
248C4×C22⋊C4—101no—
249C4×C22⋊C4—101no—
250C4×C22⋊C4—101no—
251C43C2×D511yescharacteristic
252#340—51no—
253#340—51no—
254#340—51no—
255#340—51no—
256#340—51no—
257#340—51no—
258#340—51no—
259#340—51no—
260#336—51no—
261#336—51no—
262C23×C5C22×D411yescharacteristic
263C22×D5—22no—
264C22×D5—22no—
265C22×D5—22no—
266C22×D5—41no—
267C22×D5—41no—
268C22×D5—41no—
269C22×D5—41no—
270C2×C4×C5—21no—
271C2×C4×C5—21no—
272C2×C4×C5—21no—
273C2×C4×C5—21no—
274C2×C4×C5—21no—
275C2×C4×C5—21no—
276C2×C4×C5—21no—
277C2×C4×C5—21no—
278C2×C4×C5—21no—
279C2×C4×C5—21no—
280C2×C4×C5—22no—
281C2×C4×C5—22no—
282C2×C4×C5—21no—
283C2×C4×C5—21no—
284C2×C4×C5—21no—
285C2×C4×C5—41no—
286C2×C4×C5—41no—
287C2×C4×C5—41no—
288C2×C4×C5—41no—
289C2×C4×C5—41no—
290C2×C4×C5—41no—
291C2×C4×C5—41no—
292C2×C4×C5—41no—
293C2×C4×C5—41no—
294C2×C4×C5—41no—
295C2×C4×C5C4×D412yes—
296C2×C4×C5C4×D412yes—
297C2×C4×C5C22⋊Q812yes—
298C2×C4×C5C22⋊Q812yes—
299C2×C4×C5AGL(1,ℤ/8)12yes—
300C2×C4×C5C23×C411yescharacteristic
301C2×C4×C5C22×Q811yescharacteristic
302C2×C4×C5C2×#4111yescharacteristic
303C2×C4×C5C2×#4111yescharacteristic
304C2×C4×C5C2×#4111yescharacteristic
305C2×C4×C5C2×#4111yescharacteristic
306C2×Dic5—22no—
307C2×Dic5—22no—
308C2×Dic5—22no—
309C2×Dic5—41no—
310C2×Dic5—41no—
311C2×Dic5—41no—
312C2×Dic5—41no—
313C2×Dic5—41no—
314C2×Dic5—41no—
315D20—22no—
316D20—22no—
317D20—22no—
318D20C4×Q814yes—
319C4×D5—48no—
320C4×D5—48no—
321C4×D5—48no—
322#168—22no—
323#168—22no—
324#168—41no—
325#168—41no—
326C22×D4—51no—
327C23×C4—101no—
328C23×C4—101no—
329C23×C4—101no—
330C22×C8—51no—
331C22×C8—51no—
332C22×C8—51no—
333C22×C8—51no—
334#125—22no—
335#125C4×D514yescomplemented
336C4×D4—54no—
337C4×D4—54no—
338C4×D4—102no—
339C4×D4—102no—
340C4×D4—102no—
341C4×D4—102no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—51no—
347C2×C4⋊C4—51no—
348C2×C4⋊C4—51no—
349C2×C4⋊C4C22×D511yescharacteristic
350C2×C4⋊C4C22×D511yescharacteristic
351C2×C4⋊C4C22×D511yescharacteristic
352C2×C4⋊C4C22×D511yescharacteristic
353C2×C22⋊C4—101no—
354C2×C22⋊C4—101no—
355C2×C22⋊C4—101no—
356C2×C42—21no—
357C2×C42—21no—
358C2×C42—101no—
359C2×C42—101no—
360C2×C42—101no—
361C2×C42—204no—
362C2×C42C22⋊D511yescharacteristic
363C2×C42C22⋊D511yescharacteristic
364C2×C42C22⋊D511yescharacteristic
365C2×C42C22⋊D511yescharacteristic
366C2×C42C22×D511yescharacteristic
367C2×C42C22×D511yescharacteristic
368C2×C42C22×D511yescharacteristic
369#107—54no—
370#107—102no—
371#106—54no—
372#106—102no—
373C4⋊C8—54no—
374C4⋊C8—102no—
375#102—54no—
376#102—54no—
377#102—102no—
378#102—102no—
379#97—102no—
380#97—102no—
381#95—21no—
382#95—21no—
383#95—21no—
384#95—21no—
385#95—21no—
386#95—21no—
387#95—101no—
388#95—101no—
389#95—101no—
390C22×C5C2×C4×D411yescharacteristic
391C22×C5C2×C22⋊Q811yescharacteristic
392C22×C5#52511yescharacteristic
393C22×C5C2×AGL(1,ℤ/8)11yescharacteristic
394C22×C5#57511yescharacteristic
395C22×C5#57511yescharacteristic
396C22×C5#57511yescharacteristic
397C2×D5—24no—
398C2×D5—42no—
399C2×D5—42no—
400C2×D5—42no—
401C2×D5—42no—
402C2×D5—42no—
403C2×D5—42no—
404C4×C5—22no—
405C4×C5—22no—
406C4×C5—22no—
407C4×C5—22no—
408C4×C5—22no—
409C4×C5—41no—
410C4×C5—42no—
411C4×C5—42no—
412C4×C5—81no—
413C4×C5—81no—
414C4×C5C2×C4×Q811yescharacteristic
415C4×C5C4×#4111yescharacteristic
416C4×C5#52911yescharacteristic
417C4×C5#53311yescharacteristic
418Dic5—42no—
419Dic5—42no—
420Dic5—42no—
421C24—101no—
422C2×D4—52no—
423C2×D4—52no—
424C2×D4—52no—
425C2×D4—101no—
426C2×D4—101no—
427C2×D4—101no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—104no—
433C22×C4—101no—
434C22×C4—101no—
435C22×C4—101no—
436C22×C4—104no—
437C22×C4—104no—
438C22×C4—202no—
439C22×C4—202no—
440C22×C4—202no—
441C22×C4—202no—
442C22×C4—202no—
443C22×C4—202no—
444C22×C4C2×C22⋊D511yescharacteristic
445C22×C4C2×C22⋊D511yescharacteristic
446C22×C4C2×C22⋊D511yescharacteristic
447C22×C4C2×C22⋊D511yescharacteristic
448C22×C4C2×C22⋊D511yescharacteristic
449C22×C4C2×C22⋊D511yescharacteristic
450C22×C4C23×D511yescharacteristic
451C2×C8—52no—
452C2×C8—52no—
453C2×C8—101no—
454C2×C8—101no—
455C2×C8—101no—
456C2×C8—101no—
457C2×C8—101no—
458C2×C8—101no—
459C2×C8—101no—
460C2×C8—101no—
461C2×C8—101no—
462C2×C8—101no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—24no—
466C4⋊C4—24no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—42no—
472C4⋊C4—42no—
473C4⋊C4—52no—
474C4⋊C4—52no—
475C4⋊C4—52no—
476C4⋊C4—101no—
477C4⋊C4—101no—
478C4⋊C4—101no—
479C4⋊C4C2×C4×D512yes—
480C4⋊C4C2×C4×D512yes—
481C22⋊C4—104no—
482C22⋊C4—104no—
483C22⋊C4—104no—
484C42—21no—
485C42—21no—
486C42—22no—
487C42—41no—
488C42—41no—
489C42—41no—
490C42—42no—
491C42—42no—
492C42—202no—
493C42—202no—
494C42—202no—
495C42C2×C4×D512yes—
496C42#70912yes—
497C42Q8×D512yes—
498C42#71312yes—
499C2×C5C4×C22⋊Q811yescharacteristic
500C2×C5#294311yescharacteristic
501C2×C5C4×AGL(1,ℤ/8)11yescharacteristic
502C2×C5#307711yescharacteristic
503C2×C5#308011yescharacteristic
504C2×C5#311111yescharacteristic
505C2×C5#311411yescharacteristic
506D5—44no—
507C23—102no—
508C23—102no—
509C23—102no—
510C23—201no—
511C23—201no—
512C23—201no—
513C23—201no—
514C23C22×C22⋊D511yescharacteristic
515D4—54no—
516D4—102no—
517D4—102no—
518D4—102no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—102no—
545C2×C4—102no—
546C2×C4—102no—
547C2×C4—208no—
548C2×C4—208no—
549C2×C4—208no—
550C2×C4—201no—
551C2×C4—201no—
552C2×C4—201no—
553C2×C4—201no—
554C2×C4—201no—
555C2×C4—201no—
556C2×C4C4×C22⋊D512yes—
557C2×C4C4×C22⋊D512yes—
558C2×C4#409212yes—
559C2×C4#409212yes—
560C2×C4#409512yes—
561C2×C4C22×C4×D511yescharacteristic
562C2×C4C2×#70911yescharacteristic
563C2×C4C2×Q8×D511yescharacteristic
564C2×C4C2×#71311yescharacteristic
565C2×C4D5×#4111yescharacteristic
566C2×C4D5×#4111yescharacteristic
567C8—102no—
568C8—102no—
569C8—201no—
570C8—201no—
571C5#2161711yescharacteristic, complemented, Sylow
572C22—104no—
573C22—202no—
574C22—202no—
575C22—202no—
576C22—202no—
577C22—202no—
578C22—202no—
579C22C2×C4×C22⋊D511yescharacteristic
580C22C2×#409211yescharacteristic
581C22C2×#409511yescharacteristic
582C22#6615611yescharacteristic
583C22#6615611yescharacteristic
584C22#6615611yescharacteristic
585C22#6616211yescharacteristic
586C4—22no—
587C4—22no—
588C4—22no—
589C4—22no—
590C4—22no—
591C4—41no—
592C4—42no—
593C4—42no—
594C4—81no—
595C4—81no—
596C4—202no—
597C4—202no—
598C4—202no—
599C4C4×Q8×D511yescharacteristic
600C4C4×#71311yescharacteristic
601C4#6591211yescharacteristic
602C4#6591411yescharacteristic
603C2—204no—
604C2C4×#409211yescharacteristic
605C2#1061423711yescharacteristic
606C2C4×#409511yescharacteristic
607C2#1061474811yescharacteristic
608C2#1061487311yescharacteristic
609C2#1061487411yescharacteristic
610C2#1061508111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D5
commutatorC2×C4×C5C23×C4
FrattiniC22×C4C23×D5
FittingC4×C5×#125C2
socleC23×C5C22×D4
prime radicalC22×D20C23
cosocleC22×C4×C5C24
hypercenterC4×#125D5
hypocenterC5#21617
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C43 ◁ C4×#125

Complements

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

NH ≅ G/Ntype
1. C4×C5×#125C2semidirect
4. #10602531C2semidirect
7. #10600395C2semidirect
8. #10600393C2semidirect
10. #10600333C2semidirect
11. #10600274C2semidirect
12. #10600274C2semidirect
15. #10600184C2semidirect
31. #65355C4semidirect
66. C5×#125C2×C4semidirect
118. #3940C2×C4semidirect
120. #3939C2×C4semidirect
122. C4⋊#168C2×C4semidirect
126. C4×#125D5semidirect
335. #125C4×D5semidirect
571. C5#21617semidirect

Maximal subgroups

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

subgroupindex
C4×C5×#1252
C2×#653552
C42×D202
#106025312
#106004192
#106004182
#106003952
#106003932
#106003492
#106003332
#106002742
#106002672
#106001842
#216175