Finite Group Databasebeta

← C5×A4×#121 #14511322

Subgroups — C5×A4×#121 #14511322

Order 1920.

1156 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×D4×A4C212yesmaximal, complemented
2C2×C5×D4×A4C211yesmaximal, characteristic, complemented
3C22×C4×C5×A4C211yesmaximal, characteristic, complemented
4C5×A4×C4⋊C4C211yesmaximal, characteristic, complemented
5C5×A4×C22⋊C4C212yesmaximal, complemented
6C22×C5×#121C311yesmaximal, characteristic, complemented, Hall
7C23×C5×A4C2212yes—
8C23×C5×A4C2211yescharacteristic
9C5×D4×A4—24no—
10C5×D4×A4—22no—
11C2×C4×C5×A4—22no—
12C2×C4×C5×A4C2211yescharacteristic
13C2×C4×C5×A4C2212yes—
14C2×C4×C5×A4C2211yescharacteristic
15C3×C5×#121—41nomaximal
16A4×#121C511yesmaximal, characteristic, direct product factor, Hall
17C23×C5×D4C2×C312yescomplemented
18C23×C5×D4C2×C311yescharacteristic, complemented
19C24×C4×C5C2×C311yescharacteristic, complemented
20C2×C5×#121—31no—
21C2×C5×#121—32no—
22C2×C5×#121—31no—
23C2×C5×#121—31no—
24C2×C5×#121—32no—
25C2×C5×#121—31no—
26C22×C5×C4⋊C4C2×C311yescharacteristic, complemented
27C22×C5×C22⋊C4C2×C312yescomplemented
28C22×C5×A4—21no—
29C22×C5×A4—21no—
30C22×C5×A4—22no—
31C22×C5×A4—22no—
32C22×C5×A4—22no—
33C22×C5×A4D412yescomplemented
34C22×C5×A4C2311yescharacteristic
35C2×C3×C5×D4—41no—
36C2×C3×C5×D4—42no—
37C22×C3×C4×C5—41no—
38C4×C5×A4—21no—
39C4×C5×A4—22no—
40C4×C5×A4D412yescomplemented
41C3×C5×C4⋊C4—41no—
42C3×C5×C22⋊C4—42no—
43C2×D4×A4C2×C512yescomplemented
44C2×D4×A4C2×C511yescharacteristic, complemented
45C22×C4×A4C2×C511yescharacteristic, complemented
46A4×C4⋊C4C2×C511yescharacteristic, complemented
47A4×C22⋊C4C2×C512yescomplemented
48C25×C5C22×C312yes—
49C25×C5C22×C311yescharacteristic
50C22×C5×D4—24no—
51C22×C5×D4—22no—
52C22×C5×D4—31no—
53C22×C5×D4—32no—
54C22×C5×D4—31no—
55C22×C5×D4—32no—
56C22×C5×D4—32no—
57C22×C5×D4—32no—
58C22×C5×D4—32no—
59C22×C5×D4—62no—
60C22×C5×D4—64no—
61C23×C4×C5—22no—
62C23×C4×C5—31no—
63C23×C4×C5—31no—
64C23×C4×C5—31no—
65C23×C4×C5—31no—
66C23×C4×C5—62no—
67C23×C4×C5C22×C311yescharacteristic
68C23×C4×C5C22×C312yes—
69C23×C4×C5C22×C311yescharacteristic
70C5×#121—32no—
71C5×#121—32no—
72C5×#121—34no—
73C5×#121—34no—
74C5×#121—32no—
75C5×#121—31no—
76C5×#121—32no—
77C5×#121—31no—
78C5×#121—31no—
79C5×#121—32no—
80C5×#121A411yescharacteristic, direct product factor
81C2×C5×C4⋊C4—31no—
82C2×C5×C4⋊C4—31no—
83C2×C5×C4⋊C4—32no—
84C2×C5×C22⋊C4—32no—
85C2×C5×C22⋊C4—32no—
86C2×C5×C22⋊C4—32no—
87C2×C5×C22⋊C4—32no—
88C22×#121C3×C511yescharacteristic, complemented, Sylow
89C23×C3×C5—41no—
90C23×C3×C5—42no—
91C2×C5×A4—22no—
92C2×C5×A4—42no—
93C2×C5×A4C2×D411yescharacteristic
94C2×C5×A4C2×D411yescharacteristic
95C2×C5×A4#4111yescharacteristic
96C3×C5×D4—82no—
97C3×C5×D4—84no—
98C2×C3×C4×C5—41no—
99C2×C3×C4×C5—41no—
100C2×C3×C4×C5—42no—
101C2×C3×C4×C5—82no—
102C23×A4C22×C512yes—
103C23×A4C22×C511yescharacteristic
104D4×A4—24no—
105D4×A4—22no—
106C2×C4×A4—22no—
107C2×C4×A4C22×C511yescharacteristic
108C2×C4×A4C22×C512yes—
109C2×C4×A4C22×C511yescharacteristic
110C3×#121—41no—
111C24×C5—21no—
112C24×C5—21no—
113C24×C5—22no—
114C24×C5—22no—
115C24×C5—22no—
116C24×C5—31no—
117C24×C5—32no—
118C24×C5—31no—
119C24×C5—32no—
120C24×C5—32no—
121C24×C5—61no—
122C24×C5—61no—
123C24×C5—62no—
124C24×C5—62no—
125C24×C5—62no—
126C24×C5C3×D412yescomplemented
127C24×C5C23×C311yescharacteristic
128C2×C5×D4—32no—
129C2×C5×D4—34no—
130C2×C5×D4—32no—
131C2×C5×D4—32no—
132C2×C5×D4—32no—
133C2×C5×D4—32no—
134C2×C5×D4—31no—
135C2×C5×D4—62no—
136C2×C5×D4—62no—
137C2×C5×D4—64no—
138C2×C5×D4—62no—
139C2×C5×D4—64no—
140C2×C5×D4—62no—
141C2×C5×D4—64no—
142C2×C5×D4—64no—
143C2×C5×D4—64no—
144C2×C5×D4—64no—
145C2×C5×D4—64no—
146C2×C5×D4—64no—
147C2×C5×D4—64no—
148C2×C5×D4—64no—
149C2×C5×D4C2×A412yescomplemented
150C2×C5×D4C2×A411yescharacteristic, complemented
151C22×C4×C5—21no—
152C22×C4×C5—22no—
153C22×C4×C5—31no—
154C22×C4×C5—31no—
155C22×C4×C5—32no—
156C22×C4×C5—32no—
157C22×C4×C5—31no—
158C22×C4×C5—31no—
159C22×C4×C5—32no—
160C22×C4×C5—31no—
161C22×C4×C5—31no—
162C22×C4×C5—31no—
163C22×C4×C5—32no—
164C22×C4×C5—62no—
165C22×C4×C5—62no—
166C22×C4×C5—62no—
167C22×C4×C5—62no—
168C22×C4×C5—62no—
169C22×C4×C5—62no—
170C22×C4×C5—62no—
171C22×C4×C5—62no—
172C22×C4×C5—61no—
173C22×C4×C5—62no—
174C22×C4×C5C3×D412yescomplemented
175C22×C4×C5C2×A411yescharacteristic, complemented
176C5×C4⋊C4—32no—
177C5×C4⋊C4—32no—
178C5×C4⋊C4—31no—
179C5×C4⋊C4C2×A411yescharacteristic, complemented
180C5×C22⋊C4—34no—
181C5×C22⋊C4—32no—
182C5×C22⋊C4—32no—
183C5×C22⋊C4—32no—
184C5×C22⋊C4C2×A412yescomplemented
185C23×D4C2×C3×C512yescomplemented
186C23×D4C2×C3×C511yescharacteristic, complemented
187C24×C4C2×C3×C511yescharacteristic, complemented
188C2×#121—31no—
189C2×#121—32no—
190C2×#121—31no—
191C2×#121—31no—
192C2×#121—32no—
193C2×#121—31no—
194C22×C4⋊C4C2×C3×C511yescharacteristic, complemented
195C22×C22⋊C4C2×C3×C512yescomplemented
196C22×C3×C5—42no—
197C22×C3×C5—41no—
198C22×C3×C5—81no—
199C22×C3×C5—81no—
200C22×C3×C5—82no—
201C22×C3×C5—82no—
202C22×C3×C5—82no—
203C5×A4#12111yescharacteristic, direct product factor
204C3×C4×C5—42no—
205C3×C4×C5—81no—
206C3×C4×C5—82no—
207C22×A4—21no—
208C22×A4—21no—
209C22×A4—22no—
210C22×A4—22no—
211C22×A4—22no—
212C22×A4C5×D412yescomplemented
213C22×A4C23×C511yescharacteristic
214C2×C3×D4—41no—
215C2×C3×D4—42no—
216C22×C3×C4—41no—
217C4×A4—21no—
218C4×A4—22no—
219C4×A4C5×D412yescomplemented
220C3×C4⋊C4—41no—
221C3×C22⋊C4—42no—
222C23×C5—22no—
223C23×C5—31no—
224C23×C5—31no—
225C23×C5—31no—
226C23×C5—31no—
227C23×C5—32no—
228C23×C5—32no—
229C23×C5—32no—
230C23×C5—32no—
231C23×C5—31no—
232C23×C5—32no—
233C23×C5—42no—
234C23×C5—61no—
235C23×C5—61no—
236C23×C5—61no—
237C23×C5—61no—
238C23×C5—62no—
239C23×C5—62no—
240C23×C5—62no—
241C23×C5—62no—
242C23×C5—62no—
243C23×C5—62no—
244C23×C5—62no—
245C23×C5—61no—
246C23×C5—61no—
247C23×C5—62no—
248C23×C5—62no—
249C23×C5—61no—
250C23×C5—61no—
251C23×C5—64no—
252C23×C5—62no—
253C23×C5—62no—
254C23×C5—62no—
255C23×C5—62no—
256C23×C5—62no—
257C23×C5—62no—
258C23×C5—122no—
259C23×C5—122no—
260C23×C5—122no—
261C23×C5—124no—
262C23×C5C2×C3×D411yescharacteristic
263C23×C5C2×C3×D411yescharacteristic
264C23×C5C3×#4111yescharacteristic
265C23×C5C22×A412yes—
266C23×C5C22×A411yescharacteristic
267C5×D4—24no—
268C5×D4—22no—
269C5×D4—64no—
270C5×D4—64no—
271C5×D4—64no—
272C5×D4—64no—
273C5×D4—68no—
274C5×D4—64no—
275C5×D4—62no—
276C2×C4×C5—22no—
277C2×C4×C5—32no—
278C2×C4×C5—31no—
279C2×C4×C5—32no—
280C2×C4×C5—32no—
281C2×C4×C5—32no—
282C2×C4×C5—31no—
283C2×C4×C5—32no—
284C2×C4×C5—62no—
285C2×C4×C5—61no—
286C2×C4×C5—62no—
287C2×C4×C5—61no—
288C2×C4×C5—62no—
289C2×C4×C5—62no—
290C2×C4×C5—64no—
291C2×C4×C5—62no—
292C2×C4×C5—61no—
293C2×C4×C5—62no—
294C2×C4×C5—61no—
295C2×C4×C5—62no—
296C2×C4×C5C22×A411yescharacteristic
297C2×C4×C5C22×A412yes—
298C2×C4×C5C22×A411yescharacteristic
299C25C22×C3×C512yes—
300C25C22×C3×C511yescharacteristic
301C22×D4—24no—
302C22×D4—22no—
303C22×D4—31no—
304C22×D4—32no—
305C22×D4—31no—
306C22×D4—32no—
307C22×D4—32no—
308C22×D4—32no—
309C22×D4—32no—
310C22×D4—62no—
311C22×D4—64no—
312C23×C4—22no—
313C23×C4—31no—
314C23×C4—31no—
315C23×C4—31no—
316C23×C4—31no—
317C23×C4—62no—
318C23×C4C22×C3×C511yescharacteristic
319C23×C4C22×C3×C512yes—
320C23×C4C22×C3×C511yescharacteristic
321#121—32no—
322#121—32no—
323#121—34no—
324#121—34no—
325#121—32no—
326#121—31no—
327#121—32no—
328#121—31no—
329#121—31no—
330#121—32no—
331#121C5×A411yescharacteristic, direct product factor
332C2×C4⋊C4—31no—
333C2×C4⋊C4—31no—
334C2×C4⋊C4—32no—
335C2×C22⋊C4—32no—
336C2×C22⋊C4—32no—
337C2×C22⋊C4—32no—
338C2×C22⋊C4—32no—
339C2×C3×C5—41no—
340C2×C3×C5—41no—
341C2×C3×C5—41no—
342C2×C3×C5—82no—
343C2×C3×C5—162no—
344C23×C3—41no—
345C23×C3—42no—
346C2×A4—22no—
347C2×A4—42no—
348C2×A4C2×C5×D411yescharacteristic
349C2×A4C2×C5×D411yescharacteristic
350C2×A4C5×#4111yescharacteristic
351C3×D4—82no—
352C3×D4—84no—
353C2×C3×C4—41no—
354C2×C3×C4—41no—
355C2×C3×C4—42no—
356C2×C3×C4—82no—
357C22×C5—21no—
358C22×C5—21no—
359C22×C5—22no—
360C22×C5—22no—
361C22×C5—22no—
362C22×C5—31no—
363C22×C5—31no—
364C22×C5—31no—
365C22×C5—32no—
366C22×C5—31no—
367C22×C5—31no—
368C22×C5—31no—
369C22×C5—31no—
370C22×C5—31no—
371C22×C5—31no—
372C22×C5—32no—
373C22×C5—62no—
374C22×C5—62no—
375C22×C5—62no—
376C22×C5—62no—
377C22×C5—62no—
378C22×C5—62no—
379C22×C5—62no—
380C22×C5—62no—
381C22×C5—61no—
382C22×C5—61no—
383C22×C5—62no—
384C22×C5—62no—
385C22×C5—62no—
386C22×C5—122no—
387C22×C5—122no—
388C22×C5—122no—
389C22×C5—122no—
390C22×C5—122no—
391C22×C5—122no—
392C22×C5—122no—
393C22×C5—122no—
394C22×C5C3×#12111yescharacteristic, complemented
395C22×C5D4×A412yescomplemented
396C22×C5C23×A411yescharacteristic
397C4×C5—21no—
398C4×C5—22no—
399C4×C5—32no—
400C4×C5—61no—
401C4×C5—62no—
402C4×C5D4×A412yescomplemented
403C24—21no—
404C24—21no—
405C24—22no—
406C24—22no—
407C24—22no—
408C24—31no—
409C24—32no—
410C24—31no—
411C24—32no—
412C24—32no—
413C24—61no—
414C24—61no—
415C24—62no—
416C24—62no—
417C24—62no—
418C24C3×C5×D412yescomplemented
419C24C23×C3×C511yescharacteristic
420C2×D4—32no—
421C2×D4—34no—
422C2×D4—32no—
423C2×D4—32no—
424C2×D4—32no—
425C2×D4—32no—
426C2×D4—31no—
427C2×D4—62no—
428C2×D4—62no—
429C2×D4—64no—
430C2×D4—62no—
431C2×D4—64no—
432C2×D4—62no—
433C2×D4—64no—
434C2×D4—64no—
435C2×D4—64no—
436C2×D4—64no—
437C2×D4—64no—
438C2×D4—64no—
439C2×D4—64no—
440C2×D4—64no—
441C2×D4C2×C5×A412yescomplemented
442C2×D4C2×C5×A411yescharacteristic, complemented
443C22×C4—21no—
444C22×C4—22no—
445C22×C4—31no—
446C22×C4—31no—
447C22×C4—32no—
448C22×C4—32no—
449C22×C4—31no—
450C22×C4—31no—
451C22×C4—32no—
452C22×C4—31no—
453C22×C4—31no—
454C22×C4—31no—
455C22×C4—32no—
456C22×C4—62no—
457C22×C4—62no—
458C22×C4—62no—
459C22×C4—62no—
460C22×C4—62no—
461C22×C4—62no—
462C22×C4—62no—
463C22×C4—62no—
464C22×C4—61no—
465C22×C4—62no—
466C22×C4C3×C5×D412yescomplemented
467C22×C4C2×C5×A411yescharacteristic, complemented
468C4⋊C4—32no—
469C4⋊C4—32no—
470C4⋊C4—31no—
471C4⋊C4C2×C5×A411yescharacteristic, complemented
472C22⋊C4—34no—
473C22⋊C4—32no—
474C22⋊C4—32no—
475C22⋊C4—32no—
476C22⋊C4C2×C5×A412yescomplemented
477C3×C5—41noHall
478C22×C3—42no—
479C22×C3—41no—
480C22×C3—81no—
481C22×C3—81no—
482C22×C3—82no—
483C22×C3—82no—
484C22×C3—82no—
485A4C5×#12111yescharacteristic, direct product factor
486C3×C4—42no—
487C3×C4—81no—
488C3×C4—82no—
489C2×C5—22no—
490C2×C5—31no—
491C2×C5—31no—
492C2×C5—31no—
493C2×C5—31no—
494C2×C5—42no—
495C2×C5—62no—
496C2×C5—122no—
497C2×C5C2×D4×A411yescharacteristic
498C2×C5C2×D4×A411yescharacteristic
499C2×C5A4×#4111yescharacteristic
500C23—22no—
501C23—31no—
502C23—31no—
503C23—31no—
504C23—31no—
505C23—32no—
506C23—32no—
507C23—32no—
508C23—32no—
509C23—31no—
510C23—32no—
511C23—42no—
512C23—61no—
513C23—61no—
514C23—61no—
515C23—61no—
516C23—62no—
517C23—62no—
518C23—62no—
519C23—62no—
520C23—62no—
521C23—62no—
522C23—62no—
523C23—61no—
524C23—61no—
525C23—62no—
526C23—62no—
527C23—61no—
528C23—61no—
529C23—64no—
530C23—62no—
531C23—62no—
532C23—62no—
533C23—62no—
534C23—62no—
535C23—62no—
536C23—122no—
537C23—122no—
538C23—122no—
539C23—124no—
540C23C2×C3×C5×D411yescharacteristic
541C23C2×C3×C5×D411yescharacteristic
542C23C3×C5×#4111yescharacteristic
543C23C22×C5×A412yes—
544C23C22×C5×A411yescharacteristic
545D4—24no—
546D4—22no—
547D4—64no—
548D4—64no—
549D4—64no—
550D4—64no—
551D4—68no—
552D4—64no—
553D4—62no—
554C2×C4—22no—
555C2×C4—32no—
556C2×C4—31no—
557C2×C4—32no—
558C2×C4—32no—
559C2×C4—32no—
560C2×C4—31no—
561C2×C4—32no—
562C2×C4—62no—
563C2×C4—61no—
564C2×C4—62no—
565C2×C4—61no—
566C2×C4—62no—
567C2×C4—62no—
568C2×C4—64no—
569C2×C4—62no—
570C2×C4—61no—
571C2×C4—62no—
572C2×C4—61no—
573C2×C4—62no—
574C2×C4C22×C5×A411yescharacteristic
575C2×C4C22×C5×A412yes—
576C2×C4C22×C5×A411yescharacteristic
577C2×C3—41no—
578C2×C3—41no—
579C2×C3—41no—
580C2×C3—82no—
581C2×C3—162no—
582C5A4×#12111yescharacteristic, direct product factor, Sylow
583C22—21no—
584C22—21no—
585C22—22no—
586C22—22no—
587C22—22no—
588C22—31no—
589C22—31no—
590C22—31no—
591C22—32no—
592C22—31no—
593C22—31no—
594C22—31no—
595C22—31no—
596C22—31no—
597C22—31no—
598C22—32no—
599C22—62no—
600C22—62no—
601C22—62no—
602C22—62no—
603C22—62no—
604C22—62no—
605C22—62no—
606C22—62no—
607C22—61no—
608C22—61no—
609C22—62no—
610C22—62no—
611C22—62no—
612C22—122no—
613C22—122no—
614C22—122no—
615C22—122no—
616C22—122no—
617C22—122no—
618C22—122no—
619C22—122no—
620C22C3×C5×#12111yescharacteristic, complemented
621C22C5×D4×A412yescomplemented
622C22C23×C5×A411yescharacteristic
623C4—21no—
624C4—22no—
625C4—32no—
626C4—61no—
627C4—62no—
628C4C5×D4×A412yescomplemented
629C3—41noSylow
630C2—22no—
631C2—31no—
632C2—31no—
633C2—31no—
634C2—31no—
635C2—42no—
636C2—62no—
637C2—122no—
638C2C2×C5×D4×A411yescharacteristic
639C2C2×C5×D4×A411yescharacteristic
640C2C5×A4×#4111yescharacteristic
subgroupG/H
centerC22×C5C23×A4
commutator, cosocleC24C23×C3×C5
FrattiniC22C23×C5×A4
FittingC22×C5×#121C3
socleC24×C5C23×C3
hypercenterC5×#121A4
hypocenterC22C3×C5×#121
LCSG ▷ C24 ▷ C22
UCSC1 ◁ C22×C5 ◁ C5×#121

Complements

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

NH ≅ G/Ntype
1. C2×C5×D4×A4C2semidirect
2. C2×C5×D4×A4C2semidirect
3. C22×C4×C5×A4C2semidirect
4. C5×A4×C4⋊C4C2semidirect
5. C5×A4×C22⋊C4C2semidirect
6. C22×C5×#121C3semidirect
16. A4×#121C5direct (N × H)
17. C23×C5×D4C2×C3semidirect
18. C23×C5×D4C2×C3semidirect
19. C24×C4×C5C2×C3semidirect
26. C22×C5×C4⋊C4C2×C3semidirect
27. C22×C5×C22⋊C4C2×C3semidirect
33. C22×C5×A4D4semidirect
40. C4×C5×A4D4semidirect
43. C2×D4×A4C2×C5semidirect
44. C2×D4×A4C2×C5semidirect
45. C22×C4×A4C2×C5semidirect
46. A4×C4⋊C4C2×C5semidirect
47. A4×C22⋊C4C2×C5semidirect
80. C5×#121A4direct (N × H)
88. C22×#121C3×C5semidirect
126. C24×C5C3×D4semidirect
149. C2×C5×D4C2×A4semidirect
150. C2×C5×D4C2×A4semidirect
174. C22×C4×C5C3×D4semidirect
175. C22×C4×C5C2×A4semidirect
179. C5×C4⋊C4C2×A4semidirect
184. C5×C22⋊C4C2×A4semidirect
185. C23×D4C2×C3×C5semidirect
186. C23×D4C2×C3×C5semidirect
187. C24×C4C2×C3×C5semidirect
194. C22×C4⋊C4C2×C3×C5semidirect
195. C22×C22⋊C4C2×C3×C5semidirect
203. C5×A4#121direct (N × H)
212. C22×A4C5×D4semidirect
219. C4×A4C5×D4semidirect
331. #121C5×A4direct (N × H)
394. C22×C5C3×#121semidirect
395. C22×C5D4×A4semidirect
402. C4×C5D4×A4semidirect
418. C24C3×C5×D4semidirect
441. C2×D4C2×C5×A4semidirect
442. C2×D4C2×C5×A4semidirect
466. C22×C4C3×C5×D4semidirect
467. C22×C4C2×C5×A4semidirect
471. C4⋊C4C2×C5×A4semidirect
476. C22⋊C4C2×C5×A4semidirect
485. A4C5×#121direct (N × H)
582. C5A4×#121direct (N × H)
620. C22C3×C5×#121semidirect
621. C22C5×D4×A4semidirect
628. C4C5×D4×A4semidirect

Maximal subgroups

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

subgroupindex
C2×C5×D4×A42
C22×C4×C5×A42
C5×A4×C4⋊C42
C5×A4×C22⋊C42
C22×C5×#1213
C3×C5×#1214
A4×#1215