Finite Group Databasebeta

← C4×A4×C22⋊D5 #14514180

Subgroups — C4×A4×C22⋊D5 #14514180

Order 1920.

1156 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C5×A4C211yesmaximal, characteristic, complemented
2C2×A4×C22⋊D5C211yesmaximal, characteristic
3C2×C4×D5×A4C211yesmaximal, characteristic, complemented
4A4×C22⋊Dic5C211yesmaximal, characteristic, complemented
5A4×#685C211yesmaximal, characteristic, complemented
6A4×#683C211yesmaximal, characteristic, complemented
7C4×A4×Dic5C211yesmaximal, characteristic, complemented
8C22×C4×C22⋊D5C311yesmaximal, characteristic, complemented, Hall
9C23×C5×A4C2211yescharacteristic
10C22×D5×A4C2211yescharacteristic
11C2×C4×C5×A4—22no—
12C2×C4×C5×A4C2211yescharacteristic
13C2×C4×C5×A4C2211yescharacteristic
14A4×C22⋊D5C414yesdirect product factor
15C2×A4×Dic5C2211yescharacteristic
16C2×A4×Dic5C2211yescharacteristic
17C2×A4×Dic5C2211yescharacteristic
18C4×D5×A4—22no—
19C3×C4×C22⋊D5—41nomaximal
20C4×D4×A4—51nomaximal, Hall
21C24×C4×C5C2×C311yescharacteristic, complemented
22C23×C22⋊D5C2×C311yescharacteristic
23C23×C4×D5C2×C311yescharacteristic, complemented
24C22×C22⋊Dic5C2×C311yescharacteristic, complemented
25C2×C4×C22⋊D5—31no—
26C2×C4×C22⋊D5—31no—
27C2×C4×C22⋊D5—31no—
28C2×C4×C22⋊D5—31no—
29C2×C4×C22⋊D5—31no—
30C2×C4×C22⋊D5—31no—
31C2×C4×C22⋊D5—31no—
32C2×C4×C22⋊D5—31no—
33C22×#685C2×C311yescharacteristic, complemented
34C22×#683C2×C311yescharacteristic, complemented
35C22×C4×Dic5C2×C311yescharacteristic, complemented
36C22×C5×A4—21no—
37C22×C5×A4—21no—
38C22×C5×A4C2×C412yescomplemented
39C22×C5×A4C2311yescharacteristic
40C2×D5×A4—21no—
41C2×D5×A4—21no—
42C2×D5×A4C2×C412yescomplemented
43C22×C3×C4×C5—41no—
44C2×C3×C22⋊D5—41no—
45C2×C3×C4×D5—41no—
46C4×C5×A4—21no—
47C4×C5×A4D412yescomplemented
48A4×Dic5—21no—
49A4×Dic5—21no—
50A4×Dic5C2×C412yescomplemented
51C3×C22⋊Dic5—41no—
52C3×#685—41no—
53C3×#683—41no—
54C3×C4×Dic5—41no—
55C2×D4×A4—51no—
56C22×C4×A4—51no—
57C22×C4×A4D511yescharacteristic, complemented
58A4×C4⋊C4—51no—
59A4×C22⋊C4—51no—
60A4×C22⋊C4—51no—
61C42×A4—51no—
62C25×C5C22×C311yescharacteristic
63C24×D5C22×C311yescharacteristic
64C23×C4×C5—22no—
65C23×C4×C5—31no—
66C23×C4×C5—31no—
67C23×C4×C5—31no—
68C23×C4×C5—31no—
69C23×C4×C5—62no—
70C23×C4×C5C22×C311yescharacteristic
71C23×C4×C5C22×C311yescharacteristic
72C22×C22⋊D5—31no—
73C22×C22⋊D5—31no—
74C22×C22⋊D5—31no—
75C22×C22⋊D5—31no—
76C22×C22⋊D5—34no—
77C22×C22⋊D5C3×C414yescomplemented
78C23×Dic5C22×C311yescharacteristic
79C23×Dic5C22×C311yescharacteristic
80C23×Dic5C22×C311yescharacteristic
81C22×C4×D5—22no—
82C22×C4×D5—31no—
83C22×C4×D5—31no—
84C22×C4×D5—31no—
85C22×C4×D5—31no—
86C22×C4×D5—62no—
87C2×C22⋊Dic5—31no—
88C2×C22⋊Dic5—31no—
89C2×C22⋊Dic5—31no—
90C2×C22⋊Dic5—31no—
91C4×C22⋊D5—32no—
92C4×C22⋊D5—32no—
93C4×C22⋊D5—32no—
94C4×C22⋊D5—32no—
95C4×C22⋊D5—32no—
96C4×C22⋊D5—32no—
97C4×C22⋊D5—32no—
98C4×C22⋊D5—31no—
99C4×C22⋊D5—31no—
100C4×C22⋊D5—31no—
101C4×C22⋊D5—31no—
102C4×C22⋊D5—31no—
103C4×C22⋊D5—31no—
104C4×C22⋊D5—31no—
105C4×C22⋊D5A411yescharacteristic, direct product factor
106C2×#685—31no—
107C2×#685—31no—
108C2×#685—31no—
109C2×#685—31no—
110C2×#683—31no—
111C2×#683—31no—
112C2×#683—31no—
113C2×#683—31no—
114C2×C4×Dic5—31no—
115C2×C4×Dic5—31no—
116C2×C4×Dic5—31no—
117C2×C4×Dic5—31no—
118C22×C4×D4—51noSylow
119C23×C3×C5—41no—
120C22×C3×D5—41no—
121C2×C5×A4—22no—
122C2×C5×A4C22×C411yescharacteristic
123C2×C5×A4C2×D411yescharacteristic
124C2×C5×A4#4111yescharacteristic
125D5×A4—22no—
126C2×C3×C4×C5—41no—
127C2×C3×C4×C5—41no—
128C2×C3×C4×C5—82no—
129C3×C22⋊D5—44no—
130C2×C3×Dic5—41no—
131C2×C3×Dic5—41no—
132C2×C3×Dic5—41no—
133C3×C4×D5—82no—
134C23×A4—51no—
135C23×A4C2×D511yescharacteristic
136D4×A4—54no—
137C2×C4×A4—22no—
138C2×C4×A4—51no—
139C2×C4×A4—51no—
140C2×C4×A4—51no—
141C2×C4×A4—102no—
142C2×C4×A4C2×D511yescharacteristic
143C2×C4×A4C2×D511yescharacteristic
144C3×C4×D4—201no—
145C24×C5—21no—
146C24×C5—21no—
147C24×C5—31no—
148C24×C5—32no—
149C24×C5—31no—
150C24×C5—61no—
151C24×C5—61no—
152C24×C5C2×C3×C412yescomplemented
153C24×C5C23×C311yescharacteristic
154C23×D5—21no—
155C23×D5—21no—
156C23×D5—31no—
157C23×D5—31no—
158C23×D5—32no—
159C23×D5—61no—
160C23×D5—61no—
161C23×D5C2×C3×C412yescomplemented
162C22×C4×C5—21no—
163C22×C4×C5—31no—
164C22×C4×C5—31no—
165C22×C4×C5—32no—
166C22×C4×C5—32no—
167C22×C4×C5—31no—
168C22×C4×C5—31no—
169C22×C4×C5—31no—
170C22×C4×C5—31no—
171C22×C4×C5—31no—
172C22×C4×C5—62no—
173C22×C4×C5—62no—
174C22×C4×C5—62no—
175C22×C4×C5—62no—
176C22×C4×C5—62no—
177C22×C4×C5—62no—
178C22×C4×C5—62no—
179C22×C4×C5—62no—
180C22×C4×C5—61no—
181C22×C4×C5C3×D412yescomplemented
182C22×C4×C5C2×A411yescharacteristic, complemented
183C2×C22⋊D5—34no—
184C2×C22⋊D5—34no—
185C2×C22⋊D5—34no—
186C2×C22⋊D5—32no—
187C2×C22⋊D5—31no—
188C2×C22⋊D5—31no—
189C2×C22⋊D5—34no—
190C2×C22⋊D5—34no—
191C2×C22⋊D5—34no—
192C2×C22⋊D5—34no—
193C2×C22⋊D5—34no—
194C2×C22⋊D5—31no—
195C2×C22⋊D5C2×A411yescharacteristic
196C22×Dic5—21no—
197C22×Dic5—21no—
198C22×Dic5—31no—
199C22×Dic5—32no—
200C22×Dic5—31no—
201C22×Dic5—31no—
202C22×Dic5—31no—
203C22×Dic5—31no—
204C22×Dic5—31no—
205C22×Dic5—61no—
206C22×Dic5—61no—
207C22×Dic5C2×C3×C412yescomplemented
208C2×C4×D5—32no—
209C2×C4×D5—31no—
210C2×C4×D5—31no—
211C2×C4×D5—31no—
212C2×C4×D5—62no—
213C2×C4×D5—62no—
214C2×C4×D5—62no—
215C2×C4×D5—62no—
216C2×C4×D5—62no—
217C2×C4×D5—62no—
218C2×C4×D5—62no—
219C2×C4×D5—62no—
220C2×C4×D5C2×A411yescharacteristic, complemented
221C22⋊Dic5—32no—
222C22⋊Dic5—31no—
223C22⋊Dic5—31no—
224C22⋊Dic5—31no—
225C22⋊Dic5C2×A411yescharacteristic, complemented
226#685—32no—
227#685—31no—
228#685—31no—
229#685—31no—
230#685C2×A411yescharacteristic, complemented
231#683—32no—
232#683—31no—
233#683—31no—
234#683—31no—
235#683C2×A411yescharacteristic, complemented
236C4×Dic5—32no—
237C4×Dic5—31no—
238C4×Dic5—31no—
239C4×Dic5—31no—
240C4×Dic5C2×A411yescharacteristic, complemented
241C23×D4—51no—
242C24×C4—51no—
243C24×C4C3×D511yescharacteristic, complemented
244C2×C4×D4—151no—
245C2×C4×D4—151no—
246C2×C4×D4—151no—
247C2×C4×D4—151no—
248C2×C4×D4—151no—
249C2×C4×D4—151no—
250C2×C4×D4—151no—
251C2×C4×D4—151no—
252C22×C4⋊C4—51no—
253C22×C22⋊C4—51no—
254C22×C22⋊C4—51no—
255C22×C42—51no—
256C22×C3×C5—42no—
257C22×C3×C5—41no—
258C22×C3×C5—81no—
259C22×C3×C5—81no—
260C2×C3×D5—42no—
261C2×C3×D5—81no—
262C2×C3×D5—81no—
263C5×A4C4×D411yescharacteristic, complemented
264C3×C4×C5—42no—
265C3×C4×C5—81no—
266C3×Dic5—42no—
267C3×Dic5—81no—
268C3×Dic5—81no—
269C22×A4—21no—
270C22×A4—21no—
271C22×A4—52no—
272C22×A4—101no—
273C22×A4—101no—
274C22×A4C4×D512yescomplemented
275C22×A4C22×D511yescharacteristic
276C2×C3×D4—201no—
277C22×C3×C4—41no—
278C22×C3×C4—201no—
279C4×A4—21no—
280C4×A4—52no—
281C4×A4—101no—
282C4×A4—101no—
283C4×A4C22⋊D512yesdirect product factor
284C3×C4⋊C4—201no—
285C3×C22⋊C4—201no—
286C3×C22⋊C4—201no—
287C3×C42—201no—
288C23×C5—22no—
289C23×C5—31no—
290C23×C5—31no—
291C23×C5—31no—
292C23×C5—31no—
293C23×C5—32no—
294C23×C5—32no—
295C23×C5—32no—
296C23×C5—32no—
297C23×C5—31no—
298C23×C5—61no—
299C23×C5—61no—
300C23×C5—61no—
301C23×C5—61no—
302C23×C5—62no—
303C23×C5—61no—
304C23×C5—61no—
305C23×C5—62no—
306C23×C5—62no—
307C23×C5—61no—
308C23×C5—61no—
309C23×C5—64no—
310C23×C5C22×C3×C411yescharacteristic
311C23×C5C2×C3×D411yescharacteristic
312C23×C5C3×#4111yescharacteristic
313C23×C5C22×A411yescharacteristic
314C22×D5—22no—
315C22×D5—32no—
316C22×D5—31no—
317C22×D5—32no—
318C22×D5—32no—
319C22×D5—32no—
320C22×D5—61no—
321C22×D5—61no—
322C22×D5—61no—
323C22×D5—61no—
324C22×D5—64no—
325C22×D5—61no—
326C22×D5—61no—
327C22×D5—62no—
328C22×D5—62no—
329C22×D5—61no—
330C22×D5—61no—
331C22×D5—62no—
332C22×D5C22×A411yescharacteristic
333C2×C4×C5—22no—
334C2×C4×C5—32no—
335C2×C4×C5—31no—
336C2×C4×C5—32no—
337C2×C4×C5—32no—
338C2×C4×C5—32no—
339C2×C4×C5—31no—
340C2×C4×C5—62no—
341C2×C4×C5—61no—
342C2×C4×C5—61no—
343C2×C4×C5—62no—
344C2×C4×C5—64no—
345C2×C4×C5—62no—
346C2×C4×C5—61no—
347C2×C4×C5—61no—
348C2×C4×C5C22×A411yescharacteristic
349C2×C4×C5C22×A411yescharacteristic
350C22⋊D5—38no—
351C22⋊D5—34no—
352C22⋊D5—34no—
353C22⋊D5—34no—
354C22⋊D5C4×A414yesdirect product factor
355C2×Dic5—32no—
356C2×Dic5—31no—
357C2×Dic5—32no—
358C2×Dic5—32no—
359C2×Dic5—32no—
360C2×Dic5—31no—
361C2×Dic5—31no—
362C2×Dic5—61no—
363C2×Dic5—61no—
364C2×Dic5—61no—
365C2×Dic5—61no—
366C2×Dic5—61no—
367C2×Dic5—61no—
368C2×Dic5—61no—
369C2×Dic5—61no—
370C2×Dic5C22×A411yescharacteristic
371C2×Dic5C22×A411yescharacteristic
372C2×Dic5C22×A411yescharacteristic
373C4×D5—22no—
374C4×D5—62no—
375C4×D5—62no—
376C4×D5—64no—
377C4×D5—62no—
378C25—51no—
379C25C2×C3×D511yescharacteristic
380C22×D4—54no—
381C22×D4—151no—
382C22×D4—151no—
383C22×D4—151no—
384C22×D4—151no—
385C22×D4—154no—
386C23×C4—22no—
387C23×C4—31no—
388C23×C4—31no—
389C23×C4—31no—
390C23×C4—31no—
391C23×C4—51no—
392C23×C4—51no—
393C23×C4—51no—
394C23×C4—62no—
395C23×C4—102no—
396C23×C4—151no—
397C23×C4—151no—
398C23×C4—151no—
399C23×C4—151no—
400C23×C4—302no—
401C23×C4C2×C3×D511yescharacteristic
402C23×C4C2×C3×D511yescharacteristic
403C4×D4—51no—
404C4×D4—151no—
405C4×D4—151no—
406C4×D4—151no—
407C4×D4—151no—
408C4×D4—151no—
409C4×D4—151no—
410C4×D4—152no—
411C4×D4—152no—
412C4×D4—152no—
413C4×D4—152no—
414C4×D4—152no—
415C4×D4—152no—
416C4×D4—152no—
417C4×D4—151no—
418C2×C4⋊C4—151no—
419C2×C4⋊C4—151no—
420C2×C4⋊C4—151no—
421C2×C4⋊C4—151no—
422C2×C22⋊C4—151no—
423C2×C22⋊C4—151no—
424C2×C22⋊C4—151no—
425C2×C22⋊C4—151no—
426C2×C22⋊C4—151no—
427C2×C22⋊C4—151no—
428C2×C22⋊C4—151no—
429C2×C22⋊C4—151no—
430C2×C42—151no—
431C2×C42—151no—
432C2×C42—151no—
433C2×C42—151no—
434C2×C3×C5—41no—
435C2×C3×C5—41no—
436C2×C3×C5—41no—
437C2×C3×C5—82no—
438C3×D5—82no—
439C23×C3—41no—
440C23×C3—201no—
441C2×A4—22no—
442C2×A4—102no—
443C2×A4C2×C4×D511yescharacteristic
444C2×A4#70911yescharacteristic
445C2×A4C2×C22⋊D511yescharacteristic
446C3×D4—204no—
447C2×C3×C4—41no—
448C2×C3×C4—41no—
449C2×C3×C4—82no—
450C2×C3×C4—201no—
451C2×C3×C4—201no—
452C2×C3×C4—201no—
453C2×C3×C4—402no—
454C22×C5—21no—
455C22×C5—21no—
456C22×C5—31no—
457C22×C5—31no—
458C22×C5—31no—
459C22×C5—32no—
460C22×C5—31no—
461C22×C5—31no—
462C22×C5—31no—
463C22×C5—31no—
464C22×C5—31no—
465C22×C5—31no—
466C22×C5—32no—
467C22×C5—62no—
468C22×C5—62no—
469C22×C5—62no—
470C22×C5—62no—
471C22×C5—62no—
472C22×C5—62no—
473C22×C5—62no—
474C22×C5—62no—
475C22×C5—61no—
476C22×C5—61no—
477C22×C5C3×C4×D411yescharacteristic, complemented
478C22×C5C2×C4×A412yescomplemented
479C22×C5C23×A411yescharacteristic
480C2×D5—21no—
481C2×D5—21no—
482C2×D5—32no—
483C2×D5—62no—
484C2×D5—62no—
485C2×D5—62no—
486C2×D5—62no—
487C2×D5—62no—
488C2×D5—62no—
489C2×D5—61no—
490C2×D5—61no—
491C2×D5—62no—
492C2×D5—62no—
493C2×D5C2×C4×A412yescomplemented
494C4×C5—21no—
495C4×C5—32no—
496C4×C5—61no—
497C4×C5D4×A412yescomplemented
498Dic5—21no—
499Dic5—21no—
500Dic5—32no—
501Dic5—61no—
502Dic5—61no—
503Dic5C2×C4×A412yescomplemented
504C24—21no—
505C24—21no—
506C24—31no—
507C24—32no—
508C24—31no—
509C24—52no—
510C24—61no—
511C24—61no—
512C24—101no—
513C24—101no—
514C24—151no—
515C24—151no—
516C24—152no—
517C24—301no—
518C24—301no—
519C24C3×C4×D512yescomplemented
520C24C22×C3×D511yescharacteristic
521C2×D4—51no—
522C2×D4—151no—
523C2×D4—154no—
524C2×D4—154no—
525C2×D4—151no—
526C2×D4—152no—
527C2×D4—154no—
528C2×D4—154no—
529C2×D4—154no—
530C2×D4—151no—
531C2×D4—154no—
532C2×D4—154no—
533C2×D4—154no—
534C22×C4—21no—
535C22×C4—31no—
536C22×C4—31no—
537C22×C4—32no—
538C22×C4—32no—
539C22×C4—31no—
540C22×C4—31no—
541C22×C4—31no—
542C22×C4—31no—
543C22×C4—31no—
544C22×C4—51no—
545C22×C4—52no—
546C22×C4—62no—
547C22×C4—62no—
548C22×C4—62no—
549C22×C4—62no—
550C22×C4—62no—
551C22×C4—62no—
552C22×C4—62no—
553C22×C4—62no—
554C22×C4—61no—
555C22×C4—101no—
556C22×C4—101no—
557C22×C4—151no—
558C22×C4—151no—
559C22×C4—152no—
560C22×C4—151no—
561C22×C4—151no—
562C22×C4—151no—
563C22×C4—151no—
564C22×C4—152no—
565C22×C4—151no—
566C22×C4—151no—
567C22×C4—151no—
568C22×C4—302no—
569C22×C4—302no—
570C22×C4—302no—
571C22×C4—302no—
572C22×C4—302no—
573C22×C4—302no—
574C22×C4—302no—
575C22×C4—302no—
576C22×C4—301no—
577C22×C4—301no—
578C22×C4C3×C22⋊D512yescomplemented
579C22×C4D5×A411yescharacteristic, complemented
580C4⋊C4—51no—
581C4⋊C4—151no—
582C4⋊C4—151no—
583C4⋊C4—152no—
584C4⋊C4—151no—
585C22⋊C4—51no—
586C22⋊C4—51no—
587C22⋊C4—151no—
588C22⋊C4—151no—
589C22⋊C4—152no—
590C22⋊C4—151no—
591C22⋊C4—151no—
592C22⋊C4—152no—
593C22⋊C4—151no—
594C22⋊C4—151no—
595C42—51no—
596C42—151no—
597C42—151no—
598C42—152no—
599C42—151no—
600C3×C5—41noHall
601C22×C3—42no—
602C22×C3—41no—
603C22×C3—81no—
604C22×C3—81no—
605C22×C3—202no—
606C22×C3—401no—
607C22×C3—401no—
608A4C4×C22⋊D511yescharacteristic, direct product factor
609C3×C4—42no—
610C3×C4—81no—
611C3×C4—202no—
612C3×C4—401no—
613C3×C4—401no—
614C2×C5—22no—
615C2×C5—31no—
616C2×C5—31no—
617C2×C5—31no—
618C2×C5—31no—
619C2×C5—62no—
620C2×C5C22×C4×A411yescharacteristic
621C2×C5C2×D4×A411yescharacteristic
622C2×C5A4×#4111yescharacteristic
623D5—22no—
624D5—62no—
625C23—22no—
626C23—31no—
627C23—31no—
628C23—31no—
629C23—31no—
630C23—32no—
631C23—32no—
632C23—32no—
633C23—32no—
634C23—31no—
635C23—51no—
636C23—61no—
637C23—61no—
638C23—61no—
639C23—61no—
640C23—62no—
641C23—61no—
642C23—61no—
643C23—62no—
644C23—62no—
645C23—61no—
646C23—61no—
647C23—64no—
648C23—102no—
649C23—152no—
650C23—152no—
651C23—152no—
652C23—152no—
653C23—151no—
654C23—301no—
655C23—301no—
656C23—301no—
657C23—301no—
658C23—302no—
659C23—301no—
660C23—301no—
661C23—302no—
662C23—302no—
663C23—301no—
664C23—301no—
665C23—304no—
666C23C2×C3×C4×D511yescharacteristic
667C23C3×#70911yescharacteristic
668C23C2×C3×C22⋊D511yescharacteristic
669C23C2×D5×A411yescharacteristic
670D4—54no—
671D4—154no—
672D4—154no—
673D4—158no—
674D4—154no—
675C2×C4—22no—
676C2×C4—32no—
677C2×C4—31no—
678C2×C4—32no—
679C2×C4—32no—
680C2×C4—32no—
681C2×C4—31no—
682C2×C4—51no—
683C2×C4—51no—
684C2×C4—51no—
685C2×C4—62no—
686C2×C4—61no—
687C2×C4—61no—
688C2×C4—62no—
689C2×C4—64no—
690C2×C4—62no—
691C2×C4—61no—
692C2×C4—61no—
693C2×C4—102no—
694C2×C4—152no—
695C2×C4—152no—
696C2×C4—152no—
697C2×C4—151no—
698C2×C4—152no—
699C2×C4—151no—
700C2×C4—151no—
701C2×C4—302no—
702C2×C4—302no—
703C2×C4—304no—
704C2×C4—301no—
705C2×C4—301no—
706C2×C4—301no—
707C2×C4—301no—
708C2×C4—302no—
709C2×C4—301no—
710C2×C4—301no—
711C2×C4—301no—
712C2×C4—301no—
713C2×C4C2×D5×A411yescharacteristic
714C2×C4C2×D5×A411yescharacteristic
715C2×C3—41no—
716C2×C3—41no—
717C2×C3—41no—
718C2×C3—82no—
719C2×C3—402no—
720C5C4×D4×A411yescharacteristic, complemented, Sylow
721C22—21no—
722C22—21no—
723C22—31no—
724C22—31no—
725C22—31no—
726C22—32no—
727C22—31no—
728C22—31no—
729C22—31no—
730C22—31no—
731C22—31no—
732C22—31no—
733C22—32no—
734C22—52no—
735C22—62no—
736C22—62no—
737C22—62no—
738C22—62no—
739C22—62no—
740C22—62no—
741C22—62no—
742C22—62no—
743C22—61no—
744C22—61no—
745C22—101no—
746C22—101no—
747C22—152no—
748C22—302no—
749C22—302no—
750C22—302no—
751C22—302no—
752C22—302no—
753C22—302no—
754C22—302no—
755C22—302no—
756C22—301no—
757C22—301no—
758C22C3×C4×C22⋊D511yescharacteristic, complemented
759C22C4×D5×A412yescomplemented
760C22C22×D5×A411yescharacteristic
761C4—21no—
762C4—32no—
763C4—52no—
764C4—61no—
765C4—101no—
766C4—101no—
767C4—152no—
768C4—301no—
769C4—301no—
770C4A4×C22⋊D512yesdirect product factor
771C3—41noSylow
772C2—22no—
773C2—31no—
774C2—31no—
775C2—31no—
776C2—31no—
777C2—62no—
778C2—102no—
779C2—302no—
780C2C2×C4×D5×A411yescharacteristic
781C2A4×#70911yescharacteristic
782C2C2×A4×C22⋊D511yescharacteristic
subgroupG/H
centerC2×C4C2×D5×A4
commutatorC23×C5C22×C3×C4
FrattiniC22C22×D5×A4
FittingC24×C4×C5C2×C3
socle, cosocleC24×C5C23×C3
prime radicalC2×A4×C22⋊D5C2
hypercenterC22×C4D5×A4
hypocenterC22×C5C3×C4×D4
LCSG ▷ C23×C5 ▷ C22×C5
UCSC1 ◁ C2×C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. C22×C4×C5×A4C2semidirect
3. C2×C4×D5×A4C2semidirect
4. A4×C22⋊Dic5C2semidirect
5. A4×#685C2semidirect
6. A4×#683C2semidirect
7. C4×A4×Dic5C2semidirect
8. C22×C4×C22⋊D5C3semidirect
14. A4×C22⋊D5C4direct (N × H)
21. C24×C4×C5C2×C3semidirect
23. C23×C4×D5C2×C3semidirect
24. C22×C22⋊Dic5C2×C3semidirect
33. C22×#685C2×C3semidirect
34. C22×#683C2×C3semidirect
35. C22×C4×Dic5C2×C3semidirect
38. C22×C5×A4C2×C4semidirect
42. C2×D5×A4C2×C4semidirect
47. C4×C5×A4D4semidirect
50. A4×Dic5C2×C4semidirect
57. C22×C4×A4D5semidirect
77. C22×C22⋊D5C3×C4semidirect
105. C4×C22⋊D5A4direct (N × H)
152. C24×C5C2×C3×C4semidirect
161. C23×D5C2×C3×C4semidirect
181. C22×C4×C5C3×D4semidirect
182. C22×C4×C5C2×A4semidirect
207. C22×Dic5C2×C3×C4semidirect
220. C2×C4×D5C2×A4semidirect
225. C22⋊Dic5C2×A4semidirect
230. #685C2×A4semidirect
235. #683C2×A4semidirect
240. C4×Dic5C2×A4semidirect
243. C24×C4C3×D5semidirect
263. C5×A4C4×D4semidirect
274. C22×A4C4×D5semidirect
283. C4×A4C22⋊D5direct (N × H)
354. C22⋊D5C4×A4direct (N × H)
477. C22×C5C3×C4×D4semidirect
478. C22×C5C2×C4×A4semidirect
493. C2×D5C2×C4×A4semidirect
497. C4×C5D4×A4semidirect
503. Dic5C2×C4×A4semidirect
519. C24C3×C4×D5semidirect
578. C22×C4C3×C22⋊D5semidirect
579. C22×C4D5×A4semidirect
608. A4C4×C22⋊D5direct (N × H)
720. C5C4×D4×A4semidirect
758. C22C3×C4×C22⋊D5semidirect
759. C22C4×D5×A4semidirect
770. C4A4×C22⋊D5direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×C5×A42
C2×A4×C22⋊D52
C2×C4×D5×A42
A4×C22⋊Dic52
A4×#6852
A4×#6832
C4×A4×Dic52
C22×C4×C22⋊D53
C3×C4×C22⋊D54
C4×D4×A45