Finite Group Databasebeta

← A4×#4027 #14513987

Subgroups — A4×#4027 #14513987

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
1C2×A4×C22⋊D5C211yesmaximal, characteristic
2C22×A4×Dic5C211yesmaximal, characteristic, complemented
3C2×C4×D5×A4C211yesmaximal, characteristic, complemented
4C5×A4×C22⋊C4C211yesmaximal, characteristic, complemented
5A4×#685C211yesmaximal, characteristic, complemented
6A4×#683C211yesmaximal, characteristic, complemented
7C4×A4×Dic5C211yesmaximal, characteristic, complemented
8C22×#4027C311yesmaximal, characteristic, complemented, Hall
9C23×C5×A4C2211yescharacteristic
10C22×D5×A4C2211yescharacteristic
11C2×C4×C5×A4C2211yescharacteristic
12C2×C4×C5×A4C2211yescharacteristic
13A4×C22⋊D5C414yescomplemented
14C2×A4×Dic5—22no—
15C2×A4×Dic5C2211yescharacteristic
16C2×A4×Dic5C2211yescharacteristic
17C2×A4×Dic5C2211yescharacteristic
18C4×D5×A4—22no—
19C3×#4027—41nomaximal
20C4×D4×A4—51nomaximal, Hall
21C23×C22⋊D5C2×C311yescharacteristic
22C24×Dic5C2×C311yescharacteristic, complemented
23C23×C4×D5C2×C311yescharacteristic, complemented
24C22×C5×C22⋊C4C2×C311yescharacteristic, complemented
25C22×#685C2×C311yescharacteristic, complemented
26C22×#683C2×C311yescharacteristic, complemented
27C22×C4×Dic5C2×C311yescharacteristic, complemented
28C2×#4027—31no—
29C2×#4027—31no—
30C2×#4027—31no—
31C2×#4027—31no—
32C2×#4027—31no—
33C2×#4027—31no—
34C2×#4027—31no—
35C2×#4027—31no—
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
43C2×C3×C22⋊D5—41no—
44C22×C3×Dic5—41no—
45C2×C3×C4×D5—41no—
46C4×C5×A4—21no—
47C4×C5×A4—21no—
48A4×Dic5—21no—
49A4×Dic5C2×C412yescomplemented
50A4×Dic5D412yescomplemented
51C3×C5×C22⋊C4—41no—
52C3×#685—41no—
53C3×#683—41no—
54C3×C4×Dic5—41no—
55C2×D4×A4—51no—
56C22×C4×A4—51no—
57C22×C4×A4—51no—
58A4×C4⋊C4—51no—
59A4×C22⋊C4—51no—
60A4×C22⋊C4D511yescharacteristic, complemented
61C42×A4—51no—
62C25×C5C22×C311yescharacteristic
63C24×D5C22×C311yescharacteristic
64C23×C4×C5C22×C311yescharacteristic
65C23×C4×C5C22×C311yescharacteristic
66C22×C22⋊D5—31no—
67C22×C22⋊D5—31no—
68C22×C22⋊D5—31no—
69C22×C22⋊D5—31no—
70C22×C22⋊D5—34no—
71C22×C22⋊D5C3×C414yescomplemented
72C23×Dic5—22no—
73C23×Dic5—31no—
74C23×Dic5—31no—
75C23×Dic5—31no—
76C23×Dic5—31no—
77C23×Dic5—62no—
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×C5×C22⋊C4—31no—
88C2×C5×C22⋊C4—31no—
89C2×C5×C22⋊C4—31no—
90C2×C5×C22⋊C4—31no—
91C2×#685—31no—
92C2×#685—31no—
93C2×#685—31no—
94C2×#685—31no—
95C2×#683—31no—
96C2×#683—31no—
97C2×#683—31no—
98C2×#683—31no—
99C2×C4×Dic5—31no—
100C2×C4×Dic5—31no—
101C2×C4×Dic5—31no—
102C2×C4×Dic5—31no—
103#4027—32no—
104#4027—32no—
105#4027—32no—
106#4027—32no—
107#4027—32no—
108#4027—32no—
109#4027—32no—
110#4027—31no—
111#4027—31no—
112#4027—31no—
113#4027—31no—
114#4027—31no—
115#4027—31no—
116#4027—31no—
117#4027A411yescharacteristic, direct product factor
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—
128C3×C22⋊D5—44no—
129C2×C3×Dic5—41no—
130C2×C3×Dic5—41no—
131C2×C3×Dic5—41no—
132C2×C3×Dic5—82no—
133C3×C4×D5—82no—
134C23×A4—51no—
135C23×A4C2×D511yescharacteristic
136D4×A4—54no—
137C2×C4×A4—51no—
138C2×C4×A4—51no—
139C2×C4×A4—51no—
140C2×C4×A4—102no—
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—21no—
164C22×C4×C5—31no—
165C22×C4×C5—31no—
166C22×C4×C5—31no—
167C22×C4×C5—31no—
168C22×C4×C5—61no—
169C22×C4×C5—61no—
170C2×C22⋊D5—34no—
171C2×C22⋊D5—34no—
172C2×C22⋊D5—34no—
173C2×C22⋊D5—32no—
174C2×C22⋊D5—31no—
175C2×C22⋊D5—31no—
176C2×C22⋊D5—34no—
177C2×C22⋊D5—34no—
178C2×C22⋊D5—34no—
179C2×C22⋊D5—34no—
180C2×C22⋊D5—34no—
181C2×C22⋊D5—31no—
182C2×C22⋊D5C2×A411yescharacteristic
183C22×Dic5—21no—
184C22×Dic5—31no—
185C22×Dic5—31no—
186C22×Dic5—31no—
187C22×Dic5—32no—
188C22×Dic5—32no—
189C22×Dic5—31no—
190C22×Dic5—32no—
191C22×Dic5—31no—
192C22×Dic5—31no—
193C22×Dic5—31no—
194C22×Dic5—31no—
195C22×Dic5—31no—
196C22×Dic5—62no—
197C22×Dic5—62no—
198C22×Dic5—62no—
199C22×Dic5—62no—
200C22×Dic5—62no—
201C22×Dic5—62no—
202C22×Dic5—62no—
203C22×Dic5—62no—
204C22×Dic5—61no—
205C22×Dic5C2×C3×C412yescomplemented
206C22×Dic5C3×D412yescomplemented
207C22×Dic5C2×A411yescharacteristic, complemented
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
221C5×C22⋊C4—32no—
222C5×C22⋊C4—31no—
223C5×C22⋊C4—31no—
224C5×C22⋊C4—31no—
225C5×C22⋊C4C2×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×C4—51no—
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⋊C4C3×D511yescharacteristic, complemented
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—81no—
265C3×C4×C5—81no—
266C3×Dic5—42no—
267C3×Dic5—42no—
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—201no—
278C22×C3×C4—201no—
279C4×A4—21no—
280C4×A4—21no—
281C4×A4—52no—
282C4×A4—52no—
283C4×A4—101no—
284C3×C4⋊C4—201no—
285C3×C22⋊C4—41no—
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—31no—
334C2×C4×C5—31no—
335C2×C4×C5—61no—
336C2×C4×C5—61no—
337C2×C4×C5—61no—
338C2×C4×C5—61no—
339C2×C4×C5—61no—
340C2×C4×C5—61no—
341C2×C4×C5—61no—
342C2×C4×C5—61no—
343C2×C4×C5C22×A411yescharacteristic
344C2×C4×C5C22×A411yescharacteristic
345C22⋊D5—38no—
346C22⋊D5—34no—
347C22⋊D5—34no—
348C22⋊D5—34no—
349C22⋊D5C4×A414yescomplemented
350C2×Dic5—22no—
351C2×Dic5—32no—
352C2×Dic5—32no—
353C2×Dic5—31no—
354C2×Dic5—31no—
355C2×Dic5—32no—
356C2×Dic5—32no—
357C2×Dic5—32no—
358C2×Dic5—32no—
359C2×Dic5—32no—
360C2×Dic5—32no—
361C2×Dic5—31no—
362C2×Dic5—62no—
363C2×Dic5—61no—
364C2×Dic5—61no—
365C2×Dic5—62no—
366C2×Dic5—64no—
367C2×Dic5—62no—
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—51no—
387C23×C4—51no—
388C23×C4—51no—
389C23×C4—102no—
390C23×C4—102no—
391C23×C4—151no—
392C23×C4—151no—
393C23×C4—151no—
394C23×C4—151no—
395C23×C4—151no—
396C23×C4—151no—
397C23×C4—151no—
398C23×C4—151no—
399C23×C4—302no—
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—31no—
423C2×C22⋊C4—31no—
424C2×C22⋊C4—31no—
425C2×C22⋊C4—31no—
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×A4D4×D511yescharacteristic
445C2×A4#71111yescharacteristic
446C3×D4—204no—
447C2×C3×C4—41no—
448C2×C3×C4—41no—
449C2×C3×C4—201no—
450C2×C3×C4—201no—
451C2×C3×C4—201no—
452C2×C3×C4—402no—
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—21no—
496C4×C5—61no—
497C4×C5—61no—
498Dic5—21no—
499Dic5—32no—
500Dic5—32no—
501Dic5—61no—
502Dic5C2×C4×A412yescomplemented
503Dic5D4×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—21no—
536C22×C4—31no—
537C22×C4—31no—
538C22×C4—31no—
539C22×C4—31no—
540C22×C4—51no—
541C22×C4—51no—
542C22×C4—52no—
543C22×C4—52no—
544C22×C4—61no—
545C22×C4—61no—
546C22×C4—101no—
547C22×C4—151no—
548C22×C4—151no—
549C22×C4—152no—
550C22×C4—151no—
551C22×C4—151no—
552C22×C4—151no—
553C22×C4—151no—
554C22×C4—151no—
555C22×C4—151no—
556C22×C4—151no—
557C22×C4—152no—
558C22×C4—152no—
559C22×C4—152no—
560C22×C4—151no—
561C22×C4—151no—
562C22×C4—151no—
563C22×C4—302no—
564C22×C4—302no—
565C22×C4—302no—
566C22×C4—302no—
567C22×C4—302no—
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—302no—
577C22×C4—302no—
578C22×C4—302no—
579C22×C4—301no—
580C4⋊C4—51no—
581C4⋊C4—151no—
582C4⋊C4—151no—
583C4⋊C4—152no—
584C4⋊C4—151no—
585C22⋊C4—32no—
586C22⋊C4—31no—
587C22⋊C4—31no—
588C22⋊C4—31no—
589C22⋊C4—51no—
590C22⋊C4—151no—
591C22⋊C4—151no—
592C22⋊C4—152no—
593C22⋊C4—151no—
594C22⋊C4D5×A411yescharacteristic, complemented
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—
608A4#402711yescharacteristic, direct product factor
609C3×C4—81no—
610C3×C4—81no—
611C3×C4—202no—
612C3×C4—202no—
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×D4×D511yescharacteristic
668C23C3×#71111yescharacteristic
669C23C2×D5×A411yescharacteristic
670D4—54no—
671D4—154no—
672D4—154no—
673D4—158no—
674D4—154no—
675C2×C4—31no—
676C2×C4—31no—
677C2×C4—51no—
678C2×C4—51no—
679C2×C4—51no—
680C2×C4—61no—
681C2×C4—61no—
682C2×C4—61no—
683C2×C4—61no—
684C2×C4—61no—
685C2×C4—61no—
686C2×C4—61no—
687C2×C4—61no—
688C2×C4—102no—
689C2×C4—102no—
690C2×C4—152no—
691C2×C4—152no—
692C2×C4—152no—
693C2×C4—152no—
694C2×C4—152no—
695C2×C4—152no—
696C2×C4—151no—
697C2×C4—151no—
698C2×C4—152no—
699C2×C4—152no—
700C2×C4—151no—
701C2×C4—302no—
702C2×C4—302no—
703C2×C4—302no—
704C2×C4—302no—
705C2×C4—304no—
706C2×C4—302no—
707C2×C4—301no—
708C2×C4—301no—
709C2×C4—302no—
710C2×C4—304no—
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×#402711yescharacteristic, complemented
759C22C4×D5×A412yescomplemented
760C22C22×D5×A411yescharacteristic
761C4—21no—
762C4—21no—
763C4—52no—
764C4—52no—
765C4—61no—
766C4—61no—
767C4—101no—
768C4—152no—
769C4—152no—
770C4—301no—
771C3—41noSylow
772C2—22no—
773C2—31no—
774C2—31no—
775C2—31no—
776C2—31no—
777C2—62no—
778C2—102no—
779C2—302no—
780C2C2×C4×D5×A411yescharacteristic
781C2D4×D5×A411yescharacteristic
782C2A4×#71111yescharacteristic
subgroupG/H
center, FrattiniC22C22×D5×A4
commutatorC23×C5C22×C3×C4
FittingC22×C5×C22⋊C4C2×C3
socle, cosocleC24×C5C23×C3
prime radicalC2×A4×C22⋊D5C2
hypercenterC22⋊C4D5×A4
hypocenterC22×C5C3×C4×D4
LCSG ▷ C23×C5 ▷ C22×C5
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C22×A4×Dic5C2semidirect
3. C2×C4×D5×A4C2semidirect
4. C5×A4×C22⋊C4C2semidirect
5. A4×#685C2semidirect
6. A4×#683C2semidirect
7. C4×A4×Dic5C2semidirect
8. C22×#4027C3semidirect
13. A4×C22⋊D5C4semidirect
22. C24×Dic5C2×C3semidirect
23. C23×C4×D5C2×C3semidirect
24. C22×C5×C22⋊C4C2×C3semidirect
25. C22×#685C2×C3semidirect
26. C22×#683C2×C3semidirect
27. C22×C4×Dic5C2×C3semidirect
38. C22×C5×A4C2×C4semidirect
42. C2×D5×A4C2×C4semidirect
49. A4×Dic5C2×C4semidirect
50. A4×Dic5D4semidirect
60. A4×C22⋊C4D5semidirect
71. C22×C22⋊D5C3×C4semidirect
117. #4027A4direct (N × H)
152. C24×C5C2×C3×C4semidirect
161. C23×D5C2×C3×C4semidirect
205. C22×Dic5C2×C3×C4semidirect
206. C22×Dic5C3×D4semidirect
207. C22×Dic5C2×A4semidirect
220. C2×C4×D5C2×A4semidirect
225. C5×C22⋊C4C2×A4semidirect
230. #685C2×A4semidirect
235. #683C2×A4semidirect
240. C4×Dic5C2×A4semidirect
254. C22×C22⋊C4C3×D5semidirect
263. C5×A4C4×D4semidirect
274. C22×A4C4×D5semidirect
349. C22⋊D5C4×A4semidirect
477. C22×C5C3×C4×D4semidirect
478. C22×C5C2×C4×A4semidirect
493. C2×D5C2×C4×A4semidirect
502. Dic5C2×C4×A4semidirect
503. Dic5D4×A4semidirect
519. C24C3×C4×D5semidirect
594. C22⋊C4D5×A4semidirect
608. A4#4027direct (N × H)
720. C5C4×D4×A4semidirect
758. C22C3×#4027semidirect
759. C22C4×D5×A4semidirect

Maximal subgroups

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

subgroupindex
C2×A4×C22⋊D52
C22×A4×Dic52
C2×C4×D5×A42
C5×A4×C22⋊C42
A4×#6852
A4×#6832
C4×A4×Dic52
C22×#40273
C3×#40274
C4×D4×A45