Finite Group Databasebeta

← #12022395

Subgroups — #12022395

Order 1280.

1802 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C5×C4⋊C4C211yesmaximal, characteristic, complemented
2C2×#65276C211yesmaximal, characteristic
3C2×#65276C211yesmaximal, characteristic
4C2×#65262C211yesmaximal, characteristic, complemented
5C2×#65229C212yesmaximal
6C2×C4×#685C211yesmaximal, characteristic
7#10602356C211yesmaximal, characteristic, complemented
8#10602328C211yesmaximal, characteristic, complemented
9#10602327C212yesmaximal, complemented
10#10600222C212yesmaximal
11#10600206C212yesmaximal, complemented
12C23×C4×D5C2211yescharacteristic
13C22×C5×C4⋊C4C2211yescharacteristic
14C22×C5×C4⋊C4C2211yescharacteristic
15C22×C42×C5C2212yes—
16C22×C42×C5C2211yescharacteristic
17C22×#685C2211yescharacteristic
18C22×#685C2212yes—
19C22×#685C2212yes—
20C22×#685C2211yescharacteristic
21C22×C4⋊Dic5C2211yescharacteristic
22C22×C4⋊Dic5C2211yescharacteristic
23C22×#683C2212yes—
24C22×C4×Dic5C2211yescharacteristic
25C4×C5×C4⋊C4—24no—
26C2×C5×#95C2212yes—
27C2×#3963C2211yescharacteristic
28C2×#3963C2212yes—
29C2×#3963C2212yes—
30C2×#3963C2211yescharacteristic
31C2×#3963C2212yes—
32C2×#3963C2212yes—
33C2×#3963C2212yes—
34C2×#3963C2212yes—
35C2×#3963C2212yes—
36#65276—24no—
37#65276C418yescomplemented
38#65262—24no—
39#65229—28no—
40C4×#685—24no—
41#13994—51nomaximal, Sylow
42C24×D5C2311yescharacteristic
43C23×C4×C5C2312yes—
44C23×C4×C5C2311yescharacteristic
45C23×C4×C5C2312yes—
46C23×C4×C5C2311yescharacteristic
47C23×C4×C5C2311yescharacteristic
48C23×Dic5C2312yes—
49C23×Dic5C2312yes—
50C23×Dic5C2311yescharacteristic
51C23×Dic5C2311yescharacteristic
52C23×Dic5C2311yescharacteristic
53C22×C4×D5—22no—
54C22×C4×D5—22no—
55C22×C4×D5—22no—
56C22×C4×D5—22no—
57C22×C4×D5—22no—
58C22×C4×D5—22no—
59C22×C4×D5C2×C414yes—
60C2×C5×C4⋊C4—22no—
61C2×C5×C4⋊C4—22no—
62C2×C5×C4⋊C4—22no—
63C2×C5×C4⋊C4—22no—
64C2×C5×C4⋊C4C2×C414yes—
65C2×C5×C4⋊C4D414yes—
66C2×C42×C5—22no—
67C2×C42×C5—22no—
68C2×C42×C5—24no—
69C2×C42×C5—24no—
70C2×C42×C5—24no—
71C2×C42×C5D414yes—
72C2×#685—24no—
73C2×#685—22no—
74C2×#685—24no—
75C2×#685—22no—
76C2×#685—22no—
77C2×#685—22no—
78C2×#685—22no—
79C2×#685—24no—
80C2×#685—24no—
81C2×#685—42no—
82C2×#685C2×C418yes—
83C2×#685D414yes—
84C2×C4⋊Dic5—22no—
85C2×C4⋊Dic5—22no—
86C2×C4⋊Dic5—22no—
87C2×C4⋊Dic5—22no—
88C2×C4⋊Dic5—22no—
89C2×C4⋊Dic5C2×C414yes—
90C2×#683—24no—
91C2×#683—24no—
92C2×#683—42no—
93C2×C4×Dic5—22no—
94C2×C4×Dic5—22no—
95C2×C4×Dic5—22no—
96C5×#95—24no—
97#3963—22no—
98#3963—22no—
99#3963—24no—
100#3963—24no—
101#3963—24no—
102#3963—24no—
103#3963—24no—
104#3963—42no—
105#3963C2×C418yes—
106C2×#389—51no—
107C2×#388—52no—
108C2×#380—51no—
109C2×#380—51no—
110C2×C4×C4⋊C4D511yescharacteristic, complemented
111C2×C4×C22⋊C4—51no—
112#1442—52no—
113#1440—52no—
114C4⋊#95—51no—
115C4⋊#95—51no—
116#1434—52no—
117C24×C5C2411yescharacteristic
118C23×D5—21no—
119C23×D5—21no—
120C23×D5—21no—
121C23×D5—21no—
122C23×D5—21no—
123C23×D5—21no—
124C23×D5—21no—
125C23×D5—21no—
126C23×D5—21no—
127C23×D5—21no—
128C23×D5—21no—
129C23×D5—21no—
130C23×D5C22×C412yes—
131C23×D5C2×D412yes—
132C23×D5#4112yes—
133C22×C4×C5—21no—
134C22×C4×C5—21no—
135C22×C4×C5—21no—
136C22×C4×C5—21no—
137C22×C4×C5—22no—
138C22×C4×C5—22no—
139C22×C4×C5—22no—
140C22×C4×C5—22no—
141C22×C4×C5—21no—
142C22×C4×C5—21no—
143C22×C4×C5—22no—
144C22×C4×C5—22no—
145C22×C4×C5—22no—
146C22×C4×C5—22no—
147C22×C4×C5—22no—
148C22×C4×C5—22no—
149C22×C4×C5—21no—
150C22×C4×C5—21no—
151C22×C4×C5—21no—
152C22×C4×C5—22no—
153C22×C4×C5—21no—
154C22×C4×C5—22no—
155C22×C4×C5C22×C414yes—
156C22×C4×C5C22×C412yes—
157C22×C4×C5C2×D414yes—
158C22×C4×C5C2×D412yes—
159C22×C4×C5C2×D412yes—
160C22×C4×C5C2×D412yes—
161C22×C4×C5C2×D412yes—
162C22×C4×C5C2×D412yes—
163C22×C4×C5#4112yes—
164C22×C4×C5#4112yes—
165C22×C4×C5#4112yes—
166C22×C4×C5#4112yes—
167C22×C4×C5#4112yes—
168C22×Dic5—21no—
169C22×Dic5—21no—
170C22×Dic5—21no—
171C22×Dic5—21no—
172C22×Dic5—21no—
173C22×Dic5—22no—
174C22×Dic5—22no—
175C22×Dic5—21no—
176C22×Dic5—21no—
177C22×Dic5—21no—
178C22×Dic5—21no—
179C22×Dic5—21no—
180C22×Dic5—21no—
181C22×Dic5—21no—
182C22×Dic5—22no—
183C22×Dic5—21no—
184C22×Dic5—22no—
185C22×Dic5—21no—
186C22×Dic5—22no—
187C22×Dic5—21no—
188C22×Dic5—22no—
189C22×Dic5—21no—
190C22×Dic5—21no—
191C22×Dic5—21no—
192C22×Dic5—22no—
193C22×Dic5—22no—
194C22×Dic5—22no—
195C22×Dic5—22no—
196C22×Dic5—22no—
197C22×Dic5—22no—
198C22×Dic5—22no—
199C22×Dic5C22×C412yes—
200C22×Dic5C22×C414yes—
201C22×Dic5C2×D412yes—
202C22×Dic5#4112yes—
203C2×C4×D5—28no—
204C2×C4×D5—28no—
205C2×C4×D5—28no—
206C2×C4×D5—44no—
207C2×C4×D5—44no—
208C2×C4×D5—44no—
209C2×C4×D5—44no—
210C5×C4⋊C4—28no—
211C5×C4⋊C4—28no—
212C42×C5—28no—
213C42×C5—48no—
214#685—28no—
215#685—216no—
216#685—28no—
217#685—48no—
218C4⋊Dic5—28no—
219C4⋊Dic5—44no—
220#683—48no—
221C4×Dic5—44no—
222C24×C4—51no—
223C22×C4⋊C4—51no—
224C22×C4⋊C4—51no—
225C22×C4⋊C4—52no—
226C22×C4⋊C4C2×D511yescharacteristic
227C22×C4⋊C4C2×D511yescharacteristic
228C22×C22⋊C4—52no—
229C22×C22⋊C4—51no—
230C22×C22⋊C4—51no—
231C22×C22⋊C4—52no—
232C22×C42—51no—
233C22×C42C2×D512yes—
234C22×C42C2×D511yescharacteristic
235#389—104no—
236#388—108no—
237#380—58no—
238#380—104no—
239C4×C4⋊C4—24no—
240C4×C22⋊C4—104no—
241C2×#95—52no—
242C2×#95—51no—
243C2×#95—52no—
244C2×#95—52no—
245C2×#95—52no—
246C2×#95—52no—
247C2×#95—52no—
248C2×#95—51no—
249C2×#95—52no—
250C2×#95C2×D512yes—
251C23×C5C23×C411yescharacteristic
252C23×C5C22×D411yescharacteristic
253C23×C5C22×D411yescharacteristic
254C23×C5C22×D411yescharacteristic
255C23×C5C2×#4111yescharacteristic
256C23×C5C2×#4111yescharacteristic
257C23×C5C2×#4111yescharacteristic
258C23×C5C2×#4111yescharacteristic
259C23×C5C2×#4111yescharacteristic
260C23×C5C2×#4111yescharacteristic
261C23×C5C2×#4111yescharacteristic
262C23×C5H(5,𝔽2)11yescharacteristic
263C23×C52−1+411yescharacteristic
264C23×C52−1+411yescharacteristic
265C23×C52−1+411yescharacteristic
266C22×D5—22no—
267C22×D5—22no—
268C22×D5—22no—
269C22×D5—22no—
270C22×D5—22no—
271C22×D5—22no—
272C22×D5—22no—
273C22×D5—22no—
274C22×D5—22no—
275C22×D5—22no—
276C22×D5—22no—
277C22×D5—22no—
278C22×D5—22no—
279C22×D5—22no—
280C22×D5—22no—
281C22×D5—22no—
282C22×D5—22no—
283C22×D5—22no—
284C22×D5—41no—
285C22×D5—41no—
286C22×D5—41no—
287C22×D5—41no—
288C22×D5—41no—
289C22×D5—41no—
290C22×D5—41no—
291C22×D5—41no—
292C22×D5—41no—
293C22×D5—41no—
294C22×D5—41no—
295C22×D5—41no—
296C22×D5—41no—
297C22×D5—41no—
298C22×D5—41no—
299C22×D5—41no—
300C22×D5C4×D414yes—
301C2×C4×C5—22no—
302C2×C4×C5—22no—
303C2×C4×C5—22no—
304C2×C4×C5—22no—
305C2×C4×C5—22no—
306C2×C4×C5—22no—
307C2×C4×C5—24no—
308C2×C4×C5—24no—
309C2×C4×C5—24no—
310C2×C4×C5—24no—
311C2×C4×C5—22no—
312C2×C4×C5—22no—
313C2×C4×C5—22no—
314C2×C4×C5—24no—
315C2×C4×C5—24no—
316C2×C4×C5—42no—
317C2×C4×C5—42no—
318C2×C4×C5—42no—
319C2×C4×C5—42no—
320C2×C4×C5—42no—
321C2×C4×C5—42no—
322C2×C4×C5—42no—
323C2×C4×C5—41no—
324C2×C4×C5—41no—
325C2×C4×C5—41no—
326C2×C4×C5—42no—
327C2×C4×C5—41no—
328C2×C4×C5#11714yes—
329C2×C4×C5C4×D414yes—
330C2×C4×C5C4×D414yes—
331C2×C4×C5#12114yes—
332C2×C4×C5#12114yes—
333C2×C4×C5#12314yes—
334C2×C4×C5#12414yes—
335C2×C4×C5#12614yes—
336C2×Dic5—22no—
337C2×Dic5—24no—
338C2×Dic5—24no—
339C2×Dic5—22no—
340C2×Dic5—22no—
341C2×Dic5—24no—
342C2×Dic5—22no—
343C2×Dic5—22no—
344C2×Dic5—22no—
345C2×Dic5—22no—
346C2×Dic5—22no—
347C2×Dic5—22no—
348C2×Dic5—41no—
349C2×Dic5—41no—
350C2×Dic5—41no—
351C2×Dic5—41no—
352C2×Dic5—41no—
353C2×Dic5—41no—
354C2×Dic5—41no—
355C2×Dic5—41no—
356C2×Dic5—42no—
357C2×Dic5—42no—
358C2×Dic5—41no—
359C2×Dic5—42no—
360C2×Dic5—41no—
361C2×Dic5—41no—
362C2×Dic5—42no—
363C2×Dic5—41no—
364C2×Dic5—42no—
365C2×Dic5—42no—
366C2×Dic5—42no—
367C2×Dic5—42no—
368C2×Dic5—42no—
369C2×Dic5—42no—
370C2×Dic5—42no—
371C4×D5—416no—
372C25—51no—
373C23×C4—52no—
374C23×C4—51no—
375C23×C4—51no—
376C23×C4—51no—
377C23×C4—54no—
378C23×C4—52no—
379C23×C4—102no—
380C23×C4—102no—
381C23×C4—102no—
382C23×C4—102no—
383C23×C4—102no—
384C23×C4—102no—
385C23×C4C22×D512yes—
386C23×C4C22×D512yes—
387C23×C4C22×D511yescharacteristic
388C23×C4C22×D511yescharacteristic
389C23×C4C22×D511yescharacteristic
390C2×C4⋊C4—22no—
391C2×C4⋊C4—22no—
392C2×C4⋊C4—22no—
393C2×C4⋊C4—22no—
394C2×C4⋊C4—54no—
395C2×C4⋊C4—102no—
396C2×C4⋊C4—102no—
397C2×C4⋊C4—104no—
398C2×C4⋊C4—102no—
399C2×C4⋊C4—104no—
400C2×C4⋊C4—102no—
401C2×C4⋊C4—102no—
402C2×C4⋊C4—202no—
403C2×C4⋊C4C4×D514yes—
404C2×C4⋊C4D2014yes—
405C2×C22⋊C4—58no—
406C2×C22⋊C4—54no—
407C2×C22⋊C4—102no—
408C2×C22⋊C4—104no—
409C2×C22⋊C4—104no—
410C2×C22⋊C4—102no—
411C2×C22⋊C4—102no—
412C2×C22⋊C4—102no—
413C2×C22⋊C4—102no—
414C2×C22⋊C4—104no—
415C2×C22⋊C4—104no—
416C2×C22⋊C4—202no—
417C2×C42—22no—
418C2×C42—22no—
419C2×C42—24no—
420C2×C42—24no—
421C2×C42—24no—
422C2×C42—102no—
423C2×C42—102no—
424C2×C42—102no—
425C2×C42C22⋊D514yes—
426#95—24no—
427#95—58no—
428#95—104no—
429#95—104no—
430#95—104no—
431#95—104no—
432#95—104no—
433#95—102no—
434#95—102no—
435#95—202no—
436C22×C5C2×#11711yescharacteristic
437C22×C5C2×C4×D411yescharacteristic
438C22×C5C2×C4×D411yescharacteristic
439C22×C5C2×C4×D411yescharacteristic
440C22×C5C4×#4111yescharacteristic
441C22×C5#51911yescharacteristic
442C22×C5#52011yescharacteristic
443C22×C5C2×#12111yescharacteristic
444C22×C5C2×#12111yescharacteristic
445C22×C5C2×#12311yescharacteristic
446C22×C5#52511yescharacteristic
447C22×C5C2×#12411yescharacteristic
448C22×C5C2×#12611yescharacteristic
449C22×C5#52911yescharacteristic
450C22×C5#53211yescharacteristic
451C22×C5#53611yescharacteristic
452C22×C5#53711yescharacteristic
453C22×C5#54111yescharacteristic
454C22×C5#54211yescharacteristic
455C22×C5D4211yescharacteristic
456C22×C5#54711yescharacteristic
457C22×C5#54711yescharacteristic
458C22×C5#54711yescharacteristic
459C22×C5#54711yescharacteristic
460C22×C5#54811yescharacteristic
461C22×C5#54811yescharacteristic
462C22×C5#55211yescharacteristic
463C22×C5#55211yescharacteristic
464C22×C5#55211yescharacteristic
465C22×C5#55211yescharacteristic
466C22×C5#55211yescharacteristic
467C22×C5#55311yescharacteristic
468C22×C5#55511yescharacteristic
469C22×C5#55511yescharacteristic
470C22×C5#55611yescharacteristic
471C2×D5—24no—
472C2×D5—24no—
473C2×D5—24no—
474C2×D5—42no—
475C2×D5—42no—
476C2×D5—42no—
477C2×D5—42no—
478C2×D5—42no—
479C2×D5—42no—
480C2×D5—42no—
481C2×D5—42no—
482C2×D5—42no—
483C2×D5—42no—
484C2×D5—42no—
485C2×D5—42no—
486C4×C5—24no—
487C4×C5—42no—
488C4×C5—44no—
489C4×C5—44no—
490C4×C5#38818yescomplemented
491Dic5—44no—
492Dic5—42no—
493Dic5—42no—
494Dic5—42no—
495Dic5—82no—
496C24—52no—
497C24—52no—
498C24—52no—
499C24—101no—
500C24—101no—
501C24—101no—
502C24—101no—
503C24—101no—
504C24—101no—
505C24—101no—
506C24—101no—
507C24—101no—
508C24—101no—
509C24—101no—
510C24—101no—
511C24C23×D511yescharacteristic
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—21no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—52no—
535C22×C4—54no—
536C22×C4—52no—
537C22×C4—52no—
538C22×C4—101no—
539C22×C4—101no—
540C22×C4—102no—
541C22×C4—101no—
542C22×C4—101no—
543C22×C4—101no—
544C22×C4—102no—
545C22×C4—101no—
546C22×C4—101no—
547C22×C4—101no—
548C22×C4—101no—
549C22×C4—102no—
550C22×C4—101no—
551C22×C4—102no—
552C22×C4—101no—
553C22×C4—101no—
554C22×C4—102no—
555C22×C4—101no—
556C22×C4—102no—
557C22×C4—101no—
558C22×C4—101no—
559C22×C4—101no—
560C22×C4—101no—
561C22×C4—101no—
562C22×C4—108no—
563C22×C4—108no—
564C22×C4—108no—
565C22×C4—102no—
566C22×C4—102no—
567C22×C4—102no—
568C22×C4—102no—
569C22×C4—102no—
570C22×C4—102no—
571C22×C4—102no—
572C22×C4—204no—
573C22×C4—204no—
574C22×C4—204no—
575C22×C4—204no—
576C22×C4C2×C4×D514yes—
577C22×C4C2×C4×D512yes—
578C22×C4C2×D2014yes—
579C22×C4C2×D2012yes—
580C22×C4#70912yes—
581C22×C4#70912yes—
582C22×C4#70912yes—
583C22×C4#70912yes—
584C22×C4D4×D512yes—
585C22×C4#71112yes—
586C22×C4C2×C22⋊D512yes—
587C22×C4C2×C22⋊D512yes—
588C22×C4C2×C22⋊D512yes—
589C4⋊C4—28no—
590C4⋊C4—28no—
591C4⋊C4—108no—
592C4⋊C4—208no—
593C4⋊C4—204no—
594C22⋊C4—1016no—
595C22⋊C4—108no—
596C22⋊C4—108no—
597C22⋊C4—208no—
598C42—28no—
599C42—48no—
600C42—204no—
601C2×C5C2×#38811yescharacteristic
602C2×C5C4×#12111yescharacteristic
603C2×C5#232311yescharacteristic
604C2×C5#234411yescharacteristic
605C2×C5#234611yescharacteristic
606C2×C5#236111yescharacteristic
607C2×C5#236211yescharacteristic
608C2×C5#248511yescharacteristic
609C2×C5#248611yescharacteristic
610C2×C5#248911yescharacteristic
611C2×C5#249111yescharacteristic
612C2×C5#249511yescharacteristic
613C2×C5#249611yescharacteristic
614C2×C5#253611yescharacteristic
615C2×C5#253711yescharacteristic
616D5—44no—
617C23—54no—
618C23—102no—
619C23—102no—
620C23—102no—
621C23—102no—
622C23—102no—
623C23—102no—
624C23—102no—
625C23—102no—
626C23—102no—
627C23—102no—
628C23—102no—
629C23—102no—
630C23—102no—
631C23—102no—
632C23—102no—
633C23—102no—
634C23—102no—
635C23—102no—
636C23—201no—
637C23—201no—
638C23—201no—
639C23—201no—
640C23—201no—
641C23—201no—
642C23—201no—
643C23—201no—
644C23—201no—
645C23—201no—
646C23—201no—
647C23—201no—
648C23—201no—
649C23—201no—
650C23—201no—
651C23—201no—
652C23C22×C4×D511yescharacteristic
653C23C22×D2011yescharacteristic
654C23C2×#70911yescharacteristic
655C23C2×#70911yescharacteristic
656C23C2×#70911yescharacteristic
657C23C2×#70911yescharacteristic
658C23C2×D4×D511yescharacteristic
659C23C2×#71111yescharacteristic
660C23#414711yescharacteristic
661C23#414711yescharacteristic
662C23D5×#4111yescharacteristic
663C23D5×#4111yescharacteristic
664C23#414911yescharacteristic
665C23#415011yescharacteristic
666C23C22×C22⋊D511yescharacteristic
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—24no—
674C2×C4—22no—
675C2×C4—24no—
676C2×C4—24no—
677C2×C4—24no—
678C2×C4—24no—
679C2×C4—24no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—102no—
695C2×C4—104no—
696C2×C4—102no—
697C2×C4—102no—
698C2×C4—104no—
699C2×C4—102no—
700C2×C4—102no—
701C2×C4—102no—
702C2×C4—102no—
703C2×C4—104no—
704C2×C4—102no—
705C2×C4—102no—
706C2×C4—201no—
707C2×C4—201no—
708C2×C4—202no—
709C2×C4—202no—
710C2×C4—201no—
711C2×C4—201no—
712C2×C4—201no—
713C2×C4—201no—
714C2×C4—202no—
715C2×C4—201no—
716C2×C4—201no—
717C2×C4—201no—
718C2×C4—202no—
719C2×C4—201no—
720C2×C4—201no—
721C2×C4—201no—
722C2×C4—2016no—
723C2×C4—202no—
724C2×C4—202no—
725C2×C4—202no—
726C2×C4—202no—
727C2×C4—202no—
728C2×C4—202no—
729C2×C4—202no—
730C2×C4#401814yes—
731C2×C4C4×D2014yes—
732C2×C4#402114yes—
733C2×C4#402214yes—
734C2×C4C4×C22⋊D514yes—
735C2×C4#407514yes—
736C2×C4#407614yes—
737C2×C4#408414yes—
738C5#1399411yescharacteristic, complemented, Sylow
739C22—104no—
740C22—104no—
741C22—104no—
742C22—202no—
743C22—202no—
744C22—202no—
745C22—202no—
746C22—202no—
747C22—202no—
748C22—202no—
749C22—202no—
750C22—202no—
751C22—202no—
752C22—202no—
753C22—202no—
754C22C2×#401811yescharacteristic
755C22C2×C4×D2011yescharacteristic
756C22C2×#402111yescharacteristic
757C22C2×#402211yescharacteristic
758C22#6584111yescharacteristic
759C22#6584111yescharacteristic
760C22#6584711yescharacteristic
761C22#6584711yescharacteristic
762C22#6586311yescharacteristic
763C22#6586411yescharacteristic
764C22#6586611yescharacteristic
765C22#6586711yescharacteristic
766C22C4×#71111yescharacteristic
767C22C4×D4×D511yescharacteristic
768C22#6588211yescharacteristic
769C22D4×D2011yescharacteristic
770C22#6588511yescharacteristic
771C22#6588911yescharacteristic
772C22#6589111yescharacteristic
773C22#6589711yescharacteristic
774C22#6590611yescharacteristic
775C22#6590811yescharacteristic
776C22#6591011yescharacteristic
777C22#6591011yescharacteristic
778C22#6591511yescharacteristic
779C22#6591511yescharacteristic
780C22#6591611yescharacteristic
781C22#6591711yescharacteristic
782C22C2×C4×C22⋊D511yescharacteristic
783C22C2×#407511yescharacteristic
784C22C2×#407611yescharacteristic
785C22C2×#408411yescharacteristic
786C22#6615011yescharacteristic
787C22#6616211yescharacteristic
788C22#6616711yescharacteristic
789C4—24no—
790C4—44no—
791C4—44no—
792C4—42no—
793C4—202no—
794C4—202no—
795C4—204no—
796C4—202no—
797C4—402no—
798C4#6522918yescomplemented
799C2—204no—
800C2#1060536411yescharacteristic
801C2#1060537811yescharacteristic
802C2#1060549811yescharacteristic
803C2#1060550511yescharacteristic
804C2#1060551711yescharacteristic
805C2#1060551911yescharacteristic
806C2#1060552211yescharacteristic
807C2#1060552311yescharacteristic
808C2C2×#6522911yescharacteristic
809C2#1061392711yescharacteristic
810C2#1061401411yescharacteristic
811C2C4×#408411yescharacteristic
812C2#1061414811yescharacteristic
813C2#1061421911yescharacteristic
814C2#1061423011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D5
commutatorC23×C5C23×C4
FittingC2×C4×C5×C4⋊C4C2
socle, cosocleC24×C5C24
prime radicalC24×D5C23
hypercenterC2×C4×C4⋊C4D5
hypocenterC5#13994
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C4×C5×C4⋊C4C2semidirect
4. C2×#65262C2semidirect
7. #10602356C2semidirect
8. #10602328C2semidirect
9. #10602327C2semidirect
11. #10600206C2semidirect
37. #65276C4semidirect
110. C2×C4×C4⋊C4D5semidirect
490. C4×C5#388semidirect
738. C5#13994semidirect
798. C4#65229semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C5×C4⋊C42
C2×#652762
C2×#652622
C2×#652292
C2×C4×#6852
#106023562
#106023282
#106023272
#106002222
#106002062
#139945