Finite Group Databasebeta

← #12022735

Subgroups — #12022735

Order 1280.

1954 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C5×C4⋊C4C211yesmaximal, characteristic, complemented
2C2×#65277C211yesmaximal, characteristic
3C2×#65277C211yesmaximal, characteristic
4C2×#65228C211yesmaximal, characteristic
5C2×#65229C212yesmaximal, complemented
6C2×C4×#683C211yesmaximal, characteristic, complemented
7#10602356C211yesmaximal, characteristic, complemented
8#10602356C211yesmaximal, characteristic, complemented
9#10602330C212yesmaximal, complemented
10#10600222C212yesmaximal, complemented
11#10600221C212yesmaximal, complemented
12C23×D20C2211yescharacteristic
13C22×C5×C4⋊C4C2211yescharacteristic
14C22×C5×C4⋊C4C2211yescharacteristic
15C22×C42×C5C2212yes—
16C22×C42×C5C2211yescharacteristic
17C22×#685C2212yes—
18C22×#685C2212yes—
19C22×#685C2212yes—
20C22×#685C2212yes—
21C22×#685C2212yes—
22C22×#685C2212yes—
23C22×C4⋊Dic5C2211yescharacteristic
24C22×#683C2211yescharacteristic
25C22×#683C2211yescharacteristic
26C22×C4×Dic5C2211yescharacteristic
27C22×C4×Dic5C2211yescharacteristic
28C4×C5×C4⋊C4—24no—
29C2×C5×#95C2212yes—
30C2×#3963C2211yescharacteristic
31C2×#3963C2211yescharacteristic
32C2×#3963C2212yes—
33C2×#3963C2212yes—
34C2×#3963C2212yes—
35C2×#3963C2212yes—
36#65277—24no—
37#65277C418yescomplemented
38#65229—28no—
39#65228—24no—
40C4×#683—24no—
41#14022—51nomaximal, Sylow
42C24×D5C2312yes—
43C23×C4×C5C2312yes—
44C23×C4×C5C2311yescharacteristic
45C23×C4×C5C2312yes—
46C23×C4×C5C2311yescharacteristic
47C23×C4×C5C2311yescharacteristic
48C23×Dic5C2312yes—
49C23×Dic5C2311yescharacteristic
50C23×Dic5C2311yescharacteristic
51C23×Dic5C2311yescharacteristic
52C23×Dic5C2311yescharacteristic
53C22×D20—22no—
54C22×D20—22no—
55C22×D20—22no—
56C22×D20—22no—
57C22×D20—22no—
58C22×D20—22no—
59C22×D20C2×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—42no—
71C2×C42×C5D414yes—
72C2×#685—24no—
73C2×#685—24no—
74C2×#685—24no—
75C2×#685—24no—
76C2×#685—24no—
77C2×#685—24no—
78C2×#685—24no—
79C2×#685—24no—
80C2×#685—24no—
81C2×#685—24no—
82C2×#685—42no—
83C2×#685—42no—
84C2×#685—42no—
85C2×#685—42no—
86C2×#685—42no—
87C2×#685—42no—
88C2×#685C2×C418yes—
89C2×#685C2×C418yes—
90C2×C4⋊Dic5—22no—
91C2×C4⋊Dic5—22no—
92C2×C4⋊Dic5—22no—
93C2×#683—22no—
94C2×#683—22no—
95C2×#683—22no—
96C2×#683—22no—
97C2×#683—22no—
98C2×#683D414yescomplemented
99C2×C4×Dic5—22no—
100C2×C4×Dic5—22no—
101C2×C4×Dic5—22no—
102C2×C4×Dic5—22no—
103C2×C4×Dic5—22no—
104C2×C4×Dic5C2×C414yes—
105C5×#95—24no—
106#3963—22no—
107#3963—22no—
108#3963—24no—
109#3963—24no—
110#3963—42no—
111#3963—42no—
112C2×#390—51no—
113C2×#390—51no—
114C2×#390—51no—
115C2×#388—52no—
116C2×C4×C4⋊C4—51no—
117C2×C4×C4⋊C4D511yescharacteristic, complemented
118#1440—52no—
119#1439—52no—
120#1437—52no—
121C4⋊#95—51no—
122C4⋊#95—51no—
123C24×C5C2411yescharacteristic
124C23×D5—22no—
125C23×D5—22no—
126C23×D5—22no—
127C23×D5—22no—
128C23×D5—22no—
129C23×D5—22no—
130C23×D5—22no—
131C23×D5—22no—
132C23×D5—22no—
133C23×D5—22no—
134C23×D5—22no—
135C23×D5—22no—
136C23×D5—22no—
137C23×D5—22no—
138C23×D5C22×C414yes—
139C22×C4×C5—21no—
140C22×C4×C5—21no—
141C22×C4×C5—21no—
142C22×C4×C5—21no—
143C22×C4×C5—22no—
144C22×C4×C5—22no—
145C22×C4×C5—22no—
146C22×C4×C5—21no—
147C22×C4×C5—21no—
148C22×C4×C5—22no—
149C22×C4×C5—22no—
150C22×C4×C5—22no—
151C22×C4×C5—21no—
152C22×C4×C5—21no—
153C22×C4×C5—22no—
154C22×C4×C5—22no—
155C22×C4×C5—22no—
156C22×C4×C5—22no—
157C22×C4×C5—22no—
158C22×C4×C5—22no—
159C22×C4×C5—21no—
160C22×C4×C5—21no—
161C22×C4×C5C22×C414yes—
162C22×C4×C5C22×C412yes—
163C22×C4×C5C2×D412yes—
164C22×C4×C5C2×D412yes—
165C22×C4×C5C2×D412yes—
166C22×C4×C5C2×D412yes—
167C22×C4×C5C2×D414yes—
168C22×C4×C5C2×D412yes—
169C22×C4×C5#4112yes—
170C22×C4×C5#4112yes—
171C22×C4×C5#4112yes—
172C22×C4×C5#4112yes—
173C22×C4×C5#4112yes—
174C22×Dic5—21no—
175C22×Dic5—21no—
176C22×Dic5—21no—
177C22×Dic5—21no—
178C22×Dic5—21no—
179C22×Dic5—21no—
180C22×Dic5—21no—
181C22×Dic5—21no—
182C22×Dic5—21no—
183C22×Dic5—21no—
184C22×Dic5—21no—
185C22×Dic5—21no—
186C22×Dic5—21no—
187C22×Dic5—21no—
188C22×Dic5—21no—
189C22×Dic5—21no—
190C22×Dic5—21no—
191C22×Dic5—21no—
192C22×Dic5—21no—
193C22×Dic5—21no—
194C22×Dic5—21no—
195C22×Dic5—21no—
196C22×Dic5—22no—
197C22×Dic5—22no—
198C22×Dic5—22no—
199C22×Dic5—22no—
200C22×Dic5—22no—
201C22×Dic5—22no—
202C22×Dic5—22no—
203C22×Dic5C22×C412yes—
204C22×Dic5C22×C412yes—
205C22×Dic5C2×D412yes—
206C22×Dic5C2×D412yes—
207C22×Dic5#4112yes—
208C22×Dic5#4112yes—
209C2×D20—28no—
210C2×D20—28no—
211C2×D20—28no—
212C2×D20—44no—
213C2×D20—44no—
214C2×D20—44no—
215C2×D20—44no—
216C5×C4⋊C4—28no—
217C5×C4⋊C4—28no—
218C42×C5—28no—
219C42×C5—48no—
220#685—216no—
221#685—48no—
222#685—48no—
223#685—48no—
224#685—48no—
225#685—48no—
226C4⋊Dic5—44no—
227#683—28no—
228#683—28no—
229C4×Dic5—28no—
230C4×Dic5—44no—
231C23×D4—51no—
232C22×C4⋊C4—51no—
233C22×C4⋊C4—51no—
234C22×C4⋊C4—51no—
235C22×C4⋊C4C2×D511yescharacteristic
236C22×C4⋊C4C2×D511yescharacteristic
237C22×C22⋊C4—52no—
238C22×C22⋊C4—52no—
239C22×C22⋊C4—52no—
240C22×C22⋊C4—52no—
241C22×C22⋊C4—52no—
242C22×C22⋊C4—52no—
243C22×C42—51no—
244C22×C42—51no—
245C22×C42C2×D512yes—
246C22×C42C2×D511yescharacteristic
247#390—58no—
248#390—104no—
249#390—104no—
250#388—108no—
251C4×C4⋊C4—24no—
252C4×C4⋊C4—104no—
253C2×#95—52no—
254C2×#95—52no—
255C2×#95—51no—
256C2×#95—51no—
257C2×#95—52no—
258C2×#95—52no—
259C2×#95C2×D512yes—
260C23×C5C23×C411yescharacteristic
261C23×C5C22×D411yescharacteristic
262C23×C5C22×D411yescharacteristic
263C23×C5C22×D411yescharacteristic
264C23×C5C2×#4111yescharacteristic
265C23×C5C2×#4111yescharacteristic
266C23×C5C2×#4111yescharacteristic
267C23×C5C2×#4111yescharacteristic
268C23×C5C2×#4111yescharacteristic
269C23×C5C2×#4111yescharacteristic
270C23×C5C2×#4111yescharacteristic
271C23×C5H(5,𝔽2)11yescharacteristic
272C23×C5H(5,𝔽2)11yescharacteristic
273C23×C5H(5,𝔽2)11yescharacteristic
274C23×C52−1+411yescharacteristic
275C22×D5—24no—
276C22×D5—24no—
277C22×D5—24no—
278C22×D5—24no—
279C22×D5—24no—
280C22×D5—24no—
281C22×D5—24no—
282C22×D5—42no—
283C22×D5—42no—
284C22×D5—42no—
285C22×D5—42no—
286C22×D5—42no—
287C22×D5—42no—
288C22×D5—42no—
289C22×D5—42no—
290C22×D5—42no—
291C22×D5—42no—
292C22×D5—42no—
293C22×D5—42no—
294C22×D5—42no—
295C22×D5—42no—
296C22×D5—42no—
297C22×D5—42no—
298C22×D5—42no—
299C22×D5—42no—
300C22×D5—42no—
301C22×D5—42no—
302C22×D5—42no—
303C22×D5—42no—
304C22×D5—42no—
305C22×D5—42no—
306C22×D5—42no—
307C22×D5—42no—
308C22×D5—42no—
309C22×D5—42no—
310C2×C4×C5—22no—
311C2×C4×C5—22no—
312C2×C4×C5—22no—
313C2×C4×C5—22no—
314C2×C4×C5—22no—
315C2×C4×C5—22no—
316C2×C4×C5—24no—
317C2×C4×C5—24no—
318C2×C4×C5—24no—
319C2×C4×C5—22no—
320C2×C4×C5—24no—
321C2×C4×C5—22no—
322C2×C4×C5—22no—
323C2×C4×C5—24no—
324C2×C4×C5—24no—
325C2×C4×C5—42no—
326C2×C4×C5—42no—
327C2×C4×C5—42no—
328C2×C4×C5—41no—
329C2×C4×C5—42no—
330C2×C4×C5—42no—
331C2×C4×C5—42no—
332C2×C4×C5—41no—
333C2×C4×C5—41no—
334C2×C4×C5—41no—
335C2×C4×C5—42no—
336C2×C4×C5—42no—
337C2×C4×C5#11714yes—
338C2×C4×C5C4×D414yes—
339C2×C4×C5C4×D414yes—
340C2×C4×C5#12114yes—
341C2×C4×C5#12114yes—
342C2×C4×C5#12314yes—
343C2×C4×C5#12414yes—
344C2×C4×C5#12614yes—
345C2×Dic5—22no—
346C2×Dic5—22no—
347C2×Dic5—22no—
348C2×Dic5—22no—
349C2×Dic5—22no—
350C2×Dic5—22no—
351C2×Dic5—22no—
352C2×Dic5—22no—
353C2×Dic5—22no—
354C2×Dic5—22no—
355C2×Dic5—22no—
356C2×Dic5—22no—
357C2×Dic5—22no—
358C2×Dic5—22no—
359C2×Dic5—22no—
360C2×Dic5—41no—
361C2×Dic5—41no—
362C2×Dic5—41no—
363C2×Dic5—41no—
364C2×Dic5—41no—
365C2×Dic5—41no—
366C2×Dic5—41no—
367C2×Dic5—41no—
368C2×Dic5—41no—
369C2×Dic5—41no—
370C2×Dic5—41no—
371C2×Dic5—41no—
372C2×Dic5—42no—
373C2×Dic5—42no—
374C2×Dic5—42no—
375C2×Dic5—42no—
376C2×Dic5—42no—
377C2×Dic5—42no—
378C2×Dic5—42no—
379C2×Dic5C4×D414yes—
380D20—416no—
381C25—52no—
382C22×D4—54no—
383C22×D4—102no—
384C22×D4—102no—
385C22×D4—102no—
386C22×D4—102no—
387C22×D4—102no—
388C22×D4—102no—
389C23×C4—51no—
390C23×C4—51no—
391C23×C4—51no—
392C23×C4—51no—
393C23×C4—52no—
394C23×C4C22×D512yes—
395C23×C4C22×D511yescharacteristic
396C23×C4C22×D512yes—
397C23×C4C22×D511yescharacteristic
398C23×C4C22×D511yescharacteristic
399C2×C4⋊C4—22no—
400C2×C4⋊C4—22no—
401C2×C4⋊C4—22no—
402C2×C4⋊C4—22no—
403C2×C4⋊C4—54no—
404C2×C4⋊C4—102no—
405C2×C4⋊C4—102no—
406C2×C4⋊C4—102no—
407C2×C4⋊C4—102no—
408C2×C4⋊C4—102no—
409C2×C4⋊C4—102no—
410C2×C4⋊C4—102no—
411C2×C4⋊C4—102no—
412C2×C4⋊C4C4×D514yes—
413C2×C4⋊C4C22⋊D514yes—
414C2×C22⋊C4—58no—
415C2×C22⋊C4—58no—
416C2×C22⋊C4—104no—
417C2×C22⋊C4—104no—
418C2×C22⋊C4—104no—
419C2×C22⋊C4—104no—
420C2×C22⋊C4—104no—
421C2×C22⋊C4—104no—
422C2×C22⋊C4—104no—
423C2×C22⋊C4—104no—
424C2×C22⋊C4—104no—
425C2×C22⋊C4—104no—
426C2×C22⋊C4—202no—
427C2×C22⋊C4—202no—
428C2×C22⋊C4—202no—
429C2×C22⋊C4—202no—
430C2×C22⋊C4—202no—
431C2×C22⋊C4—202no—
432C2×C42—22no—
433C2×C42—22no—
434C2×C42—24no—
435C2×C42—24no—
436C2×C42—42no—
437C2×C42—54no—
438C2×C42—102no—
439C2×C42—102no—
440C2×C42—102no—
441C2×C42—102no—
442C2×C42—102no—
443C2×C42D2014yes—
444#95—24no—
445#95—104no—
446#95—104no—
447#95—102no—
448#95—102no—
449#95—202no—
450#95—202no—
451C22×C5C2×#11711yescharacteristic
452C22×C5C2×C4×D411yescharacteristic
453C22×C5C2×C4×D411yescharacteristic
454C22×C5C2×C4×D411yescharacteristic
455C22×C5C4×#4111yescharacteristic
456C22×C5#51811yescharacteristic
457C22×C5#52011yescharacteristic
458C22×C5C2×#12111yescharacteristic
459C22×C5C2×#12111yescharacteristic
460C22×C5C2×#12311yescharacteristic
461C22×C5#52511yescharacteristic
462C22×C5C2×#12411yescharacteristic
463C22×C5C2×#12611yescharacteristic
464C22×C5#52911yescharacteristic
465C22×C5#53211yescharacteristic
466C22×C5#53511yescharacteristic
467C22×C5#53711yescharacteristic
468C22×C5#54011yescharacteristic
469C22×C5#54211yescharacteristic
470C22×C5D4211yescharacteristic
471C22×C5#54611yescharacteristic
472C22×C5#54711yescharacteristic
473C22×C5#54811yescharacteristic
474C22×C5#55011yescharacteristic
475C22×C5#55011yescharacteristic
476C22×C5#55011yescharacteristic
477C22×C5#55311yescharacteristic
478C22×C5#55311yescharacteristic
479C22×C5#55511yescharacteristic
480C22×C5#55611yescharacteristic
481C22×C5#55611yescharacteristic
482C22×C5#55911yescharacteristic
483C22×C5#55911yescharacteristic
484C22×C5#55911yescharacteristic
485C22×C5#55911yescharacteristic
486C2×D5—44no—
487C2×D5—44no—
488C2×D5—44no—
489C2×D5—44no—
490C2×D5—44no—
491C2×D5—44no—
492C2×D5—44no—
493C2×D5—82no—
494C2×D5—82no—
495C2×D5—82no—
496C2×D5—82no—
497C2×D5—82no—
498C2×D5—82no—
499C2×D5—82no—
500C2×D5—82no—
501C4×C5—24no—
502C4×C5—44no—
503C4×C5—42no—
504C4×C5—44no—
505C4×C5#38818yescomplemented
506Dic5—24no—
507Dic5—42no—
508Dic5—42no—
509Dic5—42no—
510Dic5—82no—
511C24—54no—
512C24—102no—
513C24—102no—
514C24—102no—
515C24—102no—
516C24—102no—
517C24—102no—
518C24—102no—
519C24—102no—
520C24—102no—
521C24—102no—
522C24—102no—
523C24—102no—
524C24—102no—
525C24—102no—
526C24C23×D511yescharacteristic
527C2×D4—108no—
528C2×D4—108no—
529C2×D4—108no—
530C2×D4—204no—
531C2×D4—204no—
532C2×D4—204no—
533C2×D4—204no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—22no—
556C22×C4—52no—
557C22×C4—52no—
558C22×C4—52no—
559C22×C4—52no—
560C22×C4—52no—
561C22×C4—52no—
562C22×C4—101no—
563C22×C4—101no—
564C22×C4—101no—
565C22×C4—101no—
566C22×C4—101no—
567C22×C4—101no—
568C22×C4—101no—
569C22×C4—101no—
570C22×C4—101no—
571C22×C4—101no—
572C22×C4—101no—
573C22×C4—101no—
574C22×C4—101no—
575C22×C4—101no—
576C22×C4—101no—
577C22×C4—101no—
578C22×C4—101no—
579C22×C4—101no—
580C22×C4—101no—
581C22×C4—101no—
582C22×C4—101no—
583C22×C4—101no—
584C22×C4—102no—
585C22×C4—102no—
586C22×C4—102no—
587C22×C4—102no—
588C22×C4—102no—
589C22×C4—102no—
590C22×C4—102no—
591C22×C4C2×C4×D514yes—
592C22×C4C2×C4×D512yes—
593C22×C4C2×D2012yes—
594C22×C4C2×D2012yes—
595C22×C4C2×D2012yes—
596C22×C4#70912yes—
597C22×C4#70912yes—
598C22×C4#70912yes—
599C22×C4#70912yes—
600C22×C4D4×D512yes—
601C22×C4#71312yes—
602C22×C4C2×C22⋊D514yes—
603C22×C4C2×C22⋊D512yes—
604C4⋊C4—28no—
605C4⋊C4—28no—
606C4⋊C4—108no—
607C4⋊C4—108no—
608C4⋊C4—204no—
609C22⋊C4—1016no—
610C22⋊C4—208no—
611C22⋊C4—208no—
612C22⋊C4—208no—
613C22⋊C4—208no—
614C22⋊C4—208no—
615C42—28no—
616C42—48no—
617C42—108no—
618C42—204no—
619C2×C5C2×#38811yescharacteristic
620C2×C5C4×#12111yescharacteristic
621C2×C5#232411yescharacteristic
622C2×C5#235411yescharacteristic
623C2×C5#235711yescharacteristic
624C2×C5#236611yescharacteristic
625C2×C5#236711yescharacteristic
626C2×C5#241411yescharacteristic
627C2×C5#241611yescharacteristic
628C2×C5#244511yescharacteristic
629C2×C5#244811yescharacteristic
630C2×C5#251211yescharacteristic
631C2×C5#251311yescharacteristic
632C2×C5#254811yescharacteristic
633C2×C5#259211yescharacteristic
634D5—84no—
635C23—104no—
636C23—104no—
637C23—104no—
638C23—104no—
639C23—104no—
640C23—104no—
641C23—104no—
642C23—202no—
643C23—202no—
644C23—202no—
645C23—202no—
646C23—202no—
647C23—202no—
648C23—202no—
649C23—202no—
650C23—202no—
651C23—202no—
652C23—202no—
653C23—202no—
654C23—202no—
655C23—202no—
656C23—202no—
657C23—202no—
658C23—202no—
659C23—202no—
660C23—202no—
661C23—202no—
662C23—202no—
663C23—202no—
664C23—202no—
665C23—202no—
666C23—202no—
667C23—202no—
668C23—202no—
669C23—202no—
670C23C22×C4×D511yescharacteristic
671C23C22×D2011yescharacteristic
672C23C2×#70911yescharacteristic
673C23C2×#70911yescharacteristic
674C23C2×#70911yescharacteristic
675C23C2×#70911yescharacteristic
676C23C2×D4×D511yescharacteristic
677C23#414411yescharacteristic
678C23C2×#71311yescharacteristic
679C23#414711yescharacteristic
680C23D5×#4111yescharacteristic
681C23D5×#4111yescharacteristic
682C23#414911yescharacteristic
683C23#414911yescharacteristic
684C23C22×C22⋊D511yescharacteristic
685D4—2016no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—24no—
695C2×C4—24no—
696C2×C4—22no—
697C2×C4—24no—
698C2×C4—24no—
699C2×C4—24no—
700C2×C4—24no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—41no—
711C2×C4—42no—
712C2×C4—41no—
713C2×C4—54no—
714C2×C4—102no—
715C2×C4—102no—
716C2×C4—102no—
717C2×C4—102no—
718C2×C4—102no—
719C2×C4—102no—
720C2×C4—102no—
721C2×C4—102no—
722C2×C4—102no—
723C2×C4—102no—
724C2×C4—102no—
725C2×C4—102no—
726C2×C4—102no—
727C2×C4—102no—
728C2×C4—102no—
729C2×C4—201no—
730C2×C4—201no—
731C2×C4—201no—
732C2×C4—201no—
733C2×C4—201no—
734C2×C4—201no—
735C2×C4—201no—
736C2×C4—201no—
737C2×C4—201no—
738C2×C4—201no—
739C2×C4—201no—
740C2×C4—201no—
741C2×C4—202no—
742C2×C4—202no—
743C2×C4—202no—
744C2×C4—202no—
745C2×C4—202no—
746C2×C4—202no—
747C2×C4—202no—
748C2×C4#401814yes—
749C2×C4C4×D2014yes—
750C2×C4#402114yes—
751C2×C4#402214yes—
752C2×C4#404114yes—
753C2×C4C4×C22⋊D514yes—
754C2×C4#407514yes—
755C2×C4#407614yes—
756C5#1402211yescharacteristic, complemented, Sylow
757C22—204no—
758C22—204no—
759C22—204no—
760C22—204no—
761C22—204no—
762C22—204no—
763C22—204no—
764C22—402no—
765C22—402no—
766C22—402no—
767C22—402no—
768C22—402no—
769C22—402no—
770C22—402no—
771C22—402no—
772C22C2×#401811yescharacteristic
773C22C2×C4×D2011yescharacteristic
774C22C2×#402111yescharacteristic
775C22C2×#402211yescharacteristic
776C22C2×#404111yescharacteristic
777C22#6584111yescharacteristic
778C22#6584411yescharacteristic
779C22#6584811yescharacteristic
780C22#6585811yescharacteristic
781C22#6585911yescharacteristic
782C22#6586411yescharacteristic
783C22#6586611yescharacteristic
784C22C4×D4×D511yescharacteristic
785C22#6587911yescharacteristic
786C22#6588211yescharacteristic
787C22#6588711yescharacteristic
788C22#6588711yescharacteristic
789C22#6589311yescharacteristic
790C22#6589311yescharacteristic
791C22#6589611yescharacteristic
792C22#6590211yescharacteristic
793C22#6590211yescharacteristic
794C22C4×#71311yescharacteristic
795C22#6590811yescharacteristic
796C22#6591411yescharacteristic
797C22#6591611yescharacteristic
798C22#6591911yescharacteristic
799C22#6591911yescharacteristic
800C22C2×C4×C22⋊D511yescharacteristic
801C22C2×#407511yescharacteristic
802C22C2×#407611yescharacteristic
803C22D4×C22⋊D511yescharacteristic
804C22#6615111yescharacteristic
805C22#6616311yescharacteristic
806C22#6616811yescharacteristic
807C4—24no—
808C4—44no—
809C4—44no—
810C4—42no—
811C4—104no—
812C4—202no—
813C4—202no—
814C4—202no—
815C4—402no—
816C4#6522918yescomplemented
817C2—404no—
818C2#1060537011yescharacteristic
819C2#1060537711yescharacteristic
820C2#1060542411yescharacteristic
821C2#1060542611yescharacteristic
822C2#1060544311yescharacteristic
823C2#1060546611yescharacteristic
824C2C4×#404111yescharacteristic
825C2#1060549411yescharacteristic
826C2C2×#6522911yescharacteristic
827C2#1061392411yescharacteristic
828C2#1061400711yescharacteristic
829C2#1061407411yescharacteristic
830C2#1061408911yescharacteristic
831C2#1061419711yescharacteristic
832C2#1061420011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D5
commutatorC23×C5C23×C4
FittingC2×C4×C5×C4⋊C4C2
socle, cosocleC24×C5C24
prime radicalC23×D20C22
hypercenterC2×C4×C4⋊C4D5
hypocenterC5#14022
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
5. C2×#65229C2semidirect
6. C2×C4×#683C2semidirect
7. #10602356C2semidirect
8. #10602356C2semidirect
9. #10602330C2semidirect
10. #10600222C2semidirect
11. #10600221C2semidirect
37. #65277C4semidirect
98. C2×#683D4semidirect
117. C2×C4×C4⋊C4D5semidirect
505. C4×C5#388semidirect
756. C5#14022semidirect
816. 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×#652772
C2×#652282
C2×#652292
C2×C4×#6832
#106023562
#106023302
#106002222
#106002212
#140225