Finite Group Databasebeta

← C2×#10609876 #12266919

Subgroups — C2×#10609876 #12266919

Order 1280.

3114 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D5×C4⋊C4C211yesmaximal, characteristic, complemented
2C22×#4044C211yesmaximal, characteristic, complemented
3C2×C5×#400C211yesmaximal, characteristic, complemented
4C2×#65283C211yesmaximal, characteristic, complemented
5C2×#65276C211yesmaximal, characteristic, complemented
6#10609876C2116yesmaximal, direct product factor
7C2×#64964C211yesmaximal, characteristic, complemented
8C2×#64954C211yesmaximal, characteristic
9C2×#64954C211yesmaximal, characteristic
10C2×#64954C211yesmaximal, characteristic
11C2×#64957C211yesmaximal, characteristic, complemented
12C2×#64949C211yesmaximal, characteristic, complemented
13C2×#64959C211yesmaximal, characteristic, complemented
14C2×#64944C211yesmaximal, characteristic, complemented
15C2×#64944C211yesmaximal, characteristic, complemented
16C2×#64955C211yesmaximal, characteristic, complemented
17C23×D20C2211yescharacteristic
18C23×C4×D5C2211yescharacteristic
19C23×C4×D5C2211yescharacteristic
20C23×C4×D5C2211yescharacteristic
21C22×C5×C4⋊C4C2211yescharacteristic
22C22×C5×C4⋊C4C2211yescharacteristic
23C22×#685C2211yescharacteristic
24C22×#685C2211yescharacteristic
25C22×#685C2211yescharacteristic
26C22×#685C2211yescharacteristic
27C22×#685C2211yescharacteristic
28C22×#685C2211yescharacteristic
29C22×#685C2211yescharacteristic
30C22×#685C2211yescharacteristic
31C22×#685C2211yescharacteristic
32C22×C4⋊Dic5C2211yescharacteristic
33C22×C4⋊Dic5C2211yescharacteristic
34C22×C4⋊Dic5C2211yescharacteristic
35C22×#683C2211yescharacteristic
36C22×#683C2211yescharacteristic
37C22×#683C2211yescharacteristic
38C22×C4×Dic5C2211yescharacteristic
39C22×C4×Dic5C2211yescharacteristic
40C2×#4044—28no—
41C2×#4044C2218yescomplemented
42C2×D5×C4⋊C4—28no—
43C2×D5×C4⋊C4C2218yescomplemented
44C5×#400C2218yescomplemented
45C2×C5×#95C2211yescharacteristic
46C2×C5×#95C2211yescharacteristic
47C2×C5×#95C2211yescharacteristic
48C2×C5×#95C2211yescharacteristic
49C2×C5×#95C2211yescharacteristic
50C2×#3963C2211yescharacteristic
51C2×#3963C2211yescharacteristic
52C2×#3963C2211yescharacteristic
53C2×#3963C2211yescharacteristic
54C2×#3963C2211yescharacteristic
55C2×#3963C2211yescharacteristic
56C2×#3963C2211yescharacteristic
57#65283C2218yescomplemented
58#65276C2218yescomplemented
59#64964C2218yescomplemented
60#64959C2218yescomplemented
61#64957C2218yescomplemented
62#64955C2218yescomplemented
63#64954C2218yes—
64#64954C2218yes—
65#64954C2218yes—
66#64949C2218yescomplemented
67#64944C2218yescomplemented
68#64944C2218yescomplemented
69C2×#2481—51nomaximal, Sylow
70C24×D5C2311yescharacteristic
71C24×D5C2311yescharacteristic
72C23×C4×C5C2311yescharacteristic
73C23×C4×C5C2311yescharacteristic
74C23×C4×C5C2311yescharacteristic
75C23×C4×C5C2311yescharacteristic
76C23×C4×C5C2311yescharacteristic
77C23×C4×C5C2311yescharacteristic
78C23×C4×C5C2311yescharacteristic
79C23×Dic5C2311yescharacteristic
80C23×Dic5C2311yescharacteristic
81C23×Dic5C2311yescharacteristic
82C23×Dic5C2311yescharacteristic
83C23×Dic5C2311yescharacteristic
84C23×Dic5C2311yescharacteristic
85C22×D20—24no—
86C22×D20—24no—
87C22×D20—24no—
88C22×D20C2314yes—
89C22×C4×D5—24no—
90C22×C4×D5—24no—
91C22×C4×D5—24no—
92C22×C4×D5—24no—
93C22×C4×D5—24no—
94C22×C4×D5—24no—
95C22×C4×D5—24no—
96C22×C4×D5—42no—
97C22×C4×D5—42no—
98C22×C4×D5C2314yes—
99C22×C4×D5C2314yes—
100C22×C4×D5C2314yes—
101C2×C5×C4⋊C4—24no—
102C2×C5×C4⋊C4—24no—
103C2×C5×C4⋊C4C2314yes—
104C2×C5×C4⋊C4C2314yes—
105C2×#685—24no—
106C2×#685—24no—
107C2×#685—24no—
108C2×#685—24no—
109C2×#685—24no—
110C2×#685—24no—
111C2×#685—24no—
112C2×#685—42no—
113C2×#685—42no—
114C2×#685C2314yes—
115C2×#685C2314yes—
116C2×#685C2314yes—
117C2×#685C2314yes—
118C2×#685C2314yes—
119C2×#685C2314yes—
120C2×#685C2314yes—
121C2×#685C2314yes—
122C2×#685C2314yes—
123C2×C4⋊Dic5—24no—
124C2×C4⋊Dic5—24no—
125C2×C4⋊Dic5—42no—
126C2×C4⋊Dic5C2314yes—
127C2×C4⋊Dic5C2314yes—
128C2×C4⋊Dic5C2314yes—
129C2×#683—24no—
130C2×#683—24no—
131C2×#683D418yescomplemented
132C2×#683C2314yes—
133C2×#683C2314yes—
134C2×#683C2314yes—
135C2×C4×Dic5—24no—
136C2×C4×Dic5—42no—
137C2×C4×Dic5C2314yes—
138C2×C4×Dic5C2314yes—
139#4044—232no—
140D5×C4⋊C4—232no—
141C5×#95C2314yes—
142C5×#95C2314yes—
143C5×#95C2314yes—
144C5×#95C2314yes—
145C5×#95C2314yes—
146#3963C2314yes—
147#3963C2314yes—
148#3963C2314yes—
149#3963C2314yes—
150#3963C2314yes—
151#3963C2314yes—
152#3963C2314yes—
153C22×#126—51no—
154C23×C4⋊C4—51no—
155#2481—516no—
156C2×#400—51no—
157C2×#400D511yescharacteristic, complemented
158C2×#397—51no—
159C2×#396—51no—
160C2×#388—51no—
161C2×#387—51no—
162C2×#387—51no—
163C2×#386—51no—
164C2×#386—51no—
165C2×#386—51no—
166C2×#385—51no—
167C2×#380—51no—
168C2×C4×C22⋊C4—51no—
169C24×C5C2411yescharacteristic
170C23×D5—22no—
171C23×D5—22no—
172C23×D5—22no—
173C23×D5—22no—
174C23×D5—22no—
175C23×D5—22no—
176C23×D5—22no—
177C23×D5—22no—
178C23×D5—22no—
179C23×D5—22no—
180C23×D5—22no—
181C23×D5#4114yes—
182C23×D5#4114yes—
183C23×D5#4114yes—
184C23×D5C2412yes—
185C23×D5C2412yes—
186C22×C4×C5—22no—
187C22×C4×C5—22no—
188C22×C4×C5—22no—
189C22×C4×C5—22no—
190C22×C4×C5—22no—
191C22×C4×C5—22no—
192C22×C4×C5—22no—
193C22×C4×C5—22no—
194C22×C4×C5—22no—
195C22×C4×C5—22no—
196C22×C4×C5—22no—
197C22×C4×C5—22no—
198C22×C4×C5—22no—
199C22×C4×C5—22no—
200C22×C4×C5—22no—
201C22×C4×C5—22no—
202C22×C4×C5—22no—
203C22×C4×C5—22no—
204C22×C4×C5—22no—
205C22×C4×C5C2×D414yes—
206C22×C4×C5#4114yes—
207C22×C4×C5C2412yes—
208C22×C4×C5C2412yes—
209C22×C4×C5C2412yes—
210C22×C4×C5C2412yes—
211C22×C4×C5C2412yes—
212C22×C4×C5C2412yes—
213C22×C4×C5C2412yes—
214C22×Dic5—22no—
215C22×Dic5—22no—
216C22×Dic5—22no—
217C22×Dic5—22no—
218C22×Dic5—22no—
219C22×Dic5—22no—
220C22×Dic5—22no—
221C22×Dic5—22no—
222C22×Dic5—22no—
223C22×Dic5—22no—
224C22×Dic5—22no—
225C22×Dic5—22no—
226C22×Dic5—22no—
227C22×Dic5—22no—
228C22×Dic5—22no—
229C22×Dic5—22no—
230C22×Dic5C2×D414yes—
231C22×Dic5C2×D414yes—
232C22×Dic5C2412yes—
233C22×Dic5C2412yes—
234C22×Dic5C2412yes—
235C22×Dic5C2412yes—
236C22×Dic5C2412yes—
237C22×Dic5C2412yes—
238C2×D20—28no—
239C2×D20—28no—
240C2×D20—28no—
241C2×D20—416no—
242C2×C4×D5—232no—
243C2×C4×D5—28no—
244C2×C4×D5—28no—
245C2×C4×D5—28no—
246C2×C4×D5—28no—
247C2×C4×D5—28no—
248C2×C4×D5—28no—
249C2×C4×D5—28no—
250C2×C4×D5—44no—
251C2×C4×D5—44no—
252C2×C4×D5—416no—
253C2×C4×D5—416no—
254C5×C4⋊C4—28no—
255C5×C4⋊C4—28no—
256#685—28no—
257#685—28no—
258#685—28no—
259#685—28no—
260#685—28no—
261#685—28no—
262#685—28no—
263#685—44no—
264#685—44no—
265C4⋊Dic5—28no—
266C4⋊Dic5—28no—
267C4⋊Dic5—44no—
268#683—28no—
269#683—28no—
270#683C2×D4116yescomplemented
271C4×Dic5—28no—
272C4×Dic5—44no—
273C23×D4—51no—
274C24×C4—51no—
275C24×C4—51no—
276C24×C4—51no—
277C2×#126—58no—
278C2×#126—108no—
279C22×C4⋊C4—51no—
280C22×C4⋊C4—51no—
281C22×C4⋊C4—51no—
282C22×C4⋊C4—51no—
283C22×C4⋊C4—51no—
284C22×C4⋊C4—51no—
285C22×C4⋊C4—58no—
286C22×C4⋊C4—108no—
287C22×C4⋊C4C2×D511yescharacteristic
288C22×C4⋊C4C2×D511yescharacteristic
289C22×C22⋊C4—51no—
290C22×C22⋊C4—51no—
291C22×C22⋊C4—51no—
292C22×C22⋊C4—51no—
293C22×C22⋊C4—51no—
294C22×C22⋊C4—51no—
295C22×C22⋊C4—51no—
296C22×C22⋊C4—51no—
297C22×C22⋊C4—51no—
298C22×C42—51no—
299C22×C42—51no—
300#400—58no—
301#400C2×D518yescomplemented
302#397—58no—
303#396—58no—
304#388—58no—
305#387—58no—
306#387—58no—
307#386—58no—
308#386—58no—
309#386—58no—
310#385—58no—
311#380—58no—
312C4×C22⋊C4—58no—
313C2×#95—51no—
314C2×#95—51no—
315C2×#95—51no—
316C2×#95—51no—
317C2×#95—51no—
318C2×#95—51no—
319C2×#95—51no—
320C2×#95C2×D511yescharacteristic
321C2×#95C2×D511yescharacteristic
322C2×#95C2×D511yescharacteristic
323C2×#95C2×D511yescharacteristic
324C2×#95C2×D511yescharacteristic
325C23×C5C22×D412yes—
326C23×C5C2×#4112yes—
327C23×C5C2×#4112yes—
328C23×C5C2×#4112yes—
329C23×C5C2×#4112yes—
330C23×C5H(5,𝔽2)12yes—
331C23×C52−1+412yes—
332C23×C5C2511yescharacteristic
333C22×D5—28no—
334C22×D5—28no—
335C22×D5—28no—
336C22×D5—28no—
337C22×D5—28no—
338C22×D5—28no—
339C22×D5—22no—
340C22×D5—22no—
341C22×D5—22no—
342C22×D5—22no—
343C22×D5—22no—
344C22×D5—22no—
345C22×D5—22no—
346C22×D5—22no—
347C22×D5—22no—
348C22×D5—22no—
349C22×D5—22no—
350C22×D5—44no—
351C22×D5—44no—
352C22×D5—44no—
353C22×D5—44no—
354C22×D5—44no—
355C22×D5—44no—
356C22×D5—44no—
357C22×D5#126116yescomplemented
358C22×D5C2×#4114yes—
359C22×D5C2×#4114yes—
360C22×D5C2×#4114yes—
361C2×C4×C5—28no—
362C2×C4×C5—28no—
363C2×C4×C5—22no—
364C2×C4×C5—22no—
365C2×C4×C5—22no—
366C2×C4×C5—22no—
367C2×C4×C5—22no—
368C2×C4×C5—22no—
369C2×C4×C5—22no—
370C2×C4×C5—22no—
371C2×C4×C5—22no—
372C2×C4×C5—22no—
373C2×C4×C5—22no—
374C2×C4×C5—22no—
375C2×C4×C5—22no—
376C2×C4×C5—22no—
377C2×C4×C5—22no—
378C2×C4×C5—22no—
379C2×C4×C5—22no—
380C2×C4×C5—22no—
381C2×C4×C5—22no—
382C2×C4×C5—44no—
383C2×C4×C5—44no—
384C2×C4×C5—44no—
385C2×C4×C5—44no—
386C2×C4×C5—44no—
387C2×C4×C5C22×D414yes—
388C2×C4×C5C2×#4114yes—
389C2×Dic5—28no—
390C2×Dic5—28no—
391C2×Dic5—22no—
392C2×Dic5—22no—
393C2×Dic5—22no—
394C2×Dic5—22no—
395C2×Dic5—22no—
396C2×Dic5—22no—
397C2×Dic5—22no—
398C2×Dic5—22no—
399C2×Dic5—22no—
400C2×Dic5—22no—
401C2×Dic5—22no—
402C2×Dic5—22no—
403C2×Dic5—22no—
404C2×Dic5—22no—
405C2×Dic5—22no—
406C2×Dic5—22no—
407C2×Dic5—44no—
408C2×Dic5—44no—
409C2×Dic5—44no—
410C2×Dic5—44no—
411C2×Dic5C22×D414yes—
412C2×Dic5C22×D414yes—
413D20—416no—
414C4×D5—232no—
415C4×D5—416no—
416C4×D5—416no—
417C25—51no—
418C25—51no—
419C22×D4—54no—
420C22×D4—104no—
421C22×D4—104no—
422C22×D4—104no—
423C23×C4—51no—
424C23×C4—51no—
425C23×C4—51no—
426C23×C4—51no—
427C23×C4—51no—
428C23×C4—51no—
429C23×C4—54no—
430C23×C4—54no—
431C23×C4—54no—
432C23×C4—104no—
433C23×C4—104no—
434C23×C4—104no—
435C23×C4—104no—
436C23×C4—104no—
437C23×C4—104no—
438C23×C4—104no—
439C23×C4—202no—
440C23×C4—202no—
441C23×C4C22×D511yescharacteristic
442C23×C4C22×D511yescharacteristic
443C23×C4C22×D511yescharacteristic
444C23×C4C22×D511yescharacteristic
445C23×C4C22×D511yescharacteristic
446C23×C4C22×D511yescharacteristic
447C23×C4C22×D511yescharacteristic
448#126—1032no—
449C2×C4⋊C4—24no—
450C2×C4⋊C4—24no—
451C2×C4⋊C4—58no—
452C2×C4⋊C4—54no—
453C2×C4⋊C4—54no—
454C2×C4⋊C4—54no—
455C2×C4⋊C4—54no—
456C2×C4⋊C4—54no—
457C2×C4⋊C4—54no—
458C2×C4⋊C4—1032no—
459C2×C4⋊C4—104no—
460C2×C4⋊C4—104no—
461C2×C4⋊C4—104no—
462C2×C4⋊C4—104no—
463C2×C4⋊C4—202no—
464C2×C4⋊C4C22×D514yes—
465C2×C4⋊C4C22×D514yes—
466C2×C22⋊C4—54no—
467C2×C22⋊C4—54no—
468C2×C22⋊C4—54no—
469C2×C22⋊C4—54no—
470C2×C22⋊C4—54no—
471C2×C22⋊C4—54no—
472C2×C22⋊C4—54no—
473C2×C22⋊C4—54no—
474C2×C22⋊C4—54no—
475C2×C22⋊C4—104no—
476C2×C22⋊C4—104no—
477C2×C22⋊C4—104no—
478C2×C22⋊C4—104no—
479C2×C22⋊C4—104no—
480C2×C22⋊C4—104no—
481C2×C22⋊C4—104no—
482C2×C22⋊C4—202no—
483C2×C22⋊C4—202no—
484C2×C42—54no—
485C2×C42—54no—
486C2×C42—104no—
487C2×C42—202no—
488#95—54no—
489#95—54no—
490#95—54no—
491#95—54no—
492#95—54no—
493#95—54no—
494#95—54no—
495#95C22×D514yes—
496#95C22×D514yes—
497#95C22×D514yes—
498#95C22×D514yes—
499#95C22×D514yes—
500C22×C5#52514yes—
501C22×C5C2×#12614yes—
502C22×C5#53914yes—
503C22×C5#54614yes—
504C22×C5#54814yes—
505C22×C5#55214yes—
506C22×C5#55314yes—
507C22×C5C23×D411yescharacteristic
508C22×C5C22×#4111yescharacteristic
509C22×C5C22×#4111yescharacteristic
510C22×C5C22×#4111yescharacteristic
511C22×C5C22×#4111yescharacteristic
512C22×C5C2×H(5,𝔽2)11yescharacteristic
513C22×C5C2×2−1+411yescharacteristic
514C2×D5—24no—
515C2×D5—24no—
516C2×D5—24no—
517C2×D5—24no—
518C2×D5—24no—
519C2×D5—24no—
520C2×D5—232no—
521C2×D5—42no—
522C2×D5—42no—
523C2×D5—42no—
524C2×D5—42no—
525C2×D5—42no—
526C2×D5—42no—
527C2×D5—42no—
528C2×D5—88no—
529C2×D5C2×#12618yescomplemented
530C4×C5—24no—
531C4×C5—24no—
532C4×C5—42no—
533C4×C5—42no—
534C4×C5—42no—
535C4×C5—42no—
536C4×C5—42no—
537Dic5—24no—
538Dic5—24no—
539Dic5—42no—
540Dic5—42no—
541Dic5—42no—
542Dic5—42no—
543C24—54no—
544C24—54no—
545C24—54no—
546C24—52no—
547C24—52no—
548C24—102no—
549C24—102no—
550C24—102no—
551C24—102no—
552C24—102no—
553C24—102no—
554C24—102no—
555C24—102no—
556C24—102no—
557C24—102no—
558C24—102no—
559C24C23×D511yescharacteristic
560C2×D4—108no—
561C2×D4—108no—
562C2×D4—108no—
563C2×D4—2016no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—54no—
584C22×C4—54no—
585C22×C4—52no—
586C22×C4—52no—
587C22×C4—52no—
588C22×C4—52no—
589C22×C4—52no—
590C22×C4—52no—
591C22×C4—108no—
592C22×C4—108no—
593C22×C4—108no—
594C22×C4—1032no—
595C22×C4—108no—
596C22×C4—108no—
597C22×C4—102no—
598C22×C4—102no—
599C22×C4—102no—
600C22×C4—102no—
601C22×C4—108no—
602C22×C4—102no—
603C22×C4—102no—
604C22×C4—102no—
605C22×C4—102no—
606C22×C4—102no—
607C22×C4—102no—
608C22×C4—102no—
609C22×C4—102no—
610C22×C4—102no—
611C22×C4—102no—
612C22×C4—102no—
613C22×C4—102no—
614C22×C4—108no—
615C22×C4—204no—
616C22×C4—204no—
617C22×C4—2016no—
618C22×C4—2016no—
619C22×C4D4×D514yes—
620C22×C4#71314yes—
621C22×C4C23×D512yes—
622C22×C4C23×D512yes—
623C22×C4C23×D512yes—
624C22×C4C23×D512yes—
625C22×C4C23×D512yes—
626C22×C4C23×D512yes—
627C22×C4C23×D512yes—
628C4⋊C4—28no—
629C4⋊C4—28no—
630C4⋊C4—516no—
631C4⋊C4—108no—
632C4⋊C4—108no—
633C4⋊C4—108no—
634C4⋊C4—108no—
635C4⋊C4—204no—
636C22⋊C4—108no—
637C22⋊C4—108no—
638C22⋊C4—108no—
639C22⋊C4—108no—
640C22⋊C4—108no—
641C22⋊C4—108no—
642C22⋊C4—108no—
643C22⋊C4—204no—
644C22⋊C4—204no—
645C42—108no—
646C42—204no—
647C2×C5#248118yescomplemented
648C2×C5C2×#52511yescharacteristic
649C2×C5C22×#12611yescharacteristic
650C2×C5C2×#53911yescharacteristic
651C2×C5C2×#54611yescharacteristic
652C2×C5C2×#54811yescharacteristic
653C2×C5C2×#55211yescharacteristic
654C2×C5C2×#55311yescharacteristic
655D5—28no—
656D5—82no—
657C23—54no—
658C23—54no—
659C23—54no—
660C23—516no—
661C23—108no—
662C23—108no—
663C23—108no—
664C23—102no—
665C23—102no—
666C23—102no—
667C23—102no—
668C23—108no—
669C23—108no—
670C23—108no—
671C23—102no—
672C23—102no—
673C23—102no—
674C23—102no—
675C23—102no—
676C23—102no—
677C23—102no—
678C23—204no—
679C23—204no—
680C23—204no—
681C23—204no—
682C23—204no—
683C23—204no—
684C23—204no—
685C23C2×D4×D512yes—
686C23C2×#71312yes—
687C23D5×#4112yes—
688C23D5×#4112yes—
689C23D5×#4112yes—
690C23#414912yes—
691C23#415012yes—
692C23C24×D511yescharacteristic
693D4—2016no—
694C2×C4—28no—
695C2×C4—28no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—44no—
716C2×C4—44no—
717C2×C4—44no—
718C2×C4—44no—
719C2×C4—44no—
720C2×C4—54no—
721C2×C4—54no—
722C2×C4—1032no—
723C2×C4—108no—
724C2×C4—108no—
725C2×C4—102no—
726C2×C4—102no—
727C2×C4—102no—
728C2×C4—102no—
729C2×C4—102no—
730C2×C4—102no—
731C2×C4—102no—
732C2×C4—102no—
733C2×C4—102no—
734C2×C4—102no—
735C2×C4—102no—
736C2×C4—102no—
737C2×C4—102no—
738C2×C4—102no—
739C2×C4—102no—
740C2×C4—102no—
741C2×C4—2016no—
742C2×C4—2016no—
743C2×C4—204no—
744C2×C4—204no—
745C2×C4—204no—
746C2×C4—204no—
747C2×C4C2×D4×D514yes—
748C2×C4C2×#71314yes—
749C5C2×#248111yescharacteristic, complemented, Sylow
750C22—58no—
751C22—104no—
752C22—104no—
753C22—104no—
754C22—104no—
755C22—104no—
756C22—104no—
757C22—1032no—
758C22—202no—
759C22—202no—
760C22—202no—
761C22—202no—
762C22—202no—
763C22—202no—
764C22—202no—
765C22—408no—
766C22#6596114yes—
767C22#6598814yes—
768C22#6601114yes—
769C22#6602814yes—
770C22#6602914yes—
771C22D5×#12614yes—
772C22#6604114yes—
773C22C22×D4×D511yescharacteristic
774C22C22×#71311yescharacteristic
775C22C2×D5×#4111yescharacteristic
776C22C2×D5×#4111yescharacteristic
777C22C2×D5×#4111yescharacteristic
778C22C2×#414911yescharacteristic
779C22C2×#415011yescharacteristic
780C4—24no—
781C4—24no—
782C4—42no—
783C4—42no—
784C4—42no—
785C4—42no—
786C4—42no—
787C4—104no—
788C4—104no—
789C4—202no—
790C4—202no—
791C4—202no—
792C4—202no—
793C2—108no—
794C2—402no—
795C2#1060987618yesdirect product factor
796C2C2×#6596111yescharacteristic
797C2C2×#6598811yescharacteristic
798C2C2×#6601111yescharacteristic
799C2C2×#6602811yescharacteristic
800C2C2×#6602911yescharacteristic
801C2C2×D5×#12611yescharacteristic
802C2C2×#6604111yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC2×C5×#400C2
socleC24×C5C24
prime radicalC23×D20C22
hypercenterC2×#400D5
hypocenterC5C2×#2481
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#400

Complements

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

NH ≅ G/Ntype
1. C22×D5×C4⋊C4C2semidirect
2. C22×#4044C2semidirect
3. C2×C5×#400C2semidirect
4. C2×#65283C2semidirect
5. C2×#65276C2semidirect
6. #10609876C2direct (N × H)
7. C2×#64964C2semidirect
11. C2×#64957C2semidirect
12. C2×#64949C2semidirect
13. C2×#64959C2semidirect
14. C2×#64944C2semidirect
15. C2×#64944C2semidirect
16. C2×#64955C2semidirect
41. C2×#4044C22semidirect
43. C2×D5×C4⋊C4C22semidirect
44. C5×#400C22semidirect
57. #65283C22semidirect
58. #65276C22semidirect
59. #64964C22semidirect
60. #64959C22semidirect
61. #64957C22semidirect
62. #64955C22semidirect
66. #64949C22semidirect
67. #64944C22semidirect
68. #64944C22semidirect
131. C2×#683D4semidirect
157. C2×#400D5semidirect
270. #683C2×D4semidirect
301. #400C2×D5semidirect
357. C22×D5#126semidirect
529. C2×D5C2×#126semidirect
647. C2×C5#2481semidirect
749. C5C2×#2481semidirect
795. C2#10609876direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D5×C4⋊C42
C22×#40442
C2×C5×#4002
C2×#652832
C2×#652762
#106098762
C2×#649642
C2×#649542
C2×#649572
C2×#649492
C2×#649592
C2×#649442
C2×#649552
C2×#24815