Finite Group Databasebeta

← C2×#10609214 #12266927

Subgroups — C2×#10609214 #12266927

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×#4025C211yesmaximal, characteristic, complemented
3C2×C5×#397C211yesmaximal, characteristic, complemented
4C2×#65271C211yesmaximal, characteristic, complemented
5C2×#65245C211yesmaximal, characteristic
6C2×#65245C211yesmaximal, characteristic
7C2×#65245C211yesmaximal, characteristic
8C2×#65237C211yesmaximal, characteristic, complemented
9C2×#65233C211yesmaximal, characteristic, complemented
10#10609214C2116yesmaximal, direct product factor
11C2×#64957C211yesmaximal, characteristic, complemented
12C2×#64956C211yesmaximal, characteristic, complemented
13C2×#64947C211yesmaximal, characteristic, complemented
14C2×#64943C211yesmaximal, characteristic, complemented
15C2×#64943C211yesmaximal, characteristic, complemented
16C2×#64955C211yesmaximal, characteristic, complemented
17C23×C22⋊D5C2211yescharacteristic
18C23×C4×D5C2211yescharacteristic
19C23×C4×D5C2211yescharacteristic
20C23×C4×D5C2211yescharacteristic
21C22×C5×C4⋊C4C2211yescharacteristic
22C22×C5×C22⋊C4C2211yescharacteristic
23C22×C5×C22⋊C4C2211yescharacteristic
24C22×C5×C22⋊C4C2211yescharacteristic
25C22×C22⋊Dic5C2211yescharacteristic
26C22×C22⋊Dic5C2211yescharacteristic
27C22×C22⋊Dic5C2211yescharacteristic
28C22×#685C2211yescharacteristic
29C22×#685C2211yescharacteristic
30C22×#685C2211yescharacteristic
31C22×C4⋊Dic5C2211yescharacteristic
32C22×C4⋊Dic5C2211yescharacteristic
33C22×#683C2211yescharacteristic
34C22×#683C2211yescharacteristic
35C22×#683C2211yescharacteristic
36C22×#683C2211yescharacteristic
37C22×#683C2211yescharacteristic
38C22×C4×Dic5C2211yescharacteristic
39C22×C4×Dic5C2211yescharacteristic
40C2×D5×C4⋊C4—28no—
41C2×D5×C4⋊C4C2218yescomplemented
42C2×#4025—28no—
43C2×#4025C2218yescomplemented
44C5×#397C2218yescomplemented
45C2×C5×#95C2211yescharacteristic
46C2×C5×#95C2211yescharacteristic
47C2×C5×#95C2211yescharacteristic
48C2×#3963C2211yescharacteristic
49C2×#3963C2211yescharacteristic
50C2×#3963C2211yescharacteristic
51C2×#3963C2211yescharacteristic
52C2×#3963C2211yescharacteristic
53C2×#3963C2211yescharacteristic
54C2×#3963C2211yescharacteristic
55C2×#3963C2211yescharacteristic
56C2×#3963C2211yescharacteristic
57#65271C2218yescomplemented
58#65245C2218yes—
59#65245C2218yes—
60#65245C2218yes—
61#65237C2218yescomplemented
62#65233C2218yescomplemented
63#64957C2218yescomplemented
64#64956C2218yescomplemented
65#64955C2218yescomplemented
66#64947C2218yescomplemented
67#64943C2218yescomplemented
68#64943C2218yescomplemented
69C2×#2481—51nomaximal, Sylow
70C25×C5C2311yescharacteristic
71C24×D5C2311yescharacteristic
72C23×C4×C5C2311yescharacteristic
73C23×C4×C5C2311yescharacteristic
74C23×C4×C5C2311yescharacteristic
75C23×C4×C5C2311yescharacteristic
76C23×C4×C5C2311yescharacteristic
77C23×C4×C5C2311yescharacteristic
78C22×C22⋊D5—24no—
79C22×C22⋊D5—24no—
80C22×C22⋊D5—24no—
81C22×C22⋊D5C2314yes—
82C23×Dic5C2311yescharacteristic
83C23×Dic5C2311yescharacteristic
84C23×Dic5C2311yescharacteristic
85C23×Dic5C2311yescharacteristic
86C23×Dic5C2311yescharacteristic
87C23×Dic5C2311yescharacteristic
88C23×Dic5C2311yescharacteristic
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⋊C4C2314yes—
103C2×C5×C22⋊C4—24no—
104C2×C5×C22⋊C4—42no—
105C2×C5×C22⋊C4—42no—
106C2×C5×C22⋊C4C2314yes—
107C2×C5×C22⋊C4C2314yes—
108C2×C5×C22⋊C4C2314yes—
109C2×C22⋊Dic5—24no—
110C2×C22⋊Dic5—24no—
111C2×C22⋊Dic5—24no—
112C2×C22⋊Dic5C2314yes—
113C2×C22⋊Dic5C2314yes—
114C2×C22⋊Dic5C2314yes—
115C2×#685—24no—
116C2×#685—24no—
117C2×#685—24no—
118C2×#685C2314yes—
119C2×#685C2314yes—
120C2×#685C2314yes—
121C2×C4⋊Dic5—24no—
122C2×C4⋊Dic5D418yescomplemented
123C2×C4⋊Dic5C2314yes—
124C2×C4⋊Dic5C2314yes—
125C2×#683—24no—
126C2×#683—24no—
127C2×#683—24no—
128C2×#683—24no—
129C2×#683—42no—
130C2×#683C2314yes—
131C2×#683C2314yes—
132C2×#683C2314yes—
133C2×#683C2314yes—
134C2×#683C2314yes—
135C2×C4×Dic5—24no—
136C2×C4×Dic5—42no—
137C2×C4×Dic5C2314yes—
138C2×C4×Dic5C2314yes—
139D5×C4⋊C4—232no—
140#4025—232no—
141C5×#95C2314yes—
142C5×#95C2314yes—
143C5×#95C2314yes—
144#3963C2314yes—
145#3963C2314yes—
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×#400—51no—
158C2×#397D511yescharacteristic, complemented
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×C5—22no—
170C24×C5—22no—
171C24×C5—22no—
172C24×C5—22no—
173C24×C5—22no—
174C24×C5—22no—
175C24×C5—22no—
176C24×C5C2412yes—
177C24×C5C2411yescharacteristic
178C23×D5—22no—
179C23×D5—22no—
180C23×D5—22no—
181C23×D5—22no—
182C23×D5#4114yes—
183C23×D5#4114yes—
184C23×D5#4114yes—
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×C5C2×D414yes—
204C22×C4×C5C2412yes—
205C22×C4×C5C2412yes—
206C22×C4×C5C2412yes—
207C22×C4×C5C2412yes—
208C22×C4×C5C2412yes—
209C22×C4×C5C2412yes—
210C2×C22⋊D5—28no—
211C2×C22⋊D5—28no—
212C2×C22⋊D5—28no—
213C2×C22⋊D5—416no—
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×Dic5—22no—
231C22×Dic5—22no—
232C22×Dic5C2×D414yes—
233C22×Dic5C2×D414yes—
234C22×Dic5#4114yes—
235C22×Dic5C2412yes—
236C22×Dic5C2412yes—
237C22×Dic5C2412yes—
238C22×Dic5C2412yes—
239C22×Dic5C2412yes—
240C22×Dic5C2412yes—
241C22×Dic5C2412yes—
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×C22⋊C4—28no—
256C5×C22⋊C4—44no—
257C5×C22⋊C4—44no—
258C22⋊Dic5—28no—
259C22⋊Dic5—28no—
260C22⋊Dic5—28no—
261#685—28no—
262#685—28no—
263#685—28no—
264C4⋊Dic5—28no—
265C4⋊Dic5C2×D4116yescomplemented
266#683—28no—
267#683—28no—
268#683—28no—
269#683—28no—
270#683—44no—
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—51no—
286C22×C4⋊C4—58no—
287C22×C4⋊C4—108no—
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⋊C4C2×D511yescharacteristic
296C22×C22⋊C4C2×D511yescharacteristic
297C22×C22⋊C4C2×D511yescharacteristic
298C22×C42—51no—
299C22×C42—51no—
300#400—58no—
301#400—58no—
302#397C2×D518yescomplemented
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×#95—51no—
321C2×#95—51no—
322C2×#95C2×D511yescharacteristic
323C2×#95C2×D511yescharacteristic
324C2×#95C2×D511yescharacteristic
325C23×C5—22no—
326C23×C5—22no—
327C23×C5—22no—
328C23×C5—22no—
329C23×C5—22no—
330C23×C5—22no—
331C23×C5—22no—
332C23×C5—44no—
333C23×C5—44no—
334C23×C5—44no—
335C23×C5—44no—
336C23×C5—44no—
337C23×C5—44no—
338C23×C5—44no—
339C23×C5C22×D412yes—
340C23×C5C2×#4112yes—
341C23×C5C2×#4112yes—
342C23×C5C2×#4112yes—
343C23×C5C2×#4112yes—
344C23×C5H(5,𝔽2)12yes—
345C23×C52−1+412yes—
346C23×C5C2511yescharacteristic
347C22×D5—28no—
348C22×D5—28no—
349C22×D5—28no—
350C22×D5—28no—
351C22×D5—28no—
352C22×D5—28no—
353C22×D5—22no—
354C22×D5—22no—
355C22×D5—22no—
356C22×D5—22no—
357C22×D5#126116yescomplemented
358C22×D5C2×#4114yes—
359C22×D5C2×#4114yes—
360C22×D5C2×#4114yes—
361C2×C4×C5—28no—
362C2×C4×C5—22no—
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—44no—
380C2×C4×C5—44no—
381C2×C4×C5—44no—
382C2×C4×C5—44no—
383C2×C4×C5—44no—
384C2×C4×C5C22×D414yes—
385C22⋊D5—416no—
386C2×Dic5—28no—
387C2×Dic5—28no—
388C2×Dic5—28no—
389C2×Dic5—22no—
390C2×Dic5—22no—
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—
413C2×Dic5C2×#4114yes—
414C4×D5—232no—
415C4×D5—416no—
416C4×D5—416no—
417C25—51no—
418C25C22×D511yescharacteristic
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—51no—
430C23×C4—54no—
431C23×C4—54no—
432C23×C4—54no—
433C23×C4—104no—
434C23×C4—104no—
435C23×C4—104no—
436C23×C4—104no—
437C23×C4—104no—
438C23×C4—104no—
439C23×C4—104no—
440C23×C4—202no—
441C23×C4—202no—
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—58no—
451C2×C4⋊C4—54no—
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—104no—
464C2×C4⋊C4—202no—
465C2×C4⋊C4C22×D514yes—
466C2×C22⋊C4—24no—
467C2×C22⋊C4—42no—
468C2×C22⋊C4—42no—
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⋊C4C22×D514yes—
482C2×C22⋊C4C22×D514yes—
483C2×C22⋊C4C22×D514yes—
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#95—54no—
496#95—54no—
497#95C22×D514yes—
498#95C22×D514yes—
499#95C22×D514yes—
500C22×C5—42no—
501C22×C5—42no—
502C22×C5—42no—
503C22×C5—42no—
504C22×C5—42no—
505C22×C5—42no—
506C22×C5—42no—
507C22×C5—88no—
508C22×C5#52514yes—
509C22×C5C2×#12614yes—
510C22×C5#53914yes—
511C22×C5#54614yes—
512C22×C5#54814yes—
513C22×C5#55214yes—
514C22×C5#55314yes—
515C22×C5C23×D411yescharacteristic
516C22×C5C22×#4111yescharacteristic
517C22×C5C22×#4111yescharacteristic
518C22×C5C22×#4111yescharacteristic
519C22×C5C22×#4111yescharacteristic
520C22×C5C2×H(5,𝔽2)11yescharacteristic
521C22×C5C2×2−1+411yescharacteristic
522C2×D5—24no—
523C2×D5—24no—
524C2×D5—24no—
525C2×D5—24no—
526C2×D5—24no—
527C2×D5—24no—
528C2×D5—232no—
529C2×D5C2×#12618yescomplemented
530C4×C5—24no—
531C4×C5—42no—
532C4×C5—42no—
533C4×C5—42no—
534C4×C5—42no—
535C4×C5—42no—
536Dic5—24no—
537Dic5—24no—
538Dic5—24no—
539Dic5—42no—
540Dic5—42no—
541Dic5—42no—
542Dic5—42no—
543C24—22no—
544C24—22no—
545C24—22no—
546C24—22no—
547C24—22no—
548C24—22no—
549C24—22no—
550C24—54no—
551C24—54no—
552C24—54no—
553C24—52no—
554C24—102no—
555C24—102no—
556C24—102no—
557C24—102no—
558C24C23×D512yes—
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—54no—
582C22×C4—54no—
583C22×C4—54no—
584C22×C4—52no—
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—108no—
595C22×C4—1032no—
596C22×C4—108no—
597C22×C4—108no—
598C22×C4—102no—
599C22×C4—102no—
600C22×C4—102no—
601C22×C4—102no—
602C22×C4—102no—
603C22×C4—102no—
604C22×C4—108no—
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—102no—
615C22×C4—102no—
616C22×C4—102no—
617C22×C4—204no—
618C22×C4—204no—
619C22×C4—2016no—
620C22×C4—2016no—
621C22×C4D4×D514yes—
622C22×C4C23×D512yes—
623C22×C4C23×D512yes—
624C22×C4C23×D512yes—
625C22×C4C23×D512yes—
626C22×C4C23×D512yes—
627C22×C4C23×D512yes—
628C4⋊C4—28no—
629C4⋊C4—516no—
630C4⋊C4—108no—
631C4⋊C4—108no—
632C4⋊C4—108no—
633C4⋊C4—108no—
634C4⋊C4—108no—
635C4⋊C4—204no—
636C22⋊C4—28no—
637C22⋊C4—44no—
638C22⋊C4—44no—
639C22⋊C4—108no—
640C22⋊C4—108no—
641C22⋊C4—108no—
642C22⋊C4—108no—
643C22⋊C4—108no—
644C22⋊C4—108no—
645C42—108no—
646C42—204no—
647C2×C5—82no—
648C2×C5#248118yescomplemented
649C2×C5C2×#52511yescharacteristic
650C2×C5C22×#12611yescharacteristic
651C2×C5C2×#53911yescharacteristic
652C2×C5C2×#54611yescharacteristic
653C2×C5C2×#54811yescharacteristic
654C2×C5C2×#55211yescharacteristic
655C2×C5C2×#55311yescharacteristic
656D5—28no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—22no—
664C23—44no—
665C23—44no—
666C23—44no—
667C23—44no—
668C23—44no—
669C23—44no—
670C23—44no—
671C23—54no—
672C23—54no—
673C23—54no—
674C23—516no—
675C23—108no—
676C23—108no—
677C23—108no—
678C23—108no—
679C23—108no—
680C23—102no—
681C23—102no—
682C23—102no—
683C23—102no—
684C23—108no—
685C23C2×D4×D512yes—
686C23#414412yes—
687C23D5×#4112yes—
688C23D5×#4112yes—
689C23D5×#4112yes—
690C23D5×#4112yes—
691C23#415012yes—
692C23C24×D511yescharacteristic
693D4—2016no—
694C2×C4—28no—
695C2×C4—22no—
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—44no—
713C2×C4—44no—
714C2×C4—44no—
715C2×C4—44no—
716C2×C4—44no—
717C2×C4—54no—
718C2×C4—54no—
719C2×C4—54no—
720C2×C4—1032no—
721C2×C4—108no—
722C2×C4—108no—
723C2×C4—108no—
724C2×C4—102no—
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—102no—
742C2×C4—2016no—
743C2×C4—2016no—
744C2×C4—204no—
745C2×C4—204no—
746C2×C4—204no—
747C2×C4—204no—
748C2×C4C2×D4×D514yes—
749C5C2×#248111yescharacteristic, complemented, Sylow
750C22—42no—
751C22—42no—
752C22—42no—
753C22—42no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—58no—
758C22—88no—
759C22—104no—
760C22—104no—
761C22—104no—
762C22—1032no—
763C22—104no—
764C22—104no—
765C22—104no—
766C22#6594614yes—
767C22#6599014yes—
768C22#6599414yes—
769C22#6599514yes—
770C22#6601114yes—
771C22D5×#12614yes—
772C22#6604214yes—
773C22C22×D4×D511yescharacteristic
774C22C2×#414411yescharacteristic
775C22C2×D5×#4111yescharacteristic
776C22C2×D5×#4111yescharacteristic
777C22C2×D5×#4111yescharacteristic
778C22C2×D5×#4111yescharacteristic
779C22C2×#415011yescharacteristic
780C4—24no—
781C4—42no—
782C4—42no—
783C4—42no—
784C4—42no—
785C4—42no—
786C4—104no—
787C4—104no—
788C4—104no—
789C4—202no—
790C4—202no—
791C4—202no—
792C4—202no—
793C2—82no—
794C2—108no—
795C2#1060921418yesdirect product factor
796C2C2×#6594611yescharacteristic
797C2C2×#6599011yescharacteristic
798C2C2×#6599511yescharacteristic
799C2C2×#6599411yescharacteristic
800C2C2×#6601111yescharacteristic
801C2C2×D5×#12611yescharacteristic
802C2C2×#6604211yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC2×C5×#397C2
socleC24×C5C24
prime radicalC23×C22⋊D5C22
hypercenterC2×#397D5
hypocenterC5C2×#2481
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#397

Complements

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

NH ≅ G/Ntype
1. C22×D5×C4⋊C4C2semidirect
2. C22×#4025C2semidirect
3. C2×C5×#397C2semidirect
4. C2×#65271C2semidirect
8. C2×#65237C2semidirect
9. C2×#65233C2semidirect
10. #10609214C2direct (N × H)
11. C2×#64957C2semidirect
12. C2×#64956C2semidirect
13. C2×#64947C2semidirect
14. C2×#64943C2semidirect
15. C2×#64943C2semidirect
16. C2×#64955C2semidirect
41. C2×D5×C4⋊C4C22semidirect
43. C2×#4025C22semidirect
44. C5×#397C22semidirect
57. #65271C22semidirect
61. #65237C22semidirect
62. #65233C22semidirect
63. #64957C22semidirect
64. #64956C22semidirect
65. #64955C22semidirect
66. #64947C22semidirect
67. #64943C22semidirect
68. #64943C22semidirect
122. C2×C4⋊Dic5D4semidirect
158. C2×#397D5semidirect
265. C4⋊Dic5C2×D4semidirect
302. #397C2×D5semidirect
357. C22×D5#126semidirect
529. C2×D5C2×#126semidirect
648. C2×C5#2481semidirect
749. C5C2×#2481semidirect
795. C2#10609214direct (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×#40252
C2×C5×#3972
C2×#652712
C2×#652452
C2×#652372
C2×#652332
#106092142
C2×#649572
C2×#649562
C2×#649472
C2×#649432
C2×#649552
C2×#24815