Finite Group Databasebeta

← C2×#10607065 #12267735

Subgroups — C2×#10607065 #12267735

Order 1280.

3070 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×#4042C211yesmaximal, characteristic, complemented
2C22×#4038C211yesmaximal, characteristic, complemented
3C2×C5×#387C211yesmaximal, characteristic, complemented
4C2×#65280C211yesmaximal, characteristic
5C2×#65263C211yesmaximal, characteristic, complemented
6C2×#65229C211yesmaximal, characteristic, complemented
7C2×C4×#685C211yesmaximal, characteristic, complemented
8#10607065C2116yesmaximal, direct product factor
9C2×#64962C211yesmaximal, characteristic, complemented
10C2×#64954C211yesmaximal, characteristic
11C2×#64954C211yesmaximal, characteristic
12C2×#64957C211yesmaximal, characteristic, complemented
13C2×#64948C211yesmaximal, characteristic, complemented
14C2×#64963C211yesmaximal, characteristic, complemented
15C2×#64959C211yesmaximal, characteristic, complemented
16C2×#64942C211yesmaximal, characteristic, complemented
17C23×D20C2211yescharacteristic
18C23×C4×D5C2211yescharacteristic
19C23×C4×D5C2211yescharacteristic
20C23×Dic10C2211yescharacteristic
21C22×C5×C4⋊C4C2211yescharacteristic
22C22×C5×C4⋊C4C2211yescharacteristic
23C22×C42×C5C2211yescharacteristic
24C22×#685C2211yescharacteristic
25C22×#685C2211yescharacteristic
26C22×#685C2211yescharacteristic
27C22×#685C2211yescharacteristic
28C22×#685C2211yescharacteristic
29C22×#685C2211yescharacteristic
30C22×#685C2211yescharacteristic
31C22×#685C2211yescharacteristic
32C22×#685C2211yescharacteristic
33C22×#685C2211yescharacteristic
34C22×C4⋊Dic5C2211yescharacteristic
35C22×C4⋊Dic5C2211yescharacteristic
36C22×#683C2211yescharacteristic
37C22×#683C2211yescharacteristic
38C22×C4×Dic5C2211yescharacteristic
39C22×C4×Dic5C2211yescharacteristic
40C2×#4042—28no—
41C2×#4042C2218yescomplemented
42C2×#4038—28no—
43C2×#4038C2218yescomplemented
44C5×#387C2218yescomplemented
45C2×C5×#95C2211yescharacteristic
46C2×C5×#95C2211yescharacteristic
47C2×C5×#95C2211yescharacteristic
48C2×C5×#95C2211yescharacteristic
49C2×#3963C2211yescharacteristic
50C2×#3963C2211yescharacteristic
51C2×#3963C2211yescharacteristic
52C2×#3963C2211yescharacteristic
53C2×#3963C2211yescharacteristic
54C2×#3963C2211yescharacteristic
55C2×#3963C2211yescharacteristic
56C2×#3963C2211yescharacteristic
57#65280C2218yes—
58#65263C2218yescomplemented
59#65229C2218yescomplemented
60C4×#685C2218yescomplemented
61#64963C2218yescomplemented
62#64962C2218yescomplemented
63#64959C2218yescomplemented
64#64957C2218yescomplemented
65#64954C2218yes—
66#64954C2218yes—
67#64948C2218yescomplemented
68#64942C2218yescomplemented
69C2×#2477—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—42no—
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—42no—
95C22×C4×D5C2314yes—
96C22×C4×D5C2314yes—
97C22×Dic10—24no—
98C22×Dic10—24no—
99C22×Dic10—42no—
100C22×Dic10C2314yes—
101C2×C5×C4⋊C4—42no—
102C2×C5×C4⋊C4D418yescomplemented
103C2×C5×C4⋊C4C2314yes—
104C2×C5×C4⋊C4C2314yes—
105C2×C42×C5—42no—
106C2×C42×C5C2314yes—
107C2×#685—24no—
108C2×#685—24no—
109C2×#685—24no—
110C2×#685—24no—
111C2×#685—24no—
112C2×#685—24no—
113C2×#685—24no—
114C2×#685—24no—
115C2×#685—24no—
116C2×#685—42no—
117C2×#685C2314yes—
118C2×#685C2314yes—
119C2×#685C2314yes—
120C2×#685C2314yes—
121C2×#685C2314yes—
122C2×#685C2314yes—
123C2×#685C2314yes—
124C2×#685C2314yes—
125C2×#685C2314yes—
126C2×#685C2314yes—
127C2×C4⋊Dic5—24no—
128C2×C4⋊Dic5—24no—
129C2×C4⋊Dic5C2314yes—
130C2×C4⋊Dic5C2314yes—
131C2×#683—24no—
132C2×#683—24no—
133C2×#683C2314yes—
134C2×#683C2314yes—
135C2×C4×Dic5—24no—
136C2×C4×Dic5—24no—
137C2×C4×Dic5C2314yes—
138C2×C4×Dic5C2314yes—
139#4042—232no—
140#4038—232no—
141C5×#95C2314yes—
142C5×#95C2314yes—
143C5×#95C2314yes—
144C5×#95C2314yes—
145#3963C2314yes—
146#3963C2314yes—
147#3963C2314yes—
148#3963C2314yes—
149#3963C2314yes—
150#3963C2314yes—
151#3963C2314yes—
152#3963C2314yes—
153C22×C22⋊Q8—51no—
154C22×#117—51no—
155#2477—516no—
156C2×#400—51no—
157C2×#397—51no—
158C2×#394—51no—
159C2×#393—51no—
160C2×#391—51no—
161C2×#388—51no—
162C2×#388—51no—
163C2×#387—51no—
164C2×#387D511yescharacteristic, complemented
165C2×#386—51no—
166C2×#386—51no—
167C2×#385—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—22no—
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×C5C2×D414yes—
205C22×C4×C5C2×D414yes—
206C22×C4×C5C2×D414yes—
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×Dic5#4114yes—
231C22×Dic5#4114yes—
232C22×Dic5C2412yes—
233C22×Dic5C2412yes—
234C22×Dic5C2412yes—
235C22×Dic5C2412yes—
236C22×Dic5C2412yes—
237C22×Dic5C2412yes—
238C2×D20—28no—
239C2×D20—28no—
240C2×D20—44no—
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—44no—
249C2×C4×D5—416no—
250C2×Dic10—28no—
251C2×Dic10—28no—
252C2×Dic10—44no—
253C2×Dic10—416no—
254C5×C4⋊C4—44no—
255C5×C4⋊C4C2×D4116yescomplemented
256C42×C5—44no—
257#685—28no—
258#685—28no—
259#685—28no—
260#685—28no—
261#685—28no—
262#685—28no—
263#685—28no—
264#685—28no—
265#685—28no—
266#685—44no—
267C4⋊Dic5—28no—
268C4⋊Dic5—28no—
269#683—28no—
270#683—28no—
271C4×Dic5—28no—
272C4×Dic5—28no—
273C23×Q8—51no—
274C23×D4—51no—
275C24×C4—51no—
276C24×C4—51no—
277C2×C22⋊Q8—58no—
278C2×C22⋊Q8—108no—
279C2×#117—58no—
280C2×#117—108no—
281C22×C4⋊C4—51no—
282C22×C4⋊C4—51no—
283C22×C4⋊C4—51no—
284C22×C4⋊C4—51no—
285C22×C4⋊C4C2×D511yescharacteristic
286C22×C4⋊C4C2×D511yescharacteristic
287C22×C22⋊C4—51no—
288C22×C22⋊C4—51no—
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×C42—51no—
298C22×C42—51no—
299C22×C42C2×D511yescharacteristic
300#400—58no—
301#397—58no—
302#394—58no—
303#393—58no—
304#391—58no—
305#388—58no—
306#388—58no—
307#387—58no—
308#387C2×D518yescomplemented
309#386—58no—
310#386—58no—
311#385—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×#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—22no—
351C22×D5—44no—
352C22×D5—44no—
353C22×D5—44no—
354C22×D5—44no—
355C22×D5—44no—
356C22×D5—44no—
357C22×D5—44no—
358C22×D5—44no—
359C22×D5C2×#4114yes—
360C22×D5C2×#4114yes—
361C2×C4×C5—28no—
362C2×C4×C5—28no—
363C2×C4×C5—28no—
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×C5C22×D414yes—
387C2×C4×C5C22×D414yes—
388C2×C4×C5C22×D414yes—
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×Dic5C2×#4114yes—
412C2×Dic5C2×#4114yes—
413D20—416no—
414C4×D5—232no—
415C4×D5—416no—
416Dic10—416no—
417C25—51no—
418C25—51no—
419C22×Q8—54no—
420C22×Q8—104no—
421C22×Q8—104no—
422C22×Q8—202no—
423C22×D4—54no—
424C22×D4—104no—
425C22×D4—104no—
426C22×D4—202no—
427C23×C4—51no—
428C23×C4—51no—
429C23×C4—51no—
430C23×C4—51no—
431C23×C4—51no—
432C23×C4—51no—
433C23×C4—54no—
434C23×C4—54no—
435C23×C4—104no—
436C23×C4—104no—
437C23×C4—104no—
438C23×C4—104no—
439C23×C4—104no—
440C23×C4—202no—
441C23×C4C22×D511yescharacteristic
442C23×C4C22×D511yescharacteristic
443C23×C4C22×D511yescharacteristic
444C23×C4C22×D511yescharacteristic
445C23×C4C22×D511yescharacteristic
446C23×C4C22×D511yescharacteristic
447C23×C4C22×D511yescharacteristic
448C22⋊Q8—1032no—
449#117—1032no—
450C2×C4⋊C4—42no—
451C2×C4⋊C4—54no—
452C2×C4⋊C4—54no—
453C2×C4⋊C4—54no—
454C2×C4⋊C4—54no—
455C2×C4⋊C4—104no—
456C2×C4⋊C4—104no—
457C2×C4⋊C4—104no—
458C2×C4⋊C4—104no—
459C2×C4⋊C4D2018yescomplemented
460C2×C4⋊C4C22×D514yes—
461C2×C4⋊C4C22×D514yes—
462C2×C22⋊C4—54no—
463C2×C22⋊C4—54no—
464C2×C22⋊C4—54no—
465C2×C22⋊C4—54no—
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—104no—
473C2×C22⋊C4—104no—
474C2×C22⋊C4—104no—
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—202no—
482C2×C42—42no—
483C2×C42—54no—
484C2×C42—54no—
485C2×C42—104no—
486C2×C42—104no—
487C2×C42C22×D514yes—
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#95C22×D514yes—
497#95C22×D514yes—
498#95C22×D514yes—
499#95C22×D514yes—
500C22×C5#52514yes—
501C22×C5#52914yes—
502C22×C5#54214yes—
503C22×C5#54614yes—
504C22×C5#54814yes—
505C22×C5#55114yes—
506C22×C5#55214yes—
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—42no—
521C2×D5—42no—
522C2×D5—42no—
523C2×D5—42no—
524C2×D5—42no—
525C2×D5—42no—
526C2×D5—42no—
527C2×D5—42no—
528C2×D5—416no—
529C2×D5—416no—
530C4×C5—24no—
531C4×C5—24no—
532C4×C5—24no—
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—52no—
546C24—52no—
547C24—102no—
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×Q8—108no—
561C2×Q8—108no—
562C2×Q8—204no—
563C2×Q8—2016no—
564C2×D4—108no—
565C2×D4—108no—
566C2×D4—204no—
567C2×D4—2016no—
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—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—54no—
587C22×C4—54no—
588C22×C4—52no—
589C22×C4—52no—
590C22×C4—52no—
591C22×C4—52no—
592C22×C4—52no—
593C22×C4—52no—
594C22×C4—108no—
595C22×C4—108no—
596C22×C4—108no—
597C22×C4—1032no—
598C22×C4—102no—
599C22×C4—102no—
600C22×C4—102no—
601C22×C4—102no—
602C22×C4—108no—
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—102no—
615C22×C4—108no—
616C22×C4—204no—
617C22×C4—2016no—
618C22×C4C2×D2014yes—
619C22×C4C2×D2014yes—
620C22×C4C2×D2014yes—
621C22×C4C23×D512yes—
622C22×C4C23×D512yes—
623C22×C4C23×D512yes—
624C22×C4C23×D512yes—
625C22×C4C23×D512yes—
626C22×C4C23×D512yes—
627C22×C4C23×D512yes—
628C4⋊C4—44no—
629C4⋊C4—108no—
630C4⋊C4—108no—
631C4⋊C4—108no—
632C4⋊C4—108no—
633C4⋊C4C2×D20116yescomplemented
634C22⋊C4—108no—
635C22⋊C4—108no—
636C22⋊C4—108no—
637C22⋊C4—108no—
638C22⋊C4—108no—
639C22⋊C4—108no—
640C22⋊C4—108no—
641C22⋊C4—108no—
642C22⋊C4—108no—
643C22⋊C4—204no—
644C42—44no—
645C42—108no—
646C42—108no—
647C2×C5#247718yescomplemented
648C2×C5C2×#52511yescharacteristic
649C2×C5C2×#52911yescharacteristic
650C2×C5C2×#54211yescharacteristic
651C2×C5C2×#54611yescharacteristic
652C2×C5C2×#54811yescharacteristic
653C2×C5C2×#55111yescharacteristic
654C2×C5C2×#55211yescharacteristic
655D5—44no—
656D5—44no—
657C23—54no—
658C23—54no—
659C23—108no—
660C23—108no—
661C23—108no—
662C23—108no—
663C23—102no—
664C23—102no—
665C23—102no—
666C23—102no—
667C23—102no—
668C23—102no—
669C23—102no—
670C23—102no—
671C23—102no—
672C23—102no—
673C23—102no—
674C23—102no—
675C23—108no—
676C23—108no—
677C23—204no—
678C23—204no—
679C23—204no—
680C23—204no—
681C23—204no—
682C23—204no—
683C23—204no—
684C23—204no—
685C23C22×D2012yes—
686C23#414412yes—
687C23#414712yes—
688C23D5×#4112yes—
689C23D5×#4112yes—
690C23D5×#4112yes—
691C23D5×#4112yes—
692C23C24×D511yescharacteristic
693Q8—2016no—
694D4—2016no—
695C2×C4—28no—
696C2×C4—28no—
697C2×C4—28no—
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—22no—
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—204no—
743C2×C4—204no—
744C2×C4—204no—
745C2×C4—204no—
746C2×C4C22×D2014yes—
747C2×C4C22×D2014yes—
748C2×C4C22×D2014yes—
749C5C2×#247711yescharacteristic, complemented, Sylow
750C22—104no—
751C22—104no—
752C22—104no—
753C22—104no—
754C22—104no—
755C22—104no—
756C22—202no—
757C22—202no—
758C22—202no—
759C22—202no—
760C22—202no—
761C22—202no—
762C22—202no—
763C22—202no—
764C22—2016no—
765C22—2016no—
766C22#6585814yes—
767C22#6588814yes—
768C22#6591014yes—
769C22#6597414yes—
770C22#6599314yes—
771C22#6602714yes—
772C22#6604014yes—
773C22C23×D2011yescharacteristic
774C22C2×#414411yescharacteristic
775C22C2×#414711yescharacteristic
776C22C2×D5×#4111yescharacteristic
777C22C2×D5×#4111yescharacteristic
778C22C2×D5×#4111yescharacteristic
779C22C2×D5×#4111yescharacteristic
780C4—24no—
781C4—24no—
782C4—24no—
783C4—42no—
784C4—42no—
785C4—42no—
786C4—42no—
787C4—104no—
788C4—104no—
789C4—202no—
790C4—202no—
791C4—202no—
792C4—202no—
793C2—204no—
794C2—204no—
795C2#1060706518yesdirect product factor
796C2C2×#6585811yescharacteristic
797C2C2×#6588811yescharacteristic
798C2C2×#6591011yescharacteristic
799C2C2×#6597411yescharacteristic
800C2C2×#6599311yescharacteristic
801C2C2×#6602711yescharacteristic
802C2C2×#6604011yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC2×C5×#387C2
socleC24×C5C24
prime radicalC23×D20C22
hypercenterC2×#387D5
hypocenterC5C2×#2477
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
1. C22×#4042C2semidirect
2. C22×#4038C2semidirect
3. C2×C5×#387C2semidirect
5. C2×#65263C2semidirect
6. C2×#65229C2semidirect
7. C2×C4×#685C2semidirect
8. #10607065C2direct (N × H)
9. C2×#64962C2semidirect
12. C2×#64957C2semidirect
13. C2×#64948C2semidirect
14. C2×#64963C2semidirect
15. C2×#64959C2semidirect
16. C2×#64942C2semidirect
41. C2×#4042C22semidirect
43. C2×#4038C22semidirect
44. C5×#387C22semidirect
58. #65263C22semidirect
59. #65229C22semidirect
60. C4×#685C22semidirect
61. #64963C22semidirect
62. #64962C22semidirect
63. #64959C22semidirect
64. #64957C22semidirect
67. #64948C22semidirect
68. #64942C22semidirect
102. C2×C5×C4⋊C4D4semidirect
164. C2×#387D5semidirect
255. C5×C4⋊C4C2×D4semidirect
308. #387C2×D5semidirect
459. C2×C4⋊C4D20semidirect
633. C4⋊C4C2×D20semidirect
647. C2×C5#2477semidirect
749. C5C2×#2477semidirect
795. C2#10607065direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#40422
C22×#40382
C2×C5×#3872
C2×#652802
C2×#652632
C2×#652292
C2×C4×#6852
#106070652
C2×#649622
C2×#649542
C2×#649572
C2×#649482
C2×#649632
C2×#649592
C2×#649422
C2×#24775