Finite Group Databasebeta

← C2×#10607758 #12267864

Subgroups — C2×#10607758 #12267864

Order 1280.

2898 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#4044C211yesmaximal, characteristic, complemented
2C22×#4018C211yesmaximal, characteristic, complemented
3C2×C5×#389C211yesmaximal, characteristic, complemented
4C2×#65281C211yesmaximal, characteristic, complemented
5C2×#65281C211yesmaximal, characteristic, complemented
6C2×#65280C211yesmaximal, characteristic
7C2×#65273C211yesmaximal, characteristic, complemented
8C2×#65277C211yesmaximal, characteristic
9C2×#65279C211yesmaximal, characteristic, complemented
10C2×#65267C211yesmaximal, characteristic, complemented
11C2×#65229C211yesmaximal, characteristic, complemented
12#10607758C2116yesmaximal, direct product factor
13C2×#64954C211yesmaximal, characteristic
14C2×#64957C211yesmaximal, characteristic, complemented
15C2×#64958C211yesmaximal, characteristic, complemented
16C2×#64938C211yesmaximal, characteristic, complemented
17C23×D20C2211yescharacteristic
18C23×C4×D5C2211yescharacteristic
19C22×C5×C4⋊C4C2211yescharacteristic
20C22×C5×C4⋊C4C2211yescharacteristic
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×#685C2211yescharacteristic
35C22×C4⋊Dic5C2211yescharacteristic
36C22×#683C2211yescharacteristic
37C22×#683C2211yescharacteristic
38C22×#683C2211yescharacteristic
39C22×#683C2211yescharacteristic
40C22×#683C2211yescharacteristic
41C22×C4×Dic5C2211yescharacteristic
42C22×C4×Dic5C2211yescharacteristic
43C22×C4×Dic5C2211yescharacteristic
44C2×#4044—28no—
45C2×#4044C2218yescomplemented
46C2×#4018—28no—
47C2×#4018C2218yescomplemented
48C5×#389C2218yescomplemented
49C2×C5×#95C2211yescharacteristic
50C2×C5×#95C2211yescharacteristic
51C2×#3963C2211yescharacteristic
52C2×#3963C2211yescharacteristic
53C2×#3963C2211yescharacteristic
54C2×#3963C2211yescharacteristic
55C2×#3963C2211yescharacteristic
56C2×#3963C2211yescharacteristic
57#65281C2218yescomplemented
58#65281C2218yescomplemented
59#65280C2218yes—
60#65279C2218yescomplemented
61#65277C2218yes—
62#65273C2218yescomplemented
63#65267C2218yescomplemented
64#65229C2218yescomplemented
65#64958C2218yescomplemented
66#64957C2218yescomplemented
67#64954C2218yes—
68#64938C2218yescomplemented
69C2×#2479—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×D5C2314yes—
93C2×C5×C4⋊C4—24no—
94C2×C5×C4⋊C4—24no—
95C2×C5×C4⋊C4—42no—
96C2×C5×C4⋊C4—42no—
97C2×C5×C4⋊C4C2314yes—
98C2×C5×C4⋊C4C2314yes—
99C2×C5×C4⋊C4C2314yes—
100C2×C5×C4⋊C4C2314yes—
101C2×C42×C5—24no—
102C2×C42×C5C2314yes—
103C2×#685—24no—
104C2×#685—24no—
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×#685C2314yes—
124C2×#685C2314yes—
125C2×C4⋊Dic5—24no—
126C2×C4⋊Dic5C2314yes—
127C2×#683—24no—
128C2×#683—24no—
129C2×#683—24no—
130C2×#683—42no—
131C2×#683D418yescomplemented
132C2×#683C2314yes—
133C2×#683C2314yes—
134C2×#683C2314yes—
135C2×#683C2314yes—
136C2×#683C2314yes—
137C2×C4×Dic5—24no—
138C2×C4×Dic5—24no—
139C2×C4×Dic5—24no—
140C2×C4×Dic5C2314yes—
141C2×C4×Dic5C2314yes—
142C2×C4×Dic5C2314yes—
143#4044—232no—
144#4018—232no—
145C5×#95C2314yes—
146C5×#95C2314yes—
147#3963C2314yes—
148#3963C2314yes—
149#3963C2314yes—
150#3963C2314yes—
151#3963C2314yes—
152#3963C2314yes—
153C22×#126—51no—
154C22×#117—51no—
155#2479—516no—
156C2×#399—51no—
157C2×#399—51no—
158C2×#398—51no—
159C2×#394—51no—
160C2×#390—51no—
161C2×#389D511yescharacteristic, complemented
162C2×#388—51no—
163C2×#388—51no—
164C2×#388—51no—
165C2×#387—51no—
166C2×#386—51no—
167C2×#385—51no—
168C2×C4×C4⋊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—22no—
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×C5#4114yes—
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×Dic5C2×D414yes—
230C22×Dic5C2×D414yes—
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—
246C5×C4⋊C4—28no—
247C5×C4⋊C4—28no—
248C5×C4⋊C4—44no—
249C5×C4⋊C4—44no—
250C42×C5—28no—
251#685—28no—
252#685—28no—
253#685—28no—
254#685—28no—
255#685—28no—
256#685—28no—
257#685—28no—
258#685—28no—
259#685—28no—
260#685—44no—
261#685—44no—
262C4⋊Dic5—28no—
263#683—28no—
264#683—28no—
265#683—28no—
266#683—44no—
267#683C2×D4116yescomplemented
268C4×Dic5—28no—
269C4×Dic5—28no—
270C4×Dic5—28no—
271C23×D4—51no—
272C24×C4—51no—
273C2×#126—58no—
274C2×#126—108no—
275C2×#117—58no—
276C2×#117—108no—
277C22×C4⋊C4—51no—
278C22×C4⋊C4—51no—
279C22×C4⋊C4—51no—
280C22×C4⋊C4—51no—
281C22×C4⋊C4—51no—
282C22×C4⋊C4—51no—
283C22×C4⋊C4C2×D511yescharacteristic
284C22×C4⋊C4C2×D511yescharacteristic
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×C22⋊C4—51no—
298C22×C42—51no—
299C22×C42—51no—
300C22×C42—51no—
301C22×C42C2×D511yescharacteristic
302#399—58no—
303#399—58no—
304#398—58no—
305#394—58no—
306#390—58no—
307#389C2×D518yescomplemented
308#388—58no—
309#388—58no—
310#388—58no—
311#387—58no—
312#386—58no—
313#385—58no—
314C4×C4⋊C4—58no—
315C2×#95—51no—
316C2×#95—51no—
317C2×#95—51no—
318C2×#95—51no—
319C2×#95—51no—
320C2×#95—51no—
321C2×#95C2×D511yescharacteristic
322C2×#95C2×D511yescharacteristic
323C23×C5C22×D412yes—
324C23×C5C2×#4112yes—
325C23×C5C2×#4112yes—
326C23×C5C2×#4112yes—
327C23×C5C2×#4112yes—
328C23×C5H(5,𝔽2)12yes—
329C23×C52−1+412yes—
330C23×C5C2511yescharacteristic
331C22×D5—28no—
332C22×D5—28no—
333C22×D5—28no—
334C22×D5—22no—
335C22×D5—22no—
336C22×D5—22no—
337C22×D5—22no—
338C22×D5—22no—
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—44no—
348C22×D5—44no—
349C22×D5—44no—
350C22×D5—44no—
351C22×D5—44no—
352C22×D5—44no—
353C22×D5—44no—
354C22×D5—44no—
355C22×D5—44no—
356C22×D5—44no—
357C22×D5—44no—
358C22×D5C2×#4114yes—
359C2×C4×C5—28no—
360C2×C4×C5—28no—
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—22no—
380C2×C4×C5—44no—
381C2×C4×C5—44no—
382C2×C4×C5—44no—
383C2×C4×C5—44no—
384C2×C4×C5C22×D414yes—
385C2×C4×C5C2×#4114yes—
386C2×C4×C5C2×#4114yes—
387C2×Dic5—28no—
388C2×Dic5—28no—
389C2×Dic5—28no—
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—44no—
406C2×Dic5—44no—
407C2×Dic5—44no—
408C2×Dic5C22×D414yes—
409C2×Dic5C22×D414yes—
410C2×Dic5C2×#4114yes—
411D20—416no—
412C4×D5—232no—
413C25—51no—
414C25—51no—
415C22×D4—54no—
416C22×D4—104no—
417C22×D4—104no—
418C22×D4—202no—
419C23×C4—51no—
420C23×C4—51no—
421C23×C4—51no—
422C23×C4—51no—
423C23×C4—51no—
424C23×C4—51no—
425C23×C4—54no—
426C23×C4—104no—
427C23×C4—104no—
428C23×C4—104no—
429C23×C4C22×D511yescharacteristic
430C23×C4C22×D511yescharacteristic
431C23×C4C22×D511yescharacteristic
432C23×C4C22×D511yescharacteristic
433C23×C4C22×D511yescharacteristic
434C23×C4C22×D511yescharacteristic
435C23×C4C22×D511yescharacteristic
436#126—1032no—
437#117—1032no—
438C2×C4⋊C4—24no—
439C2×C4⋊C4—24no—
440C2×C4⋊C4—42no—
441C2×C4⋊C4—42no—
442C2×C4⋊C4—58no—
443C2×C4⋊C4—54no—
444C2×C4⋊C4—54no—
445C2×C4⋊C4—54no—
446C2×C4⋊C4—54no—
447C2×C4⋊C4—54no—
448C2×C4⋊C4—54no—
449C2×C4⋊C4—104no—
450C2×C4⋊C4—104no—
451C2×C4⋊C4—104no—
452C2×C4⋊C4—104no—
453C2×C4⋊C4—202no—
454C2×C4⋊C4C22×D514yes—
455C2×C4⋊C4C22×D514yes—
456C2×C4⋊C4C22×D514yes—
457C2×C4⋊C4C22×D514yes—
458C2×C22⋊C4—54no—
459C2×C22⋊C4—54no—
460C2×C22⋊C4—54no—
461C2×C22⋊C4—54no—
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—104no—
470C2×C22⋊C4—104no—
471C2×C22⋊C4—104no—
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—202no—
479C2×C22⋊C4—202no—
480C2×C42—24no—
481C2×C42—54no—
482C2×C42—54no—
483C2×C42—54no—
484C2×C42—104no—
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#95C22×D514yes—
495#95C22×D514yes—
496C22×C5#52514yes—
497C22×C5#52914yes—
498C22×C5#54214yes—
499C22×C5#54714yes—
500C22×C5#55014yes—
501C22×C5#55114yes—
502C22×C5#55214yes—
503C22×C5C23×D411yescharacteristic
504C22×C5C22×#4111yescharacteristic
505C22×C5C22×#4111yescharacteristic
506C22×C5C22×#4111yescharacteristic
507C22×C5C22×#4111yescharacteristic
508C22×C5C2×H(5,𝔽2)11yescharacteristic
509C22×C5C2×2−1+411yescharacteristic
510C2×D5—24no—
511C2×D5—24no—
512C2×D5—24no—
513C2×D5—42no—
514C2×D5—42no—
515C2×D5—42no—
516C2×D5—42no—
517C2×D5—416no—
518C2×D5—42no—
519C2×D5—42no—
520C2×D5—42no—
521C2×D5—42no—
522C2×D5—42no—
523C2×D5—42no—
524C2×D5—42no—
525C2×D5—88no—
526C4×C5—24no—
527C4×C5—24no—
528C4×C5—24no—
529C4×C5—42no—
530C4×C5—42no—
531C4×C5—42no—
532C4×C5—42no—
533Dic5—24no—
534Dic5—24no—
535Dic5—24no—
536Dic5—42no—
537Dic5—42no—
538Dic5—42no—
539C24—54no—
540C24—52no—
541C24—52no—
542C24—102no—
543C24—102no—
544C24—102no—
545C24—102no—
546C24—102no—
547C24—102no—
548C24—102no—
549C24—102no—
550C24—102no—
551C24—102no—
552C24—102no—
553C24—102no—
554C24—102no—
555C24C23×D511yescharacteristic
556C2×D4—108no—
557C2×D4—108no—
558C2×D4—204no—
559C2×D4—2016no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
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—54no—
579C22×C4—54no—
580C22×C4—54no—
581C22×C4—52no—
582C22×C4—52no—
583C22×C4—52no—
584C22×C4—52no—
585C22×C4—52no—
586C22×C4—52no—
587C22×C4—108no—
588C22×C4—108no—
589C22×C4—1032no—
590C22×C4—102no—
591C22×C4—102no—
592C22×C4—102no—
593C22×C4—102no—
594C22×C4—102no—
595C22×C4—102no—
596C22×C4—108no—
597C22×C4—102no—
598C22×C4—102no—
599C22×C4—102no—
600C22×C4—102no—
601C22×C4—102no—
602C22×C4—102no—
603C22×C4—102no—
604C22×C4—102no—
605C22×C4—102no—
606C22×C4#70914yes—
607C22×C4D4×D514yes—
608C22×C4#71314yes—
609C22×C4C23×D512yes—
610C22×C4C23×D512yes—
611C22×C4C23×D512yes—
612C22×C4C23×D512yes—
613C22×C4C23×D512yes—
614C22×C4C23×D512yes—
615C22×C4C23×D512yes—
616C4⋊C4—28no—
617C4⋊C4—28no—
618C4⋊C4—44no—
619C4⋊C4—44no—
620C4⋊C4—516no—
621C4⋊C4—108no—
622C4⋊C4—108no—
623C4⋊C4—108no—
624C4⋊C4—108no—
625C4⋊C4—204no—
626C22⋊C4—108no—
627C22⋊C4—108no—
628C22⋊C4—108no—
629C22⋊C4—108no—
630C22⋊C4—108no—
631C22⋊C4—108no—
632C22⋊C4—108no—
633C22⋊C4—108no—
634C22⋊C4—108no—
635C22⋊C4—204no—
636C22⋊C4—204no—
637C42—28no—
638C42—108no—
639C42—108no—
640C42—108no—
641C2×C5#247918yescomplemented
642C2×C5C2×#52511yescharacteristic
643C2×C5C2×#52911yescharacteristic
644C2×C5C2×#54211yescharacteristic
645C2×C5C2×#54711yescharacteristic
646C2×C5C2×#55011yescharacteristic
647C2×C5C2×#55111yescharacteristic
648C2×C5C2×#55211yescharacteristic
649D5—44no—
650D5—82no—
651C23—54no—
652C23—108no—
653C23—108no—
654C23—102no—
655C23—102no—
656C23—102no—
657C23—102no—
658C23—102no—
659C23—102no—
660C23—108no—
661C23—102no—
662C23—102no—
663C23—102no—
664C23—102no—
665C23—102no—
666C23—102no—
667C23—102no—
668C23—204no—
669C23—204no—
670C23—204no—
671C23—204no—
672C23—204no—
673C23—204no—
674C23—204no—
675C23—204no—
676C23—204no—
677C23—204no—
678C23—204no—
679C23C2×#70912yes—
680C23C2×D4×D512yes—
681C23#414412yes—
682C23C2×#71312yes—
683C23#414712yes—
684C23D5×#4112yes—
685C23D5×#4112yes—
686C23C24×D511yescharacteristic
687D4—2016no—
688C2×C4—28no—
689C2×C4—28no—
690C2×C4—28no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
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—44no—
710C2×C4—44no—
711C2×C4—44no—
712C2×C4—44no—
713C2×C4—54no—
714C2×C4—54no—
715C2×C4—54no—
716C2×C4—1032no—
717C2×C4—108no—
718C2×C4—108no—
719C2×C4—108no—
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—102no—
730C2×C4—102no—
731C2×C4—102no—
732C2×C4—102no—
733C2×C4—102no—
734C2×C4—102no—
735C2×C4—204no—
736C2×C4—204no—
737C2×C4—204no—
738C2×C4C2×#70914yes—
739C2×C4C2×D4×D514yes—
740C2×C4C2×#71314yes—
741C5C2×#247911yescharacteristic, complemented, Sylow
742C22—104no—
743C22—104no—
744C22—104no—
745C22—202no—
746C22—202no—
747C22—2016no—
748C22—202no—
749C22—202no—
750C22—202no—
751C22—202no—
752C22—202no—
753C22—202no—
754C22—202no—
755C22—202no—
756C22—202no—
757C22—408no—
758C22#6584114yes—
759C22#6589014yes—
760C22#6591414yes—
761C22#6593314yes—
762C22#6596114yes—
763C22#6602714yes—
764C22#6606714yes—
765C22C22×#70911yescharacteristic
766C22C22×D4×D511yescharacteristic
767C22C2×#414411yescharacteristic
768C22C22×#71311yescharacteristic
769C22C2×#414711yescharacteristic
770C22C2×D5×#4111yescharacteristic
771C22C2×D5×#4111yescharacteristic
772C4—24no—
773C4—24no—
774C4—24no—
775C4—42no—
776C4—42no—
777C4—42no—
778C4—42no—
779C4—104no—
780C4—104no—
781C4—104no—
782C4—202no—
783C4—202no—
784C4—202no—
785C2—204no—
786C2—402no—
787C2#1060775818yesdirect product factor
788C2C2×#6584111yescharacteristic
789C2C2×#6589011yescharacteristic
790C2C2×#6591411yescharacteristic
791C2C2×#6593311yescharacteristic
792C2C2×#6596111yescharacteristic
793C2C2×#6602711yescharacteristic
794C2C2×#6606711yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC2×C5×#389C2
socleC24×C5C24
prime radicalC23×D20C22
hypercenterC2×#389D5
hypocenterC5C2×#2479
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
1. C22×#4044C2semidirect
2. C22×#4018C2semidirect
3. C2×C5×#389C2semidirect
4. C2×#65281C2semidirect
5. C2×#65281C2semidirect
7. C2×#65273C2semidirect
9. C2×#65279C2semidirect
10. C2×#65267C2semidirect
11. C2×#65229C2semidirect
12. #10607758C2direct (N × H)
14. C2×#64957C2semidirect
15. C2×#64958C2semidirect
16. C2×#64938C2semidirect
45. C2×#4044C22semidirect
47. C2×#4018C22semidirect
48. C5×#389C22semidirect
57. #65281C22semidirect
58. #65281C22semidirect
60. #65279C22semidirect
62. #65273C22semidirect
63. #65267C22semidirect
64. #65229C22semidirect
65. #64958C22semidirect
66. #64957C22semidirect
68. #64938C22semidirect
131. C2×#683D4semidirect
161. C2×#389D5semidirect
267. #683C2×D4semidirect
307. #389C2×D5semidirect
641. C2×C5#2479semidirect
741. C5C2×#2479semidirect
787. C2#10607758direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#40442
C22×#40182
C2×C5×#3892
C2×#652812
C2×#652802
C2×#652732
C2×#652772
C2×#652792
C2×#652672
C2×#652292
#106077582
C2×#649542
C2×#649572
C2×#649582
C2×#649382
C2×#24795