Finite Group Databasebeta

← C2×#10609522 #12269458

Subgroups — C2×#10609522 #12269458

Order 1280.

2898 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#4043C211yesmaximal, characteristic, complemented
2C22×#4044C211yesmaximal, characteristic, complemented
3C2×C5×#398C211yesmaximal, characteristic, complemented
4C2×#65280C211yesmaximal, characteristic
5C2×#65277C211yesmaximal, characteristic
6C2×#65279C211yesmaximal, characteristic, complemented
7C2×#65279C211yesmaximal, characteristic, complemented
8C2×#65270C211yesmaximal, characteristic, complemented
9C2×C4⋊C4×Dic5C211yesmaximal, characteristic, complemented
10#10609522C2116yesmaximal, direct product factor
11C2×#64964C211yesmaximal, characteristic, complemented
12C2×#64962C211yesmaximal, characteristic, complemented
13C2×#64954C211yesmaximal, characteristic
14C2×#64935C211yesmaximal, characteristic, complemented
15C2×#64959C211yesmaximal, characteristic, complemented
16C2×#64955C211yesmaximal, characteristic, complemented
17C23×D20C2211yescharacteristic
18C23×C4×D5C2211yescharacteristic
19C23×Dic10C2211yescharacteristic
20C22×C5×C4⋊C4C2211yescharacteristic
21C22×C5×C4⋊C4C2211yescharacteristic
22C22×C5×C4⋊C4C2211yescharacteristic
23C22×C5×C4⋊C4C2211yescharacteristic
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×C4⋊Dic5C2211yescharacteristic
37C22×#683C2211yescharacteristic
38C22×C4×Dic5C2211yescharacteristic
39C22×C4×Dic5C2211yescharacteristic
40C22×C4×Dic5C2211yescharacteristic
41C22×C4×Dic5C2211yescharacteristic
42C2×#4044—28no—
43C2×#4044C2218yescomplemented
44C2×#4043—28no—
45C2×#4043C2218yescomplemented
46C5×#398C2218yescomplemented
47C2×C5×#95C2211yescharacteristic
48C2×C5×#95C2211yescharacteristic
49C2×C5×#95C2211yescharacteristic
50C2×#3963C2211yescharacteristic
51C2×#3963C2211yescharacteristic
52C2×#3963C2211yescharacteristic
53C2×#3963C2211yescharacteristic
54C2×#3963C2211yescharacteristic
55C2×#3963C2211yescharacteristic
56C2×#3963C2211yescharacteristic
57#65280C2218yes—
58#65279C2218yescomplemented
59#65279C2218yescomplemented
60#65277C2218yes—
61#65270C2218yescomplemented
62C4⋊C4×Dic5C2218yescomplemented
63#64964C2218yescomplemented
64#64962C2218yescomplemented
65#64959C2218yescomplemented
66#64955C2218yescomplemented
67#64954C2218yes—
68#64935C2218yescomplemented
69C2×#2560—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—42no—
92C22×C4×D5C2314yes—
93C22×Dic10—24no—
94C22×Dic10—24no—
95C22×Dic10—42no—
96C22×Dic10C2314yes—
97C2×C5×C4⋊C4—24no—
98C2×C5×C4⋊C4—24no—
99C2×C5×C4⋊C4—24no—
100C2×C5×C4⋊C4—24no—
101C2×C5×C4⋊C4C2314yes—
102C2×C5×C4⋊C4C2314yes—
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—24no—
113C2×#685—24no—
114C2×#685—24no—
115C2×#685—42no—
116C2×#685C2314yes—
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⋊Dic5D418yescomplemented
129C2×C4⋊Dic5C2314yes—
130C2×C4⋊Dic5C2314yes—
131C2×#683—24no—
132C2×#683C2314yes—
133C2×C4×Dic5—24no—
134C2×C4×Dic5—24no—
135C2×C4×Dic5—42no—
136C2×C4×Dic5—42no—
137C2×C4×Dic5C2314yes—
138C2×C4×Dic5C2314yes—
139C2×C4×Dic5C2314yes—
140C2×C4×Dic5C2314yes—
141#4044—232no—
142#4043—232no—
143C5×#95C2314yes—
144C5×#95C2314yes—
145C5×#95C2314yes—
146#3963C2314yes—
147#3963C2314yes—
148#3963C2314yes—
149#3963C2314yes—
150#3963C2314yes—
151#3963C2314yes—
152#3963C2314yes—
153C22×#126—51no—
154C22×C22⋊Q8—51no—
155#2560—516no—
156C2×#398D511yescharacteristic, complemented
157C2×#397—51no—
158C2×#394—51no—
159C2×#393—51no—
160C2×#391—51no—
161C2×#390—51no—
162C2×#388—51no—
163C2×#388—51no—
164C2×#388—51no—
165C2×#387—51no—
166C2×#386—51no—
167C2×C4×C4⋊C4—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—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—28no—
243C2×C4×D5—28no—
244C2×C4×D5—44no—
245C2×C4×D5—416no—
246C2×Dic10—28no—
247C2×Dic10—28no—
248C2×Dic10—44no—
249C2×Dic10—416no—
250C5×C4⋊C4—28no—
251C5×C4⋊C4—28no—
252C5×C4⋊C4—28no—
253C5×C4⋊C4—28no—
254#685—28no—
255#685—28no—
256#685—28no—
257#685—28no—
258#685—28no—
259#685—28no—
260#685—28no—
261#685—28no—
262#685—28no—
263#685—28no—
264#685—44no—
265C4⋊Dic5—28no—
266C4⋊Dic5C2×D4116yescomplemented
267#683—28no—
268C4×Dic5—28no—
269C4×Dic5—28no—
270C4×Dic5—44no—
271C4×Dic5—44no—
272C23×Q8—51no—
273C23×D4—51no—
274C24×C4—51no—
275C2×#126—58no—
276C2×#126—108no—
277C2×C22⋊Q8—58no—
278C2×C22⋊Q8—108no—
279C22×C4⋊C4—51no—
280C22×C4⋊C4—51no—
281C22×C4⋊C4—51no—
282C22×C4⋊C4C2×D511yescharacteristic
283C22×C4⋊C4C2×D511yescharacteristic
284C22×C4⋊C4C2×D511yescharacteristic
285C22×C4⋊C4C2×D511yescharacteristic
286C22×C22⋊C4—51no—
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×C42—51no—
300C22×C42—51no—
301#398C2×D518yescomplemented
302#397—58no—
303#394—58no—
304#393—58no—
305#391—58no—
306#390—58no—
307#388—58no—
308#388—58no—
309#388—58no—
310#387—58no—
311#386—58no—
312C4×C4⋊C4—58no—
313C4×C22⋊C4—58no—
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
324C23×C5C22×D412yes—
325C23×C5C2×#4112yes—
326C23×C5C2×#4112yes—
327C23×C5C2×#4112yes—
328C23×C5C2×#4112yes—
329C23×C5H(5,𝔽2)12yes—
330C23×C52−1+412yes—
331C23×C5C2511yescharacteristic
332C22×D5—28no—
333C22×D5—28no—
334C22×D5—28no—
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—22no—
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×D5—44no—
359C22×D5C2×#4114yes—
360C2×C4×C5—28no—
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—44no—
382C2×C4×C5—44no—
383C2×C4×C5—44no—
384C2×C4×C5—44no—
385C2×C4×C5C22×D414yes—
386C2×C4×C5C2×#4114yes—
387C2×C4×C5C2×#4114yes—
388C2×Dic5—28no—
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—44no—
407C2×Dic5—44no—
408C2×Dic5—44no—
409C2×Dic5C22×D414yes—
410C2×Dic5C22×D414yes—
411C2×Dic5C2×#4114yes—
412D20—416no—
413C4×D5—416no—
414Dic10—416no—
415C25—51no—
416C25—51no—
417C22×Q8—54no—
418C22×Q8—104no—
419C22×Q8—104no—
420C22×Q8—202no—
421C22×D4—54no—
422C22×D4—104no—
423C22×D4—104no—
424C22×D4—202no—
425C23×C4—51no—
426C23×C4—51no—
427C23×C4—51no—
428C23×C4—51no—
429C23×C4—51no—
430C23×C4—51no—
431C23×C4—54no—
432C23×C4—104no—
433C23×C4—104no—
434C23×C4—202no—
435C23×C4C22×D511yescharacteristic
436C23×C4C22×D511yescharacteristic
437C23×C4C22×D511yescharacteristic
438C23×C4C22×D511yescharacteristic
439C23×C4C22×D511yescharacteristic
440C23×C4C22×D511yescharacteristic
441C23×C4C22×D511yescharacteristic
442#126—1032no—
443C22⋊Q8—1032no—
444C2×C4⋊C4—24no—
445C2×C4⋊C4—24no—
446C2×C4⋊C4—24no—
447C2×C4⋊C4—24no—
448C2×C4⋊C4—58no—
449C2×C4⋊C4—54no—
450C2×C4⋊C4—54no—
451C2×C4⋊C4—54no—
452C2×C4⋊C4—104no—
453C2×C4⋊C4—104no—
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—104no—
479C2×C22⋊C4—202no—
480C2×C42—54no—
481C2×C42—54no—
482C2×C42—54no—
483C2×C42—54no—
484C2×C42—104no—
485C2×C42—104no—
486C2×C42—202no—
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—
498C22×C5#52914yes—
499C22×C5#53214yes—
500C22×C5#53914yes—
501C22×C5#54614yes—
502C22×C5#54814yes—
503C22×C5#55114yes—
504C22×C5#55614yes—
505C22×C5C23×D411yescharacteristic
506C22×C5C22×#4111yescharacteristic
507C22×C5C22×#4111yescharacteristic
508C22×C5C22×#4111yescharacteristic
509C22×C5C22×#4111yescharacteristic
510C22×C5C2×H(5,𝔽2)11yescharacteristic
511C22×C5C2×2−1+411yescharacteristic
512C2×D5—24no—
513C2×D5—24no—
514C2×D5—24no—
515C2×D5—416no—
516C2×D5—42no—
517C2×D5—42no—
518C2×D5—42no—
519C2×D5—42no—
520C2×D5—42no—
521C2×D5—42no—
522C2×D5—42no—
523C2×D5—42no—
524C2×D5—42no—
525C2×D5—42no—
526C2×D5—42no—
527C2×D5—88no—
528C4×C5—24no—
529C4×C5—24no—
530C4×C5—24no—
531C4×C5—42no—
532C4×C5—42no—
533C4×C5—42no—
534C4×C5—42no—
535Dic5—24no—
536Dic5—24no—
537Dic5—24no—
538Dic5—42no—
539Dic5—42no—
540Dic5—42no—
541C24—54no—
542C24—52no—
543C24—52no—
544C24—102no—
545C24—102no—
546C24—102no—
547C24—102no—
548C24—102no—
549C24—102no—
550C24—102no—
551C24—102no—
552C24—102no—
553C24—102no—
554C24—102no—
555C24—102no—
556C24—102no—
557C24C23×D511yescharacteristic
558C2×Q8—108no—
559C2×Q8—108no—
560C2×Q8—204no—
561C2×Q8—2016no—
562C2×D4—108no—
563C2×D4—108no—
564C2×D4—204no—
565C2×D4—2016no—
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—22no—
584C22×C4—54no—
585C22×C4—54no—
586C22×C4—54no—
587C22×C4—52no—
588C22×C4—52no—
589C22×C4—52no—
590C22×C4—52no—
591C22×C4—52no—
592C22×C4—52no—
593C22×C4—108no—
594C22×C4—102no—
595C22×C4—102no—
596C22×C4—102no—
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—102no—
607C22×C4—102no—
608C22×C4—102no—
609C22×C4—108no—
610C22×C4—204no—
611C22×C4—2016no—
612C22×C4D4×D514yes—
613C22×C4#71114yes—
614C22×C4#71314yes—
615C22×C4C23×D512yes—
616C22×C4C23×D512yes—
617C22×C4C23×D512yes—
618C22×C4C23×D512yes—
619C22×C4C23×D512yes—
620C22×C4C23×D512yes—
621C22×C4C23×D512yes—
622C4⋊C4—28no—
623C4⋊C4—28no—
624C4⋊C4—28no—
625C4⋊C4—28no—
626C4⋊C4—516no—
627C4⋊C4—108no—
628C4⋊C4—108no—
629C22⋊C4—108no—
630C22⋊C4—108no—
631C22⋊C4—108no—
632C22⋊C4—108no—
633C22⋊C4—108no—
634C22⋊C4—108no—
635C22⋊C4—108no—
636C22⋊C4—108no—
637C22⋊C4—108no—
638C22⋊C4—108no—
639C22⋊C4—204no—
640C42—108no—
641C42—108no—
642C42—204no—
643C42—204no—
644C2×C5#256018yescomplemented
645C2×C5C2×#52911yescharacteristic
646C2×C5C2×#53211yescharacteristic
647C2×C5C2×#53911yescharacteristic
648C2×C5C2×#54611yescharacteristic
649C2×C5C2×#54811yescharacteristic
650C2×C5C2×#55111yescharacteristic
651C2×C5C2×#55611yescharacteristic
652D5—44no—
653D5—82no—
654C23—54no—
655C23—108no—
656C23—108no—
657C23—102no—
658C23—102no—
659C23—102no—
660C23—102no—
661C23—102no—
662C23—108no—
663C23—102no—
664C23—102no—
665C23—102no—
666C23—102no—
667C23—102no—
668C23—102no—
669C23—102no—
670C23—102no—
671C23—204no—
672C23—204no—
673C23—204no—
674C23—204no—
675C23—204no—
676C23—204no—
677C23—204no—
678C23—204no—
679C23—204no—
680C23—204no—
681C23—204no—
682C23C2×D4×D512yes—
683C23C2×#71112yes—
684C23C2×#71312yes—
685C23#414712yes—
686C23D5×#4112yes—
687C23D5×#4112yes—
688C23#414912yes—
689C23C24×D511yescharacteristic
690Q8—2016no—
691D4—2016no—
692C2×C4—28no—
693C2×C4—28no—
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—22no—
713C2×C4—44no—
714C2×C4—44no—
715C2×C4—44no—
716C2×C4—44no—
717C2×C4—54no—
718C2×C4—54no—
719C2×C4—54no—
720C2×C4—108no—
721C2×C4—108no—
722C2×C4—102no—
723C2×C4—102no—
724C2×C4—102no—
725C2×C4—102no—
726C2×C4—102no—
727C2×C4—102no—
728C2×C4—108no—
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—2016no—
739C2×C4—204no—
740C2×C4—204no—
741C2×C4—204no—
742C2×C4C2×D4×D514yes—
743C2×C4C2×#71114yes—
744C2×C4C2×#71314yes—
745C5C2×#256011yescharacteristic, complemented, Sylow
746C22—104no—
747C22—104no—
748C22—104no—
749C22—202no—
750C22—2016no—
751C22—202no—
752C22—202no—
753C22—202no—
754C22—202no—
755C22—202no—
756C22—202no—
757C22—202no—
758C22—202no—
759C22—202no—
760C22—202no—
761C22—408no—
762C22#6593014yes—
763C22#6596414yes—
764C22#6596714yes—
765C22#6599214yes—
766C22#6602514yes—
767C22#6602614yes—
768C22#6606614yes—
769C22C22×D4×D511yescharacteristic
770C22C22×#71111yescharacteristic
771C22C22×#71311yescharacteristic
772C22C2×#414711yescharacteristic
773C22C2×D5×#4111yescharacteristic
774C22C2×D5×#4111yescharacteristic
775C22C2×#414911yescharacteristic
776C4—24no—
777C4—24no—
778C4—24no—
779C4—42no—
780C4—42no—
781C4—42no—
782C4—42no—
783C4—104no—
784C4—104no—
785C4—104no—
786C4—202no—
787C4—202no—
788C4—202no—
789C2—204no—
790C2—402no—
791C2#1060952218yesdirect product factor
792C2C2×#6593011yescharacteristic
793C2C2×#6596411yescharacteristic
794C2C2×#6596711yescharacteristic
795C2C2×#6599211yescharacteristic
796C2C2×#6602511yescharacteristic
797C2C2×#6602611yescharacteristic
798C2C2×#6606611yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC2×C5×#398C2
socleC24×C5C24
prime radicalC23×D20C22
hypercenterC2×#398D5
hypocenterC5C2×#2560
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#398

Complements

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

NH ≅ G/Ntype
1. C22×#4043C2semidirect
2. C22×#4044C2semidirect
3. C2×C5×#398C2semidirect
6. C2×#65279C2semidirect
7. C2×#65279C2semidirect
8. C2×#65270C2semidirect
9. C2×C4⋊C4×Dic5C2semidirect
10. #10609522C2direct (N × H)
11. C2×#64964C2semidirect
12. C2×#64962C2semidirect
14. C2×#64935C2semidirect
15. C2×#64959C2semidirect
16. C2×#64955C2semidirect
43. C2×#4044C22semidirect
45. C2×#4043C22semidirect
46. C5×#398C22semidirect
58. #65279C22semidirect
59. #65279C22semidirect
61. #65270C22semidirect
62. C4⋊C4×Dic5C22semidirect
63. #64964C22semidirect
64. #64962C22semidirect
65. #64959C22semidirect
66. #64955C22semidirect
68. #64935C22semidirect
128. C2×C4⋊Dic5D4semidirect
156. C2×#398D5semidirect
266. C4⋊Dic5C2×D4semidirect
301. #398C2×D5semidirect
644. C2×C5#2560semidirect
745. C5C2×#2560semidirect
791. C2#10609522direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#40432
C22×#40442
C2×C5×#3982
C2×#652802
C2×#652772
C2×#652792
C2×#652702
C2×C4⋊C4×Dic52
#106095222
C2×#649642
C2×#649622
C2×#649542
C2×#649352
C2×#649592
C2×#649552
C2×#25605