Finite Group Databasebeta

← C2×#10608516 #12267519

Subgroups — C2×#10608516 #12267519

Order 1280.

2962 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×Q8×Dic5C211yesmaximal, characteristic, complemented
2C22×#4029C211yesmaximal, characteristic
3C2×C5×#393C211yesmaximal, characteristic, complemented
4C2×#65520C211yesmaximal, characteristic, complemented
5C2×#65250C211yesmaximal, characteristic
6C2×#65246C211yesmaximal, characteristic
7C2×#65233C211yesmaximal, characteristic, complemented
8C2×#65240C211yesmaximal, characteristic, complemented
9C2×#65240C211yesmaximal, characteristic, complemented
10#10608516C2116yesmaximal, direct product factor
11C2×#64957C211yesmaximal, characteristic, complemented
12C2×#64946C211yesmaximal, characteristic, complemented
13C2×#64959C211yesmaximal, characteristic, complemented
14C2×#64943C211yesmaximal, characteristic, complemented
15C2×#64942C211yesmaximal, characteristic, complemented
16C2×#64955C211yesmaximal, characteristic, complemented
17C23×C5×Q8C2211yescharacteristic
18C23×C22⋊D5C2211yescharacteristic
19C23×C4×D5C2211yescharacteristic
20C22×C5×C22⋊C4C2211yescharacteristic
21C22×C5×C22⋊C4C2211yescharacteristic
22C22×C5×C22⋊C4C2211yescharacteristic
23C22×C22⋊Dic5C2211yescharacteristic
24C22×C22⋊Dic5C2211yescharacteristic
25C22×C22⋊Dic5C2211yescharacteristic
26C2×Q8×Dic5—28no—
27C2×Q8×Dic5C2218yescomplemented
28C22×#685C2211yescharacteristic
29C22×#685C2211yescharacteristic
30C22×#685C2211yescharacteristic
31C22×#685C2211yescharacteristic
32C22×#685C2211yescharacteristic
33C22×C4⋊Dic5C2211yescharacteristic
34C22×C4⋊Dic5C2211yescharacteristic
35C22×C4⋊Dic5C2211yescharacteristic
36C22×C4⋊Dic5C2211yescharacteristic
37C22×#683C2211yescharacteristic
38C22×#683C2211yescharacteristic
39C22×#683C2211yescharacteristic
40C22×C4×Dic5C2211yescharacteristic
41C22×C4×Dic5C2211yescharacteristic
42C22×C4×Dic5C2211yescharacteristic
43C22×C4×Dic5C2211yescharacteristic
44C2×#4029—28no—
45C2×#4029C2218yes—
46C5×#393C2218yescomplemented
47C2×C5×#95C2211yescharacteristic
48C2×C5×#95C2211yescharacteristic
49C2×C5×#95C2211yescharacteristic
50#65520C2218yescomplemented
51C2×#3963C2211yescharacteristic
52C2×#3963C2211yescharacteristic
53C2×#3963C2211yescharacteristic
54C2×#3963C2211yescharacteristic
55C2×#3963C2211yescharacteristic
56C2×#3963C2211yescharacteristic
57C2×#3963C2211yescharacteristic
58#65250C2218yes—
59#65246C2218yes—
60#65240C2218yescomplemented
61#65240C2218yescomplemented
62#65233C2218yescomplemented
63#64959C2218yescomplemented
64#64957C2218yescomplemented
65#64955C2218yescomplemented
66#64946C2218yescomplemented
67#64943C2218yescomplemented
68#64942C2218yescomplemented
69C2×#2458—51nomaximal, Sylow
70C25×C5C2311yescharacteristic
71C24×D5C2311yescharacteristic
72C22×C5×Q8—24no—
73C22×C5×Q8—24no—
74C22×C5×Q8—24no—
75C22×C5×Q8C2314yes—
76C23×C4×C5C2311yescharacteristic
77C23×C4×C5C2311yescharacteristic
78C23×C4×C5C2311yescharacteristic
79C23×C4×C5C2311yescharacteristic
80C23×C4×C5C2311yescharacteristic
81C23×C4×C5C2311yescharacteristic
82C22×C22⋊D5—24no—
83C22×C22⋊D5—24no—
84C22×C22⋊D5—42no—
85C22×C22⋊D5C2314yes—
86C23×Dic5C2311yescharacteristic
87C23×Dic5C2311yescharacteristic
88C23×Dic5C2311yescharacteristic
89C23×Dic5C2311yescharacteristic
90C23×Dic5C2311yescharacteristic
91C23×Dic5C2311yescharacteristic
92C23×Dic5C2311yescharacteristic
93C22×C4×D5—24no—
94C22×C4×D5—24no—
95C22×C4×D5—42no—
96C22×C4×D5C2314yes—
97C2×C5×C22⋊C4—24no—
98C2×C5×C22⋊C4—24no—
99C2×C5×C22⋊C4—24no—
100C2×C5×C22⋊C4C2314yes—
101C2×C5×C22⋊C4C2314yes—
102C2×C5×C22⋊C4C2314yes—
103C2×C22⋊Dic5—24no—
104C2×C22⋊Dic5—24no—
105C2×C22⋊Dic5—42no—
106C2×C22⋊Dic5C2314yes—
107C2×C22⋊Dic5C2314yes—
108C2×C22⋊Dic5C2314yes—
109Q8×Dic5—232no—
110C2×#685—24no—
111C2×#685—24no—
112C2×#685—24no—
113C2×#685—24no—
114C2×#685—24no—
115C2×#685C2314yes—
116C2×#685C2314yes—
117C2×#685C2314yes—
118C2×#685C2314yes—
119C2×#685C2314yes—
120C2×C4⋊Dic5—24no—
121C2×C4⋊Dic5—24no—
122C2×C4⋊Dic5—24no—
123C2×C4⋊Dic5D418yes—
124C2×C4⋊Dic5C2314yes—
125C2×C4⋊Dic5C2314yes—
126C2×C4⋊Dic5C2314yes—
127C2×C4⋊Dic5C2314yes—
128C2×#683—24no—
129C2×#683—42no—
130C2×#683—42no—
131C2×#683C2314yes—
132C2×#683C2314yes—
133C2×#683C2314yes—
134C2×C4×Dic5—24no—
135C2×C4×Dic5—24no—
136C2×C4×Dic5—24no—
137C2×C4×Dic5—42no—
138C2×C4×Dic5C2314yes—
139C2×C4×Dic5C2314yes—
140C2×C4×Dic5C2314yes—
141C2×C4×Dic5C2314yes—
142#4029—232no—
143C5×#95C2314yes—
144C5×#95C2314yes—
145C5×#95C2314yes—
146#3963C2314yes—
147#3963C2314yes—
148#3963C2314yes—
149#3963C2314yes—
150#3963C2314yes—
151#3963C2314yes—
152#3963C2314yes—
153C22×#123—51no—
154C22×C4×Q8—51no—
155#2458—516no—
156C2×#398—51no—
157C2×#394—51no—
158C2×#393—51no—
159C2×#393D511yescharacteristic, complemented
160C2×#390—51no—
161C2×#388—51no—
162C2×#388—51no—
163C2×#388—51no—
164C2×#388—51no—
165C2×#387—51no—
166C2×#387—51no—
167C2×#385—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—22no—
183C23×D5—22no—
184C23×D5#4114yes—
185C23×D5C2412yes—
186C2×C5×Q8—232no—
187C2×C5×Q8—28no—
188C2×C5×Q8—28no—
189C2×C5×Q8—28no—
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×C5#4114yes—
208C22×C4×C5C2412yes—
209C22×C4×C5C2412yes—
210C22×C4×C5C2412yes—
211C22×C4×C5C2412yes—
212C22×C4×C5C2412yes—
213C22×C4×C5C2412yes—
214C2×C22⋊D5—28no—
215C2×C22⋊D5—28no—
216C2×C22⋊D5—44no—
217C2×C22⋊D5—416no—
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×Dic5—22no—
233C22×Dic5—22no—
234C22×Dic5—22no—
235C22×Dic5—22no—
236C22×Dic5C2×D414yes—
237C22×Dic5C2×D414yes—
238C22×Dic5#4114yes—
239C22×Dic5C2412yes—
240C22×Dic5C2412yes—
241C22×Dic5C2412yes—
242C22×Dic5C2412yes—
243C22×Dic5C2412yes—
244C22×Dic5C2412yes—
245C22×Dic5C2412yes—
246C2×C4×D5—28no—
247C2×C4×D5—28no—
248C2×C4×D5—44no—
249C2×C4×D5—416no—
250C5×C22⋊C4—28no—
251C5×C22⋊C4—28no—
252C5×C22⋊C4—28no—
253C22⋊Dic5—28no—
254C22⋊Dic5—28no—
255C22⋊Dic5—44no—
256#685—28no—
257#685—28no—
258#685—28no—
259#685—28no—
260#685—28no—
261C4⋊Dic5—28no—
262C4⋊Dic5—28no—
263C4⋊Dic5—28no—
264C4⋊Dic5C2×D4116yes—
265#683—28no—
266#683—44no—
267#683—44no—
268C4×Dic5—28no—
269C4×Dic5—28no—
270C4×Dic5—28no—
271C4×Dic5—44no—
272C23×Q8C2×D511yescharacteristic
273C23×D4—51no—
274C24×C4—51no—
275C2×#123—58no—
276C2×#123—108no—
277C2×C4×Q8—58no—
278C2×C4×Q8—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×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⋊C4C2×D511yescharacteristic
295C22×C22⋊C4C2×D511yescharacteristic
296C22×C22⋊C4C2×D511yescharacteristic
297C22×C42—51no—
298C22×C42—51no—
299C22×C42—51no—
300C22×C42—51no—
301#398—58no—
302#394—58no—
303#393—58no—
304#393C2×D518yescomplemented
305#390—58no—
306#388—58no—
307#388—58no—
308#388—58no—
309#388—58no—
310#387—58no—
311#387—58no—
312#385—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×C5—22no—
325C23×C5—22no—
326C23×C5—22no—
327C23×C5—22no—
328C23×C5—22no—
329C23×C5—22no—
330C23×C5—22no—
331C23×C5—44no—
332C23×C5—44no—
333C23×C5—44no—
334C23×C5—44no—
335C23×C5—44no—
336C23×C5—44no—
337C23×C5—44no—
338C23×C5C22×D412yes—
339C23×C5C2×#4112yes—
340C23×C5C2×#4112yes—
341C23×C5C2×#4112yes—
342C23×C5C2×#4112yes—
343C23×C5H(5,𝔽2)12yes—
344C23×C52−1+412yes—
345C23×C5C2511yescharacteristic
346C22×D5—28no—
347C22×D5—28no—
348C22×D5—28no—
349C22×D5—22no—
350C22×D5—22no—
351C22×D5—22no—
352C22×D5—22no—
353C22×D5—22no—
354C22×D5—22no—
355C22×D5—44no—
356C22×D5—44no—
357C22×D5—44no—
358C22×D5—44no—
359C22×D5C2×#4114yes—
360C5×Q8—232no—
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—44no—
380C2×C4×C5—44no—
381C2×C4×C5—44no—
382C2×C4×C5C22×D414yes—
383C2×C4×C5C2×#4114yes—
384C2×C4×C5C2×#4114yes—
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—416no—
415C25—51no—
416C25C22×D511yescharacteristic
417C22×Q8—24no—
418C22×Q8—24no—
419C22×Q8—24no—
420C22×Q8C22×D514yes—
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—51no—
432C23×C4—54no—
433C23×C4—104no—
434C23×C4—104no—
435C23×C4—202no—
436C23×C4C22×D511yescharacteristic
437C23×C4C22×D511yescharacteristic
438C23×C4C22×D511yescharacteristic
439C23×C4C22×D511yescharacteristic
440C23×C4C22×D511yescharacteristic
441C23×C4C22×D511yescharacteristic
442#123—1032no—
443C4×Q8—1032no—
444C2×C4⋊C4—58no—
445C2×C4⋊C4—54no—
446C2×C4⋊C4—54no—
447C2×C4⋊C4—54no—
448C2×C4⋊C4—54no—
449C2×C4⋊C4—54no—
450C2×C4⋊C4—54no—
451C2×C4⋊C4—54no—
452C2×C4⋊C4—104no—
453C2×C4⋊C4—104no—
454C2×C4⋊C4—104no—
455C2×C4⋊C4—104no—
456C2×C4⋊C4—202no—
457C2×C4⋊C4—202no—
458C2×C22⋊C4—24no—
459C2×C22⋊C4—24no—
460C2×C22⋊C4—24no—
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—202no—
477C2×C22⋊C4C22×D514yes—
478C2×C22⋊C4C22×D514yes—
479C2×C22⋊C4C22×D514yes—
480C2×C42—54no—
481C2×C42—54no—
482C2×C42—54no—
483C2×C42—54no—
484C2×C42—104no—
485C2×C42—104no—
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—
498C22×C5—42no—
499C22×C5—42no—
500C22×C5—42no—
501C22×C5—42no—
502C22×C5—42no—
503C22×C5—42no—
504C22×C5—42no—
505C22×C5—88no—
506C22×C5#52514yes—
507C22×C5#52914yes—
508C22×C5#54214yes—
509C22×C5#54614yes—
510C22×C5#54814yes—
511C22×C5#55214yes—
512C22×C5#55914yes—
513C22×C5C23×D411yescharacteristic
514C22×C5C22×#4111yescharacteristic
515C22×C5C22×#4111yescharacteristic
516C22×C5C22×#4111yescharacteristic
517C22×C5C22×#4111yescharacteristic
518C22×C5C2×H(5,𝔽2)11yescharacteristic
519C22×C5C2×2−1+411yescharacteristic
520C2×D5—24no—
521C2×D5—24no—
522C2×D5—24no—
523C2×D5—42no—
524C2×D5—42no—
525C2×D5—42no—
526C2×D5—42no—
527C2×D5—416no—
528C4×C5—24no—
529C4×C5—24no—
530C4×C5—24no—
531C4×C5—42no—
532C4×C5—42no—
533C4×C5—42no—
534Dic5—24no—
535Dic5—24no—
536Dic5—24no—
537Dic5—42no—
538Dic5—42no—
539Dic5—42no—
540Dic5—42no—
541C24—22no—
542C24—22no—
543C24—22no—
544C24—22no—
545C24—22no—
546C24—22no—
547C24—22no—
548C24—54no—
549C24—52no—
550C24—102no—
551C24—102no—
552C24—102no—
553C24—102no—
554C24—102no—
555C24—102no—
556C24C23×D512yes—
557C24C23×D511yescharacteristic
558C2×Q8—232no—
559C2×Q8—28no—
560C2×Q8—28no—
561C2×Q8—28no—
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—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—102no—
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—102no—
610C22×C4—102no—
611C22×C4—204no—
612C22×C4—2016no—
613C22×C4D4×D514yes—
614C22×C4#71114yes—
615C22×C4#71114yes—
616C22×C4C23×D512yes—
617C22×C4C23×D512yes—
618C22×C4C23×D512yes—
619C22×C4C23×D512yes—
620C22×C4C23×D512yes—
621C22×C4C23×D512yes—
622C4⋊C4—516no—
623C4⋊C4—108no—
624C4⋊C4—108no—
625C4⋊C4—108no—
626C4⋊C4—108no—
627C4⋊C4—204no—
628C4⋊C4—204no—
629C22⋊C4—28no—
630C22⋊C4—28no—
631C22⋊C4—28no—
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—108no—
643C42—204no—
644C2×C5—82no—
645C2×C5#245818yescomplemented
646C2×C5C2×#52511yescharacteristic
647C2×C5C2×#52911yescharacteristic
648C2×C5C2×#54211yescharacteristic
649C2×C5C2×#54611yescharacteristic
650C2×C5C2×#54811yescharacteristic
651C2×C5C2×#55211yescharacteristic
652C2×C5C2×#55911yescharacteristic
653D5—44no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—44no—
662C23—44no—
663C23—44no—
664C23—44no—
665C23—44no—
666C23—44no—
667C23—44no—
668C23—54no—
669C23—108no—
670C23—108no—
671C23—108no—
672C23—102no—
673C23—102no—
674C23—102no—
675C23—102no—
676C23—102no—
677C23—102no—
678C23—204no—
679C23—204no—
680C23—204no—
681C23—204no—
682C23C2×D4×D512yes—
683C23C2×#71112yes—
684C23C2×#71112yes—
685C23#414712yes—
686C23D5×#4112yes—
687C23D5×#4112yes—
688C23#414912yes—
689C23C24×D511yescharacteristic
690Q8—232no—
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—44no—
711C2×C4—44no—
712C2×C4—44no—
713C2×C4—54no—
714C2×C4—54no—
715C2×C4—54no—
716C2×C4—108no—
717C2×C4—108no—
718C2×C4—108no—
719C2×C4—102no—
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—102no—
736C2×C4—102no—
737C2×C4—2016no—
738C2×C4—204no—
739C2×C4—204no—
740C2×C4—204no—
741C2×C4—204no—
742C2×C4C2×D4×D514yes—
743C2×C4C2×#71114yes—
744C2×C4C2×#71114yes—
745C5C2×#245811yescharacteristic, complemented, Sylow
746C22—42no—
747C22—42no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—88no—
754C22—104no—
755C22—104no—
756C22—104no—
757C22—202no—
758C22—202no—
759C22—202no—
760C22—2016no—
761C22—202no—
762C22#6592014yes—
763C22#6596714yes—
764C22#6597314yes—
765C22#6597714yes—
766C22#6601014yes—
767C22#6601414yes—
768C22#6601514yes—
769C22C22×D4×D511yescharacteristic
770C22C22×#71111yescharacteristic
771C22C22×#71111yescharacteristic
772C22C2×#414711yescharacteristic
773C22C2×D5×#4111yescharacteristic
774C22C2×D5×#4111yescharacteristic
775C22C2×#414911yescharacteristic
776C4—24no—
777C4—24no—
778C4—24no—
779C4—42no—
780C4—42no—
781C4—42no—
782C4—104no—
783C4—104no—
784C4—104no—
785C4—202no—
786C4—202no—
787C4—202no—
788C4—202no—
789C2—82no—
790C2—204no—
791C2#1060851618yesdirect product factor
792C2C2×#6592011yescharacteristic
793C2C2×#6597711yescharacteristic
794C2C2×#6596711yescharacteristic
795C2C2×#6597311yescharacteristic
796C2C2×#6601411yescharacteristic
797C2C2×#6601511yescharacteristic
798C2C2×#6601011yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC2×C5×#393C2
socleC24×C5C24
prime radicalC23×C22⋊D5C22
hypercenterC2×#393D5
hypocenterC5C2×#2458
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#393

Complements

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

NH ≅ G/Ntype
1. C22×Q8×Dic5C2semidirect
3. C2×C5×#393C2semidirect
4. C2×#65520C2semidirect
7. C2×#65233C2semidirect
8. C2×#65240C2semidirect
9. C2×#65240C2semidirect
10. #10608516C2direct (N × H)
11. C2×#64957C2semidirect
12. C2×#64946C2semidirect
13. C2×#64959C2semidirect
14. C2×#64943C2semidirect
15. C2×#64942C2semidirect
16. C2×#64955C2semidirect
27. C2×Q8×Dic5C22semidirect
46. C5×#393C22semidirect
50. #65520C22semidirect
60. #65240C22semidirect
61. #65240C22semidirect
62. #65233C22semidirect
63. #64959C22semidirect
64. #64957C22semidirect
65. #64955C22semidirect
66. #64946C22semidirect
67. #64943C22semidirect
68. #64942C22semidirect
159. C2×#393D5semidirect
304. #393C2×D5semidirect
645. C2×C5#2458semidirect
745. C5C2×#2458semidirect
791. C2#10608516direct (N × H)

Maximal subgroups

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

subgroupindex
C22×Q8×Dic52
C22×#40292
C2×C5×#3932
C2×#655202
C2×#652502
C2×#652462
C2×#652332
C2×#652402
#106085162
C2×#649572
C2×#649462
C2×#649592
C2×#649432
C2×#649422
C2×#649552
C2×#24585