Finite Group Databasebeta

← C2×D5×#478 #12966765

Subgroups — C2×D5×#478 #12966765

Order 1280.

2574 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D5×#125C211yesmaximal, characteristic, complemented
2C2×C4×D4×D5C211yesmaximal, characteristic
3C2×C5×#478C211yesmaximal, characteristic, complemented
4C2×#65355C211yesmaximal, characteristic, complemented
5C2×#65298C211yesmaximal, characteristic, complemented
6D5×#478C2116yesmaximal, direct product factor
7C2×#65180C211yesmaximal, characteristic, complemented
8C2×D5×#107C211yesmaximal, characteristic, complemented
9C2×#65160C211yesmaximal, characteristic, complemented
10C2×D5×#106C211yesmaximal, characteristic, complemented
11C2×#65136C211yesmaximal, characteristic, complemented
12C2×D5×C4⋊C8C211yesmaximal, characteristic, complemented
13C2×D5×#102C211yesmaximal, characteristic
14C2×D5×#102C211yesmaximal, characteristic
15C2×#65052C211yesmaximal, characteristic, complemented
16C2×#65055C211yesmaximal, characteristic, complemented
17C22×D4×D5C2211yescharacteristic
18C23×C4×D5—21no—
19C2×C5×#125C2211yescharacteristic, complemented
20C2×C4×C5×D4C2211yescharacteristic
21C2×D4×Dic5C2211yescharacteristic
22C2×C4×C22⋊D5—21no—
23C22×C8×D5C2211yescharacteristic
24C22×C8×D5C2211yescharacteristic
25D5×#125—24no—
26D5×#125C2218yescomplemented
27C4×D4×D5—24no—
28C4×D4×D5C2218yes—
29C2×#4039C2211yescharacteristic
30C2×D5×C4⋊C4—21no—
31C2×D5×C4⋊C4—21no—
32C2×D5×C4⋊C4C2211yescharacteristic
33C2×D5×C4⋊C4C2211yescharacteristic
34C2×D5×C4⋊C4C2211yescharacteristic
35C2×#4036C2211yescharacteristic, complemented
36C2×#4036C2211yescharacteristic, complemented
37C2×#4035—21no—
38C2×#4035—21no—
39C2×#4027—21no—
40C2×D5×C22⋊C4—21no—
41C2×C4×D20C2211yescharacteristic
42C2×C42×D5C2211yescharacteristic
43C2×#4016C2211yescharacteristic, complemented
44C5×#478C2218yescomplemented
45C2×C5×#107C2211yescharacteristic, complemented
46C2×C5×#106C2211yescharacteristic, complemented
47C2×C5×C4⋊C8C2211yescharacteristic, complemented
48C2×C5×#102C2211yescharacteristic
49C2×C5×#102C2211yescharacteristic
50C2×#3964C2211yescharacteristic
51C2×#3964C2211yescharacteristic
52C2×#3953C2211yescharacteristic
53C2×#3953C2211yescharacteristic
54C2×#3950C2211yescharacteristic, complemented
55C2×#3949C2211yescharacteristic, complemented
56C2×#3946C2211yescharacteristic, complemented
57C2×#3946C2211yescharacteristic, complemented
58#65355C2218yescomplemented
59#65298C2218yescomplemented
60C2×#3941C2211yescharacteristic
61C2×#3941C2211yescharacteristic
62C2×#3940C2211yescharacteristic, complemented
63C2×#3940C2211yescharacteristic, complemented
64C2×#3939C2211yescharacteristic, complemented
65C2×#3939C2211yescharacteristic, complemented
66C2×C4⋊#168C2211yescharacteristic, complemented
67#65180C2218yescomplemented
68D5×#107C2218yescomplemented
69#65160C2218yescomplemented
70D5×#106C2218yescomplemented
71#65136C2218yescomplemented
72D5×C4⋊C8C2218yescomplemented
73D5×#102C2218yes—
74D5×#102C2218yes—
75#65055C2218yescomplemented
76#65052C2218yescomplemented
77C22×#478—51nomaximal, Sylow
78C24×D5—21no—
79C22×C5×D4C2311yescharacteristic
80C23×C4×C5—21no—
81C22×C22⋊D5—21no—
82C23×Dic5—21no—
83C2×D4×D5—22no—
84C2×D4×D5—24no—
85C2×D4×D5Q818yes—
86C2×D4×D5C2314yes—
87C22×D20C2311yescharacteristic
88C22×C4×D5—21no—
89C22×C4×D5—21no—
90C22×C4×D5—21no—
91C22×C4×D5—21no—
92C22×C4×D5—21no—
93C22×C4×D5—28no—
94C22×C4×D5—48no—
95C22×C4×D5D411yescharacteristic
96C22×C4×D5D411yescharacteristic
97C22×C4×D5C2311yescharacteristic
98C22×C5×C8C2311yescharacteristic
99C22×C5×C8C2311yescharacteristic
100C5×#125—22no—
101C5×#125C2314yescomplemented
102C4×C5×D4—22no—
103C4×C5×D4C2314yes—
104C2×C5×C4⋊C4—21no—
105C2×C5×C4⋊C4—21no—
106C2×C5×C4⋊C4C2311yescharacteristic
107C2×C5×C4⋊C4C2311yescharacteristic
108C2×C5×C4⋊C4C2311yescharacteristic
109C2×C5×C22⋊C4—21no—
110C2×C42×C5C2311yescharacteristic
111C2×C22⋊Dic5—21no—
112D4×Dic5—22no—
113D4×Dic5C2314yes—
114C4×C22⋊D5—28no—
115C2×#685—21no—
116C2×#685—21no—
117C2×C4⋊Dic5—21no—
118C2×C4⋊Dic5—21no—
119C2×C4⋊Dic5C2311yescharacteristic
120C2×C4⋊Dic5C2311yescharacteristic
121C2×C4⋊Dic5C2311yescharacteristic
122C2×#683—21no—
123C2×#683—21no—
124C2×#683—21no—
125C2×#683—21no—
126C2×#683—21no—
127C2×#683—21no—
128C2×#683—21no—
129C2×C4×Dic5D411yescharacteristic
130C2×C4×Dic5D411yescharacteristic
131C2×C4×Dic5C2311yescharacteristic
132C22×#168C2311yescharacteristic
133C22×#168C2311yescharacteristic
134C2×C8×D5—24no—
135C2×C8×D5—24no—
136C2×C8×D5C2314yes—
137C2×C8×D5C2314yes—
138#4039—22no—
139#4039C2314yes—
140D5×C4⋊C4—28no—
141D5×C4⋊C4—28no—
142D5×C4⋊C4—22no—
143D5×C4⋊C4—22no—
144D5×C4⋊C4—22no—
145D5×C4⋊C4C2314yes—
146D5×C4⋊C4C2314yes—
147D5×C4⋊C4C2314yes—
148#4036—22no—
149#4036—22no—
150#4036C2314yescomplemented
151#4036C2314yescomplemented
152#4035—28no—
153#4035—28no—
154#4027—28no—
155D5×C22⋊C4—28no—
156C4×D20—22no—
157C4×D20C2314yes—
158C42×D5D414yes—
159C42×D5C2314yes—
160#4016—22no—
161#4016C2314yescomplemented
162C5×#107C2314yescomplemented
163C5×#106C2314yescomplemented
164C5×C4⋊C8C2314yescomplemented
165C5×#102C2314yes—
166C5×#102C2314yes—
167#3964C2314yes—
168#3964C2314yes—
169#3953C2314yes—
170#3953C2314yes—
171#3950C2314yescomplemented
172#3949C2314yescomplemented
173#3946C2314yescomplemented
174#3946C2314yescomplemented
175#3941C2314yes—
176#3941C2314yes—
177#3940C2314yescomplemented
178#3940C2314yescomplemented
179#3939C2314yescomplemented
180#3939C2314yescomplemented
181C4⋊#168C2314yescomplemented
182C22×#125—51no—
183C22×C4×D4—51no—
184C2×#478—516no—
185C2×#478—51no—
186C2×#478—51no—
187C2×#478—51no—
188C2×#478—51no—
189C2×#478—51no—
190C2×#478—51no—
191C2×#478—51no—
192C2×#478D511yescharacteristic, direct product factor
193C22×#107—51no—
194C22×#106—51no—
195C22×C4⋊C8—51no—
196C22×#102—51no—
197C22×#102—51no—
198C24×C5—21no—
199C23×D5—21no—
200C23×D5—28no—
201C23×D5—24no—
202C23×D5—44no—
203C23×D5—44no—
204C23×D5C2×D411yescharacteristic
205C2×C5×D4—21no—
206C2×C5×D4—22no—
207C2×C5×D4C2×Q814yes—
208C2×C5×D4C2412yes—
209C22×C4×C5—21no—
210C22×C4×C5—21no—
211C22×C4×C5—21no—
212C22×C4×C5—24no—
213C22×C4×C5—44no—
214C22×C4×C5C2×D411yescharacteristic
215C22×C4×C5C2×D411yescharacteristic
216C22×C4×C5C2411yescharacteristic
217C2×C22⋊D5—28no—
218C2×C22⋊D5—24no—
219C22×Dic5—21no—
220C22×Dic5—21no—
221C22×Dic5—21no—
222C22×Dic5—24no—
223C22×Dic5—44no—
224C22×Dic5C2×D411yescharacteristic
225C22×Dic5C2×D411yescharacteristic
226C22×Dic5C2×D411yescharacteristic
227D4×D5—216no—
228D4×D5—28no—
229D4×D5C2×Q8116yes—
230C2×D20—21no—
231C2×D20—22no—
232C2×D20C2×Q814yes—
233C2×D20C2412yes—
234C2×C4×D5—24no—
235C2×C4×D5—24no—
236C2×C4×D5—24no—
237C2×C4×D5—24no—
238C2×C4×D5—24no—
239C2×C4×D5—24no—
240C2×C4×D5—24no—
241C2×C4×D5—432no—
242C2×C4×D5—44no—
243C2×C4×D5—44no—
244C2×C4×D5—44no—
245C2×C4×D5—44no—
246C2×C4×D5—44no—
247C2×C4×D5C2×D414yes—
248C2×C4×D5C2×D414yes—
249C2×C4×D5C2×D412yes—
250C2×C4×D5C2×Q814yes—
251C2×C4×D5#4114yes—
252C2×C4×D5C2412yes—
253C2×C5×C8—22no—
254C2×C5×C8—22no—
255C2×C5×C8C2412yes—
256C2×C5×C8C2412yes—
257C5×C4⋊C4—24no—
258C5×C4⋊C4—24no—
259C5×C4⋊C4—21no—
260C5×C4⋊C4—21no—
261C5×C4⋊C4—21no—
262C5×C4⋊C4C2412yes—
263C5×C4⋊C4C2412yes—
264C5×C4⋊C4C2412yes—
265C5×C22⋊C4—24no—
266C42×C5C2×D412yes—
267C42×C5C2412yes—
268C22⋊Dic5—24no—
269#685—24no—
270#685—24no—
271C4⋊Dic5—21no—
272C4⋊Dic5—21no—
273C4⋊Dic5—21no—
274C4⋊Dic5—24no—
275C4⋊Dic5—24no—
276C4⋊Dic5C2412yes—
277C4⋊Dic5C2412yes—
278C4⋊Dic5C2412yes—
279#683—24no—
280#683—24no—
281#683—24no—
282#683—24no—
283#683—24no—
284#683—24no—
285#683—24no—
286C4×Dic5C2×D412yes—
287C4×Dic5C2×D414yes—
288C4×Dic5C2×D414yes—
289C4×Dic5C2412yes—
290C2×#168—22no—
291C2×#168—22no—
292C2×#168C2412yes—
293C2×#168C2412yes—
294C8×D5—28no—
295C8×D5—28no—
296C23×D4—51no—
297C24×C4—101no—
298C23×C8—51no—
299C23×C8—51no—
300C2×#125—58no—
301C2×#125—51no—
302C2×#125—51no—
303C2×#125—51no—
304C2×#125—101no—
305C2×#125—101no—
306C2×#125—104no—
307C2×#125C2×D511yescharacteristic, complemented
308C2×C4×D4—51no—
309C2×C4×D4—58no—
310C2×C4×D4—51no—
311C2×C4×D4—51no—
312C2×C4×D4—101no—
313C2×C4×D4—104no—
314C2×C4×D4—101no—
315C2×C4×D4C2×D511yescharacteristic
316C22×C4⋊C4—51no—
317C22×C4⋊C4—51no—
318C22×C4⋊C4—51no—
319C22×C4⋊C4—101no—
320C22×C4⋊C4—101no—
321C22×C22⋊C4—101no—
322C22×C42—51no—
323#478—58no—
324#478—58no—
325#478—58no—
326#478—58no—
327#478—58no—
328#478—58no—
329#478—58no—
330#478C2×D518yesdirect product factor
331C2×#107—51no—
332C2×#107—51no—
333C2×#107—51no—
334C2×#107—58no—
335C2×#107C2×D511yescharacteristic, complemented
336C2×#106—51no—
337C2×#106—51no—
338C2×#106—51no—
339C2×#106—58no—
340C2×#106C2×D511yescharacteristic, complemented
341C2×C4⋊C8—51no—
342C2×C4⋊C8—51no—
343C2×C4⋊C8—51no—
344C2×C4⋊C8—58no—
345C2×C4⋊C8C2×D511yescharacteristic, complemented
346C2×#102—51no—
347C2×#102—51no—
348C2×#102—51no—
349C2×#102—51no—
350C2×#102—51no—
351C2×#102—51no—
352C2×#102—58no—
353C2×#102—58no—
354C2×#102C2×D511yescharacteristic
355C2×#102C2×D511yescharacteristic
356C23×C5—24no—
357C23×C5—22no—
358C23×C5—42no—
359C23×C5—42no—
360C23×C5C22×D411yescharacteristic
361C22×D5—24no—
362C22×D5—22no—
363C22×D5—216no—
364C22×D5—42no—
365C22×D5—42no—
366C22×D5—48no—
367C22×D5—48no—
368C22×D5—432no—
369C22×D5C22⋊Q814yes—
370C22×D5#13514yes—
371C22×D5AGL(1,ℤ/8)14yes—
372C22×D5C22×D412yes—
373C5×D4—24no—
374C5×D4—22no—
375C5×D4C22×Q814yes—
376C2×C4×C5—22no—
377C2×C4×C5—22no—
378C2×C4×C5—22no—
379C2×C4×C5—22no—
380C2×C4×C5—22no—
381C2×C4×C5—48no—
382C2×C4×C5—42no—
383C2×C4×C5—42no—
384C2×C4×C5—42no—
385C2×C4×C5C22×D412yes—
386C2×C4×C5C22×D412yes—
387C2×C4×C5C22×D411yescharacteristic
388C2×C4×C5C22×Q812yes—
389C2×C4×C5C2×#4112yes—
390C2×C4×C5C2511yescharacteristic
391C22⋊D5—216no—
392C2×Dic5—22no—
393C2×Dic5—22no—
394C2×Dic5—22no—
395C2×Dic5—22no—
396C2×Dic5—22no—
397C2×Dic5—48no—
398C2×Dic5—42no—
399C2×Dic5—42no—
400C2×Dic5—42no—
401C2×Dic5C22⋊Q814yes—
402C2×Dic5C22×D412yes—
403C2×Dic5C22×D412yes—
404C2×Dic5C22×D412yes—
405D20—24no—
406D20—22no—
407D20C22×Q814yes—
408C4×D5—28no—
409C4×D5—28no—
410C4×D5—48no—
411C4×D5—48no—
412C4×D5—48no—
413C4×D5—48no—
414C4×D5—48no—
415C4×D5C22⋊Q818yes—
416C4×D5C22×Q814yes—
417C4×D5C2×#4114yes—
418C5×C8—22no—
419C5×C8—22no—
420#168—22no—
421#168—22no—
422C25—101no—
423C22×D4—58no—
424C22×D4—54no—
425C22×D4—51no—
426C22×D4—102no—
427C22×D4—104no—
428C22×D4—101no—
429C22×D4C22×D511yescharacteristic
430C23×C4—21no—
431C23×C4—51no—
432C23×C4—51no—
433C23×C4—51no—
434C23×C4—101no—
435C23×C4—108no—
436C23×C4—101no—
437C23×C4—101no—
438C23×C4—101no—
439C23×C4—101no—
440C23×C4—101no—
441C23×C4—208no—
442C22×C8—51no—
443C22×C8—51no—
444C22×C8—54no—
445C22×C8—54no—
446C22×C8—104no—
447C22×C8—104no—
448C22×C8C22×D511yescharacteristic
449C22×C8C22×D511yescharacteristic
450#125—22no—
451#125—54no—
452#125—54no—
453#125—54no—
454#125—108no—
455#125—108no—
456#125—102no—
457#125—102no—
458#125—102no—
459#125C22×D514yescomplemented
460C4×D4—22no—
461C4×D4—54no—
462C4×D4—54no—
463C4×D4—54no—
464C4×D4—108no—
465C4×D4—102no—
466C4×D4—108no—
467C4×D4—102no—
468C4×D4—102no—
469C4×D4C22×D514yes—
470C2×C4⋊C4—21no—
471C2×C4⋊C4—21no—
472C2×C4⋊C4—51no—
473C2×C4⋊C4—51no—
474C2×C4⋊C4—51no—
475C2×C4⋊C4—54no—
476C2×C4⋊C4—54no—
477C2×C4⋊C4—54no—
478C2×C4⋊C4—102no—
479C2×C4⋊C4—102no—
480C2×C4⋊C4—102no—
481C2×C4⋊C4—108no—
482C2×C4⋊C4—108no—
483C2×C4⋊C4—101no—
484C2×C4⋊C4—101no—
485C2×C4⋊C4—101no—
486C2×C4⋊C4—101no—
487C2×C4⋊C4—101no—
488C2×C4⋊C4—101no—
489C2×C4⋊C4—101no—
490C2×C4⋊C4—101no—
491C2×C4⋊C4—101no—
492C2×C4⋊C4C22×D511yescharacteristic
493C2×C4⋊C4C22×D511yescharacteristic
494C2×C4⋊C4C22×D511yescharacteristic
495C2×C22⋊C4—21no—
496C2×C22⋊C4—108no—
497C2×C22⋊C4—101no—
498C2×C22⋊C4—101no—
499C2×C22⋊C4—101no—
500C2×C42—51no—
501C2×C42—51no—
502C2×C42—51no—
503C2×C42—54no—
504C2×C42—54no—
505C2×C42C22×D511yescharacteristic
506#107—54no—
507#107—54no—
508#107—54no—
509#107C22×D514yescomplemented
510#106—54no—
511#106—54no—
512#106—54no—
513#106C22×D514yescomplemented
514C4⋊C8—54no—
515C4⋊C8—54no—
516C4⋊C8—54no—
517C4⋊C8C22×D514yescomplemented
518#102—54no—
519#102—54no—
520#102—54no—
521#102—54no—
522#102—54no—
523#102—54no—
524#102C22×D514yes—
525#102C22×D514yes—
526C22×C5—24no—
527C22×C5—48no—
528C22×C5—42no—
529C22×C5—42no—
530C22×C5C2×C22⋊Q812yes—
531C22×C5C2×#13512yes—
532C22×C5C2×AGL(1,ℤ/8)12yes—
533C22×C5C23×D411yescharacteristic
534C2×D5—24no—
535C2×D5—48no—
536C2×D5—42no—
537C2×D5—42no—
538C2×D5—432no—
539C2×D5#478116yesdirect product factor
540C2×D5C2×C22⋊Q814yes—
541C2×D5C2×#13514yes—
542C2×D5C2×AGL(1,ℤ/8)14yes—
543C4×C5—22no—
544C4×C5—22no—
545C4×C5—42no—
546C4×C5—42no—
547C4×C5—42no—
548C4×C5C2×C22⋊Q812yes—
549C4×C5C23×Q811yescharacteristic
550C4×C5C22×#4111yescharacteristic
551Dic5—22no—
552Dic5—22no—
553Dic5—42no—
554Dic5—42no—
555Dic5—42no—
556Dic5C2×C22⋊Q814yes—
557C24—21no—
558C24—51no—
559C24—104no—
560C24—108no—
561C24—101no—
562C24—204no—
563C24—204no—
564C2×D4—21no—
565C2×D4—22no—
566C2×D4—516no—
567C2×D4—54no—
568C2×D4—52no—
569C2×D4—1016no—
570C2×D4—108no—
571C2×D4—104no—
572C2×D4—108no—
573C2×D4—101no—
574C2×D4—102no—
575C2×D4Q8×D514yes—
576C2×D4C23×D512yes—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—24no—
581C22×C4—44no—
582C22×C4—51no—
583C22×C4—52no—
584C22×C4—54no—
585C22×C4—54no—
586C22×C4—52no—
587C22×C4—51no—
588C22×C4—51no—
589C22×C4—54no—
590C22×C4—54no—
591C22×C4—104no—
592C22×C4—104no—
593C22×C4—104no—
594C22×C4—104no—
595C22×C4—104no—
596C22×C4—104no—
597C22×C4—104no—
598C22×C4—101no—
599C22×C4—101no—
600C22×C4—101no—
601C22×C4—104no—
602C22×C4—204no—
603C22×C4—2032no—
604C22×C4—204no—
605C22×C4—204no—
606C22×C4—204no—
607C22×C4—204no—
608C22×C4—204no—
609C22×C4D4×D511yescharacteristic
610C22×C4D4×D511yescharacteristic
611C22×C4C23×D511yescharacteristic
612C2×C8—22no—
613C2×C8—22no—
614C2×C8—52no—
615C2×C8—52no—
616C2×C8—108no—
617C2×C8—108no—
618C2×C8—102no—
619C2×C8—102no—
620C2×C8C23×D512yes—
621C2×C8C23×D512yes—
622C4⋊C4—24no—
623C4⋊C4—24no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—52no—
628C4⋊C4—52no—
629C4⋊C4—52no—
630C4⋊C4—104no—
631C4⋊C4—104no—
632C4⋊C4—104no—
633C4⋊C4—104no—
634C4⋊C4—104no—
635C4⋊C4—104no—
636C4⋊C4—104no—
637C4⋊C4—101no—
638C4⋊C4—101no—
639C4⋊C4—101no—
640C4⋊C4—104no—
641C4⋊C4—104no—
642C4⋊C4C23×D512yes—
643C4⋊C4C23×D512yes—
644C4⋊C4C23×D512yes—
645C22⋊C4—24no—
646C22⋊C4—104no—
647C22⋊C4—104no—
648C22⋊C4—104no—
649C42—54no—
650C42—54no—
651C42—52no—
652C42—52no—
653C42D4×D512yes—
654C42C23×D512yes—
655C2×C5—44no—
656C2×C5C2×#47814yescomplemented
657C2×C5C22×C22⋊Q811yescharacteristic
658C2×C5C22×#13511yescharacteristic
659C2×C5C22×AGL(1,ℤ/8)11yescharacteristic
660D5—44no—
661D5C2×#47818yesdirect product factor
662C23—24no—
663C23—22no—
664C23—42no—
665C23—42no—
666C23—54no—
667C23—54no—
668C23—54no—
669C23—52no—
670C23—1016no—
671C23—104no—
672C23—102no—
673C23—208no—
674C23—2032no—
675C23—208no—
676C23—202no—
677C23—202no—
678C23C2×D4×D511yescharacteristic
679D4—24no—
680D4—22no—
681D4—54no—
682D4—1016no—
683D4—104no—
684D4—102no—
685D4C2×Q8×D514yes—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—48no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—54no—
696C2×C4—52no—
697C2×C4—58no—
698C2×C4—54no—
699C2×C4—54no—
700C2×C4—52no—
701C2×C4—52no—
702C2×C4—108no—
703C2×C4—108no—
704C2×C4—102no—
705C2×C4—102no—
706C2×C4—102no—
707C2×C4—102no—
708C2×C4—102no—
709C2×C4—208no—
710C2×C4—208no—
711C2×C4—208no—
712C2×C4—208no—
713C2×C4—208no—
714C2×C4—208no—
715C2×C4—202no—
716C2×C4—202no—
717C2×C4—202no—
718C2×C4C2×D4×D512yes—
719C2×C4C2×D4×D512yes—
720C2×C4C2×D4×D511yescharacteristic
721C2×C4C2×Q8×D512yes—
722C2×C4D5×#4112yes—
723C2×C4C24×D511yescharacteristic
724C8—22no—
725C8—22no—
726C8—102no—
727C8—102no—
728C5C22×#47811yescharacteristic, complemented, Sylow
729C22—24no—
730C22—48no—
731C22—42no—
732C22—42no—
733C22—54no—
734C22—516no—
735C22—54no—
736C22—54no—
737C22—104no—
738C22—2032no—
739C22—208no—
740C22—202no—
741C22—202no—
742C22D5×C22⋊Q812yes—
743C22D5×#13512yes—
744C22D5×AGL(1,ℤ/8)12yes—
745C22C22×D4×D511yescharacteristic
746C4—22no—
747C4—22no—
748C4—42no—
749C4—42no—
750C4—42no—
751C4—54no—
752C4—102no—
753C4—102no—
754C4—202no—
755C4—202no—
756C4—202no—
757C4D5×C22⋊Q812yes—
758C4C22×Q8×D511yescharacteristic
759C4C2×D5×#4111yescharacteristic
760C2—44no—
761C2—58no—
762C2—204no—
763C2D5×#47814yesdirect product factor
764C2C2×D5×C22⋊Q811yescharacteristic
765C2C2×D5×#13511yescharacteristic
766C2C2×D5×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC23C2×D4×D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×#478C2
socleC23×C5C22×D4
prime radicalC22×D4×D5C22
hypercenterC2×#478D5
hypocenterC5C22×#478
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#478

Complements

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

NH ≅ G/Ntype
1. C2×D5×#125C2semidirect
3. C2×C5×#478C2semidirect
4. C2×#65355C2semidirect
5. C2×#65298C2semidirect
6. D5×#478C2direct (N × H)
7. C2×#65180C2semidirect
8. C2×D5×#107C2semidirect
9. C2×#65160C2semidirect
10. C2×D5×#106C2semidirect
11. C2×#65136C2semidirect
12. C2×D5×C4⋊C8C2semidirect
15. C2×#65052C2semidirect
16. C2×#65055C2semidirect
19. C2×C5×#125C22semidirect
26. D5×#125C22semidirect
35. C2×#4036C22semidirect
36. C2×#4036C22semidirect
43. C2×#4016C22semidirect
44. C5×#478C22semidirect
45. C2×C5×#107C22semidirect
46. C2×C5×#106C22semidirect
47. C2×C5×C4⋊C8C22semidirect
54. C2×#3950C22semidirect
55. C2×#3949C22semidirect
56. C2×#3946C22semidirect
57. C2×#3946C22semidirect
58. #65355C22semidirect
59. #65298C22semidirect
62. C2×#3940C22semidirect
63. C2×#3940C22semidirect
64. C2×#3939C22semidirect
65. C2×#3939C22semidirect
66. C2×C4⋊#168C22semidirect
67. #65180C22semidirect
68. D5×#107C22semidirect
69. #65160C22semidirect
70. D5×#106C22semidirect
71. #65136C22semidirect
72. D5×C4⋊C8C22semidirect
75. #65055C22semidirect
76. #65052C22semidirect
101. C5×#125C23semidirect
150. #4036C23semidirect
151. #4036C23semidirect
161. #4016C23semidirect
162. C5×#107C23semidirect
163. C5×#106C23semidirect
164. C5×C4⋊C8C23semidirect
171. #3950C23semidirect
172. #3949C23semidirect
173. #3946C23semidirect
174. #3946C23semidirect
177. #3940C23semidirect
178. #3940C23semidirect
179. #3939C23semidirect
180. #3939C23semidirect
181. C4⋊#168C23semidirect
192. C2×#478D5direct (N × H)
307. C2×#125C2×D5semidirect
330. #478C2×D5direct (N × H)
335. C2×#107C2×D5semidirect
340. C2×#106C2×D5semidirect
345. C2×C4⋊C8C2×D5semidirect
459. #125C22×D5semidirect
509. #107C22×D5semidirect
513. #106C22×D5semidirect
517. C4⋊C8C22×D5semidirect
539. C2×D5#478direct (N × H)
656. C2×C5C2×#478semidirect
661. D5C2×#478direct (N × H)
728. C5C22×#478semidirect
763. C2D5×#478direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D5×#1252
C2×C4×D4×D52
C2×C5×#4782
C2×#653552
C2×#652982
D5×#4782
C2×#651802
C2×D5×#1072
C2×#651602
C2×D5×#1062
C2×#651362
C2×D5×C4⋊C82
C2×D5×#1022
C2×#650522
C2×#650552
C22×#4785