Finite Group Databasebeta

← C2×#10608905 #12267124

Subgroups — C2×#10608905 #12267124

Order 1280.

3550 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×#4092C211yesmaximal, characteristic
2C22×#4090C211yesmaximal, characteristic, complemented
3C22×#4042C211yesmaximal, characteristic
4C22×D5×C4⋊C4C211yesmaximal, characteristic
5C2×C5×#395C211yesmaximal, characteristic, complemented
6C2×#65278C211yesmaximal, characteristic
7C2×#65273C211yesmaximal, characteristic, complemented
8C2×#65261C211yesmaximal, characteristic, complemented
9C2×#65265C211yesmaximal, characteristic, complemented
10#10608905C2116yesmaximal, direct product factor
11C2×#64957C211yesmaximal, characteristic
12C2×#64956C211yesmaximal, characteristic
13C2×#64946C211yesmaximal, characteristic, complemented
14C2×#64945C211yesmaximal, characteristic, complemented
15C2×#64936C211yesmaximal, characteristic, complemented
16C2×#64955C211yesmaximal, characteristic
17C23×C5×Q8C2211yescharacteristic
18C23×C4×D5C2211yescharacteristic
19C23×C4×D5C2211yescharacteristic
20C23×C4×D5C2211yescharacteristic
21C23×Dic10C2211yescharacteristic
22C22×C5×C4⋊C4C2211yescharacteristic
23C22×C5×C4⋊C4C2211yescharacteristic
24C22×C5×C4⋊C4C2211yescharacteristic
25C2×#4092—28no—
26C2×#4092C2218yes—
27C2×#4090—28no—
28C2×#4090C2218yescomplemented
29C22×#685C2211yescharacteristic
30C22×#685C2211yescharacteristic
31C22×#685C2211yescharacteristic
32C22×#685C2211yescharacteristic
33C22×C4⋊Dic5C2211yescharacteristic
34C22×C4⋊Dic5C2211yescharacteristic
35C22×C4⋊Dic5C2211yescharacteristic
36C22×#683C2211yescharacteristic
37C22×#683C2211yescharacteristic
38C22×#683C2211yescharacteristic
39C22×#683C2211yescharacteristic
40C22×#683C2211yescharacteristic
41C22×#683C2211yescharacteristic
42C22×#683C2211yescharacteristic
43C22×#683C2211yescharacteristic
44C22×#683C2211yescharacteristic
45C22×#683C2211yescharacteristic
46C22×C4×Dic5C2211yescharacteristic
47C22×C4×Dic5C2211yescharacteristic
48C2×#4042—28no—
49C2×#4042C2218yes—
50C2×D5×C4⋊C4—28no—
51C2×D5×C4⋊C4C2218yes—
52C5×#395C2218yescomplemented
53C2×C5×#95C2211yescharacteristic
54C2×C5×#95C2211yescharacteristic
55C2×C5×#95C2211yescharacteristic
56C2×#3963C2211yescharacteristic
57C2×#3963C2211yescharacteristic
58C2×#3963C2211yescharacteristic
59C2×#3963C2211yescharacteristic
60C2×#3963C2211yescharacteristic
61#65278C2218yes—
62#65273C2218yescomplemented
63#65265C2218yescomplemented
64#65261C2218yescomplemented
65#64957C2218yes—
66#64956C2218yes—
67#64955C2218yes—
68#64946C2218yescomplemented
69#64945C2218yescomplemented
70#64936C2218yescomplemented
71C2×#2440—51nomaximal, Sylow
72C24×D5C2311yescharacteristic
73C22×C5×Q8—24no—
74C22×C5×Q8—24no—
75C22×C5×Q8—42no—
76C22×C5×Q8C2314yes—
77C23×C4×C5C2311yescharacteristic
78C23×C4×C5C2311yescharacteristic
79C23×C4×C5C2311yescharacteristic
80C23×C4×C5C2311yescharacteristic
81C23×C4×C5C2311yescharacteristic
82C23×C4×C5C2311yescharacteristic
83C23×C4×C5C2311yescharacteristic
84C23×Dic5C2311yescharacteristic
85C23×Dic5C2311yescharacteristic
86C23×Dic5C2311yescharacteristic
87C23×Dic5C2311yescharacteristic
88C23×Dic5C2311yescharacteristic
89C23×Dic5C2311yescharacteristic
90C23×Dic5C2311yescharacteristic
91C22×C4×D5—24no—
92C22×C4×D5—24no—
93C22×C4×D5—24no—
94C22×C4×D5—24no—
95C22×C4×D5—24no—
96C22×C4×D5—24no—
97C22×C4×D5—42no—
98C22×C4×D5—42no—
99C22×C4×D5Q818yescomplemented
100C22×C4×D5C2314yes—
101C22×C4×D5C2314yes—
102C22×C4×D5C2314yes—
103C22×Dic10—24no—
104C22×Dic10—24no—
105C22×Dic10—42no—
106C22×Dic10C2314yes—
107C2×C5×C4⋊C4—24no—
108C2×C5×C4⋊C4—24no—
109C2×C5×C4⋊C4—42no—
110C2×C5×C4⋊C4C2314yes—
111C2×C5×C4⋊C4C2314yes—
112C2×C5×C4⋊C4C2314yes—
113#4092—232no—
114#4090—232no—
115C2×#685—24no—
116C2×#685—24no—
117C2×#685D418yes—
118C2×#685Q818yescomplemented
119C2×#685C2314yes—
120C2×#685C2314yes—
121C2×#685C2314yes—
122C2×#685C2314yes—
123C2×C4⋊Dic5—24no—
124C2×C4⋊Dic5—24no—
125C2×C4⋊Dic5—42no—
126C2×C4⋊Dic5C2314yes—
127C2×C4⋊Dic5C2314yes—
128C2×C4⋊Dic5C2314yes—
129C2×#683—24no—
130C2×#683—24no—
131C2×#683—24no—
132C2×#683—24no—
133C2×#683—24no—
134C2×#683—24no—
135C2×#683—24no—
136C2×#683—24no—
137C2×#683—24no—
138C2×#683D418yes—
139C2×#683C2314yes—
140C2×#683C2314yes—
141C2×#683C2314yes—
142C2×#683C2314yes—
143C2×#683C2314yes—
144C2×#683C2314yes—
145C2×#683C2314yes—
146C2×#683C2314yes—
147C2×#683C2314yes—
148C2×#683C2314yes—
149C2×C4×Dic5—24no—
150C2×C4×Dic5—24no—
151C2×C4×Dic5C2314yes—
152C2×C4×Dic5C2314yes—
153#4042—232no—
154D5×C4⋊C4—232no—
155C5×#95C2314yes—
156C5×#95C2314yes—
157C5×#95C2314yes—
158#3963C2314yes—
159#3963C2314yes—
160#3963C2314yes—
161#3963C2314yes—
162#3963C2314yes—
163C22×C4⋊Q8—51no—
164C22×C22⋊Q8—51no—
165C22×C22⋊Q8—51no—
166C23×C4⋊C4—51no—
167#2440—516no—
168C2×#398—51no—
169C2×#398—51no—
170C2×#395—51no—
171C2×#395D511yescharacteristic, complemented
172C2×#389—51no—
173C2×#389—51no—
174C2×#385—51no—
175C2×#385—51no—
176C2×#384—51no—
177C2×#380—51no—
178C2×C4×C22⋊C4—51no—
179C24×C5C2411yescharacteristic
180C23×D5—22no—
181C23×D5—22no—
182C23×D5—22no—
183C23×D5—22no—
184C23×D5C2×D414yes—
185C23×D5C2×Q814yes—
186C23×D5C2×Q814yes—
187C23×D5C2412yes—
188C2×C5×Q8—28no—
189C2×C5×Q8—28no—
190C2×C5×Q8—44no—
191C2×C5×Q8—416no—
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×C5—22no—
206C22×C4×C5—22no—
207C22×C4×C5—22no—
208C22×C4×C5—22no—
209C22×C4×C5C2×D414yes—
210C22×C4×C5C2×D414yes—
211C22×C4×C5C2×Q814yes—
212C22×C4×C5C2×Q814yes—
213C22×C4×C5C2412yes—
214C22×C4×C5C2412yes—
215C22×C4×C5C2412yes—
216C22×C4×C5C2412yes—
217C22×C4×C5C2412yes—
218C22×C4×C5C2412yes—
219C22×C4×C5C2412yes—
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×Dic5C2×D414yes—
236C22×Dic5C2×D414yes—
237C22×Dic5C2×D414yes—
238C22×Dic5C2×Q814yes—
239C22×Dic5C2×Q814yes—
240C22×Dic5#4114yes—
241C22×Dic5C2412yes—
242C22×Dic5C2412yes—
243C22×Dic5C2412yes—
244C22×Dic5C2412yes—
245C22×Dic5C2412yes—
246C22×Dic5C2412yes—
247C22×Dic5C2412yes—
248C2×C4×D5—232no—
249C2×C4×D5—28no—
250C2×C4×D5—28no—
251C2×C4×D5—28no—
252C2×C4×D5—28no—
253C2×C4×D5—28no—
254C2×C4×D5—28no—
255C2×C4×D5—44no—
256C2×C4×D5—44no—
257C2×C4×D5—416no—
258C2×C4×D5—416no—
259C2×C4×D5C2×Q8116yescomplemented
260C2×Dic10—28no—
261C2×Dic10—28no—
262C2×Dic10—44no—
263C2×Dic10—416no—
264C5×C4⋊C4—28no—
265C5×C4⋊C4—28no—
266C5×C4⋊C4—44no—
267#685—28no—
268#685—28no—
269#685C2×D4116yes—
270#685C2×Q8116yescomplemented
271C4⋊Dic5—28no—
272C4⋊Dic5—28no—
273C4⋊Dic5—44no—
274#683—28no—
275#683—28no—
276#683—28no—
277#683—28no—
278#683—28no—
279#683—28no—
280#683—28no—
281#683—28no—
282#683—28no—
283#683C2×D4116yes—
284C4×Dic5—28no—
285C4×Dic5—28no—
286C23×Q8—51no—
287C23×Q8C2×D511yescharacteristic
288C24×C4—51no—
289C24×C4—51no—
290C24×C4—51no—
291C2×C4⋊Q8—58no—
292C2×C4⋊Q8—108no—
293C2×C22⋊Q8—58no—
294C2×C22⋊Q8—58no—
295C2×C22⋊Q8—108no—
296C2×C22⋊Q8—108no—
297C22×C4⋊C4—51no—
298C22×C4⋊C4—51no—
299C22×C4⋊C4—51no—
300C22×C4⋊C4—51no—
301C22×C4⋊C4—51no—
302C22×C4⋊C4—51no—
303C22×C4⋊C4—51no—
304C22×C4⋊C4—51no—
305C22×C4⋊C4—51no—
306C22×C4⋊C4—51no—
307C22×C4⋊C4—51no—
308C22×C4⋊C4—51no—
309C22×C4⋊C4—51no—
310C22×C4⋊C4—58no—
311C22×C4⋊C4—108no—
312C22×C4⋊C4C2×D511yescharacteristic
313C22×C4⋊C4C2×D511yescharacteristic
314C22×C4⋊C4C2×D511yescharacteristic
315C22×C22⋊C4—51no—
316C22×C22⋊C4—51no—
317C22×C22⋊C4—51no—
318C22×C22⋊C4—51no—
319C22×C42—51no—
320C22×C42—51no—
321#398—58no—
322#398—58no—
323#395—58no—
324#395C2×D518yescomplemented
325#389—58no—
326#389—58no—
327#385—58no—
328#385—58no—
329#384—58no—
330#380—58no—
331C4×C22⋊C4—58no—
332C2×#95—51no—
333C2×#95—51no—
334C2×#95—51no—
335C2×#95—51no—
336C2×#95—51no—
337C2×#95C2×D511yescharacteristic
338C2×#95C2×D511yescharacteristic
339C2×#95C2×D511yescharacteristic
340C23×C5C22×D412yes—
341C23×C5C22×D412yes—
342C23×C5C22×Q812yes—
343C23×C5C22×Q812yes—
344C23×C5C2×#4112yes—
345C23×C5H(5,𝔽2)12yes—
346C23×C52−1+412yes—
347C23×C5C2511yescharacteristic
348C22×D5—28no—
349C22×D5—28no—
350C22×D5—28no—
351C22×D5—28no—
352C22×D5—28no—
353C22×D5—28no—
354C22×D5—22no—
355C22×D5—22no—
356C22×D5—22no—
357C22×D5—22no—
358C22×D5C4⋊Q8116yescomplemented
359C22×D5C22×D414yes—
360C22×D5C22×Q814yes—
361C22×D5C22×Q814yes—
362C5×Q8—416no—
363C2×C4×C5—28no—
364C2×C4×C5—28no—
365C2×C4×C5—28no—
366C2×C4×C5—28no—
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—22no—
383C2×C4×C5—22no—
384C2×C4×C5—44no—
385C2×C4×C5—44no—
386C2×C4×C5—44no—
387C2×C4×C5C22×D414yes—
388C2×C4×C5C22×D414yes—
389C2×C4×C5C22×Q814yes—
390C2×C4×C5C22×Q814yes—
391C2×Dic5—28no—
392C2×Dic5—28no—
393C2×Dic5—28no—
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—22no—
408C2×Dic5—22no—
409C2×Dic5—44no—
410C2×Dic5—44no—
411C2×Dic5—44no—
412C2×Dic5C22⋊Q8116yescomplemented
413C2×Dic5C22×D414yes—
414C2×Dic5C22×D414yes—
415C2×Dic5C22×D414yes—
416C2×Dic5C22×Q814yes—
417C2×Dic5C22×Q814yes—
418C2×Dic5C2×#4114yes—
419C4×D5—232no—
420C4×D5—416no—
421C4×D5—416no—
422Dic10—416no—
423C25—51no—
424C22×Q8—24no—
425C22×Q8—24no—
426C22×Q8—42no—
427C22×Q8—54no—
428C22×Q8—104no—
429C22×Q8—104no—
430C22×Q8—202no—
431C22×Q8C22×D514yes—
432C23×C4—51no—
433C23×C4—51no—
434C23×C4—51no—
435C23×C4—51no—
436C23×C4—58no—
437C23×C4—54no—
438C23×C4—51no—
439C23×C4—51no—
440C23×C4—51no—
441C23×C4—54no—
442C23×C4—54no—
443C23×C4—104no—
444C23×C4—104no—
445C23×C4—104no—
446C23×C4—104no—
447C23×C4—104no—
448C23×C4—104no—
449C23×C4—202no—
450C23×C4—202no—
451C23×C4C22×D511yescharacteristic
452C23×C4C22×D511yescharacteristic
453C23×C4C22×D511yescharacteristic
454C23×C4C22×D511yescharacteristic
455C23×C4C22×D511yescharacteristic
456C23×C4C22×D511yescharacteristic
457C23×C4C22×D511yescharacteristic
458C4⋊Q8—1032no—
459C22⋊Q8—1032no—
460C22⋊Q8—1032no—
461C2×C4⋊C4—24no—
462C2×C4⋊C4—24no—
463C2×C4⋊C4—42no—
464C2×C4⋊C4—58no—
465C2×C4⋊C4—54no—
466C2×C4⋊C4—54no—
467C2×C4⋊C4—54no—
468C2×C4⋊C4—54no—
469C2×C4⋊C4—54no—
470C2×C4⋊C4—54no—
471C2×C4⋊C4—54no—
472C2×C4⋊C4—54no—
473C2×C4⋊C4—54no—
474C2×C4⋊C4—54no—
475C2×C4⋊C4—54no—
476C2×C4⋊C4—54no—
477C2×C4⋊C4—54no—
478C2×C4⋊C4—1032no—
479C2×C4⋊C4—104no—
480C2×C4⋊C4—104no—
481C2×C4⋊C4—104no—
482C2×C4⋊C4—104no—
483C2×C4⋊C4—104no—
484C2×C4⋊C4—104no—
485C2×C4⋊C4—104no—
486C2×C4⋊C4—104no—
487C2×C4⋊C4—104no—
488C2×C4⋊C4—104no—
489C2×C4⋊C4—104no—
490C2×C4⋊C4—202no—
491C2×C4⋊C4C22×D514yes—
492C2×C4⋊C4C22×D514yes—
493C2×C4⋊C4C22×D514yes—
494C2×C22⋊C4—58no—
495C2×C22⋊C4—58no—
496C2×C22⋊C4—54no—
497C2×C22⋊C4—54no—
498C2×C22⋊C4—54no—
499C2×C22⋊C4—54no—
500C2×C22⋊C4—104no—
501C2×C22⋊C4—104no—
502C2×C42—54no—
503C2×C42—54no—
504C2×C42—104no—
505C2×C42—104no—
506#95—54no—
507#95—54no—
508#95—54no—
509#95—54no—
510#95—54no—
511#95C22×D514yes—
512#95C22×D514yes—
513#95C22×D514yes—
514C22×C5C2×C22⋊Q814yes—
515C22×C5C2×C4⋊Q814yes—
516C22×C5#54414yes—
517C22×C5D4214yes—
518C22×C5#54714yes—
519C22×C5D4×Q814yes—
520C22×C5#55414yes—
521C22×C5C23×D411yescharacteristic
522C22×C5C23×D411yescharacteristic
523C22×C5C23×Q811yescharacteristic
524C22×C5C23×Q811yescharacteristic
525C22×C5C22×#4111yescharacteristic
526C22×C5C2×H(5,𝔽2)11yescharacteristic
527C22×C5C2×2−1+411yescharacteristic
528C2×D5—24no—
529C2×D5—24no—
530C2×D5—24no—
531C2×D5—232no—
532C2×D5—24no—
533C2×D5—24no—
534C2×D5—24no—
535C2×D5C2×C4⋊Q818yescomplemented
536C4×C5—24no—
537C4×C5—24no—
538C4×C5—24no—
539C4×C5—24no—
540C4×C5—42no—
541C4×C5—42no—
542C4×C5—42no—
543Dic5—24no—
544Dic5—24no—
545Dic5—24no—
546Dic5—42no—
547Dic5—42no—
548Dic5—42no—
549Dic5C2×C22⋊Q818yescomplemented
550C24—54no—
551C24—54no—
552C24—54no—
553C24—52no—
554C24—102no—
555C24—102no—
556C24—102no—
557C24—102no—
558C24C23×D511yescharacteristic
559C2×Q8—28no—
560C2×Q8—28no—
561C2×Q8—44no—
562C2×Q8—416no—
563C2×Q8—108no—
564C2×Q8—108no—
565C2×Q8—204no—
566C2×Q8—2016no—
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—54no—
589C22×C4—54no—
590C22×C4—54no—
591C22×C4—52no—
592C22×C4—52no—
593C22×C4—52no—
594C22×C4—516no—
595C22×C4—52no—
596C22×C4—52no—
597C22×C4—52no—
598C22×C4—108no—
599C22×C4—1032no—
600C22×C4—108no—
601C22×C4—108no—
602C22×C4—108no—
603C22×C4—108no—
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—102no—
616C22×C4—102no—
617C22×C4—102no—
618C22×C4—102no—
619C22×C4—108no—
620C22×C4—204no—
621C22×C4—204no—
622C22×C4—2016no—
623C22×C4—2016no—
624C22×C4D4×D514yes—
625C22×C4D4×D514yes—
626C22×C4Q8×D514yes—
627C22×C4Q8×D514yes—
628C22×C4C23×D512yes—
629C22×C4C23×D512yes—
630C22×C4C23×D512yes—
631C22×C4C23×D512yes—
632C22×C4C23×D512yes—
633C22×C4C23×D512yes—
634C22×C4C23×D512yes—
635C4⋊C4—28no—
636C4⋊C4—28no—
637C4⋊C4—44no—
638C4⋊C4—516no—
639C4⋊C4—108no—
640C4⋊C4—108no—
641C4⋊C4—108no—
642C4⋊C4—108no—
643C4⋊C4—108no—
644C4⋊C4—108no—
645C4⋊C4—108no—
646C4⋊C4—108no—
647C4⋊C4—108no—
648C4⋊C4—108no—
649C4⋊C4—108no—
650C4⋊C4—204no—
651C22⋊C4—516no—
652C22⋊C4—516no—
653C22⋊C4—108no—
654C22⋊C4—108no—
655C42—108no—
656C42—108no—
657C2×C5#244018yescomplemented
658C2×C5C22×C22⋊Q811yescharacteristic
659C2×C5C22×C4⋊Q811yescharacteristic
660C2×C5C2×#54411yescharacteristic
661C2×C5C2×D4211yescharacteristic
662C2×C5C2×#54711yescharacteristic
663C2×C5C2×D4×Q811yescharacteristic
664C2×C5C2×#55411yescharacteristic
665D5—28no—
666C23—516no—
667C23—54no—
668C23—54no—
669C23—54no—
670C23—108no—
671C23—108no—
672C23—108no—
673C23—108no—
674C23—108no—
675C23—108no—
676C23—102no—
677C23—102no—
678C23—102no—
679C23—102no—
680C23C2×D4×D512yes—
681C23C2×D4×D512yes—
682C23#414412yes—
683C23C2×Q8×D512yes—
684C23C2×Q8×D512yes—
685C23#414712yes—
686C23D5×#4112yes—
687C23C24×D511yescharacteristic
688Q8—416no—
689Q8—2016no—
690C2×C4—28no—
691C2×C4—28no—
692C2×C4—28no—
693C2×C4—28no—
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—22no—
710C2×C4—22no—
711C2×C4—44no—
712C2×C4—44no—
713C2×C4—44no—
714C2×C4—516no—
715C2×C4—54no—
716C2×C4—54no—
717C2×C4—54no—
718C2×C4—54no—
719C2×C4—54no—
720C2×C4—54no—
721C2×C4—1032no—
722C2×C4—108no—
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—2016no—
741C2×C4—2016no—
742C2×C4—204no—
743C2×C4—204no—
744C2×C4—204no—
745C2×C4C2×D4×D514yes—
746C2×C4C2×D4×D514yes—
747C2×C4C2×Q8×D514yes—
748C2×C4C2×Q8×D514yes—
749C5C2×#244011yescharacteristic, complemented, Sylow
750C22—58no—
751C22—104no—
752C22—1032no—
753C22—104no—
754C22—104no—
755C22—104no—
756C22—104no—
757C22—104no—
758C22#6592414yes—
759C22D5×C22⋊Q814yes—
760C22#6596514yes—
761C22#6597014yes—
762C22D5×C4⋊Q814yes—
763C22#6606114yes—
764C22#6606314yes—
765C22C22×D4×D511yescharacteristic
766C22C22×D4×D511yescharacteristic
767C22C2×#414411yescharacteristic
768C22C22×Q8×D511yescharacteristic
769C22C22×Q8×D511yescharacteristic
770C22C2×#414711yescharacteristic
771C22C2×D5×#4111yescharacteristic
772C4—24no—
773C4—24no—
774C4—24no—
775C4—24no—
776C4—42no—
777C4—42no—
778C4—42no—
779C4—58no—
780C4—104no—
781C4—104no—
782C4—104no—
783C4—202no—
784C4—202no—
785C4—202no—
786C2—108no—
787C2#1060890518yesdirect product factor
788C2C2×#6592411yescharacteristic
789C2C2×#6597011yescharacteristic
790C2C2×D5×C22⋊Q811yescharacteristic
791C2C2×#6596511yescharacteristic
792C2C2×D5×C4⋊Q811yescharacteristic
793C2C2×#6606311yescharacteristic
794C2C2×#6606111yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC2×C5×#395C2
socleC24×C5C24
prime radicalC24×D5C23
hypercenterC2×#395D5
hypocenterC5C2×#2440
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#395

Complements

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

NH ≅ G/Ntype
2. C22×#4090C2semidirect
5. C2×C5×#395C2semidirect
7. C2×#65273C2semidirect
8. C2×#65261C2semidirect
9. C2×#65265C2semidirect
10. #10608905C2direct (N × H)
13. C2×#64946C2semidirect
14. C2×#64945C2semidirect
15. C2×#64936C2semidirect
28. C2×#4090C22semidirect
52. C5×#395C22semidirect
62. #65273C22semidirect
63. #65265C22semidirect
64. #65261C22semidirect
68. #64946C22semidirect
69. #64945C22semidirect
70. #64936C22semidirect
99. C22×C4×D5Q8semidirect
118. C2×#685Q8semidirect
171. C2×#395D5semidirect
259. C2×C4×D5C2×Q8semidirect
270. #685C2×Q8semidirect
324. #395C2×D5semidirect
358. C22×D5C4⋊Q8semidirect
412. C2×Dic5C22⋊Q8semidirect
535. C2×D5C2×C4⋊Q8semidirect
549. Dic5C2×C22⋊Q8semidirect
657. C2×C5#2440semidirect
749. C5C2×#2440semidirect
787. C2#10608905direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#40922
C22×#40902
C22×#40422
C22×D5×C4⋊C42
C2×C5×#3952
C2×#652782
C2×#652732
C2×#652612
C2×#652652
#106089052
C2×#649572
C2×#649562
C2×#649462
C2×#649452
C2×#649362
C2×#649552
C2×#24405