Finite Group Databasebeta

← C2×#10612272 #12970470

Subgroups — C2×#10612272 #12970470

Order 1280.

2294 conjugacy classes of subgroups.

The subgroup lattice has 838 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D5×#124C211yesmaximal, characteristic, complemented
2C2×#65891C211yesmaximal, characteristic, complemented
3C2×C5×#463C211yesmaximal, characteristic, complemented
4C2×#65459C211yesmaximal, characteristic, complemented
5C2×#65457C211yesmaximal, characteristic, complemented
6C2×#65445C211yesmaximal, characteristic
7C2×#65444C211yesmaximal, characteristic, complemented
8C2×#65343C211yesmaximal, characteristic, complemented
9C2×#65305C211yesmaximal, characteristic, complemented
10#10612272C2116yesmaximal, direct product factor
11C2×#65134C211yesmaximal, characteristic, complemented
12C2×#65122C211yesmaximal, characteristic, complemented
13C2×#65097C211yesmaximal, characteristic, complemented
14C2×#65089C211yesmaximal, characteristic, complemented
15C2×#65065C211yesmaximal, characteristic, complemented
16C2×#65057C211yesmaximal, characteristic, complemented
17C22×Q8×D5C2211yescharacteristic
18C22×D4×D5C2211yescharacteristic
19C22×C5×SD16C2211yescharacteristic, complemented
20C22×C5×D8C2211yescharacteristic
21C2×C5×#124C2211yescharacteristic
22C2×C4×C5×D4C2211yescharacteristic, complemented
23C2×#4093C2211yescharacteristic
24C22×#689C2211yescharacteristic, complemented
25C2×#4084C2211yescharacteristic
26C2×#4082C2211yescharacteristic
27C2×#4082C2211yescharacteristic, complemented
28C22×#687C2211yescharacteristic
29C22×#687C2211yescharacteristic, complemented
30C22×#686C2211yescharacteristic
31C2×C4×C22⋊D5—21no—
32C2×#4072—21no—
33C22×Dic20C2211yescharacteristic, complemented
34C22×#677C2211yescharacteristic
35D5×#124—24no—
36D5×#124C2218yescomplemented
37#65891—24no—
38#65891C2218yescomplemented
39C2×#4043C2211yescharacteristic
40C2×#4036C2211yescharacteristic, complemented
41C2×#4031—21no—
42C2×#4031—21no—
43C2×#4029—21no—
44C2×D5×C22⋊C4—21no—
45C2×D5×C22⋊C4—21no—
46C2×#4025—21no—
47C2×#4021C2211yescharacteristic
48C2×C42×D5C2211yescharacteristic
49C2×C4×Dic10C2211yescharacteristic, complemented
50C5×#463C2218yescomplemented
51C2×C5×C4⋊C8C2211yescharacteristic, complemented
52C2×C5×#103C2211yescharacteristic, complemented
53C2×C5×#102C2211yescharacteristic
54C2×#3967C2211yescharacteristic, complemented
55C2×#3964C2211yescharacteristic
56#65459C2218yescomplemented
57#65457C2218yescomplemented
58#65445C2218yes—
59#65444C2218yescomplemented
60C2×#3953C2211yescharacteristic
61C2×#3952C2211yescharacteristic
62C2×#3952C2211yescharacteristic
63C2×#3948C2211yescharacteristic, complemented
64C2×C8×Dic5C2211yescharacteristic, complemented
65C2×C8×Dic5C2211yescharacteristic, complemented
66#65343C2218yescomplemented
67#65305C2218yescomplemented
68C2×#3942C2211yescharacteristic, complemented
69C2×#3941C2211yescharacteristic
70C2×C4⋊#168C2211yescharacteristic, complemented
71#65134C2218yescomplemented
72#65122C2218yescomplemented
73#65097C2218yescomplemented
74#65089C2218yescomplemented
75#65065C2218yescomplemented
76#65057C2218yescomplemented
77C2×#3211—51nomaximal, Sylow
78C24×D5—21no—
79C22×C5×Q8C2311yescharacteristic
80C22×C5×D4C2311yescharacteristic
81C22×C5×D4C2311yescharacteristic
82C23×C4×C5—21no—
83C22×C22⋊D5—21no—
84C22×C22⋊D5—21no—
85C2×Q8×D5—22no—
86C2×Q8×D5—42no—
87C2×Q8×D5—42no—
88C2×Q8×D5C2314yes—
89C2×D4×D5—22no—
90C2×D4×D5—42no—
91C2×D4×D5—42no—
92C2×D4×D5C2314yes—
93C22×D20C2311yescharacteristic
94C22×C4×D5—21no—
95C22×C4×D5D411yescharacteristic
96C22×C4×D5D411yescharacteristic
97C22×C4×D5C2311yescharacteristic
98C22×Dic10—21no—
99C22×Dic10C2311yescharacteristic
100C22×Dic10C2311yescharacteristic
101C2×C5×SD16—42no—
102C2×C5×SD16C2314yescomplemented
103C2×C5×D8—42no—
104C2×C5×D8C2314yes—
105C22×C5×C8C2311yescharacteristic
106C22×C5×C8C2311yescharacteristic
107C5×#124—22no—
108C5×#124C2314yes—
109C4×C5×D4—22no—
110C4×C5×D4C2314yescomplemented
111C2×C5×C4⋊C4C2311yescharacteristic
112C2×C5×C22⋊C4—21no—
113C2×C5×C22⋊C4—21no—
114C2×C5×C22⋊C4—21no—
115C2×C42×C5C2311yescharacteristic
116C2×C22⋊Dic5—21no—
117C2×C22⋊Dic5—21no—
118C2×C22⋊Dic5—21no—
119C2×C22⋊Dic5—21no—
120C2×C22⋊Dic5—21no—
121#4093—22no—
122#4093C2314yes—
123C2×#689—42no—
124C2×#689C2314yescomplemented
125#4084—22no—
126#4084C2314yes—
127#4082—22no—
128#4082—22no—
129#4082C2314yes—
130#4082C2314yescomplemented
131C2×#687—42no—
132C2×#687—42no—
133C2×#687C2314yes—
134C2×#687C2314yescomplemented
135C2×#686—42no—
136C2×#686C2314yes—
137C4×C22⋊D5—28no—
138C2×#685—21no—
139C2×#685—21no—
140C2×#685—21no—
141C2×#685—21no—
142C2×#685—21no—
143#4072—28no—
144C2×C4⋊Dic5—21no—
145C2×C4⋊Dic5—21no—
146C2×C4⋊Dic5C2311yescharacteristic
147C2×#683—21no—
148C2×#683—21no—
149C2×C4×Dic5—21no—
150C2×C4×Dic5D411yescharacteristic
151C2×C4×Dic5D411yescharacteristic
152C2×C4×Dic5C2311yescharacteristic
153C22×#168C2311yescharacteristic
154C22×#168C2311yescharacteristic
155C2×Dic20—42no—
156C2×Dic20C2314yescomplemented
157C2×#677—42no—
158C2×#677C2314yes—
159#4043—22no—
160#4043C2314yes—
161#4036—22no—
162#4036C2314yescomplemented
163#4031—28no—
164#4031—28no—
165#4029—28no—
166D5×C22⋊C4—28no—
167D5×C22⋊C4—28no—
168#4025—28no—
169#4021—22no—
170#4021C2314yes—
171C42×D5D414yes—
172C42×D5C2314yes—
173C4×Dic10—22no—
174C4×Dic10C2314yescomplemented
175C5×C4⋊C8C2314yescomplemented
176C5×#103C2314yescomplemented
177C5×#102C2314yes—
178#3967C2314yescomplemented
179#3964C2314yes—
180#3953C2314yes—
181#3952C2314yes—
182#3952C2314yes—
183#3948C2314yescomplemented
184C8×Dic5C2314yescomplemented
185C8×Dic5C2314yescomplemented
186#3942C2314yescomplemented
187#3941C2314yes—
188C4⋊#168C2314yescomplemented
189C2×#529—51no—
190C22×#124—51no—
191#3211—516no—
192C2×#495—51no—
193C2×#495—51no—
194C2×#488—51no—
195C2×#488—51no—
196C2×#464—51no—
197C2×#464—51no—
198C2×#463—51no—
199C2×#463D511yescharacteristic, complemented
200C2×#451—51no—
201C2×#448—51no—
202C2×#450—51no—
203C2×#447—51no—
204C2×#431—51no—
205C24×C5—21no—
206C24×C5—21no—
207C23×D5—21no—
208C23×D5—24no—
209C23×D5—44no—
210C23×D5—44no—
211C23×D5—44no—
212C23×D5C2×D411yescharacteristic
213C2×C5×Q8—21no—
214C2×C5×Q8—22no—
215C2×C5×Q8—22no—
216C2×C5×Q8C2412yes—
217C2×C5×D4—21no—
218C2×C5×D4—21no—
219C2×C5×D4—22no—
220C2×C5×D4—22no—
221C2×C5×D4—22no—
222C2×C5×D4—22no—
223C2×C5×D4C2412yes—
224C2×C5×D4C2412yes—
225C22×C4×C5—21no—
226C22×C4×C5—21no—
227C22×C4×C5—24no—
228C22×C4×C5—44no—
229C22×C4×C5C2×D411yescharacteristic
230C22×C4×C5C2×D411yescharacteristic
231C22×C4×C5C2411yescharacteristic
232C2×C22⋊D5—24no—
233C2×C22⋊D5—24no—
234C2×C22⋊D5—44no—
235C2×C22⋊D5—44no—
236C22×Dic5—21no—
237C22×Dic5—21no—
238C22×Dic5—21no—
239C22×Dic5C2×D411yescharacteristic
240C22×Dic5C2×D411yescharacteristic
241C22×Dic5C2×D411yescharacteristic
242Q8×D5—44no—
243Q8×D5—44no—
244Q8×D5—48no—
245D4×D5—44no—
246D4×D5—44no—
247D4×D5—48no—
248C2×D20—22no—
249C2×D20—22no—
250C2×D20—21no—
251C2×D20C2412yes—
252C2×C4×D5—24no—
253C2×C4×D5—22no—
254C2×C4×D5—22no—
255C2×C4×D5—24no—
256C2×C4×D5—42no—
257C2×C4×D5—44no—
258C2×C4×D5C2×D414yes—
259C2×C4×D5C2×D412yes—
260C2×C4×D5C2×D414yes—
261C2×C4×D5C2412yes—
262C2×Dic10—22no—
263C2×Dic10—22no—
264C2×Dic10—22no—
265C2×Dic10—22no—
266C2×Dic10—21no—
267C2×Dic10—21no—
268C2×Dic10—24no—
269C2×Dic10—44no—
270C2×Dic10C2412yes—
271C2×Dic10C2412yes—
272C5×SD16—44no—
273C5×D8—44no—
274C2×C5×C8—22no—
275C2×C5×C8—22no—
276C2×C5×C8C2412yes—
277C2×C5×C8C2412yes—
278C5×C4⋊C4—21no—
279C5×C4⋊C4C2412yes—
280C5×C22⋊C4—24no—
281C5×C22⋊C4—24no—
282C5×C22⋊C4—24no—
283C42×C5C2×D412yes—
284C42×C5C2412yes—
285C22⋊Dic5—24no—
286C22⋊Dic5—24no—
287C22⋊Dic5—24no—
288C22⋊Dic5—24no—
289C22⋊Dic5—24no—
290#689—44no—
291#687—44no—
292#687—44no—
293#686—44no—
294#685—24no—
295#685—24no—
296#685—24no—
297#685—24no—
298#685—24no—
299C4⋊Dic5—21no—
300C4⋊Dic5—24no—
301C4⋊Dic5—24no—
302C4⋊Dic5C2412yes—
303#683—24no—
304#683—24no—
305C4×Dic5—24no—
306C4×Dic5C2×D412yes—
307C4×Dic5C2×D414yes—
308C4×Dic5C2×D414yes—
309C4×Dic5C2412yes—
310C2×#168—22no—
311C2×#168—22no—
312C2×#168C2412yes—
313C2×#168C2412yes—
314Dic20—44no—
315#677—44no—
316C23×Q8—51no—
317C23×D4—51no—
318C22×Q16—51no—
319C22×Q16—51no—
320C22×SD16—51no—
321C22×SD16—51no—
322C22×SD16—51no—
323C22×SD16C2×D511yescharacteristic, complemented
324C22×D8—51no—
325C22×D8C2×D511yescharacteristic
326#529—58no—
327#529—104no—
328C2×#126—101no—
329C2×#125—51no—
330C2×#124—51no—
331C2×#124—51no—
332C2×#124—51no—
333C2×#124—58no—
334C2×#124—51no—
335C2×#124—101no—
336C2×#124—101no—
337C2×#124—104no—
338C2×#124C2×D511yescharacteristic
339C2×#123—101no—
340C2×C22⋊Q8—51no—
341C2×#121—51no—
342C2×C4×Q8—51no—
343C2×C4×D4—101no—
344C2×C4×D4C2×D511yescharacteristic, complemented
345C2×#117—101no—
346C22×C22⋊C4—101no—
347C22×C22⋊C4—101no—
348C22×C42—51no—
349#495—58no—
350#495—58no—
351#488—58no—
352#488—58no—
353#464—58no—
354#464—58no—
355#463—58no—
356#463C2×D518yescomplemented
357#451—58no—
358#450—58no—
359#448—58no—
360#447—58no—
361#431—58no—
362C2×C4⋊C8—51no—
363C2×C4⋊C8C2×D511yescharacteristic, complemented
364C2×#103—51no—
365C2×#103—51no—
366C2×#103—51no—
367C2×#103C2×D511yescharacteristic, complemented
368C2×#102—51no—
369C2×#102—51no—
370C2×#102—51no—
371C2×#102C2×D511yescharacteristic
372C2×C22⋊C8—51no—
373C2×C22⋊C8—51no—
374C2×C4×C8—51no—
375C2×C4×C8—51no—
376C23×C5—22no—
377C23×C5—22no—
378C23×C5—42no—
379C23×C5—42no—
380C23×C5—42no—
381C23×C5—42no—
382C23×C5—42no—
383C23×C5—42no—
384C23×C5C22×D411yescharacteristic
385C22×D5—22no—
386C22×D5—22no—
387C22×D5—22no—
388C22×D5—48no—
389C22×D5—48no—
390C22×D5—42no—
391C22×D5—42no—
392C22×D5—42no—
393C22×D5—48no—
394C22×D5—816no—
395C22×D5#13514yes—
396C22×D5C22×D412yes—
397C5×Q8—22no—
398C5×Q8—22no—
399C5×Q8—42no—
400C5×D4—22no—
401C5×D4—22no—
402C5×D4—22no—
403C5×D4—22no—
404C5×D4—42no—
405C5×D4—42no—
406C2×C4×C5—22no—
407C2×C4×C5—22no—
408C2×C4×C5—22no—
409C2×C4×C5—22no—
410C2×C4×C5—48no—
411C2×C4×C5—42no—
412C2×C4×C5—42no—
413C2×C4×C5C22×D412yes—
414C2×C4×C5C22×D412yes—
415C2×C4×C5C22×D411yescharacteristic
416C2×C4×C5H(5,𝔽2)12yes—
417C2×C4×C5H(5,𝔽2)12yes—
418C2×C4×C5C2511yescharacteristic
419C22⋊D5—48no—
420C22⋊D5—48no—
421C2×Dic5—22no—
422C2×Dic5—22no—
423C2×Dic5—22no—
424C2×Dic5—22no—
425C2×Dic5—22no—
426C2×Dic5—22no—
427C2×Dic5—42no—
428C2×Dic5—42no—
429C2×Dic5—42no—
430C2×Dic5C22×D412yes—
431C2×Dic5C22×D412yes—
432C2×Dic5C22×D412yes—
433D20—22no—
434D20—22no—
435D20—42no—
436C4×D5—28no—
437C4×D5—24no—
438C4×D5—22no—
439C4×D5—22no—
440C4×D5—44no—
441C4×D5—48no—
442Dic10—22no—
443Dic10—22no—
444Dic10—22no—
445Dic10—22no—
446Dic10—48no—
447Dic10—42no—
448Dic10—42no—
449C5×C8—22no—
450C5×C8—22no—
451#168—22no—
452#168—22no—
453C25—101no—
454C22×Q8—54no—
455C22×Q8—51no—
456C22×Q8—51no—
457C22×Q8—101no—
458C22×Q8—102no—
459C22×Q8—202no—
460C22×Q8—202no—
461C22×Q8C22×D511yescharacteristic
462C22×D4—54no—
463C22×D4—51no—
464C22×D4—102no—
465C22×D4—101no—
466C22×D4—101no—
467C22×D4—202no—
468C22×D4—202no—
469C22×D4C22×D511yescharacteristic
470C22×D4C22×D511yescharacteristic
471C23×C4—21no—
472C23×C4—51no—
473C23×C4—51no—
474C23×C4—51no—
475C23×C4—101no—
476C2×Q16—54no—
477C2×Q16—54no—
478C2×Q16—202no—
479C2×Q16—202no—
480C2×SD16—42no—
481C2×SD16—54no—
482C2×SD16—54no—
483C2×SD16—54no—
484C2×SD16—202no—
485C2×SD16—202no—
486C2×SD16—202no—
487C2×SD16C22×D514yescomplemented
488C2×D8—42no—
489C2×D8—54no—
490C2×D8—202no—
491C2×D8C22×D514yes—
492C22×C8—51no—
493C22×C8—51no—
494C22×C8C22×D511yescharacteristic
495C22×C8C22×D511yescharacteristic
496#126—108no—
497#125—54no—
498#125—102no—
499#124—22no—
500#124—54no—
501#124—54no—
502#124—54no—
503#124—54no—
504#124—108no—
505#124—108no—
506#124—102no—
507#124—102no—
508#124—102no—
509#124—102no—
510#124C22×D514yes—
511#123—108no—
512C22⋊Q8—54no—
513C22⋊Q8—102no—
514#121—54no—
515#121—102no—
516C4×Q8—54no—
517C4×Q8—102no—
518C4×D4—22no—
519C4×D4—108no—
520C4×D4C22×D514yescomplemented
521#117—108no—
522C2×C4⋊C4—51no—
523C2×C4⋊C4—101no—
524C2×C4⋊C4—101no—
525C2×C4⋊C4—101no—
526C2×C4⋊C4—101no—
527C2×C4⋊C4C22×D511yescharacteristic
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—108no—
532C2×C22⋊C4—108no—
533C2×C22⋊C4—101no—
534C2×C22⋊C4—101no—
535C2×C22⋊C4—101no—
536C2×C22⋊C4—101no—
537C2×C22⋊C4—101no—
538C2×C22⋊C4—101no—
539C2×C22⋊C4—101no—
540C2×C22⋊C4—101no—
541C2×C22⋊C4—101no—
542C2×C22⋊C4—101no—
543C2×C42—51no—
544C2×C42—51no—
545C2×C42—51no—
546C2×C42—54no—
547C2×C42—54no—
548C2×C42—101no—
549C2×C42C22×D511yescharacteristic
550C4⋊C8—54no—
551C4⋊C8C22×D514yescomplemented
552#103—54no—
553#103—54no—
554#103—54no—
555#103C22×D514yescomplemented
556#102—54no—
557#102—54no—
558#102—54no—
559#102C22×D514yes—
560C22⋊C8—54no—
561C22⋊C8—54no—
562C4×C8—54no—
563C4×C8—54no—
564C22×C5—42no—
565C22×C5—42no—
566C22×C5—42no—
567C22×C5—42no—
568C22×C5—42no—
569C22×C5—42no—
570C22×C5—84no—
571C22×C5—84no—
572C22×C5#53512yes—
573C22×C5C2×#13512yes—
574C22×C5#57512yes—
575C22×C5C23×D411yescharacteristic
576C2×D5—22no—
577C2×D5—28no—
578C2×D5—22no—
579C2×D5—42no—
580C2×D5—42no—
581C2×D5—42no—
582C2×D5—816no—
583C2×D5—84no—
584C2×D5C2×#13514yes—
585C4×C5—22no—
586C4×C5—22no—
587C4×C5—42no—
588C4×C5—42no—
589C4×C5#53512yes—
590C4×C5C2×H(5,𝔽2)11yescharacteristic
591C4×C5C2×H(5,𝔽2)11yescharacteristic
592Dic5—22no—
593Dic5—22no—
594Dic5—22no—
595Dic5—42no—
596Dic5—42no—
597Dic5—42no—
598C24—21no—
599C24—21no—
600C24—51no—
601C24—104no—
602C24—101no—
603C24—204no—
604C24—204no—
605C24—204no—
606C2×Q8—21no—
607C2×Q8—22no—
608C2×Q8—22no—
609C2×Q8—52no—
610C2×Q8—52no—
611C2×Q8—104no—
612C2×Q8—101no—
613C2×Q8—101no—
614C2×Q8—102no—
615C2×Q8—102no—
616C2×Q8—102no—
617C2×Q8—102no—
618C2×Q8—204no—
619C2×Q8—204no—
620C2×Q8—204no—
621C2×Q8—208no—
622C2×Q8C23×D512yes—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—22no—
626C2×D4—22no—
627C2×D4—22no—
628C2×D4—22no—
629C2×D4—52no—
630C2×D4—104no—
631C2×D4—104no—
632C2×D4—101no—
633C2×D4—102no—
634C2×D4—102no—
635C2×D4—204no—
636C2×D4—204no—
637C2×D4—208no—
638C2×D4—204no—
639C2×D4—204no—
640C2×D4C23×D512yes—
641C2×D4C23×D512yes—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—24no—
645C22×C4—44no—
646C22×C4—51no—
647C22×C4—51no—
648C22×C4—51no—
649C22×C4—54no—
650C22×C4—52no—
651C22×C4—52no—
652C22×C4—54no—
653C22×C4—104no—
654C22×C4—104no—
655C22×C4—102no—
656C22×C4—102no—
657C22×C4—101no—
658C22×C4—101no—
659C22×C4—101no—
660C22×C4—202no—
661C22×C4—204no—
662C22×C4D4×D511yescharacteristic
663C22×C4D4×D511yescharacteristic
664C22×C4C23×D511yescharacteristic
665Q16—204no—
666Q16—204no—
667SD16—44no—
668SD16—204no—
669SD16—204no—
670SD16—204no—
671D8—44no—
672D8—204no—
673C2×C8—22no—
674C2×C8—22no—
675C2×C8—52no—
676C2×C8—52no—
677C2×C8—102no—
678C2×C8—102no—
679C2×C8C23×D512yes—
680C2×C8C23×D512yes—
681C4⋊C4—21no—
682C4⋊C4—52no—
683C4⋊C4—104no—
684C4⋊C4—104no—
685C4⋊C4—104no—
686C4⋊C4—101no—
687C4⋊C4—104no—
688C4⋊C4C23×D512yes—
689C22⋊C4—24no—
690C22⋊C4—24no—
691C22⋊C4—24no—
692C22⋊C4—104no—
693C22⋊C4—104no—
694C22⋊C4—104no—
695C22⋊C4—104no—
696C22⋊C4—104no—
697C22⋊C4—104no—
698C22⋊C4—104no—
699C22⋊C4—104no—
700C22⋊C4—104no—
701C22⋊C4—104no—
702C42—54no—
703C42—52no—
704C42—54no—
705C42—52no—
706C42—104no—
707C42D4×D512yes—
708C42C23×D512yes—
709C2×C5—82no—
710C2×C5—82no—
711C2×C5#321114yescomplemented
712C2×C5C2×#53511yescharacteristic
713C2×C5C22×#13511yescharacteristic
714C2×C5C2×#57511yescharacteristic
715D5—24no—
716D5—82no—
717C23—22no—
718C23—22no—
719C23—42no—
720C23—42no—
721C23—42no—
722C23—42no—
723C23—42no—
724C23—42no—
725C23—54no—
726C23—52no—
727C23—102no—
728C23—102no—
729C23—102no—
730C23—208no—
731C23—208no—
732C23—208no—
733C23—202no—
734C23—202no—
735C23—202no—
736C23—4016no—
737C23C2×D4×D511yescharacteristic
738Q8—22no—
739Q8—22no—
740Q8—42no—
741Q8—102no—
742Q8—102no—
743Q8—102no—
744Q8—102no—
745Q8—208no—
746Q8—202no—
747Q8—202no—
748D4—22no—
749D4—22no—
750D4—22no—
751D4—22no—
752D4—42no—
753D4—42no—
754D4—102no—
755D4—102no—
756D4—208no—
757D4—208no—
758D4—202no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—48no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—52no—
767C2×C4—52no—
768C2×C4—52no—
769C2×C4—108no—
770C2×C4—102no—
771C2×C4—102no—
772C2×C4—102no—
773C2×C4—104no—
774C2×C4—102no—
775C2×C4—102no—
776C2×C4—102no—
777C2×C4—102no—
778C2×C4—102no—
779C2×C4—204no—
780C2×C4—208no—
781C2×C4—202no—
782C2×C4—202no—
783C2×C4—202no—
784C2×C4C2×D4×D512yes—
785C2×C4C2×D4×D512yes—
786C2×C4C2×D4×D511yescharacteristic
787C2×C4#414412yes—
788C2×C4#414912yes—
789C2×C4C24×D511yescharacteristic
790C8—22no—
791C8—22no—
792C8—102no—
793C8—102no—
794C5C2×#321111yescharacteristic, complemented, Sylow
795C22—42no—
796C22—42no—
797C22—42no—
798C22—42no—
799C22—42no—
800C22—42no—
801C22—54no—
802C22—84no—
803C22—84no—
804C22—108no—
805C22—102no—
806C22—102no—
807C22—202no—
808C22—202no—
809C22—202no—
810C22—4016no—
811C22—404no—
812C22#6594112yes—
813C22D5×#13512yes—
814C22#6610712yes—
815C22C22×D4×D511yescharacteristic
816C4—22no—
817C4—22no—
818C4—42no—
819C4—42no—
820C4—102no—
821C4—102no—
822C4—102no—
823C4—202no—
824C4—202no—
825C4—202no—
826C4#6594112yes—
827C4C2×#414411yescharacteristic
828C4C2×#414911yescharacteristic
829C2—82no—
830C2—82no—
831C2—104no—
832C2—402no—
833C2#1061227214yesdirect product factor
834C2C2×#6594111yescharacteristic
835C2C2×D5×#13511yescharacteristic
836C2C2×#6610711yescharacteristic
subgroupG/H
centerC23C2×D4×D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×#463C2
socleC23×C5C22×D4
prime radicalC2×#65445C2
hypercenterC2×#463D5
hypocenterC5C2×#3211
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#463

Complements

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

NH ≅ G/Ntype
1. C2×D5×#124C2semidirect
2. C2×#65891C2semidirect
3. C2×C5×#463C2semidirect
4. C2×#65459C2semidirect
5. C2×#65457C2semidirect
7. C2×#65444C2semidirect
8. C2×#65343C2semidirect
9. C2×#65305C2semidirect
10. #10612272C2direct (N × H)
11. C2×#65134C2semidirect
12. C2×#65122C2semidirect
13. C2×#65097C2semidirect
14. C2×#65089C2semidirect
15. C2×#65065C2semidirect
16. C2×#65057C2semidirect
19. C22×C5×SD16C22semidirect
22. C2×C4×C5×D4C22semidirect
24. C22×#689C22semidirect
27. C2×#4082C22semidirect
29. C22×#687C22semidirect
33. C22×Dic20C22semidirect
36. D5×#124C22semidirect
38. #65891C22semidirect
40. C2×#4036C22semidirect
49. C2×C4×Dic10C22semidirect
50. C5×#463C22semidirect
51. C2×C5×C4⋊C8C22semidirect
52. C2×C5×#103C22semidirect
54. C2×#3967C22semidirect
56. #65459C22semidirect
57. #65457C22semidirect
59. #65444C22semidirect
63. C2×#3948C22semidirect
64. C2×C8×Dic5C22semidirect
65. C2×C8×Dic5C22semidirect
66. #65343C22semidirect
67. #65305C22semidirect
68. C2×#3942C22semidirect
70. C2×C4⋊#168C22semidirect
71. #65134C22semidirect
72. #65122C22semidirect
73. #65097C22semidirect
74. #65089C22semidirect
75. #65065C22semidirect
76. #65057C22semidirect
102. C2×C5×SD16C23semidirect
110. C4×C5×D4C23semidirect
124. C2×#689C23semidirect
130. #4082C23semidirect
134. C2×#687C23semidirect
156. C2×Dic20C23semidirect
162. #4036C23semidirect
174. C4×Dic10C23semidirect
175. C5×C4⋊C8C23semidirect
176. C5×#103C23semidirect
178. #3967C23semidirect
183. #3948C23semidirect
184. C8×Dic5C23semidirect
185. C8×Dic5C23semidirect
186. #3942C23semidirect
188. C4⋊#168C23semidirect
199. C2×#463D5semidirect
323. C22×SD16C2×D5semidirect
344. C2×C4×D4C2×D5semidirect
356. #463C2×D5semidirect
363. C2×C4⋊C8C2×D5semidirect
367. C2×#103C2×D5semidirect
487. C2×SD16C22×D5semidirect
520. C4×D4C22×D5semidirect
551. C4⋊C8C22×D5semidirect
555. #103C22×D5semidirect
711. C2×C5#3211semidirect
794. C5C2×#3211semidirect
833. C2#10612272direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D5×#1242
C2×#658912
C2×C5×#4632
C2×#654592
C2×#654572
C2×#654452
C2×#654442
C2×#653432
C2×#653052
#106122722
C2×#651342
C2×#651222
C2×#650972
C2×#650892
C2×#650652
C2×#650572
C2×#32115