Finite Group Databasebeta

← #12114780

Subgroups — #12114780

Order 1280.

1670 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#546C211yesmaximal, characteristic
2C2×#65521C211yesmaximal, characteristic, complemented
3C22×#3964C211yesmaximal, characteristic, complemented
4D4×C4⋊Dic5C211yesmaximal, characteristic, complemented
5C2×#65300C211yesmaximal, characteristic, complemented
6#10602928C211yesmaximal, characteristic, complemented
7#10602921C211yesmaximal, characteristic, complemented
8#10602519C211yesmaximal, characteristic, complemented
9#10602514C211yesmaximal, characteristic, complemented
10#10602489C211yesmaximal, characteristic, complemented
11#10602485C211yesmaximal, characteristic, complemented
12#10602475C211yesmaximal, characteristic, complemented
13#10602470C211yesmaximal, characteristic, complemented
14#10602402C211yesmaximal, characteristic, complemented
15#10602397C211yesmaximal, characteristic, complemented
16C22×C5×#41C2211yescharacteristic
17C23×C5×D4C2211yescharacteristic
18C5×#546—24no—
19C5×#546C418yescomplemented
20C2×C5×#124C2211yescharacteristic
21C2×C5×#123—21no—
22C2×C5×C22⋊Q8C2211yescharacteristic
23C2×C5×#121—21no—
24C2×C5×#121C2211yescharacteristic
25C2×C5×#120—21no—
26C2×C4×C5×D4C2211yescharacteristic
27C2×C4×C5×D4C2211yescharacteristic
28C22×C5×C22⋊C4—21no—
29C2×D4×Dic5—21no—
30C22×C4⋊Dic5C2211yescharacteristic
31C22×C4⋊Dic5C2211yescharacteristic, complemented
32C22×#681C2211yescharacteristic, complemented
33C23×#168C2211yescharacteristic
34#65521—24no—
35C2×#3967C2211yescharacteristic, complemented
36C2×#3967C2211yescharacteristic, complemented
37C2×#3967C2211yescharacteristic, complemented
38C2×#3967C2211yescharacteristic, complemented
39C2×#3964—24no—
40C2×#3964C2211yescharacteristic
41C2×#3964C2211yescharacteristic
42C2×#3964C2211yescharacteristic
43C2×#3964C2211yescharacteristic
44C2×#3964C2211yescharacteristic
45C2×#3964C2211yescharacteristic
46C2×#3964C2211yescharacteristic
47C2×#3964C2211yescharacteristic
48#65501C2211yescharacteristic
49#65501C2211yescharacteristic, complemented
50C2×C22⋊#168C2211yescharacteristic
51C2×C22⋊#168C2211yescharacteristic, complemented
52#65300—24no—
53#65274—21no—
54#65239—21no—
55#65239—21no—
56#65224C2211yescharacteristic, complemented
57C4×C4⋊Dic5C2211yescharacteristic, complemented
58C2×C4⋊#168C2211yescharacteristic, complemented
59C2×#3935C2211yescharacteristic, complemented
60#64749C2211yescharacteristic, complemented
61#64749C2211yescharacteristic, complemented
62#64749C2211yescharacteristic, complemented
63#64749C2211yescharacteristic, complemented
64#22419—51nomaximal, Sylow
65C25×C5—21no—
66C2×C5×#41—22no—
67C2×C5×#41—22no—
68C2×C5×#41—22no—
69C2×C5×#41—41no—
70C2×C5×#41—41no—
71C2×C5×#41C2×C414yescomplemented
72C22×C5×Q8C2311yescharacteristic
73C22×C5×D4—22no—
74C22×C5×D4—22no—
75C22×C5×D4—21no—
76C22×C5×D4—21no—
77C22×C5×D4—21no—
78C22×C5×D4—22no—
79C22×C5×D4—41no—
80C22×C5×D4—41no—
81C22×C5×D4C2×C414yescomplemented
82C22×C5×D4D411yescharacteristic
83C22×C5×D4C2311yescharacteristic
84C22×C5×D4C2311yescharacteristic
85C23×C4×C5—21no—
86C23×C4×C5—21no—
87C23×C4×C5C2311yescharacteristic
88C23×C4×C5C2311yescharacteristic
89C23×Dic5—21no—
90C23×Dic5—21no—
91C5×#124—22no—
92C5×#124C2×C414yescomplemented
93C5×#123—28no—
94C5×C22⋊Q8—22no—
95C5×C22⋊Q8C2×C414yescomplemented
96C5×#121—22no—
97C5×#121—28no—
98C5×#121C2×C414yescomplemented
99C5×#120—28no—
100C4×C5×D4—22no—
101C4×C5×D4C2×C414yes—
102C4×C5×D4C2×C414yescomplemented
103C4×C5×D4D414yes—
104C2×C5×C4⋊C4—21no—
105C2×C5×C4⋊C4D411yescharacteristic
106C2×C5×C4⋊C4C2311yescharacteristic
107C2×C5×C22⋊C4—21no—
108C2×C5×C22⋊C4—21no—
109C2×C5×C22⋊C4—21no—
110C2×C5×C22⋊C4—21no—
111C2×C5×C22⋊C4—21no—
112C2×C5×C22⋊C4—28no—
113C2×C5×C22⋊C4D411yescharacteristic
114C2×C5×C22⋊C4D411yescharacteristic
115C2×C42×C5C2311yescharacteristic
116C2×C22⋊Dic5—21no—
117C2×C22⋊Dic5—21no—
118D4×Dic5—44no—
119C2×C4⋊Dic5—22no—
120C2×C4⋊Dic5—22no—
121C2×C4⋊Dic5—21no—
122C2×C4⋊Dic5—21no—
123C2×C4⋊Dic5—21no—
124C2×C4⋊Dic5—21no—
125C2×C4⋊Dic5—41no—
126C2×C4⋊Dic5—41no—
127C2×C4⋊Dic5C2311yescharacteristic
128C2×C4⋊Dic5C2311yescharacteristic
129C2×C4⋊Dic5C2311yescharacteristic
130C2×C4⋊Dic5C2311yescharacteristic
131C2×C4×Dic5—21no—
132C2×#681—22no—
133C2×#681—22no—
134C2×#681—41no—
135C22×#168—22no—
136C22×#168—22no—
137C22×#168—41no—
138C22×#168C2311yescharacteristic
139C22×#168C2311yescharacteristic
140C22×#168C2311yescharacteristic
141C22×#168C2311yescharacteristic
142#3967—22no—
143#3967—22no—
144#3967—41no—
145#3967—41no—
146#3964—22no—
147#3964—22no—
148#3964—22no—
149#3964—22no—
150#3964—22no—
151#3964—41no—
152#3964—41no—
153#3964D414yescomplemented
154#3963—21no—
155#3963—21no—
156#3963—21no—
157C22⋊#168—22no—
158C22⋊#168—22no—
159C4⋊#168—22no—
160#3935—22no—
161C2×#546D511yescharacteristic
162C2×#435—51no—
163C2×#417—51no—
164C22×#102—51no—
165D4×C4⋊C4—51no—
166#1983—51no—
167#1959—51no—
168#1895—51no—
169#1892—51no—
170#1874—51no—
171#1872—51no—
172#1802—51no—
173#1788—51no—
174#1786—51no—
175#1762—51no—
176C24×C5—21no—
177C24×C5—21no—
178C24×C5—24no—
179C24×C5—42no—
180C24×C5—42no—
181C24×C5—42no—
182C24×C5—42no—
183C24×C5—81no—
184C24×C5—81no—
185C24×C5C2×D411yescharacteristic
186C24×C5C2×D411yescharacteristic
187C5×#41—28no—
188C5×#41—44no—
189C5×#41—44no—
190C5×#41—44no—
191C2×C5×Q8—21no—
192C2×C5×Q8—21no—
193C2×C5×Q8—21no—
194C2×C5×Q8—21no—
195C2×C5×Q8—21no—
196C2×C5×Q8C22×C412yes—
197C2×C5×D4—22no—
198C2×C5×D4—22no—
199C2×C5×D4—28no—
200C2×C5×D4—24no—
201C2×C5×D4—24no—
202C2×C5×D4—24no—
203C2×C5×D4—21no—
204C2×C5×D4—21no—
205C2×C5×D4—21no—
206C2×C5×D4—21no—
207C2×C5×D4—21no—
208C2×C5×D4—21no—
209C2×C5×D4—21no—
210C2×C5×D4—21no—
211C2×C5×D4—44no—
212C2×C5×D4—44no—
213C2×C5×D4—44no—
214C2×C5×D4—42no—
215C2×C5×D4—42no—
216C2×C5×D4—42no—
217C2×C5×D4—42no—
218C2×C5×D4—81no—
219C2×C5×D4—81no—
220C2×C5×D4C22⋊C414yes—
221C2×C5×D4C22×C412yes—
222C2×C5×D4C22×C412yes—
223C2×C5×D4C2×D412yes—
224C2×C5×D4#4112yes—
225C22×C4×C5—21no—
226C22×C4×C5—21no—
227C22×C4×C5—21no—
228C22×C4×C5—21no—
229C22×C4×C5—21no—
230C22×C4×C5—21no—
231C22×C4×C5—21no—
232C22×C4×C5—21no—
233C22×C4×C5—21no—
234C22×C4×C5—21no—
235C22×C4×C5—24no—
236C22×C4×C5—24no—
237C22×C4×C5—42no—
238C22×C4×C5—42no—
239C22×C4×C5—81no—
240C22×C4×C5—81no—
241C22×C4×C5C22×C412yes—
242C22×C4×C5C22×C412yes—
243C22×C4×C5C2×D411yescharacteristic
244C22×C4×C5C2×D411yescharacteristic
245C22×C4×C5C2×D411yescharacteristic
246C22×C4×C5C2×D411yescharacteristic
247C22×C4×C5C2×D412yes—
248C22×C4×C5C2×D412yes—
249C22×C4×C5C2411yescharacteristic
250C22×Dic5—21no—
251C22×Dic5—21no—
252C22×Dic5—21no—
253C22×Dic5—21no—
254C22×Dic5—42no—
255C22×Dic5—42no—
256C22×Dic5—42no—
257C22×Dic5—42no—
258C22×Dic5—81no—
259C22×Dic5—81no—
260C5×C4⋊C4—24no—
261C5×C4⋊C4—21no—
262C5×C4⋊C4C22⋊C414yes—
263C5×C4⋊C4C22×C412yes—
264C5×C22⋊C4—24no—
265C5×C22⋊C4—24no—
266C5×C22⋊C4—24no—
267C5×C22⋊C4—24no—
268C5×C22⋊C4—24no—
269C5×C22⋊C4C22⋊C414yes—
270C5×C22⋊C4C22⋊C414yes—
271C42×C5C22×C412yes—
272C42×C5C2×D412yes—
273C22⋊Dic5—42no—
274C22⋊Dic5—42no—
275C4⋊Dic5—21no—
276C4⋊Dic5—21no—
277C4⋊Dic5—21no—
278C4⋊Dic5—21no—
279C4⋊Dic5—21no—
280C4⋊Dic5—21no—
281C4⋊Dic5—21no—
282C4⋊Dic5—42no—
283C4⋊Dic5—42no—
284C4⋊Dic5—42no—
285C4⋊Dic5—81no—
286C4⋊Dic5C2×D412yes—
287C4×Dic5—42no—
288#681—44no—
289C2×#168—21no—
290C2×#168—21no—
291C2×#168—21no—
292C2×#168—21no—
293C2×#168—21no—
294C2×#168—21no—
295C2×#168—21no—
296C2×#168—21no—
297C2×#168—21no—
298C2×#168—21no—
299C2×#168—21no—
300C2×#168—44no—
301C2×#168C2×D412yes—
302C22×#41C2×D511yescharacteristic
303C23×D4C2×D511yescharacteristic
304C22×M16—51no—
305C23×C8—51no—
306#546—24no—
307#546Dic518yescomplemented
308C2×#124C2×D511yescharacteristic
309C2×#123—21no—
310C2×C22⋊Q8C2×D511yescharacteristic
311C2×#121—21no—
312C2×#121C2×D511yescharacteristic
313C2×#120—21no—
314C2×C4×D4—101no—
315C2×C4×D4C2×D511yescharacteristic
316C2×C4×D4C2×D511yescharacteristic
317C22×C4⋊C4—51no—
318C22×C4⋊C4—51no—
319C22×C22⋊C4—21no—
320#435—104no—
321C2×C4⋊C8—51no—
322#417—104no—
323C2×#103—51no—
324C2×#103—51no—
325C2×#103—51no—
326C2×#103—51no—
327C2×#102—51no—
328C2×#102—51no—
329C2×#102—51no—
330C2×#102—51no—
331C2×#102—51no—
332C2×#102—51no—
333C2×#102—51no—
334C2×#102—51no—
335C2×#102—104no—
336C2×C22⋊C8—51no—
337C2×C22⋊C8—51no—
338C2×#97—51no—
339#389—101no—
340#385—101no—
341#385—101no—
342#384—51no—
343#380—51no—
344#380—51no—
345C4×C4⋊C4—51no—
346#340—51no—
347#340—51no—
348#340—51no—
349#340—51no—
350C23×C5—21no—
351C23×C5—21no—
352C23×C5—21no—
353C23×C5—21no—
354C23×C5—22no—
355C23×C5—21no—
356C23×C5—22no—
357C23×C5—21no—
358C23×C5—22no—
359C23×C5—21no—
360C23×C5—21no—
361C23×C5—21no—
362C23×C5—21no—
363C23×C5—22no—
364C23×C5—48no—
365C23×C5—41no—
366C23×C5—41no—
367C23×C5—41no—
368C23×C5—41no—
369C23×C5—41no—
370C23×C5—41no—
371C23×C5—41no—
372C23×C5—41no—
373C23×C5—41no—
374C23×C5—41no—
375C23×C5—48no—
376C23×C5—84no—
377C23×C5—84no—
378C23×C5—84no—
379C23×C5—84no—
380C23×C5—84no—
381C23×C5C2×C22⋊C412yes—
382C23×C5C2×C22⋊C412yes—
383C23×C5AGL(1,ℤ/8)12yes—
384C23×C5#13712yes—
385C23×C5C22×D411yescharacteristic
386C5×Q8—22no—
387C5×Q8—22no—
388C5×Q8—41no—
389C5×Q8—41no—
390C5×D4—28no—
391C5×D4—22no—
392C5×D4—22no—
393C5×D4—22no—
394C5×D4—22no—
395C5×D4—22no—
396C5×D4—48no—
397C5×D4—48no—
398C5×D4—41no—
399C5×D4—41no—
400C5×D4—84no—
401C5×D4C4×D414yescomplemented
402C2×C4×C5—21no—
403C2×C4×C5—21no—
404C2×C4×C5—21no—
405C2×C4×C5—21no—
406C2×C4×C5—21no—
407C2×C4×C5—21no—
408C2×C4×C5—21no—
409C2×C4×C5—21no—
410C2×C4×C5—22no—
411C2×C4×C5—22no—
412C2×C4×C5—22no—
413C2×C4×C5—22no—
414C2×C4×C5—22no—
415C2×C4×C5—22no—
416C2×C4×C5—22no—
417C2×C4×C5—22no—
418C2×C4×C5—22no—
419C2×C4×C5—22no—
420C2×C4×C5—48no—
421C2×C4×C5—41no—
422C2×C4×C5—41no—
423C2×C4×C5—41no—
424C2×C4×C5—41no—
425C2×C4×C5—84no—
426C2×C4×C5C2×C22⋊C412yes—
427C2×C4×C5C2×C22⋊C412yes—
428C2×C4×C5C2×C22⋊C412yes—
429C2×C4×C5C2×C22⋊C412yes—
430C2×C4×C5C23×C411yescharacteristic
431C2×C4×C5C22×D411yescharacteristic
432C2×C4×C5C22×D411yescharacteristic
433C2×C4×C5C2×#4111yescharacteristic
434C2×C4×C5H(5,𝔽2)11yescharacteristic
435C2×C4×C5H(5,𝔽2)11yescharacteristic
436C2×Dic5—22no—
437C2×Dic5—41no—
438C2×Dic5—41no—
439C2×Dic5—41no—
440C2×Dic5—41no—
441C2×Dic5—41no—
442C2×Dic5—41no—
443C2×Dic5—41no—
444C2×Dic5—41no—
445C2×Dic5—41no—
446C2×Dic5—41no—
447C2×Dic5—41no—
448C2×Dic5—84no—
449C2×Dic5—84no—
450#168—22no—
451#168—41no—
452#168—41no—
453#168—41no—
454C25—21no—
455C2×#41—22no—
456C2×#41—22no—
457C2×#41—22no—
458C2×#41—41no—
459C2×#41—41no—
460C2×#41C2×Dic514yescomplemented
461C22×Q8C22×D511yescharacteristic
462C22×D4—22no—
463C22×D4—22no—
464C22×D4—21no—
465C22×D4—21no—
466C22×D4—21no—
467C22×D4—22no—
468C22×D4—41no—
469C22×D4—41no—
470C22×D4C2×Dic514yescomplemented
471C22×D4C22⋊D511yescharacteristic
472C22×D4C22×D511yescharacteristic
473C22×D4C22×D511yescharacteristic
474C23×C4—21no—
475C23×C4—21no—
476C23×C4—101no—
477C23×C4—101no—
478C23×C4C22×D511yescharacteristic
479C23×C4C22×D511yescharacteristic
480C2×M16—102no—
481C2×M16—102no—
482C2×M16—201no—
483C22×C8—51no—
484C22×C8—51no—
485C22×C8—51no—
486C22×C8—51no—
487C22×C8—102no—
488C22×C8—102no—
489C22×C8—201no—
490#124—22no—
491#124C2×Dic514yescomplemented
492#123—28no—
493C22⋊Q8—22no—
494C22⋊Q8C2×Dic514yescomplemented
495#121—22no—
496#121—28no—
497#121C2×Dic514yescomplemented
498#120—28no—
499C4×D4—22no—
500C4×D4—204no—
501C4×D4C2×Dic514yes—
502C4×D4C2×Dic514yescomplemented
503C4×D4C22⋊D514yes—
504C2×C4⋊C4—21no—
505C2×C4⋊C4—51no—
506C2×C4⋊C4—51no—
507C2×C4⋊C4—51no—
508C2×C4⋊C4—51no—
509C2×C4⋊C4—102no—
510C2×C4⋊C4—102no—
511C2×C4⋊C4—101no—
512C2×C4⋊C4—101no—
513C2×C4⋊C4—101no—
514C2×C4⋊C4—101no—
515C2×C4⋊C4—201no—
516C2×C4⋊C4—201no—
517C2×C4⋊C4C22⋊D511yescharacteristic
518C2×C4⋊C4C22×D511yescharacteristic
519C2×C22⋊C4—21no—
520C2×C22⋊C4—21no—
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—21no—
524C2×C22⋊C4—28no—
525C2×C22⋊C4—101no—
526C2×C22⋊C4—101no—
527C2×C22⋊C4C22⋊D511yescharacteristic
528C2×C22⋊C4C22⋊D511yescharacteristic
529C2×C42—101no—
530C2×C42C22×D511yescharacteristic
531C4⋊C8—102no—
532#103—102no—
533#103—102no—
534#103—201no—
535#103—201no—
536#102—54no—
537#102—102no—
538#102—102no—
539#102—102no—
540#102—102no—
541#102—102no—
542#102—201no—
543#102—201no—
544C22⋊C8—102no—
545C22⋊C8—102no—
546#97—102no—
547#95—101no—
548#95—101no—
549#95—101no—
550C22×C5—22no—
551C22×C5—22no—
552C22×C5—22no—
553C22×C5—22no—
554C22×C5—22no—
555C22×C5—22no—
556C22×C5—22no—
557C22×C5—24no—
558C22×C5—22no—
559C22×C5—22no—
560C22×C5—42no—
561C22×C5—42no—
562C22×C5—41no—
563C22×C5—42no—
564C22×C5—41no—
565C22×C5—42no—
566C22×C5—41no—
567C22×C5—42no—
568C22×C5—41no—
569C22×C5—42no—
570C22×C5—42no—
571C22×C5—42no—
572C22×C5—42no—
573C22×C5—816no—
574C22×C5—81no—
575C22×C5—81no—
576C22×C5—81no—
577C22×C5—81no—
578C22×C5#41714yescomplemented
579C22×C5C22×C22⋊C411yescharacteristic
580C22×C5D4211yescharacteristic
581C22×C5#54611yescharacteristic
582C22×C5C2×AGL(1,ℤ/8)11yescharacteristic
583C22×C5C2×#13711yescharacteristic
584C22×C5#57611yescharacteristic
585C22×C5#57711yescharacteristic
586C4×C5—22no—
587C4×C5—22no—
588C4×C5—22no—
589C4×C5—22no—
590C4×C5—42no—
591C4×C5—42no—
592C4×C5C2×C4×D411yescharacteristic
593C4×C5#51811yescharacteristic
594C4×C5D4211yescharacteristic
595C4×C5#54611yescharacteristic
596Dic5—42no—
597Dic5—81no—
598Dic5—81no—
599Dic5—81no—
600C24—21no—
601C24—21no—
602C24—24no—
603C24—42no—
604C24—42no—
605C24—42no—
606C24—42no—
607C24—81no—
608C24—81no—
609C24C2×C22⋊D511yescharacteristic
610C24C2×C22⋊D511yescharacteristic
611#41—28no—
612#41—44no—
613#41—44no—
614#41—44no—
615C2×Q8—21no—
616C2×Q8—21no—
617C2×Q8—21no—
618C2×Q8—21no—
619C2×Q8—21no—
620C2×Q8C22×Dic512yes—
621C2×D4—22no—
622C2×D4—22no—
623C2×D4—28no—
624C2×D4—24no—
625C2×D4—24no—
626C2×D4—24no—
627C2×D4—21no—
628C2×D4—21no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—21no—
633C2×D4—21no—
634C2×D4—21no—
635C2×D4—44no—
636C2×D4—44no—
637C2×D4—44no—
638C2×D4—42no—
639C2×D4—42no—
640C2×D4—42no—
641C2×D4—42no—
642C2×D4—81no—
643C2×D4—81no—
644C2×D4C22⋊Dic514yes—
645C2×D4D4×D512yes—
646C2×D4#71112yes—
647C2×D4C22×Dic512yes—
648C2×D4C22×Dic512yes—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—24no—
660C22×C4—24no—
661C22×C4—42no—
662C22×C4—42no—
663C22×C4—81no—
664C22×C4—81no—
665C22×C4—101no—
666C22×C4—101no—
667C22×C4—101no—
668C22×C4—101no—
669C22×C4—202no—
670C22×C4—202no—
671C22×C4—202no—
672C22×C4—202no—
673C22×C4—401no—
674C22×C4—401no—
675C22×C4C22×Dic512yes—
676C22×C4C22×Dic512yes—
677C22×C4C2×C22⋊D511yescharacteristic
678C22×C4C2×C22⋊D511yescharacteristic
679C22×C4C2×C22⋊D511yescharacteristic
680C22×C4C2×C22⋊D511yescharacteristic
681C22×C4C2×C22⋊D512yes—
682C22×C4C2×C22⋊D512yes—
683C22×C4C23×D511yescharacteristic
684M16—204no—
685C2×C8—52no—
686C2×C8—101no—
687C2×C8—101no—
688C2×C8—101no—
689C2×C8—101no—
690C2×C8—101no—
691C2×C8—101no—
692C2×C8—101no—
693C2×C8—101no—
694C2×C8—101no—
695C2×C8—101no—
696C2×C8—101no—
697C2×C8—204no—
698C4⋊C4—24no—
699C4⋊C4—21no—
700C4⋊C4—52no—
701C4⋊C4—101no—
702C4⋊C4—101no—
703C4⋊C4—101no—
704C4⋊C4—101no—
705C4⋊C4—101no—
706C4⋊C4—101no—
707C4⋊C4—101no—
708C4⋊C4—202no—
709C4⋊C4—202no—
710C4⋊C4—202no—
711C4⋊C4—401no—
712C4⋊C4C22⋊Dic514yes—
713C4⋊C4C22×Dic512yes—
714C22⋊C4—24no—
715C22⋊C4—24no—
716C22⋊C4—24no—
717C22⋊C4—24no—
718C22⋊C4—24no—
719C22⋊C4—202no—
720C22⋊C4—202no—
721C22⋊C4C22⋊Dic514yes—
722C22⋊C4C22⋊Dic514yes—
723C42—202no—
724C42C22×Dic512yes—
725C42C2×C22⋊D512yes—
726C2×C5—24no—
727C2×C5—42no—
728C2×C5—44no—
729C2×C5—82no—
730C2×C5D4×C22⋊C411yescharacteristic
731C2×C5C2×#41711yescharacteristic
732C2×C5#289711yescharacteristic
733C2×C5#326411yescharacteristic
734C2×C5#326611yescharacteristic
735C2×C5#330611yescharacteristic
736C2×C5#331411yescharacteristic
737C23—21no—
738C23—21no—
739C23—21no—
740C23—21no—
741C23—21no—
742C23—22no—
743C23—21no—
744C23—22no—
745C23—21no—
746C23—21no—
747C23—21no—
748C23—21no—
749C23—22no—
750C23—22no—
751C23—48no—
752C23—41no—
753C23—41no—
754C23—41no—
755C23—41no—
756C23—41no—
757C23—41no—
758C23—41no—
759C23—41no—
760C23—41no—
761C23—41no—
762C23—48no—
763C23—84no—
764C23—84no—
765C23—84no—
766C23—84no—
767C23—84no—
768C23#409512yes—
769C23#409712yes—
770C23C2×C22⋊Dic512yes—
771C23C2×C22⋊Dic512yes—
772C23C22×C22⋊D511yescharacteristic
773Q8—22no—
774Q8—22no—
775Q8—41no—
776Q8—41no—
777D4—28no—
778D4—22no—
779D4—22no—
780D4—22no—
781D4—22no—
782D4—22no—
783D4—48no—
784D4—48no—
785D4—41no—
786D4—41no—
787D4—84no—
788D4D4×Dic514yescomplemented
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—48no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—84no—
813C2×C4—102no—
814C2×C4—201no—
815C2×C4—201no—
816C2×C4—201no—
817C2×C4—201no—
818C2×C4—201no—
819C2×C4—201no—
820C2×C4—201no—
821C2×C4—201no—
822C2×C4—201no—
823C2×C4—201no—
824C2×C4—201no—
825C2×C4—404no—
826C2×C4—404no—
827C2×C4C2×C22⋊Dic512yes—
828C2×C4C2×C22⋊Dic512yes—
829C2×C4C2×C22⋊Dic512yes—
830C2×C4C2×C22⋊Dic512yes—
831C2×C4C2×D4×D511yescharacteristic
832C2×C4C2×#71111yescharacteristic
833C2×C4#414411yescharacteristic
834C2×C4#414411yescharacteristic
835C2×C4C23×Dic511yescharacteristic
836C2×C4C22×C22⋊D511yescharacteristic
837C8—102no—
838C8—201no—
839C8—201no—
840C8—201no—
841C5#2241911yescharacteristic, complemented, Sylow
842C22—22no—
843C22—22no—
844C22—22no—
845C22—22no—
846C22—22no—
847C22—22no—
848C22—22no—
849C22—22no—
850C22—24no—
851C22—22no—
852C22—42no—
853C22—41no—
854C22—42no—
855C22—41no—
856C22—42no—
857C22—41no—
858C22—42no—
859C22—41no—
860C22—42no—
861C22—42no—
862C22—42no—
863C22—42no—
864C22—42no—
865C22—816no—
866C22—81no—
867C22—81no—
868C22—81no—
869C22—81no—
870C22#6552114yescomplemented
871C22D4×C22⋊D511yescharacteristic
872C22#6614011yescharacteristic
873C22C2×#409511yescharacteristic
874C22C2×#409711yescharacteristic
875C22#6616911yescharacteristic
876C22#6617011yescharacteristic
877C22C22×C22⋊Dic511yescharacteristic
878C4—22no—
879C4—22no—
880C4—22no—
881C4—22no—
882C4—42no—
883C4—42no—
884C4—202no—
885C4—401no—
886C4—401no—
887C4—401no—
888C4C2×D4×Dic511yescharacteristic
889C4#6613211yescharacteristic
890C4D4×C22⋊D511yescharacteristic
891C4#6614011yescharacteristic
892C2—24no—
893C2—42no—
894C2—44no—
895C2—82no—
896C2#1061522711yescharacteristic
897C2#1061522911yescharacteristic
898C2#1061523311yescharacteristic
899C2#1061523711yescharacteristic
900C2D4×C22⋊Dic511yescharacteristic
901C2C2×#6552111yescharacteristic
902C2#1061583011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D5
commutatorC2×C4×C5C23×C4
FrattiniC22×C4C23×D5
Fitting, prime radicalC2×C5×#546C2
socleC23×C5C22×D4
cosocleC22×C4×C5C24
hypercenterC2×#546D5
hypocenterC5#22419
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#546

Complements

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

NH ≅ G/Ntype
2. C2×#65521C2semidirect
3. C22×#3964C2semidirect
4. D4×C4⋊Dic5C2semidirect
5. C2×#65300C2semidirect
6. #10602928C2semidirect
7. #10602921C2semidirect
8. #10602519C2semidirect
9. #10602514C2semidirect
10. #10602489C2semidirect
11. #10602485C2semidirect
12. #10602475C2semidirect
13. #10602470C2semidirect
14. #10602402C2semidirect
15. #10602397C2semidirect
19. C5×#546C4semidirect
31. C22×C4⋊Dic5C22semidirect
32. C22×#681C22semidirect
35. C2×#3967C22semidirect
36. C2×#3967C22semidirect
37. C2×#3967C22semidirect
38. C2×#3967C22semidirect
49. #65501C22semidirect
51. C2×C22⋊#168C22semidirect
56. #65224C22semidirect
57. C4×C4⋊Dic5C22semidirect
58. C2×C4⋊#168C22semidirect
59. C2×#3935C22semidirect
60. #64749C22semidirect
61. #64749C22semidirect
62. #64749C22semidirect
63. #64749C22semidirect
71. C2×C5×#41C2×C4semidirect
81. C22×C5×D4C2×C4semidirect
92. C5×#124C2×C4semidirect
95. C5×C22⋊Q8C2×C4semidirect
98. C5×#121C2×C4semidirect
102. C4×C5×D4C2×C4semidirect
153. #3964D4semidirect
307. #546Dic5semidirect
401. C5×D4C4×D4semidirect
460. C2×#41C2×Dic5semidirect
470. C22×D4C2×Dic5semidirect
491. #124C2×Dic5semidirect
494. C22⋊Q8C2×Dic5semidirect
497. #121C2×Dic5semidirect
502. C4×D4C2×Dic5semidirect
578. C22×C5#417semidirect
788. D4D4×Dic5semidirect
841. C5#22419semidirect
870. C22#65521semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#5462
C2×#655212
C22×#39642
D4×C4⋊Dic52
C2×#653002
#106029282
#106029212
#106025192
#106025142
#106024892
#106024852
#106024752
#106024702
#106024022
#106023972
#224195