Finite Group Databasebeta

← C2×#10611390 #12967601

Subgroups — C2×#10611390 #12967601

Order 1280.

2210 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65917C211yesmaximal, characteristic, complemented
2C2×#65879C211yesmaximal, characteristic
3C2×C4×C5×SD16C211yesmaximal, characteristic, complemented
4C2×#65458C211yesmaximal, characteristic
5C2×#65451C211yesmaximal, characteristic, complemented
6C2×#65315C211yesmaximal, characteristic, complemented
7C2×#65307C211yesmaximal, characteristic, complemented
8#10611390C2116yesmaximal, direct product factor
9C2×#65160C211yesmaximal, characteristic, complemented
10C2×#65156C211yesmaximal, characteristic, complemented
11C2×#65107C211yesmaximal, characteristic, complemented
12C2×#65104C211yesmaximal, characteristic, complemented
13C2×#65065C211yesmaximal, characteristic
14C2×#65052C211yesmaximal, characteristic, complemented
15C2×C4×#677C211yesmaximal, characteristic, complemented
16C2×#64979C211yesmaximal, characteristic, complemented
17C22×D4×D5C2211yescharacteristic
18C22×C5×SD16C2211yescharacteristic
19C2×C4×C5×Q8C2211yescharacteristic, complemented
20C2×C4×C5×D4C2211yescharacteristic
21C2×#4092C2211yescharacteristic
22C2×#4090C2211yescharacteristic, complemented
23C22×#688C2211yescharacteristic
24C2×D4×Dic5C2211yescharacteristic
25C22×#687C2211yescharacteristic
26C2×C4×C22⋊D5—21no—
27C22×#685—21no—
28C22×#677C2211yescharacteristic
29#65917—24no—
30#65917C2218yescomplemented
31#65879—24no—
32#65879C2218yes—
33C2×#4044—21no—
34C2×#4043C2211yescharacteristic
35C2×#4039C2211yescharacteristic
36C2×#4038C2211yescharacteristic
37C2×#4036C2211yescharacteristic, complemented
38C2×#4035—21no—
39C2×#4027—21no—
40C2×D5×C22⋊C4—21no—
41C2×#4022—21no—
42C2×C4×D20C2211yescharacteristic
43C2×#4018C2211yescharacteristic
44C2×#4016—21no—
45C2×C4×Dic10C2211yescharacteristic, complemented
46C4×C5×SD16C2218yescomplemented
47C2×C5×#106C2211yescharacteristic, complemented
48C2×C5×#103C2211yescharacteristic, complemented
49C2×C5×#102C2211yescharacteristic
50C2×C4×C5×C8C2211yescharacteristic, complemented
51C2×#3967C2211yescharacteristic, complemented
52C2×#3964C2211yescharacteristic
53#65458C2218yes—
54#65451C2218yescomplemented
55C2×#3953C2211yescharacteristic
56C2×#3952C2211yescharacteristic
57C2×#3952C2211yescharacteristic
58C2×#3949C2211yescharacteristic, complemented
59C2×#3948C2211yescharacteristic, complemented
60C2×#3946C2211yescharacteristic, complemented
61C2×#3946C2211yescharacteristic, complemented
62#65315C2218yescomplemented
63#65307C2218yescomplemented
64C2×#3942C2211yescharacteristic, complemented
65C2×#3941C2211yescharacteristic
66C2×#3939C2211yescharacteristic, complemented
67C2×#3939C2211yescharacteristic, complemented
68C2×#3935C2211yescharacteristic, complemented
69#65160C2218yescomplemented
70#65156C2218yescomplemented
71#65107C2218yescomplemented
72#65104C2218yescomplemented
73#65065C2218yes—
74#65052C2218yescomplemented
75C4×#677C2218yescomplemented
76#64979C2218yescomplemented
77C2×#3123—51nomaximal, Sylow
78C24×D5—21no—
79C22×C5×Q8C2311yescharacteristic
80C22×C5×D4C2311yescharacteristic
81C23×C4×C5—21no—
82C22×C22⋊D5—21no—
83C23×Dic5—21no—
84C2×D4×D5—24no—
85C2×D4×D5—24no—
86C2×D4×D5—22no—
87C2×D4×D5C2314yes—
88C22×D20C2311yescharacteristic
89C22×C4×D5—21no—
90C22×C4×D5—21no—
91C22×C4×D5C2311yescharacteristic
92C22×Dic10C2311yescharacteristic
93C2×C5×SD16—24no—
94C2×C5×SD16C2314yes—
95C22×C5×C8C2311yescharacteristic
96C22×C5×C8C2311yescharacteristic
97C4×C5×Q8—22no—
98C4×C5×Q8C2314yescomplemented
99C4×C5×D4—22no—
100C4×C5×D4C2314yes—
101C2×C5×C4⋊C4—21no—
102C2×C5×C4⋊C4C2311yescharacteristic
103C2×C5×C4⋊C4C2311yescharacteristic
104C2×C5×C22⋊C4—21no—
105C2×C42×C5—21no—
106C2×C42×C5C2311yescharacteristic
107C2×C22⋊Dic5—21no—
108#4092—22no—
109#4092C2314yes—
110#4090—22no—
111#4090C2314yescomplemented
112C2×#688—24no—
113C2×#688C2314yes—
114D4×Dic5—22no—
115D4×Dic5C2314yes—
116C2×#687—24no—
117C2×#687C2314yes—
118C4×C22⋊D5—28no—
119C2×#685—21no—
120C2×#685—21no—
121C2×#685—21no—
122C2×#685—21no—
123C2×#685—21no—
124C2×#685—28no—
125C2×#685D411yescharacteristic
126C2×#685D411yescharacteristic
127C2×C4⋊Dic5—21no—
128C2×C4⋊Dic5—21no—
129C2×C4⋊Dic5C2311yescharacteristic
130C2×C4⋊Dic5C2311yescharacteristic
131C2×#683—21no—
132C2×#683—21no—
133C2×#683—21no—
134C2×#683—21no—
135C2×#683—21no—
136C2×#683D411yescharacteristic
137C2×#683D411yescharacteristic
138C2×C4×Dic5—21no—
139C2×C4×Dic5—21no—
140C2×C4×Dic5C2311yescharacteristic
141C22×#168C2311yescharacteristic
142C22×#168C2311yescharacteristic
143C2×#677—24no—
144C2×#677C2314yes—
145#4044—28no—
146#4043—22no—
147#4043C2314yes—
148#4039—22no—
149#4039C2314yes—
150#4038—22no—
151#4038C2314yes—
152#4036—22no—
153#4036C2314yescomplemented
154#4035—28no—
155#4027—28no—
156D5×C22⋊C4—28no—
157#4022—28no—
158C4×D20—22no—
159C4×D20C2314yes—
160#4018D414yes—
161#4018C2314yes—
162#4016—28no—
163C4×Dic10—22no—
164C4×Dic10C2314yescomplemented
165C5×#106C2314yescomplemented
166C5×#103C2314yescomplemented
167C5×#102C2314yes—
168C4×C5×C8C2314yescomplemented
169#3967C2314yescomplemented
170#3964C2314yes—
171#3953C2314yes—
172#3952C2314yes—
173#3952C2314yes—
174#3949C2314yescomplemented
175#3948C2314yescomplemented
176#3946C2314yescomplemented
177#3946C2314yescomplemented
178#3942C2314yescomplemented
179#3941C2314yes—
180#3939C2314yescomplemented
181#3939C2314yescomplemented
182#3935C2314yescomplemented
183C2×#541—51no—
184C2×#518—51no—
185#3123—516no—
186C2×#485—51no—
187C2×#485—51no—
188C2×#478—51no—
189C2×#478—51no—
190C2×#461—51no—
191C2×#461—51no—
192C2×#450—51no—
193C2×#450—51no—
194C2×#440—51no—
195C2×#440—51no—
196C2×C4×SD16—51no—
197C2×C4×SD16D511yescharacteristic, complemented
198C2×#433—51no—
199C24×C5—21no—
200C23×D5—21no—
201C23×D5—28no—
202C23×D5—24no—
203C23×D5—82no—
204C23×D5—82no—
205C23×D5C2×D411yescharacteristic
206C2×C5×Q8—21no—
207C2×C5×Q8—22no—
208C2×C5×Q8—22no—
209C2×C5×Q8C2412yes—
210C2×C5×D4—21no—
211C2×C5×D4—22no—
212C2×C5×D4#4114yes—
213C2×C5×D4C2412yes—
214C22×C4×C5—21no—
215C22×C4×C5—21no—
216C22×C4×C5—21no—
217C22×C4×C5—24no—
218C22×C4×C5—82no—
219C22×C4×C5C2×D411yescharacteristic
220C22×C4×C5C2×D411yescharacteristic
221C22×C4×C5C2411yescharacteristic
222C2×C22⋊D5—28no—
223C2×C22⋊D5—24no—
224C22×Dic5—21no—
225C22×Dic5—21no—
226C22×Dic5—21no—
227C22×Dic5—24no—
228C22×Dic5—82no—
229C22×Dic5C2×D411yescharacteristic
230C22×Dic5C2×D411yescharacteristic
231C22×Dic5C2×D411yescharacteristic
232D4×D5—216no—
233D4×D5—28no—
234D4×D5—28no—
235C2×D20—21no—
236C2×D20—22no—
237C2×D20#4114yes—
238C2×D20C2412yes—
239C2×C4×D5—22no—
240C2×C4×D5—22no—
241C2×C4×D5—24no—
242C2×C4×D5—24no—
243C2×C4×D5—82no—
244C2×C4×D5—82no—
245C2×C4×D5C2×D412yes—
246C2×C4×D5C2412yes—
247C2×Dic10—22no—
248C2×Dic10—22no—
249C2×Dic10—21no—
250C2×Dic10C2412yes—
251C5×SD16—28no—
252C2×C5×C8—22no—
253C2×C5×C8—22no—
254C2×C5×C8C2412yes—
255C2×C5×C8C2412yes—
256C5×C4⋊C4—24no—
257C5×C4⋊C4—21no—
258C5×C4⋊C4—21no—
259C5×C4⋊C4C2412yes—
260C5×C4⋊C4C2412yes—
261C5×C22⋊C4—24no—
262C42×C5—24no—
263C42×C5C2×D412yes—
264C42×C5C2412yes—
265C22⋊Dic5—24no—
266#688—28no—
267#687—28no—
268#685—24no—
269#685—24no—
270#685—24no—
271#685—24no—
272#685—24no—
273#685C2×D414yes—
274#685C2×D414yes—
275C4⋊Dic5—21no—
276C4⋊Dic5—21no—
277C4⋊Dic5—24no—
278C4⋊Dic5—24no—
279C4⋊Dic5C2412yes—
280C4⋊Dic5C2412yes—
281#683—24no—
282#683—24no—
283#683—24no—
284#683—24no—
285#683—24no—
286#683C2×D414yes—
287#683C2×D414yes—
288C4×Dic5—24no—
289C4×Dic5—24no—
290C4×Dic5C2×D412yes—
291C4×Dic5C2412yes—
292C2×#168—22no—
293C2×#168—22no—
294C2×#168C2412yes—
295C2×#168C2412yes—
296#677—28no—
297C23×D4—51no—
298C22×SD16—51no—
299C22×SD16—51no—
300C22×SD16—51no—
301C22×SD16C2×D511yescharacteristic
302#541—58no—
303#541—104no—
304C2×C4⋊Q8—51no—
305C2×#126—101no—
306C2×#126—101no—
307C2×#125—51no—
308C2×#125—101no—
309C2×#125—101no—
310C2×C22⋊Q8—51no—
311C2×C22⋊Q8—51no—
312#518—58no—
313#518—104no—
314C2×C4×Q8—51no—
315C2×C4×Q8C2×D511yescharacteristic, complemented
316C2×C4×D4—51no—
317C2×C4×D4—51no—
318C2×C4×D4—51no—
319C2×C4×D4—101no—
320C2×C4×D4—101no—
321C2×C4×D4C2×D511yescharacteristic
322C2×#117—51no—
323C2×#117—51no—
324C22×C22⋊C4—101no—
325C22×C22⋊C4—101no—
326#485—58no—
327#485—58no—
328#478—58no—
329#478—58no—
330#461—58no—
331#461—58no—
332#450—58no—
333#450—58no—
334#440—58no—
335#440—58no—
336C4×SD16—58no—
337C4×SD16C2×D518yescomplemented
338#433—58no—
339C2×#107—51no—
340C2×#107—51no—
341C2×#106—51no—
342C2×#106C2×D511yescharacteristic, complemented
343C2×C4⋊C8—51no—
344C2×C4⋊C8—51no—
345C2×#103—51no—
346C2×#103—51no—
347C2×#103—51no—
348C2×#103C2×D511yescharacteristic, complemented
349C2×#102—51no—
350C2×#102—51no—
351C2×#102—51no—
352C2×#102C2×D511yescharacteristic
353C2×C22⋊C8—51no—
354C2×C22⋊C8—51no—
355C2×#97—51no—
356C2×C4×C8C2×D511yescharacteristic, complemented
357C23×C5—24no—
358C23×C5—22no—
359C23×C5—42no—
360C23×C5—42no—
361C23×C5C22×D411yescharacteristic
362C22×D5—22no—
363C22×D5—24no—
364C22×D5—22no—
365C22×D5—22no—
366C22×D5—22no—
367C22×D5—216no—
368C22×D5—42no—
369C22×D5—42no—
370C22×D5—84no—
371C22×D5—84no—
372C22×D5—816no—
373C22×D5C22×D412yes—
374C5×Q8—22no—
375C5×Q8—22no—
376C5×Q8—42no—
377C5×D4—24no—
378C5×D4—22no—
379C5×D4C2×#4114yes—
380C2×C4×C5—22no—
381C2×C4×C5—22no—
382C2×C4×C5—22no—
383C2×C4×C5—22no—
384C2×C4×C5—22no—
385C2×C4×C5—42no—
386C2×C4×C5—42no—
387C2×C4×C5—42no—
388C2×C4×C5—84no—
389C2×C4×C5C22×D412yes—
390C2×C4×C5C22×D412yes—
391C2×C4×C5C22×D411yescharacteristic
392C2×C4×C5C2×#4112yes—
393C2×C4×C5C2×#4112yes—
394C2×C4×C5C2511yescharacteristic
395C22⋊D5—216no—
396C2×Dic5—22no—
397C2×Dic5—22no—
398C2×Dic5—22no—
399C2×Dic5—22no—
400C2×Dic5—22no—
401C2×Dic5—22no—
402C2×Dic5—42no—
403C2×Dic5—42no—
404C2×Dic5—42no—
405C2×Dic5—84no—
406C2×Dic5C22×D412yes—
407C2×Dic5C22×D412yes—
408C2×Dic5C22×D412yes—
409D20—24no—
410D20—22no—
411D20C2×#4114yes—
412C4×D5—24no—
413C4×D5—22no—
414C4×D5—22no—
415C4×D5—84no—
416C4×D5—84no—
417Dic10—22no—
418Dic10—22no—
419Dic10—42no—
420C5×C8—22no—
421C5×C8—22no—
422#168—22no—
423#168—22no—
424C25—101no—
425C22×Q8—51no—
426C22×Q8C22×D511yescharacteristic
427C22×D4—54no—
428C22×D4—51no—
429C22×D4—102no—
430C22×D4—101no—
431C22×D4—104no—
432C22×D4—104no—
433C22×D4C22×D511yescharacteristic
434C23×C4—21no—
435C23×C4—51no—
436C23×C4—101no—
437C23×C4—101no—
438C23×C4—101no—
439C2×SD16—24no—
440C2×SD16—54no—
441C2×SD16—54no—
442C2×SD16—54no—
443C2×SD16—104no—
444C2×SD16—104no—
445C2×SD16—104no—
446C2×SD16C22×D514yes—
447C22×C8—51no—
448C22×C8—51no—
449C22×C8C22×D511yescharacteristic
450C22×C8C22×D511yescharacteristic
451C4⋊Q8—54no—
452C4⋊Q8—102no—
453#126—108no—
454#126—108no—
455#125—54no—
456#125—108no—
457#125—102no—
458#125—108no—
459C22⋊Q8—54no—
460C22⋊Q8—54no—
461C22⋊Q8—102no—
462C22⋊Q8—102no—
463C4×Q8—22no—
464C4×Q8—54no—
465C4×Q8—102no—
466C4×Q8C22×D514yescomplemented
467C4×D4—22no—
468C4×D4—54no—
469C4×D4—54no—
470C4×D4—54no—
471C4×D4—102no—
472C4×D4—102no—
473C4×D4—108no—
474C4×D4—108no—
475C4×D4—102no—
476C4×D4C22×D514yes—
477#117—54no—
478#117—54no—
479#117—54no—
480#117—102no—
481C2×C4⋊C4—21no—
482C2×C4⋊C4—51no—
483C2×C4⋊C4—51no—
484C2×C4⋊C4—51no—
485C2×C4⋊C4—51no—
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⋊C4—101no—
493C2×C4⋊C4C22×D511yescharacteristic
494C2×C4⋊C4C22×D511yescharacteristic
495C2×C22⋊C4—21no—
496C2×C22⋊C4—51no—
497C2×C22⋊C4—51no—
498C2×C22⋊C4—108no—
499C2×C22⋊C4—108no—
500C2×C22⋊C4—101no—
501C2×C22⋊C4—101no—
502C2×C22⋊C4—101no—
503C2×C22⋊C4—101no—
504C2×C22⋊C4—101no—
505C2×C22⋊C4—101no—
506C2×C42—21no—
507C2×C42—51no—
508C2×C42—101no—
509C2×C42—101no—
510C2×C42C22×D511yescharacteristic
511#107—54no—
512#107—54no—
513#106—54no—
514#106C22×D514yescomplemented
515C4⋊C8—54no—
516C4⋊C8—54no—
517#103—54no—
518#103—54no—
519#103—54no—
520#103C22×D514yescomplemented
521#102—54no—
522#102—54no—
523#102—54no—
524#102C22×D514yes—
525C22⋊C8—54no—
526C22⋊C8—54no—
527#97—54no—
528C4×C8C22×D514yescomplemented
529C22×C5—24no—
530C22×C5—48no—
531C22×C5—42no—
532C22×C5—42no—
533C22×C5#52512yes—
534C22×C5#57712yes—
535C22×C5#57712yes—
536C22×C5C23×D411yescharacteristic
537C2×D5—22no—
538C2×D5—24no—
539C2×D5—22no—
540C2×D5—22no—
541C2×D5—44no—
542C2×D5—48no—
543C2×D5—42no—
544C2×D5—42no—
545C2×D5—816no—
546C4×C5—22no—
547C4×C5—22no—
548C4×C5—42no—
549C4×C5—42no—
550C4×C5—42no—
551C4×C5#52512yes—
552C4×C5C22×#4111yescharacteristic
553C4×C5C22×#4111yescharacteristic
554Dic5—22no—
555Dic5—22no—
556Dic5—22no—
557Dic5—42no—
558Dic5—42no—
559Dic5—42no—
560C24—21no—
561C24—51no—
562C24—104no—
563C24—108no—
564C24—101no—
565C24—402no—
566C24—402no—
567C2×Q8—21no—
568C2×Q8—22no—
569C2×Q8—22no—
570C2×Q8—52no—
571C2×Q8—101no—
572C2×Q8—102no—
573C2×Q8—102no—
574C2×Q8C23×D512yes—
575C2×D4—21no—
576C2×D4—22no—
577C2×D4—54no—
578C2×D4—52no—
579C2×D4—104no—
580C2×D4—108no—
581C2×D4—1016no—
582C2×D4—108no—
583C2×D4—108no—
584C2×D4—102no—
585C2×D4—101no—
586C2×D4#70914yes—
587C2×D4C23×D512yes—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—24no—
592C22×C4—51no—
593C22×C4—51no—
594C22×C4—51no—
595C22×C4—52no—
596C22×C4—52no—
597C22×C4—82no—
598C22×C4—104no—
599C22×C4—104no—
600C22×C4—102no—
601C22×C4—102no—
602C22×C4—101no—
603C22×C4—101no—
604C22×C4—101no—
605C22×C4—104no—
606C22×C4—402no—
607C22×C4—402no—
608C22×C4—402no—
609C22×C4D4×D511yescharacteristic
610C22×C4D4×D511yescharacteristic
611C22×C4C23×D511yescharacteristic
612SD16—28no—
613SD16—108no—
614SD16—108no—
615SD16—108no—
616C2×C8—22no—
617C2×C8—22no—
618C2×C8—52no—
619C2×C8—52no—
620C2×C8—102no—
621C2×C8—102no—
622C2×C8C23×D512yes—
623C2×C8C23×D512yes—
624C4⋊C4—24no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—54no—
628C4⋊C4—54no—
629C4⋊C4—52no—
630C4⋊C4—52no—
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—104no—
640C4⋊C4C23×D512yes—
641C4⋊C4C23×D512yes—
642C22⋊C4—24no—
643C22⋊C4—54no—
644C22⋊C4—54no—
645C22⋊C4—104no—
646C22⋊C4—104no—
647C22⋊C4—104no—
648C22⋊C4—104no—
649C22⋊C4—104no—
650C22⋊C4—104no—
651C42—24no—
652C42—52no—
653C42—52no—
654C42—104no—
655C42—104no—
656C42D4×D512yes—
657C42C23×D512yes—
658C2×C5—44no—
659C2×C5#312314yescomplemented
660C2×C5C2×#52511yescharacteristic
661C2×C5C2×#57711yescharacteristic
662C2×C5C2×#57711yescharacteristic
663D5—42no—
664D5—44no—
665C23—24no—
666C23—22no—
667C23—42no—
668C23—42no—
669C23—52no—
670C23—1016no—
671C23—102no—
672C23—102no—
673C23—102no—
674C23—104no—
675C23—102no—
676C23—202no—
677C23—202no—
678C23—404no—
679C23—404no—
680C23—4016no—
681C23C2×D4×D511yescharacteristic
682Q8—22no—
683Q8—22no—
684Q8—42no—
685Q8—102no—
686Q8—102no—
687Q8—202no—
688D4—24no—
689D4—22no—
690D4—54no—
691D4—1016no—
692D4—104no—
693D4—102no—
694D4C2×#70914yes—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—52no—
704C2×C4—52no—
705C2×C4—52no—
706C2×C4—84no—
707C2×C4—102no—
708C2×C4—102no—
709C2×C4—102no—
710C2×C4—104no—
711C2×C4—102no—
712C2×C4—102no—
713C2×C4—102no—
714C2×C4—102no—
715C2×C4—102no—
716C2×C4—202no—
717C2×C4—202no—
718C2×C4—202no—
719C2×C4—404no—
720C2×C4—404no—
721C2×C4—404no—
722C2×C4C2×#70912yes—
723C2×C4C2×D4×D512yes—
724C2×C4C2×D4×D512yes—
725C2×C4C2×D4×D511yescharacteristic
726C2×C4D5×#4112yes—
727C2×C4C24×D511yescharacteristic
728C8—22no—
729C8—22no—
730C8—102no—
731C8—102no—
732C5C2×#312311yescharacteristic, complemented, Sylow
733C22—24no—
734C22—48no—
735C22—42no—
736C22—42no—
737C22—102no—
738C22—104no—
739C22—102no—
740C22—102no—
741C22—204no—
742C22—208no—
743C22—202no—
744C22—202no—
745C22—4016no—
746C22#6588112yes—
747C22#6609612yes—
748C22#6610412yes—
749C22C22×D4×D511yescharacteristic
750C4—22no—
751C4—22no—
752C4—42no—
753C4—42no—
754C4—42no—
755C4—102no—
756C4—102no—
757C4—102no—
758C4—202no—
759C4—202no—
760C4—202no—
761C4#6588112yes—
762C4C22×#70911yescharacteristic
763C4C2×D5×#4111yescharacteristic
764C2—44no—
765C2—202no—
766C2—204no—
767C2#1061139014yesdirect product factor
768C2C2×#6588111yescharacteristic
769C2C2×#6609611yescharacteristic
770C2C2×#6610411yescharacteristic
subgroupG/H
centerC23C2×D4×D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C4×C5×SD16C2
socleC23×C5C22×D4
prime radicalC22×D4×D5C22
hypercenterC2×C4×SD16D5
hypocenterC5C2×#3123
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#65917C2semidirect
3. C2×C4×C5×SD16C2semidirect
5. C2×#65451C2semidirect
6. C2×#65315C2semidirect
7. C2×#65307C2semidirect
8. #10611390C2direct (N × H)
9. C2×#65160C2semidirect
10. C2×#65156C2semidirect
11. C2×#65107C2semidirect
12. C2×#65104C2semidirect
14. C2×#65052C2semidirect
15. C2×C4×#677C2semidirect
16. C2×#64979C2semidirect
19. C2×C4×C5×Q8C22semidirect
22. C2×#4090C22semidirect
30. #65917C22semidirect
37. C2×#4036C22semidirect
45. C2×C4×Dic10C22semidirect
46. C4×C5×SD16C22semidirect
47. C2×C5×#106C22semidirect
48. C2×C5×#103C22semidirect
50. C2×C4×C5×C8C22semidirect
51. C2×#3967C22semidirect
54. #65451C22semidirect
58. C2×#3949C22semidirect
59. C2×#3948C22semidirect
60. C2×#3946C22semidirect
61. C2×#3946C22semidirect
62. #65315C22semidirect
63. #65307C22semidirect
64. C2×#3942C22semidirect
66. C2×#3939C22semidirect
67. C2×#3939C22semidirect
68. C2×#3935C22semidirect
69. #65160C22semidirect
70. #65156C22semidirect
71. #65107C22semidirect
72. #65104C22semidirect
74. #65052C22semidirect
75. C4×#677C22semidirect
76. #64979C22semidirect
98. C4×C5×Q8C23semidirect
111. #4090C23semidirect
153. #4036C23semidirect
164. C4×Dic10C23semidirect
165. C5×#106C23semidirect
166. C5×#103C23semidirect
168. C4×C5×C8C23semidirect
169. #3967C23semidirect
174. #3949C23semidirect
175. #3948C23semidirect
176. #3946C23semidirect
177. #3946C23semidirect
178. #3942C23semidirect
180. #3939C23semidirect
181. #3939C23semidirect
182. #3935C23semidirect
197. C2×C4×SD16D5semidirect
315. C2×C4×Q8C2×D5semidirect
337. C4×SD16C2×D5semidirect
342. C2×#106C2×D5semidirect
348. C2×#103C2×D5semidirect
356. C2×C4×C8C2×D5semidirect
466. C4×Q8C22×D5semidirect
514. #106C22×D5semidirect
520. #103C22×D5semidirect
528. C4×C8C22×D5semidirect
659. C2×C5#3123semidirect
732. C5C2×#3123semidirect
767. C2#10611390direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#659172
C2×#658792
C2×C4×C5×SD162
C2×#654582
C2×#654512
C2×#653152
C2×#653072
#106113902
C2×#651602
C2×#651562
C2×#651072
C2×#651042
C2×#650652
C2×#650522
C2×C4×#6772
C2×#649792
C2×#31235