Finite Group Databasebeta

← C2×#10614871 #12967309

Subgroups — C2×#10614871 #12967309

Order 1280.

2202 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×C5×#529C211yesmaximal, characteristic, complemented
2C2×C4×#709C211yesmaximal, characteristic, complemented
3#10614871C2116yesmaximal, direct product factor
4C2×#65352C211yesmaximal, characteristic, complemented
5C2×#65355C211yesmaximal, characteristic, complemented
6C2×#65343C211yesmaximal, characteristic, complemented
7C2×#65346C211yesmaximal, characteristic, complemented
8C2×#65336C211yesmaximal, characteristic, complemented
9C2×#65334C211yesmaximal, characteristic, complemented
10C2×#65326C211yesmaximal, characteristic
11C2×#65324C211yesmaximal, characteristic, complemented
12C2×C4×#689C211yesmaximal, characteristic, complemented
13C2×C4×#688C211yesmaximal, characteristic, complemented
14C2×C4×#687C211yesmaximal, characteristic, complemented
15C2×C4×#686C211yesmaximal, characteristic, complemented
16C2×#65214C211yesmaximal, characteristic, complemented
17C22×#709C2211yescharacteristic
18C5×#529—24no—
19C5×#529C2218yescomplemented
20C2×C5×#126—21no—
21C2×C5×#125C2211yescharacteristic
22C2×C5×#124C2211yescharacteristic
23C2×C5×#123—21no—
24C2×C5×C22⋊Q8C2211yescharacteristic
25C2×C5×#121C2211yescharacteristic
26C2×C4×C5×Q8C2211yescharacteristic
27C2×C4×C5×D4—21no—
28C2×C4×C5×D4C2211yescharacteristic
29C2×C5×#117—21no—
30C22×C42×C5C2211yescharacteristic
31C22×#689C2211yescharacteristic
32C22×#688C2211yescharacteristic
33C22×#687C2211yescharacteristic
34C22×#686C2211yescharacteristic
35C2×C4×C22⋊D5—21no—
36C2×C4×C22⋊D5—21no—
37C2×#4072C2211yescharacteristic
38C4×#709—24no—
39C4×#709C2218yescomplemented
40C2×C4×D20C2211yescharacteristic
41C2×C4×D20C2211yescharacteristic
42C2×#4018—21no—
43C2×C42×D5—21no—
44C2×C4×Dic10C2211yescharacteristic
45C2×C4×Dic10C2211yescharacteristic
46C2×#3967C2211yescharacteristic
47C2×#3967C2211yescharacteristic
48C2×#3964C2211yescharacteristic
49C2×#3964C2211yescharacteristic
50C2×C22⋊#168C2211yescharacteristic
51C2×C22⋊#168C2211yescharacteristic
52#65355C2218yescomplemented
53#65352C2218yescomplemented
54#65346C2218yescomplemented
55#65343C2218yescomplemented
56#65336C2218yescomplemented
57#65334C2218yescomplemented
58#65326C2218yes—
59#65324C2218yescomplemented
60C4×#689C2218yescomplemented
61C4×#688C2218yescomplemented
62C4×#687C2218yescomplemented
63C4×#686C2218yescomplemented
64C2×#3942C2211yescharacteristic
65C2×#3942C2211yescharacteristic
66C2×#3941C2211yescharacteristic
67C2×#3941C2211yescharacteristic
68C2×#3940C2211yescharacteristic
69C2×#3940C2211yescharacteristic
70C2×#3939C2211yescharacteristic
71C2×#3939C2211yescharacteristic
72#65214C2218yescomplemented
73C2×C4⋊#168C2211yescharacteristic
74C2×C4⋊#168C2211yescharacteristic
75C2×C4×#168C2211yescharacteristic
76C2×C4×#168C2211yescharacteristic
77C2×#3102—51nomaximal, Sylow
78C22×C5×Q8C2311yescharacteristic
79C22×C5×D4—21no—
80C22×C5×D4C2311yescharacteristic
81C23×C4×C5—21no—
82C23×C4×C5D411yescharacteristic
83C23×C4×C5D411yescharacteristic
84C23×C4×C5C2311yescharacteristic
85C22×C22⋊D5—21no—
86C2×#709—22no—
87C2×#709—24no—
88C2×#709—24no—
89C2×#709C2314yes—
90C22×D20C2311yescharacteristic
91C22×C4×D5—21no—
92C22×C4×D5—21no—
93C22×C4×D5—21no—
94C22×Dic10C2311yescharacteristic
95C5×#126—28no—
96C5×#125—22no—
97C5×#125C2314yes—
98C5×#124—22no—
99C5×#124C2314yes—
100C5×#123—28no—
101C5×C22⋊Q8—22no—
102C5×C22⋊Q8C2314yes—
103C5×#121—22no—
104C5×#121C2314yes—
105C4×C5×Q8—22no—
106C4×C5×Q8C2314yes—
107C4×C5×D4—28no—
108C4×C5×D4—22no—
109C4×C5×D4C2314yes—
110C5×#117—28no—
111C2×C5×C4⋊C4—21no—
112C2×C5×C4⋊C4—21no—
113C2×C5×C4⋊C4—21no—
114C2×C5×C4⋊C4—21no—
115C2×C5×C4⋊C4C2311yescharacteristic
116C2×C5×C4⋊C4C2311yescharacteristic
117C2×C5×C22⋊C4—21no—
118C2×C5×C22⋊C4—21no—
119C2×C5×C22⋊C4—21no—
120C2×C5×C22⋊C4—21no—
121C2×C5×C22⋊C4—21no—
122C2×C42×C5—21no—
123C2×C42×C5D411yescharacteristic
124C2×C42×C5D411yescharacteristic
125C2×C42×C5D414yes—
126C2×C42×C5C2311yescharacteristic
127C2×C42×C5C2311yescharacteristic
128C2×C42×C5C2314yes—
129C2×C22⋊Dic5—21no—
130C2×#689—24no—
131C2×#689C2314yes—
132C2×#688—24no—
133C2×#688C2314yes—
134C2×#687—24no—
135C2×#687C2314yes—
136C2×#686—24no—
137C2×#686C2314yes—
138C4×C22⋊D5—28no—
139C4×C22⋊D5—28no—
140C2×#685—21no—
141C2×#685—21no—
142#4072—22no—
143#4072C2314yes—
144C2×C4⋊Dic5C2311yescharacteristic
145C2×C4⋊Dic5C2311yescharacteristic
146C2×#683—21no—
147C2×#683—21no—
148C2×C4×Dic5—21no—
149C2×C4×Dic5—21no—
150C2×C4×Dic5—21no—
151C22×#168C2311yescharacteristic
152C22×#168C2311yescharacteristic
153C22×#168C2311yescharacteristic
154C22×#168C2311yescharacteristic
155C4×D20—22no—
156C4×D20—22no—
157C4×D20C2314yes—
158C4×D20C2314yes—
159#4018—28no—
160C42×D5—28no—
161C4×Dic10—22no—
162C4×Dic10—22no—
163C4×Dic10C2314yes—
164C4×Dic10C2314yes—
165#3967C2314yes—
166#3967C2314yes—
167#3964C2314yes—
168#3964C2314yes—
169C22⋊#168C2314yes—
170C22⋊#168C2314yes—
171#3942C2314yes—
172#3942C2314yes—
173#3941C2314yes—
174#3941C2314yes—
175#3940C2314yes—
176#3940C2314yes—
177#3939C2314yes—
178#3939C2314yes—
179C4⋊#168C2314yes—
180C4⋊#168C2314yes—
181C4×#168C2314yes—
182C4×#168C2314yes—
183C2×#529D511yescharacteristic, complemented
184C2×C4×#41—51no—
185#3102—516no—
186C2×#485—51no—
187C2×#482—51no—
188C2×#479—51no—
189C2×#478—51no—
190C2×#464—51no—
191C2×#463—51no—
192C2×#452—51no—
193C2×#449—51no—
194C2×C4×Q16—51no—
195C2×C4×SD16—51no—
196C2×C4×SD16—51no—
197C2×C4×D8—51no—
198C2×#431—51no—
199C24×C5—21no—
200C24×C5C2×D411yescharacteristic
201C23×D5—21no—
202C2×C5×Q8—21no—
203C2×C5×Q8—22no—
204C2×C5×Q8—22no—
205C2×C5×Q8C2412yes—
206C2×C5×D4—24no—
207C2×C5×D4—21no—
208C2×C5×D4—22no—
209C2×C5×D4—22no—
210C2×C5×D4—44no—
211C2×C5×D4C2412yes—
212C22×C4×C5—24no—
213C22×C4×C5—22no—
214C22×C4×C5—22no—
215C22×C4×C5—21no—
216C22×C4×C5—21no—
217C22×C4×C5—21no—
218C22×C4×C5—24no—
219C22×C4×C5—42no—
220C22×C4×C5—44no—
221C22×C4×C5C2×D411yescharacteristic
222C22×C4×C5C2×D412yes—
223C22×C4×C5C2×D411yescharacteristic
224C22×C4×C5C2×D411yescharacteristic
225C22×C4×C5C2×D411yescharacteristic
226C22×C4×C5C2×D414yes—
227C22×C4×C5C2×D414yes—
228C22×C4×C5C2×D411yescharacteristic
229C22×C4×C5C2412yes—
230C22×C4×C5C2411yescharacteristic
231C2×C22⋊D5—28no—
232C2×C22⋊D5—24no—
233C22×Dic5—21no—
234C22×Dic5—21no—
235C22×Dic5—21no—
236#709—216no—
237#709—28no—
238#709—28no—
239C2×D20—21no—
240C2×D20—22no—
241C2×D20#4114yes—
242C2×D20C2412yes—
243C2×C4×D5—28no—
244C2×C4×D5—24no—
245C2×C4×D5—24no—
246C2×C4×D5—24no—
247C2×C4×D5—44no—
248C2×C4×D5—44no—
249C2×Dic10—21no—
250C2×Dic10—22no—
251C2×Dic10#4114yes—
252C2×Dic10C2412yes—
253C5×C4⋊C4—24no—
254C5×C4⋊C4—24no—
255C5×C4⋊C4—24no—
256C5×C4⋊C4—24no—
257C5×C4⋊C4—21no—
258C5×C4⋊C4—21no—
259C5×C4⋊C4C2412yes—
260C5×C4⋊C4C2412yes—
261C5×C22⋊C4—24no—
262C5×C22⋊C4—24no—
263C5×C22⋊C4—24no—
264C5×C22⋊C4—24no—
265C5×C22⋊C4—24no—
266C42×C5—24no—
267C42×C5C2×D414yes—
268C42×C5C2×D412yes—
269C42×C5C2×D412yes—
270C42×C5C2×D414yes—
271C42×C5C2412yes—
272C42×C5C2412yes—
273C22⋊Dic5—24no—
274#689—28no—
275#688—28no—
276#687—28no—
277#686—28no—
278#685—24no—
279#685—24no—
280C4⋊Dic5—21no—
281C4⋊Dic5—21no—
282C4⋊Dic5C2412yes—
283C4⋊Dic5C2412yes—
284#683—24no—
285#683—24no—
286C4×Dic5—24no—
287C4×Dic5—24no—
288C4×Dic5—24no—
289C2×#168—22no—
290C2×#168—22no—
291C2×#168—22no—
292C2×#168—22no—
293C2×#168C2412yes—
294C2×#168C2412yes—
295C2×#168C2412yes—
296C2×#168C2412yes—
297C22×#41—51no—
298C22×Q16—51no—
299C22×SD16—51no—
300C22×SD16—51no—
301C22×D8—51no—
302#529—24no—
303#529C2×D518yescomplemented
304C2×#126—21no—
305C2×#125C2×D511yescharacteristic
306C2×#124C2×D511yescharacteristic
307C2×#123—21no—
308C2×C22⋊Q8C2×D511yescharacteristic
309C2×#121C2×D511yescharacteristic
310C4×#41—58no—
311C4×#41—104no—
312C2×C4×Q8—51no—
313C2×C4×Q8—51no—
314C2×C4×Q8C2×D511yescharacteristic
315C2×C4×D4—21no—
316C2×C4×D4—51no—
317C2×C4×D4—51no—
318C2×C4×D4—101no—
319C2×C4×D4—101no—
320C2×C4×D4C2×D511yescharacteristic
321C2×#117—21no—
322C2×#117—51no—
323C2×#117—101no—
324C22×C42—101no—
325C22×C42C2×D511yescharacteristic
326#485—58no—
327#482—58no—
328#479—58no—
329#478—58no—
330#464—58no—
331#463—58no—
332#452—58no—
333#449—58no—
334C4×Q16—58no—
335C4×SD16—58no—
336C4×SD16—58no—
337C4×D8—58no—
338#431—58no—
339C2×#107—51no—
340C2×#107—51no—
341C2×#106—51no—
342C2×#106—51no—
343C2×C4⋊C8—51no—
344C2×C4⋊C8—51no—
345C2×#103—51no—
346C2×#103—51no—
347C2×#103—51no—
348C2×#103—51no—
349C2×#102—51no—
350C2×#102—51no—
351C2×#102—51no—
352C2×#102—51no—
353C2×C22⋊C8—51no—
354C2×C22⋊C8—51no—
355C2×C4×C8—51no—
356C2×C4×C8—51no—
357C23×C5—22no—
358C23×C5—22no—
359C23×C5—22no—
360C23×C5—22no—
361C23×C5—42no—
362C23×C5—42no—
363C23×C5—42no—
364C23×C5C22×D412yes—
365C23×C5C22×D411yescharacteristic
366C22×D5—24no—
367C22×D5—22no—
368C22×D5—42no—
369C22×D5—42no—
370C5×Q8—22no—
371C5×Q8—22no—
372C5×Q8—42no—
373C5×D4—22no—
374C5×D4—22no—
375C5×D4—48no—
376C5×D4—42no—
377C2×C4×C5—22no—
378C2×C4×C5—22no—
379C2×C4×C5—22no—
380C2×C4×C5—22no—
381C2×C4×C5—24no—
382C2×C4×C5—28no—
383C2×C4×C5—22no—
384C2×C4×C5—22no—
385C2×C4×C5—22no—
386C2×C4×C5—22no—
387C2×C4×C5—22no—
388C2×C4×C5—44no—
389C2×C4×C5—42no—
390C2×C4×C5—42no—
391C2×C4×C5—42no—
392C2×C4×C5—48no—
393C2×C4×C5#13514yes—
394C2×C4×C5C22×D412yes—
395C2×C4×C5C22×D412yes—
396C2×C4×C5C22×D412yes—
397C2×C4×C5C22×D412yes—
398C2×C4×C5C22×D411yescharacteristic
399C2×C4×C5C22×D412yes—
400C2×C4×C5C2×#4112yes—
401C2×C4×C5C2×#4112yes—
402C2×C4×C5C2511yescharacteristic
403C22⋊D5—216no—
404C2×Dic5—24no—
405C2×Dic5—22no—
406C2×Dic5—22no—
407C2×Dic5—22no—
408C2×Dic5—42no—
409C2×Dic5—42no—
410D20—24no—
411D20—22no—
412D20C2×#4114yes—
413C4×D5—216no—
414C4×D5—48no—
415C4×D5—48no—
416Dic10—24no—
417Dic10—22no—
418Dic10C2×#4114yes—
419#168—22no—
420#168—22no—
421#168—22no—
422#168—22no—
423C2×#41—54no—
424C2×#41—104no—
425C2×#41—104no—
426C2×#41—102no—
427C22×Q8—51no—
428C22×Q8C22×D511yescharacteristic
429C22×D4—21no—
430C22×D4—51no—
431C22×D4—101no—
432C22×D4C22×D511yescharacteristic
433C23×C4—21no—
434C23×C4—101no—
435C23×C4—101no—
436C23×C4—101no—
437C23×C4C22⋊D511yescharacteristic
438C23×C4C22⋊D511yescharacteristic
439C23×C4C22×D511yescharacteristic
440C2×Q16—54no—
441C2×Q16—104no—
442C2×SD16—54no—
443C2×SD16—54no—
444C2×SD16—104no—
445C2×SD16—104no—
446C2×D8—54no—
447C2×D8—104no—
448C22×C8—51no—
449C22×C8—51no—
450C22×C8—51no—
451C22×C8—51no—
452#126—28no—
453#125—22no—
454#125C22×D514yes—
455#124—22no—
456#124C22×D514yes—
457#123—28no—
458C22⋊Q8—22no—
459C22⋊Q8C22×D514yes—
460#121—22no—
461#121C22×D514yes—
462C4×Q8—22no—
463C4×Q8—54no—
464C4×Q8—54no—
465C4×Q8—102no—
466C4×Q8—102no—
467C4×Q8C22×D514yes—
468C4×D4—28no—
469C4×D4—22no—
470C4×D4—54no—
471C4×D4—54no—
472C4×D4—108no—
473C4×D4—108no—
474C4×D4—102no—
475C4×D4—102no—
476C4×D4C22×D514yes—
477#117—28no—
478#117—54no—
479#117—102no—
480#117—108no—
481C2×C4⋊C4—21no—
482C2×C4⋊C4—21no—
483C2×C4⋊C4—21no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—51no—
486C2×C4⋊C4—51no—
487C2×C4⋊C4—101no—
488C2×C4⋊C4—101no—
489C2×C4⋊C4C22×D511yescharacteristic
490C2×C4⋊C4C22×D511yescharacteristic
491C2×C22⋊C4—21no—
492C2×C22⋊C4—21no—
493C2×C22⋊C4—21no—
494C2×C22⋊C4—21no—
495C2×C22⋊C4—21no—
496C2×C22⋊C4—101no—
497C2×C22⋊C4—101no—
498C2×C22⋊C4—101no—
499C2×C42—21no—
500C2×C42—101no—
501C2×C42—101no—
502C2×C42—101no—
503C2×C42—108no—
504C2×C42C22⋊D511yescharacteristic
505C2×C42C22⋊D514yes—
506C2×C42C22⋊D511yescharacteristic
507C2×C42C22×D511yescharacteristic
508C2×C42C22×D514yes—
509C2×C42C22×D511yescharacteristic
510#107—54no—
511#107—54no—
512#106—54no—
513#106—54no—
514C4⋊C8—54no—
515C4⋊C8—54no—
516#103—54no—
517#103—54no—
518#103—54no—
519#103—54no—
520#102—54no—
521#102—54no—
522#102—54no—
523#102—54no—
524C22⋊C8—54no—
525C22⋊C8—54no—
526C4×C8—54no—
527C4×C8—54no—
528C22×C5—22no—
529C22×C5—22no—
530C22×C5—22no—
531C22×C5—44no—
532C22×C5—42no—
533C22×C5—42no—
534C22×C5—42no—
535C22×C5—84no—
536C22×C5#52512yes—
537C22×C5C2×#13512yes—
538C22×C5#57512yes—
539C22×C5C23×D411yescharacteristic
540C2×D5—24no—
541C2×D5—48no—
542C2×D5—42no—
543C2×D5—42no—
544C4×C5—22no—
545C4×C5—22no—
546C4×C5—22no—
547C4×C5—22no—
548C4×C5—42no—
549C4×C5—42no—
550C4×C5—42no—
551C4×C5#52512yes—
552C4×C5C2×#13514yes—
553C4×C5C22×#4111yescharacteristic
554C4×C5C22×#4111yescharacteristic
555Dic5—24no—
556Dic5—42no—
557Dic5—42no—
558C24—21no—
559C24—101no—
560C24C2×C22⋊D511yescharacteristic
561#41—108no—
562#41—108no—
563#41—1016no—
564C2×Q8—21no—
565C2×Q8—22no—
566C2×Q8—22no—
567C2×Q8—54no—
568C2×Q8—52no—
569C2×Q8—102no—
570C2×Q8—101no—
571C2×Q8C23×D512yes—
572C2×D4—24no—
573C2×D4—22no—
574C2×D4—22no—
575C2×D4—21no—
576C2×D4—44no—
577C2×D4—54no—
578C2×D4—52no—
579C2×D4—108no—
580C2×D4—104no—
581C2×D4—102no—
582C2×D4—101no—
583C2×D4C23×D512yes—
584C22×C4—24no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—24no—
591C22×C4—42no—
592C22×C4—44no—
593C22×C4—108no—
594C22×C4—101no—
595C22×C4—104no—
596C22×C4—101no—
597C22×C4—101no—
598C22×C4—104no—
599C22×C4—104no—
600C22×C4—204no—
601C22×C4—204no—
602C22×C4C2×C22⋊D511yescharacteristic
603C22×C4C2×C22⋊D511yescharacteristic
604C22×C4C2×C22⋊D512yes—
605C22×C4C2×C22⋊D511yescharacteristic
606C22×C4C2×C22⋊D511yescharacteristic
607C22×C4C2×C22⋊D514yes—
608C22×C4C2×C22⋊D514yes—
609C22×C4C2×C22⋊D511yescharacteristic
610C22×C4C23×D512yes—
611C22×C4C23×D511yescharacteristic
612Q16—108no—
613SD16—108no—
614SD16—108no—
615D8—108no—
616C2×C8—52no—
617C2×C8—52no—
618C2×C8—52no—
619C2×C8—52no—
620C2×C8—102no—
621C2×C8—102no—
622C2×C8—102no—
623C2×C8—102no—
624C4⋊C4—24no—
625C4⋊C4—24no—
626C4⋊C4—24no—
627C4⋊C4—24no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—52no—
631C4⋊C4—52no—
632C4⋊C4—101no—
633C4⋊C4—101no—
634C4⋊C4—104no—
635C4⋊C4—104no—
636C4⋊C4C23×D512yes—
637C4⋊C4C23×D512yes—
638C22⋊C4—24no—
639C22⋊C4—24no—
640C22⋊C4—24no—
641C22⋊C4—24no—
642C22⋊C4—24no—
643C22⋊C4—104no—
644C22⋊C4—104no—
645C22⋊C4—104no—
646C42—24no—
647C42—104no—
648C42—104no—
649C42—104no—
650C42C2×C22⋊D514yes—
651C42C2×C22⋊D514yes—
652C42C2×C22⋊D512yes—
653C42C2×C22⋊D512yes—
654C42C23×D512yes—
655C42C23×D512yes—
656C2×C5—42no—
657C2×C5—82no—
658C2×C5#310214yescomplemented
659C2×C5C2×#52511yescharacteristic
660C2×C5C22×#13511yescharacteristic
661C2×C5C2×#57511yescharacteristic
662D5—44no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—104no—
671C23—102no—
672C23—202no—
673C23—202no—
674C23C22×C22⋊D512yes—
675C23C22×C22⋊D511yescharacteristic
676Q8—22no—
677Q8—22no—
678Q8—42no—
679Q8—54no—
680Q8—104no—
681Q8—102no—
682D4—22no—
683D4—22no—
684D4—48no—
685D4—42no—
686D4—54no—
687D4—1016no—
688D4—104no—
689D4—102no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—28no—
695C2×C4—24no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—44no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—48no—
706C2×C4—1016no—
707C2×C4—104no—
708C2×C4—102no—
709C2×C4—102no—
710C2×C4—102no—
711C2×C4—208no—
712C2×C4—202no—
713C2×C4—202no—
714C2×C4—208no—
715C2×C4#409614yes—
716C2×C4D5×#4112yes—
717C2×C4D5×#4112yes—
718C2×C4C22×C22⋊D512yes—
719C2×C4C22×C22⋊D512yes—
720C2×C4C22×C22⋊D512yes—
721C2×C4C22×C22⋊D512yes—
722C2×C4C22×C22⋊D512yes—
723C2×C4C22×C22⋊D511yescharacteristic
724C2×C4C24×D511yescharacteristic
725C8—102no—
726C8—102no—
727C8—102no—
728C8—102no—
729C5C2×#310211yescharacteristic, complemented, Sylow
730C22—22no—
731C22—22no—
732C22—22no—
733C22—44no—
734C22—42no—
735C22—42no—
736C22—42no—
737C22—84no—
738C22—104no—
739C22—202no—
740C22—202no—
741C22—208no—
742C22C2×#409612yes—
743C22#6615612yes—
744C22#6616212yes—
745C22C23×C22⋊D511yescharacteristic
746C4—22no—
747C4—22no—
748C4—22no—
749C4—22no—
750C4—42no—
751C4—42no—
752C4—42no—
753C4—104no—
754C4—202no—
755C4—202no—
756C4C2×#409614yes—
757C4#6616212yes—
758C4C2×D5×#4111yescharacteristic
759C4C2×D5×#4111yescharacteristic
760C2—42no—
761C2—82no—
762C2—204no—
763C2#1061487114yesdirect product factor
764C2C22×#409611yescharacteristic
765C2C2×#6615611yescharacteristic
766C2C2×#6616211yescharacteristic
subgroupG/H
centerC22×C4C2×C22⋊D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×#529C2
socleC23×C5C22×D4
prime radicalC2×#65326C2
hypercenterC2×#529D5
hypocenterC5C2×#3102
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C2×#529

Complements

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

NH ≅ G/Ntype
1. C2×C5×#529C2semidirect
2. C2×C4×#709C2semidirect
3. #10614871C2direct (N × H)
4. C2×#65352C2semidirect
5. C2×#65355C2semidirect
6. C2×#65343C2semidirect
7. C2×#65346C2semidirect
8. C2×#65336C2semidirect
9. C2×#65334C2semidirect
11. C2×#65324C2semidirect
12. C2×C4×#689C2semidirect
13. C2×C4×#688C2semidirect
14. C2×C4×#687C2semidirect
15. C2×C4×#686C2semidirect
16. C2×#65214C2semidirect
19. C5×#529C22semidirect
39. C4×#709C22semidirect
52. #65355C22semidirect
53. #65352C22semidirect
54. #65346C22semidirect
55. #65343C22semidirect
56. #65336C22semidirect
57. #65334C22semidirect
59. #65324C22semidirect
60. C4×#689C22semidirect
61. C4×#688C22semidirect
62. C4×#687C22semidirect
63. C4×#686C22semidirect
72. #65214C22semidirect
183. C2×#529D5semidirect
303. #529C2×D5semidirect
658. C2×C5#3102semidirect
729. C5C2×#3102semidirect
763. C2#10614871direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#5292
C2×C4×#7092
#106148712
C2×#653522
C2×#653552
C2×#653432
C2×#653462
C2×#653362
C2×#653342
C2×#653262
C2×#653242
C2×C4×#6892
C2×C4×#6882
C2×C4×#6872
C2×C4×#6862
C2×#652142
C2×#31025