Finite Group Databasebeta

← C2×#10611384 #12967327

Subgroups — C2×#10611384 #12967327

Order 1280.

2418 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×Q8×D5C211yesmaximal, characteristic, complemented
2C2×#65882C211yesmaximal, characteristic
3C2×C4×C5×SD16C211yesmaximal, characteristic, complemented
4C2×#65459C211yesmaximal, characteristic, complemented
5C2×#65452C211yesmaximal, characteristic, complemented
6C2×C4×#688C211yesmaximal, characteristic, complemented
7C2×C4×#687C211yesmaximal, characteristic, complemented
8#10611384C2116yesmaximal, direct product factor
9C2×#65143C211yesmaximal, characteristic, complemented
10C2×#65152C211yesmaximal, characteristic, complemented
11C2×#65095C211yesmaximal, characteristic, complemented
12C2×#65080C211yesmaximal, characteristic, complemented
13C2×#65051C211yesmaximal, characteristic, complemented
14C2×#65066C211yesmaximal, characteristic, complemented
15C2×C4×#677C211yesmaximal, characteristic, complemented
16C2×#64974C211yesmaximal, characteristic, complemented
17C22×Q8×D5C2211yescharacteristic
18C22×#709—21no—
19C22×C5×SD16C2211yescharacteristic
20C2×C4×C5×Q8C2211yescharacteristic
21C2×C4×C5×D4C2211yescharacteristic
22C2×Q8×Dic5C2211yescharacteristic
23C22×#688C2211yescharacteristic
24C2×#4086C2211yescharacteristic
25C2×#4084C2211yescharacteristic
26C22×#687C2211yescharacteristic
27C2×C4×C22⋊D5—21no—
28C22×#677C2211yescharacteristic
29C4×Q8×D5—24no—
30C4×Q8×D5C2218yescomplemented
31#65882—24no—
32#65882C2218yes—
33C2×#4041C2211yescharacteristic
34C2×D5×C4⋊C4—21no—
35C2×D5×C4⋊C4C2211yescharacteristic
36C2×#4034C2211yescharacteristic
37C2×#4033—21no—
38C2×#4033C2211yescharacteristic
39C2×#4031—21no—
40C2×#4030—21no—
41C2×C4×D20C2211yescharacteristic
42C2×C42×D5—21no—
43C2×C42×D5C2211yescharacteristic
44C2×C4×Dic10—21no—
45C2×C4×Dic10C2211yescharacteristic
46C4×C5×SD16C2218yescomplemented
47C2×C5×#106C2211yescharacteristic
48C2×C5×#103C2211yescharacteristic
49C2×C5×#102C2211yescharacteristic
50C2×C4×C5×C8C2211yescharacteristic
51C2×#3967C2211yescharacteristic
52C2×#3964C2211yescharacteristic
53#65459C2218yescomplemented
54#65452C2218yescomplemented
55C2×#3953C2211yescharacteristic
56C2×#3952C2211yescharacteristic
57C2×#3952C2211yescharacteristic
58C2×#3949C2211yescharacteristic
59C2×#3948C2211yescharacteristic
60C2×#3946C2211yescharacteristic
61C2×#3946C2211yescharacteristic
62C4×#688C2218yescomplemented
63C4×#687C2218yescomplemented
64C2×#3942C2211yescharacteristic
65C2×#3941C2211yescharacteristic
66C2×#3940C2211yescharacteristic
67C2×#3940C2211yescharacteristic
68C2×C4×#168C2211yescharacteristic
69#65152C2218yescomplemented
70#65143C2218yescomplemented
71#65095C2218yescomplemented
72#65080C2218yescomplemented
73#65066C2218yescomplemented
74#65051C2218yescomplemented
75C4×#677C2218yescomplemented
76#64974C2218yescomplemented
77C2×#3103—51nomaximal, Sylow
78C22×C5×Q8C2311yescharacteristic
79C22×C5×D4C2311yescharacteristic
80C23×C4×C5—21no—
81C22×C22⋊D5—21no—
82C22×C22⋊D5—21no—
83C22×C22⋊D5—21no—
84C2×Q8×D5—24no—
85C2×Q8×D5—22no—
86C2×Q8×D5—24no—
87C2×Q8×D5C2314yes—
88C2×#709—28no—
89C2×#709—48no—
90C22×D20—21no—
91C22×D20C2311yescharacteristic
92C22×C4×D5—21no—
93C22×C4×D5—21no—
94C22×C4×D5—21no—
95C22×C4×D5D411yescharacteristic
96C22×C4×D5D411yescharacteristic
97C22×C4×D5C2311yescharacteristic
98C22×Dic10—21no—
99C22×Dic10—21no—
100C22×Dic10C2311yescharacteristic
101C2×C5×SD16—24no—
102C2×C5×SD16C2314yes—
103C22×C5×C8C2311yescharacteristic
104C22×C5×C8C2311yescharacteristic
105C4×C5×Q8—22no—
106C4×C5×Q8C2314yes—
107C4×C5×D4—22no—
108C4×C5×D4C2314yes—
109C2×C5×C4⋊C4—21no—
110C2×C5×C4⋊C4C2311yescharacteristic
111C2×C5×C4⋊C4C2311yescharacteristic
112C2×C5×C22⋊C4—21no—
113C2×C42×C5—21no—
114C2×C42×C5C2311yescharacteristic
115C2×C22⋊Dic5—21no—
116Q8×Dic5—22no—
117Q8×Dic5C2314yes—
118C2×#688—24no—
119C2×#688C2314yes—
120#4086—22no—
121#4086C2314yes—
122#4084—22no—
123#4084C2314yes—
124C2×#687—24no—
125C2×#687C2314yes—
126C4×C22⋊D5—28no—
127C2×#685—21no—
128C2×#685—21no—
129C2×C4⋊Dic5—21no—
130C2×C4⋊Dic5C2311yescharacteristic
131C2×C4⋊Dic5C2311yescharacteristic
132C2×#683—21no—
133C2×#683—21no—
134C2×#683—21no—
135C2×#683—21no—
136C2×C4×Dic5—21no—
137C2×C4×Dic5—21no—
138C2×C4×Dic5—21no—
139C2×C4×Dic5D411yescharacteristic
140C2×C4×Dic5D411yescharacteristic
141C2×C4×Dic5C2311yescharacteristic
142C22×#168C2311yescharacteristic
143C22×#168C2311yescharacteristic
144C2×#677—24no—
145C2×#677C2314yes—
146#4041—22no—
147#4041C2314yes—
148D5×C4⋊C4—28no—
149D5×C4⋊C4—22no—
150D5×C4⋊C4C2314yes—
151#4034—22no—
152#4034C2314yes—
153#4033—28no—
154#4033—22no—
155#4033C2314yes—
156#4031—28no—
157#4030—28no—
158C4×D20—22no—
159C4×D20C2314yes—
160C42×D5—28no—
161C42×D5D414yes—
162C42×D5C2314yes—
163C4×Dic10—22no—
164C4×Dic10—28no—
165C4×Dic10C2314yes—
166C5×#106C2314yes—
167C5×#103C2314yes—
168C5×#102C2314yes—
169C4×C5×C8C2314yes—
170#3967C2314yes—
171#3964C2314yes—
172#3953C2314yes—
173#3952C2314yes—
174#3952C2314yes—
175#3949C2314yes—
176#3948C2314yes—
177#3946C2314yes—
178#3946C2314yes—
179#3942C2314yes—
180#3941C2314yes—
181#3940C2314yes—
182#3940C2314yes—
183C4×#168C2314yes—
184C2×#532—51no—
185C22×C4×Q8—51no—
186#3103—516no—
187C2×#481—51no—
188C2×#481—51no—
189C2×#475—51no—
190C2×#475—51no—
191C2×#460—51no—
192C2×#460—51no—
193C2×#448—51no—
194C2×#448—51no—
195C2×C4×SD16—51no—
196C2×C4×SD16—51no—
197C2×C4×SD16—51no—
198C2×C4×SD16D511yescharacteristic, complemented
199C2×#431—51no—
200C24×C5—21no—
201C23×D5—21no—
202C23×D5C2×D411yescharacteristic
203C2×C5×Q8—21no—
204C2×C5×Q8—22no—
205C2×C5×Q8#4114yescomplemented
206C2×C5×Q8C2412yes—
207C2×C5×D4—21no—
208C2×C5×D4—22no—
209C2×C5×D4—22no—
210C2×C5×D4C2412yes—
211C22×C4×C5—21no—
212C22×C4×C5—21no—
213C22×C4×C5—21no—
214C22×C4×C5—24no—
215C22×C4×C5—44no—
216C22×C4×C5C2×D411yescharacteristic
217C22×C4×C5C2×D411yescharacteristic
218C22×C4×C5C2411yescharacteristic
219C2×C22⋊D5—24no—
220C2×C22⋊D5—24no—
221C2×C22⋊D5—24no—
222C2×C22⋊D5—44no—
223C2×C22⋊D5—44no—
224C2×C22⋊D5—44no—
225C22×Dic5—21no—
226C22×Dic5—21no—
227C22×Dic5—21no—
228C22×Dic5C2×D411yescharacteristic
229C22×Dic5C2×D411yescharacteristic
230C22×Dic5C2×D411yescharacteristic
231Q8×D5—216no—
232Q8×D5—28no—
233Q8×D5—28no—
234#709—432no—
235C2×D20—22no—
236C2×D20—22no—
237C2×D20—24no—
238C2×D20—21no—
239C2×D20—44no—
240C2×D20C2412yes—
241C2×C4×D5—28no—
242C2×C4×D5—24no—
243C2×C4×D5—22no—
244C2×C4×D5—22no—
245C2×C4×D5—24no—
246C2×C4×D5—24no—
247C2×C4×D5—42no—
248C2×C4×D5—44no—
249C2×C4×D5—44no—
250C2×C4×D5SD1618yescomplemented
251C2×C4×D5C2×D412yes—
252C2×C4×D5C2×D414yes—
253C2×C4×D5C2×D414yes—
254C2×C4×D5C2412yes—
255C2×Dic10—28no—
256C2×Dic10—21no—
257C2×Dic10—22no—
258C2×Dic10—24no—
259C2×Dic10—24no—
260C2×Dic10—44no—
261C2×Dic10#4114yescomplemented
262C2×Dic10C2412yes—
263C5×SD16—28no—
264C2×C5×C8—22no—
265C2×C5×C8—22no—
266C2×C5×C8C2412yes—
267C2×C5×C8C2412yes—
268C5×C4⋊C4—24no—
269C5×C4⋊C4—21no—
270C5×C4⋊C4—21no—
271C5×C4⋊C4C2412yes—
272C5×C4⋊C4C2412yes—
273C5×C22⋊C4—24no—
274C42×C5—24no—
275C42×C5C2×D412yes—
276C42×C5C2412yes—
277C22⋊Dic5—24no—
278#688—28no—
279#687—28no—
280#685—24no—
281#685—24no—
282C4⋊Dic5—21no—
283C4⋊Dic5—21no—
284C4⋊Dic5—24no—
285C4⋊Dic5C2412yes—
286C4⋊Dic5C2412yes—
287#683—24no—
288#683—24no—
289#683—24no—
290#683—24no—
291C4×Dic5—24no—
292C4×Dic5—24no—
293C4×Dic5—24no—
294C4×Dic5C2×D414yes—
295C4×Dic5C2×D412yes—
296C4×Dic5C2×D414yes—
297C4×Dic5C2412yes—
298C2×#168—22no—
299C2×#168—22no—
300C2×#168C2412yes—
301C2×#168C2412yes—
302#677—28no—
303C22×#41—101no—
304C23×Q8—51no—
305C22×SD16—51no—
306C22×SD16—51no—
307C22×SD16—51no—
308C22×SD16C2×D511yescharacteristic
309#532—58no—
310#532—104no—
311C2×C4⋊Q8—51no—
312C2×#127—51no—
313C2×#124—101no—
314C2×#121—51no—
315C2×#121—51no—
316C2×#121—101no—
317C2×C4×Q8—51no—
318C2×C4×Q8—58no—
319C2×C4×Q8—51no—
320C2×C4×Q8—51no—
321C2×C4×Q8—101no—
322C2×C4×Q8—101no—
323C2×C4×Q8—104no—
324C2×C4×Q8C2×D511yescharacteristic
325C2×C4×D4—51no—
326C2×C4×D4—101no—
327C2×C4×D4C2×D511yescharacteristic
328C22×C4⋊C4—51no—
329C22×C4⋊C4—101no—
330C22×C42—51no—
331C22×C42—101no—
332#481—58no—
333#481—58no—
334#475—58no—
335#475—58no—
336#460—58no—
337#460—58no—
338#448—58no—
339#448—58no—
340C4×SD16—58no—
341C4×SD16—58no—
342C4×SD16—58no—
343C4×SD16C2×D518yescomplemented
344#431—58no—
345C2×#106—51no—
346C2×#106—51no—
347C2×#106—51no—
348C2×#106C2×D511yescharacteristic
349C2×C4⋊C8—51no—
350C2×C4⋊C8—51no—
351C2×#103—51no—
352C2×#103—51no—
353C2×#103—51no—
354C2×#103C2×D511yescharacteristic
355C2×#102—51no—
356C2×#102—51no—
357C2×#102—51no—
358C2×#102C2×D511yescharacteristic
359C2×C22⋊C8—51no—
360C2×C22⋊C8—51no—
361C2×C4×C8—51no—
362C2×C4×C8C2×D511yescharacteristic
363C23×C5—22no—
364C23×C5—42no—
365C23×C5—42no—
366C23×C5—42no—
367C23×C5C22×D411yescharacteristic
368C22×D5—22no—
369C22×D5—22no—
370C22×D5—22no—
371C22×D5—42no—
372C22×D5—42no—
373C22×D5—42no—
374C22×D5C2×SD1614yes—
375C22×D5C22×D412yes—
376C5×Q8—24no—
377C5×Q8—22no—
378C5×Q8C2×#4114yescomplemented
379C5×D4—22no—
380C5×D4—22no—
381C5×D4—42no—
382C2×C4×C5—24no—
383C2×C4×C5—22no—
384C2×C4×C5—22no—
385C2×C4×C5—22no—
386C2×C4×C5—22no—
387C2×C4×C5—42no—
388C2×C4×C5—42no—
389C2×C4×C5—48no—
390C2×C4×C5C2×SD1614yes—
391C2×C4×C5C22×D412yes—
392C2×C4×C5C22×D411yescharacteristic
393C2×C4×C5C22×D412yes—
394C2×C4×C5C2×#4112yes—
395C2×C4×C5C2×#4112yes—
396C2×C4×C5C2511yescharacteristic
397C22⋊D5—48no—
398C22⋊D5—48no—
399C22⋊D5—48no—
400C2×Dic5—22no—
401C2×Dic5—24no—
402C2×Dic5—22no—
403C2×Dic5—22no—
404C2×Dic5—22no—
405C2×Dic5—22no—
406C2×Dic5—42no—
407C2×Dic5—42no—
408C2×Dic5C2×SD1614yes—
409C2×Dic5C22×D412yes—
410C2×Dic5C22×D412yes—
411C2×Dic5C22×D412yes—
412D20—22no—
413D20—22no—
414D20—48no—
415D20—42no—
416C4×D5—216no—
417C4×D5—24no—
418C4×D5—22no—
419C4×D5—22no—
420C4×D5—44no—
421C4×D5—48no—
422C4×D5—48no—
423C4×D5C2×SD16116yescomplemented
424Dic10—216no—
425Dic10—24no—
426Dic10—22no—
427Dic10—48no—
428Dic10C2×#4114yescomplemented
429C5×C8—22no—
430C5×C8—22no—
431#168—22no—
432#168—22no—
433C2×#41—108no—
434C2×#41—208no—
435C22×Q8—54no—
436C22×Q8—51no—
437C22×Q8—101no—
438C22×Q8—101no—
439C22×Q8—102no—
440C22×Q8—104no—
441C22×Q8—104no—
442C22×Q8C22×D511yescharacteristic
443C22×D4—51no—
444C22×D4—101no—
445C22×D4—101no—
446C22×D4—101no—
447C22×D4—101no—
448C22×D4C22×D511yescharacteristic
449C23×C4—21no—
450C23×C4—51no—
451C23×C4—51no—
452C23×C4—51no—
453C23×C4—101no—
454C23×C4—101no—
455C23×C4—101no—
456C2×SD16—24no—
457C2×SD16—54no—
458C2×SD16—54no—
459C2×SD16—54no—
460C2×SD16—104no—
461C2×SD16—104no—
462C2×SD16—104no—
463C2×SD16C22×D514yes—
464C22×C8—51no—
465C22×C8—51no—
466C22×C8C22×D511yescharacteristic
467C22×C8C22×D511yescharacteristic
468C4⋊Q8—54no—
469C4⋊Q8—102no—
470#127—54no—
471#127—102no—
472#124—108no—
473#121—54no—
474#121—54no—
475#121—108no—
476#121—102no—
477#121—102no—
478C4×Q8—22no—
479C4×Q8—54no—
480C4×Q8—54no—
481C4×Q8—54no—
482C4×Q8—108no—
483C4×Q8—108no—
484C4×Q8—102no—
485C4×Q8—102no—
486C4×Q8—102no—
487C4×Q8C22×D514yes—
488C4×D4—22no—
489C4×D4—54no—
490C4×D4—108no—
491C4×D4—102no—
492C4×D4C22×D514yes—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—51no—
495C2×C4⋊C4—51no—
496C2×C4⋊C4—54no—
497C2×C4⋊C4—102no—
498C2×C4⋊C4—108no—
499C2×C4⋊C4—101no—
500C2×C4⋊C4—101no—
501C2×C4⋊C4—101no—
502C2×C4⋊C4—101no—
503C2×C4⋊C4—101no—
504C2×C4⋊C4C22×D511yescharacteristic
505C2×C4⋊C4C22×D511yescharacteristic
506C2×C22⋊C4—21no—
507C2×C22⋊C4—101no—
508C2×C22⋊C4—101no—
509C2×C22⋊C4—101no—
510C2×C42—21no—
511C2×C42—51no—
512C2×C42—51no—
513C2×C42—51no—
514C2×C42—54no—
515C2×C42—54no—
516C2×C42—108no—
517C2×C42—101no—
518C2×C42—101no—
519C2×C42—101no—
520C2×C42C22×D511yescharacteristic
521#106—54no—
522#106—54no—
523#106—54no—
524#106C22×D514yes—
525C4⋊C8—54no—
526C4⋊C8—54no—
527#103—54no—
528#103—54no—
529#103—54no—
530#103C22×D514yes—
531#102—54no—
532#102—54no—
533#102—54no—
534#102C22×D514yes—
535C22⋊C8—54no—
536C22⋊C8—54no—
537C4×C8—54no—
538C4×C8C22×D514yes—
539C22×C5—42no—
540C22×C5—42no—
541C22×C5—42no—
542C22×C5—84no—
543C22×C5#52512yes—
544C22×C5C22×SD1612yes—
545C22×C5#57512yes—
546C22×C5C23×D411yescharacteristic
547C2×D5—28no—
548C2×D5—22no—
549C2×D5—22no—
550C2×D5—42no—
551C2×D5—42no—
552C2×D5—42no—
553C2×D5—84no—
554C2×D5C22×SD1614yes—
555C4×C5—24no—
556C4×C5—22no—
557C4×C5—42no—
558C4×C5—42no—
559C4×C5#52512yes—
560C4×C5C22×SD1614yes—
561C4×C5C22×#4111yescharacteristic
562C4×C5C22×#4111yescharacteristic
563Dic5—22no—
564Dic5—24no—
565Dic5—22no—
566Dic5—42no—
567Dic5—42no—
568Dic5C22×SD1614yes—
569C24—21no—
570C24—51no—
571C24—101no—
572#41—2032no—
573C2×Q8—21no—
574C2×Q8—22no—
575C2×Q8—54no—
576C2×Q8—52no—
577C2×Q8—104no—
578C2×Q8—104no—
579C2×Q8—108no—
580C2×Q8—108no—
581C2×Q8—1016no—
582C2×Q8—108no—
583C2×Q8—102no—
584C2×Q8—101no—
585C2×Q8—204no—
586C2×Q8#70914yescomplemented
587C2×Q8C23×D512yes—
588C2×D4—22no—
589C2×D4—21no—
590C2×D4—22no—
591C2×D4—52no—
592C2×D4—104no—
593C2×D4—104no—
594C2×D4—104no—
595C2×D4—104no—
596C2×D4—102no—
597C2×D4—101no—
598C2×D4—102no—
599C2×D4—204no—
600C2×D4—204no—
601C2×D4—204no—
602C2×D4—204no—
603C2×D4C23×D512yes—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—24no—
608C22×C4—44no—
609C22×C4—51no—
610C22×C4—54no—
611C22×C4—58no—
612C22×C4—51no—
613C22×C4—51no—
614C22×C4—52no—
615C22×C4—52no—
616C22×C4—54no—
617C22×C4—104no—
618C22×C4—108no—
619C22×C4—104no—
620C22×C4—101no—
621C22×C4—102no—
622C22×C4—102no—
623C22×C4—101no—
624C22×C4—101no—
625C22×C4—104no—
626C22×C4—202no—
627C22×C4—204no—
628C22×C4—204no—
629C22×C4D4×D511yescharacteristic
630C22×C4D4×D511yescharacteristic
631C22×C4C23×D511yescharacteristic
632SD16—28no—
633SD16—108no—
634SD16—108no—
635SD16—108no—
636C2×C8—22no—
637C2×C8—22no—
638C2×C8—52no—
639C2×C8—52no—
640C2×C8—102no—
641C2×C8—102no—
642C2×C8C23×D512yes—
643C2×C8C23×D512yes—
644C4⋊C4—24no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—52no—
648C4⋊C4—52no—
649C4⋊C4—104no—
650C4⋊C4—104no—
651C4⋊C4—104no—
652C4⋊C4—104no—
653C4⋊C4—101no—
654C4⋊C4—101no—
655C4⋊C4—104no—
656C4⋊C4C23×D512yes—
657C4⋊C4C23×D512yes—
658C22⋊C4—24no—
659C22⋊C4—104no—
660C22⋊C4—104no—
661C22⋊C4—104no—
662C42—24no—
663C42—54no—
664C42—54no—
665C42—52no—
666C42—52no—
667C42—104no—
668C42—104no—
669C42—104no—
670C42D4×D512yes—
671C42C23×D512yes—
672C2×C5—82no—
673C2×C5#310314yescomplemented
674C2×C5C2×#52511yescharacteristic
675C2×C5C23×SD1611yescharacteristic
676C2×C5C2×#57511yescharacteristic
677D5—24no—
678D5—82no—
679C23—22no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—54no—
684C23—52no—
685C23—102no—
686C23—102no—
687C23—102no—
688C23—202no—
689C23—202no—
690C23—202no—
691C23C2×D4×D511yescharacteristic
692Q8—24no—
693Q8—22no—
694Q8—54no—
695Q8—1016no—
696Q8—104no—
697Q8—102no—
698Q8—208no—
699Q8C2×#70914yescomplemented
700D4—22no—
701D4—22no—
702D4—42no—
703D4—102no—
704D4—102no—
705D4—208no—
706D4—208no—
707D4—208no—
708D4—208no—
709D4—202no—
710C2×C4—22no—
711C2×C4—24no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—48no—
718C2×C4—54no—
719C2×C4—52no—
720C2×C4—516no—
721C2×C4—52no—
722C2×C4—52no—
723C2×C4—1016no—
724C2×C4—102no—
725C2×C4—102no—
726C2×C4—104no—
727C2×C4—102no—
728C2×C4—104no—
729C2×C4—102no—
730C2×C4—102no—
731C2×C4—102no—
732C2×C4—102no—
733C2×C4—204no—
734C2×C4—208no—
735C2×C4—202no—
736C2×C4—202no—
737C2×C4—208no—
738C2×C4D5×SD1614yes—
739C2×C4C2×#70912yes—
740C2×C4C2×D4×D512yes—
741C2×C4C2×D4×D512yes—
742C2×C4C2×D4×D511yescharacteristic
743C2×C4D5×#4112yes—
744C2×C4C24×D511yescharacteristic
745C8—22no—
746C8—22no—
747C8—102no—
748C8—102no—
749C5C2×#310311yescharacteristic, complemented, Sylow
750C22—42no—
751C22—42no—
752C22—42no—
753C22—54no—
754C22—84no—
755C22—102no—
756C22—108no—
757C22—102no—
758C22—202no—
759C22—202no—
760C22—202no—
761C22—404no—
762C22#6588112yes—
763C22C2×D5×SD1612yes—
764C22#6610212yes—
765C22C22×D4×D511yescharacteristic
766C4—24no—
767C4—22no—
768C4—42no—
769C4—42no—
770C4—54no—
771C4—102no—
772C4—104no—
773C4—102no—
774C4—202no—
775C4—202no—
776C4#6588112yes—
777C4C2×D5×SD1614yes—
778C4C22×#70911yescharacteristic
779C4C2×D5×#4111yescharacteristic
780C2—82no—
781C2—104no—
782C2—402no—
783C2#1061138414yesdirect product factor
784C2C2×#6588111yescharacteristic
785C2C22×D5×SD1611yescharacteristic
786C2C2×#6610211yescharacteristic
subgroupG/H
centerC22×C4D4×D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C4×C5×SD16C2
socleC23×C5C22×D4
prime radicalC2×#65882C2
hypercenterC2×C4×SD16D5
hypocenterC5C2×#3103
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×SD16

Complements

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

NH ≅ G/Ntype
1. C2×C4×Q8×D5C2semidirect
3. C2×C4×C5×SD16C2semidirect
4. C2×#65459C2semidirect
5. C2×#65452C2semidirect
6. C2×C4×#688C2semidirect
7. C2×C4×#687C2semidirect
8. #10611384C2direct (N × H)
9. C2×#65143C2semidirect
10. C2×#65152C2semidirect
11. C2×#65095C2semidirect
12. C2×#65080C2semidirect
13. C2×#65051C2semidirect
14. C2×#65066C2semidirect
15. C2×C4×#677C2semidirect
16. C2×#64974C2semidirect
30. C4×Q8×D5C22semidirect
46. C4×C5×SD16C22semidirect
53. #65459C22semidirect
54. #65452C22semidirect
62. C4×#688C22semidirect
63. C4×#687C22semidirect
69. #65152C22semidirect
70. #65143C22semidirect
71. #65095C22semidirect
72. #65080C22semidirect
73. #65066C22semidirect
74. #65051C22semidirect
75. C4×#677C22semidirect
76. #64974C22semidirect
198. C2×C4×SD16D5semidirect
205. C2×C5×Q8#41semidirect
250. C2×C4×D5SD16semidirect
261. C2×Dic10#41semidirect
343. C4×SD16C2×D5semidirect
378. C5×Q8C2×#41semidirect
423. C4×D5C2×SD16semidirect
428. Dic10C2×#41semidirect
586. C2×Q8#709semidirect
673. C2×C5#3103semidirect
699. Q8C2×#709semidirect
749. C5C2×#3103semidirect
783. C2#10611384direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×Q8×D52
C2×#658822
C2×C4×C5×SD162
C2×#654592
C2×#654522
C2×C4×#6882
C2×C4×#6872
#106113842
C2×#651432
C2×#651522
C2×#650952
C2×#650802
C2×#650512
C2×#650662
C2×C4×#6772
C2×#649742
C2×#31035