Finite Group Databasebeta

← C2×#10615165 #12967541

Subgroups — C2×#10615165 #12967541

Order 1280.

2198 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#540C211yesmaximal, characteristic, complemented
2C2×#65857C211yesmaximal, characteristic, complemented
3#10615165C2116yesmaximal, direct product factor
4C2×#65364C211yesmaximal, characteristic, complemented
5C2×#65361C211yesmaximal, characteristic, complemented
6C2×#65352C211yesmaximal, characteristic, complemented
7C2×#65355C211yesmaximal, characteristic, complemented
8C2×#65326C211yesmaximal, characteristic, complemented
9C2×#65326C211yesmaximal, characteristic, complemented
10C2×#65323C211yesmaximal, characteristic, complemented
11C2×#65322C211yesmaximal, characteristic, complemented
12C2×C4×#687C211yesmaximal, characteristic, complemented
13C2×#65303C211yesmaximal, characteristic, complemented
14C2×#65307C211yesmaximal, characteristic, complemented
15C2×C4×#686C211yesmaximal, characteristic, complemented
16C2×#65289C211yesmaximal, characteristic, complemented
17C22×#709C2211yescharacteristic
18C5×#540—24no—
19C5×#540C2218yescomplemented
20C2×C5×#127C2211yescharacteristic
21C2×C5×#125C2211yescharacteristic
22C2×C5×#123—21no—
23C2×C5×#123—21no—
24C2×C5×#121—21no—
25C2×C5×#121—21no—
26C2×C5×#121C2211yescharacteristic
27C2×C5×#121C2211yescharacteristic
28C2×C4×C5×D4C2211yescharacteristic
29C2×C4×C5×D4C2211yescharacteristic
30C2×C5×#117C2211yescharacteristic
31C22×#687C2211yescharacteristic
32C22×#687C2211yescharacteristic
33C22×#686C2211yescharacteristic
34C22×#686C2211yescharacteristic
35C22×C4⋊Dic5C2211yescharacteristic
36#65857—24no—
37#65857C2218yescomplemented
38C2×#4038—21no—
39C2×D5×C4⋊C4—21no—
40C2×#4027—21no—
41C2×#4027—21no—
42C2×C4×D20C2211yescharacteristic
43C2×C4×D20C2211yescharacteristic
44C2×C4×Dic10C2211yescharacteristic
45C2×C4×Dic10C2211yescharacteristic
46C2×#3964C2211yescharacteristic
47C2×#3964C2211yescharacteristic
48C2×#3964C2211yescharacteristic
49C2×#3964C2211yescharacteristic
50C2×C22⋊#168C2211yescharacteristic
51C2×C22⋊#168C2211yescharacteristic
52#65364C2218yescomplemented
53#65361C2218yescomplemented
54#65355C2218yescomplemented
55#65352C2218yescomplemented
56#65326C2218yescomplemented
57#65326C2218yescomplemented
58#65323C2218yescomplemented
59#65322C2218yescomplemented
60#65307C2218yescomplemented
61C4×#687C2218yescomplemented
62#65303C2218yescomplemented
63C4×#686C2218yescomplemented
64#65289C2218yescomplemented
65C2×#3942C2211yescharacteristic
66C2×#3942C2211yescharacteristic
67C2×#3941C2211yescharacteristic
68C2×#3941C2211yescharacteristic
69C2×#3940C2211yescharacteristic
70C2×#3940C2211yescharacteristic
71C2×#3939C2211yescharacteristic
72C2×#3939C2211yescharacteristic
73C2×C4⋊#168C2211yescharacteristic
74C2×C4⋊#168C2211yescharacteristic
75C2×#3935C2211yescharacteristic
76C2×C4×#168C2211yescharacteristic
77C2×#3119—51nomaximal, Sylow
78C22×C5×D4—21no—
79C22×C5×D4—21no—
80C22×C5×D4—21no—
81C22×C5×D4—21no—
82C22×C5×D4C2311yescharacteristic
83C22×C5×D4C2311yescharacteristic
84C23×C4×C5—21no—
85C23×C4×C5—21no—
86C23×C4×C5C2311yescharacteristic
87C22×C22⋊D5—21no—
88C23×Dic5—21no—
89C2×#709—22no—
90C2×#709—24no—
91C2×#709—24no—
92C2×#709C2314yes—
93C22×D20C2311yescharacteristic
94C22×C4×D5—21no—
95C22×C4×D5—21no—
96C22×C4×D5—21no—
97C22×Dic10C2311yescharacteristic
98C5×#127—22no—
99C5×#127C2314yes—
100C5×#125—22no—
101C5×#125C2314yes—
102C5×#123—28no—
103C5×#123—28no—
104C5×#121—22no—
105C5×#121—22no—
106C5×#121—28no—
107C5×#121—28no—
108C5×#121C2314yes—
109C5×#121C2314yes—
110C4×C5×D4—22no—
111C4×C5×D4—22no—
112C4×C5×D4C2314yes—
113C4×C5×D4C2314yes—
114C5×#117D414yes—
115C5×#117C2314yes—
116C2×C5×C4⋊C4—21no—
117C2×C5×C4⋊C4—21no—
118C2×C5×C4⋊C4D411yescharacteristic
119C2×C5×C4⋊C4D411yescharacteristic
120C2×C5×C4⋊C4C2311yescharacteristic
121C2×C5×C4⋊C4C2311yescharacteristic
122C2×C5×C22⋊C4—21no—
123C2×C5×C22⋊C4—21no—
124C2×C5×C22⋊C4—21no—
125C2×C5×C22⋊C4—21no—
126C2×C5×C22⋊C4D411yescharacteristic
127C2×C5×C22⋊C4D411yescharacteristic
128C2×C42×C5C2311yescharacteristic
129C2×C42×C5C2311yescharacteristic
130C2×#687—24no—
131C2×#687—24no—
132C2×#687C2314yes—
133C2×#687C2314yes—
134C2×#686—24no—
135C2×#686—24no—
136C2×#686C2314yes—
137C2×#686C2314yes—
138C2×#685—21no—
139C2×#685—21no—
140C2×C4⋊Dic5—21no—
141C2×C4⋊Dic5—22no—
142C2×C4⋊Dic5C2311yescharacteristic
143C2×C4⋊Dic5C2311yescharacteristic
144C2×C4⋊Dic5C2314yes—
145C2×#683—21no—
146C2×#683—21no—
147C2×C4×Dic5—21no—
148C2×C4×Dic5—21no—
149C22×#168C2311yescharacteristic
150C22×#168C2311yescharacteristic
151C22×#168C2311yescharacteristic
152C22×#168C2311yescharacteristic
153#4038—28no—
154D5×C4⋊C4—28no—
155#4027—28no—
156#4027—28no—
157C4×D20—22no—
158C4×D20—22no—
159C4×D20C2314yes—
160C4×D20C2314yes—
161C4×Dic10—22no—
162C4×Dic10—22no—
163C4×Dic10C2314yes—
164C4×Dic10C2314yes—
165#3964C2314yes—
166#3964C2314yes—
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—
181#3935C2314yes—
182C4×#168C2314yes—
183C2×#540D511yescharacteristic, complemented
184C2×#520—51no—
185#3119—516no—
186C2×#481—51no—
187C2×#480—51no—
188C2×#479—51no—
189C2×#478—51no—
190C2×#460—51no—
191C2×#459—51no—
192C2×#449—51no—
193C2×#449—51no—
194C2×#442—51no—
195C2×#440—51no—
196C2×C4×SD16—51no—
197C2×C4×D8—51no—
198C2×#433—51no—
199C24×C5—21no—
200C24×C5—21no—
201C24×C5C2×D411yescharacteristic
202C23×D5—21no—
203C2×C5×D4—24no—
204C2×C5×D4—24no—
205C2×C5×D4—21no—
206C2×C5×D4—21no—
207C2×C5×D4—24no—
208C2×C5×D4—24no—
209C2×C5×D4—22no—
210C2×C5×D4—22no—
211C2×C5×D4—22no—
212C2×C5×D4—22no—
213C2×C5×D4—82no—
214C2×C5×D4—82no—
215C2×C5×D4—82no—
216C2×C5×D4—82no—
217C2×C5×D4C2412yes—
218C2×C5×D4C2412yes—
219C22×C4×C5—22no—
220C22×C4×C5—22no—
221C22×C4×C5—21no—
222C22×C4×C5—21no—
223C22×C4×C5—24no—
224C22×C4×C5—24no—
225C22×C4×C5—82no—
226C22×C4×C5—82no—
227C22×C4×C5C2×D411yescharacteristic
228C22×C4×C5C2×D411yescharacteristic
229C22×C4×C5C2×D411yescharacteristic
230C22×C4×C5C2×D411yescharacteristic
231C22×C4×C5C2×D411yescharacteristic
232C22×C4×C5C2×D412yes—
233C22×C4×C5C2412yes—
234C22×C4×C5C2411yescharacteristic
235C2×C22⋊D5—28no—
236C2×C22⋊D5—24no—
237C22×Dic5—21no—
238C22×Dic5—21no—
239C22×Dic5—21no—
240C22×Dic5—24no—
241C22×Dic5—82no—
242#709—216no—
243#709—28no—
244#709—28no—
245C2×D20—21no—
246C2×D20—22no—
247C2×D20#4114yes—
248C2×D20C2412yes—
249C2×C4×D5—28no—
250C2×C4×D5—24no—
251C2×C4×D5—24no—
252C2×C4×D5—24no—
253C2×C4×D5—82no—
254C2×C4×D5—82no—
255C2×Dic10—21no—
256C2×Dic10—22no—
257C2×Dic10#4114yes—
258C2×Dic10C2412yes—
259C5×C4⋊C4—24no—
260C5×C4⋊C4—24no—
261C5×C4⋊C4—21no—
262C5×C4⋊C4—21no—
263C5×C4⋊C4C2×D414yes—
264C5×C4⋊C4C2×D414yes—
265C5×C4⋊C4C2412yes—
266C5×C4⋊C4C2412yes—
267C5×C22⋊C4—24no—
268C5×C22⋊C4—24no—
269C5×C22⋊C4—24no—
270C5×C22⋊C4—24no—
271C5×C22⋊C4C2×D414yes—
272C5×C22⋊C4C2×D414yes—
273C42×C5C2×D412yes—
274C42×C5C2×D412yes—
275C42×C5C2412yes—
276C42×C5C2412yes—
277#687—28no—
278#687—28no—
279#686—28no—
280#686—28no—
281#685—24no—
282#685—24no—
283C4⋊Dic5—21no—
284C4⋊Dic5—21no—
285C4⋊Dic5—24no—
286C4⋊Dic5C2412yes—
287C4⋊Dic5C2412yes—
288#683—24no—
289#683—24no—
290C4×Dic5—24no—
291C4×Dic5—24no—
292C2×#168—22no—
293C2×#168—22no—
294C2×#168—22no—
295C2×#168—22no—
296C2×#168C2412yes—
297C2×#168C2412yes—
298C2×#168C2412yes—
299C2×#168C2412yes—
300C22×#41—51no—
301C22×SD16—51no—
302C22×SD16—51no—
303C22×D8—51no—
304C22×D8—51no—
305#540—24no—
306#540C2×D518yescomplemented
307C2×#127C2×D511yescharacteristic
308C2×#125C2×D511yescharacteristic
309C2×#123—21no—
310C2×#123—21no—
311C2×#121—21no—
312C2×#121—21no—
313C2×#121C2×D511yescharacteristic
314C2×#121C2×D511yescharacteristic
315#520—58no—
316#520—104no—
317C2×C4×Q8—51no—
318C2×C4×Q8—51no—
319C2×C4×D4—51no—
320C2×C4×D4—51no—
321C2×C4×D4—101no—
322C2×C4×D4—101no—
323C2×C4×D4C2×D511yescharacteristic
324C2×C4×D4C2×D511yescharacteristic
325C2×#117—101no—
326C2×#117C2×D511yescharacteristic
327C22×C4⋊C4—51no—
328C22×C4⋊C4—101no—
329#481—58no—
330#480—58no—
331#479—58no—
332#478—58no—
333#460—58no—
334#459—58no—
335#449—58no—
336#449—58no—
337#442—58no—
338#440—58no—
339C4×SD16—58no—
340C4×D8—58no—
341#433—58no—
342C2×#107—51no—
343C2×#107—51no—
344C2×#106—51no—
345C2×#106—51no—
346C2×C4⋊C8—51no—
347C2×C4⋊C8—51no—
348C2×#103—51no—
349C2×#103—51no—
350C2×#102—51no—
351C2×#102—51no—
352C2×#102—51no—
353C2×#102—51no—
354C2×#102—51no—
355C2×#102—51no—
356C2×C22⋊C8—51no—
357C2×C22⋊C8—51no—
358C2×#97—51no—
359C2×C4×C8—51no—
360C23×C5—22no—
361C23×C5—22no—
362C23×C5—22no—
363C23×C5—22no—
364C23×C5—22no—
365C23×C5—42no—
366C23×C5—42no—
367C23×C5—42no—
368C23×C5—42no—
369C23×C5—42no—
370C23×C5—42no—
371C23×C5C22×D412yes—
372C23×C5C22×D411yescharacteristic
373C22×D5—24no—
374C22×D5—22no—
375C22×D5—42no—
376C22×D5—42no—
377C5×D4—22no—
378C5×D4—22no—
379C5×D4—22no—
380C5×D4—22no—
381C5×D4—42no—
382C5×D4—42no—
383C5×D4—84no—
384C5×D4—84no—
385C5×D4—84no—
386C5×D4—84no—
387C2×C4×C5—22no—
388C2×C4×C5—22no—
389C2×C4×C5—22no—
390C2×C4×C5—22no—
391C2×C4×C5—22no—
392C2×C4×C5—24no—
393C2×C4×C5—22no—
394C2×C4×C5—22no—
395C2×C4×C5—22no—
396C2×C4×C5—22no—
397C2×C4×C5—42no—
398C2×C4×C5—42no—
399C2×C4×C5—84no—
400C2×C4×C5—84no—
401C2×C4×C5C22×D412yes—
402C2×C4×C5C22×D412yes—
403C2×C4×C5C22×D412yes—
404C2×C4×C5C22×D412yes—
405C2×C4×C5C22×D412yes—
406C2×C4×C5C22×D411yescharacteristic
407C2×C4×C5C2×#4112yes—
408C2×C4×C5C2×#4112yes—
409C2×C4×C5C2511yescharacteristic
410C22⋊D5—216no—
411C2×Dic5—24no—
412C2×Dic5—22no—
413C2×Dic5—22no—
414C2×Dic5—22no—
415C2×Dic5—42no—
416C2×Dic5—42no—
417C2×Dic5—84no—
418D20—24no—
419D20—22no—
420D20C2×#4114yes—
421C4×D5—216no—
422C4×D5—84no—
423C4×D5—84no—
424Dic10—24no—
425Dic10—22no—
426Dic10C2×#4114yes—
427#168—22no—
428#168—22no—
429#168—22no—
430#168—22no—
431C2×#41—54no—
432C2×#41—104no—
433C2×#41—104no—
434C2×#41—102no—
435C22×Q8—51no—
436C22×D4—21no—
437C22×D4—21no—
438C22×D4—21no—
439C22×D4—21no—
440C22×D4—51no—
441C22×D4—101no—
442C22×D4C22×D511yescharacteristic
443C22×D4C22×D511yescharacteristic
444C23×C4—21no—
445C23×C4—21no—
446C23×C4—101no—
447C23×C4—101no—
448C23×C4—101no—
449C23×C4—101no—
450C23×C4C22×D511yescharacteristic
451C2×SD16—54no—
452C2×SD16—54no—
453C2×SD16—104no—
454C2×SD16—104no—
455C2×D8—54no—
456C2×D8—54no—
457C2×D8—104no—
458C2×D8—104no—
459C22×C8—51no—
460C22×C8—51no—
461C22×C8—51no—
462C22×C8—51no—
463#127—22no—
464#127C22×D514yes—
465#125—22no—
466#125C22×D514yes—
467#123—28no—
468#123—28no—
469#121—22no—
470#121—22no—
471#121—28no—
472#121—28no—
473#121C22×D514yes—
474#121C22×D514yes—
475C4×Q8—54no—
476C4×Q8—54no—
477C4×Q8—102no—
478C4×Q8—102no—
479C4×D4—22no—
480C4×D4—22no—
481C4×D4—54no—
482C4×D4—54no—
483C4×D4—108no—
484C4×D4—108no—
485C4×D4—102no—
486C4×D4—102no—
487C4×D4C22×D514yes—
488C4×D4C22×D514yes—
489#117—108no—
490#117C22⋊D514yes—
491#117C22×D514yes—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—51no—
495C2×C4⋊C4—51no—
496C2×C4⋊C4—54no—
497C2×C4⋊C4—101no—
498C2×C4⋊C4—102no—
499C2×C4⋊C4—101no—
500C2×C4⋊C4—101no—
501C2×C4⋊C4—108no—
502C2×C4⋊C4C22⋊D511yescharacteristic
503C2×C4⋊C4C22⋊D511yescharacteristic
504C2×C4⋊C4C22×D511yescharacteristic
505C2×C4⋊C4C22×D511yescharacteristic
506C2×C22⋊C4—21no—
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—101no—
511C2×C22⋊C4—101no—
512C2×C22⋊C4C22⋊D511yescharacteristic
513C2×C22⋊C4C22⋊D511yescharacteristic
514C2×C42—101no—
515C2×C42—101no—
516C2×C42C22×D511yescharacteristic
517C2×C42C22×D511yescharacteristic
518#107—54no—
519#107—54no—
520#106—54no—
521#106—54no—
522C4⋊C8—54no—
523C4⋊C8—54no—
524#103—54no—
525#103—54no—
526#102—54no—
527#102—54no—
528#102—54no—
529#102—54no—
530#102—54no—
531#102—54no—
532C22⋊C8—54no—
533C22⋊C8—54no—
534#97—54no—
535C4×C8—54no—
536C22×C5—22no—
537C22×C5—22no—
538C22×C5—22no—
539C22×C5—44no—
540C22×C5—42no—
541C22×C5—42no—
542C22×C5—42no—
543C22×C5—42no—
544C22×C5—42no—
545C22×C5—42no—
546C22×C5—84no—
547C22×C5—84no—
548C22×C5#52512yes—
549C22×C5#57612yes—
550C22×C5#57712yes—
551C22×C5C23×D411yescharacteristic
552C2×D5—24no—
553C2×D5—48no—
554C2×D5—42no—
555C2×D5—42no—
556C4×C5—22no—
557C4×C5—22no—
558C4×C5—22no—
559C4×C5—22no—
560C4×C5—22no—
561C4×C5—42no—
562C4×C5—42no—
563C4×C5#52512yes—
564C4×C5C22×#4111yescharacteristic
565C4×C5C22×#4111yescharacteristic
566Dic5—24no—
567Dic5—42no—
568Dic5—42no—
569C24—21no—
570C24—21no—
571C24—101no—
572C24C2×C22⋊D511yescharacteristic
573#41—108no—
574#41—108no—
575#41—1016no—
576C2×Q8—54no—
577C2×Q8—52no—
578C2×Q8—102no—
579C2×Q8—101no—
580C2×D4—24no—
581C2×D4—24no—
582C2×D4—22no—
583C2×D4—22no—
584C2×D4—22no—
585C2×D4—22no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—24no—
589C2×D4—24no—
590C2×D4—54no—
591C2×D4—52no—
592C2×D4—82no—
593C2×D4—82no—
594C2×D4—82no—
595C2×D4—82no—
596C2×D4—108no—
597C2×D4—104no—
598C2×D4—102no—
599C2×D4—101no—
600C2×D4C23×D512yes—
601C2×D4C23×D512yes—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—24no—
607C22×C4—24no—
608C22×C4—82no—
609C22×C4—82no—
610C22×C4—108no—
611C22×C4—101no—
612C22×C4—104no—
613C22×C4—101no—
614C22×C4—101no—
615C22×C4—104no—
616C22×C4—104no—
617C22×C4—104no—
618C22×C4—402no—
619C22×C4—402no—
620C22×C4—402no—
621C22×C4C2×C22⋊D512yes—
622C22×C4C2×C22⋊D511yescharacteristic
623C22×C4C2×C22⋊D511yescharacteristic
624C22×C4C2×C22⋊D511yescharacteristic
625C22×C4C2×C22⋊D511yescharacteristic
626C22×C4C2×C22⋊D511yescharacteristic
627C22×C4C23×D512yes—
628C22×C4C23×D511yescharacteristic
629SD16—108no—
630SD16—108no—
631D8—108no—
632D8—108no—
633C2×C8—52no—
634C2×C8—52no—
635C2×C8—52no—
636C2×C8—52no—
637C2×C8—102no—
638C2×C8—102no—
639C2×C8—102no—
640C2×C8—102no—
641C4⋊C4—24no—
642C4⋊C4—24no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—52no—
646C4⋊C4—52no—
647C4⋊C4—104no—
648C4⋊C4—101no—
649C4⋊C4—101no—
650C4⋊C4—104no—
651C4⋊C4—104no—
652C4⋊C4C2×C22⋊D514yes—
653C4⋊C4C2×C22⋊D514yes—
654C4⋊C4C23×D512yes—
655C4⋊C4C23×D512yes—
656C22⋊C4—24no—
657C22⋊C4—24no—
658C22⋊C4—24no—
659C22⋊C4—24no—
660C22⋊C4—104no—
661C22⋊C4—104no—
662C22⋊C4C2×C22⋊D514yes—
663C22⋊C4C2×C22⋊D514yes—
664C42—104no—
665C42—104no—
666C42C2×C22⋊D512yes—
667C42C2×C22⋊D512yes—
668C42C23×D512yes—
669C42C23×D512yes—
670C2×C5—42no—
671C2×C5—82no—
672C2×C5—82no—
673C2×C5#311914yescomplemented
674C2×C5C2×#52511yescharacteristic
675C2×C5C2×#57611yescharacteristic
676C2×C5C2×#57711yescharacteristic
677D5—44no—
678C23—22no—
679C23—22no—
680C23—22no—
681C23—22no—
682C23—22no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—104no—
690C23—102no—
691C23—202no—
692C23—202no—
693C23C22×C22⋊D512yes—
694C23C22×C22⋊D511yescharacteristic
695Q8—54no—
696Q8—104no—
697Q8—102no—
698D4—22no—
699D4—22no—
700D4—22no—
701D4—22no—
702D4—42no—
703D4—42no—
704D4—54no—
705D4—84no—
706D4—84no—
707D4—84no—
708D4—84no—
709D4—1016no—
710D4—104no—
711D4—102no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—24no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—84no—
725C2×C4—84no—
726C2×C4—1016no—
727C2×C4—104no—
728C2×C4—102no—
729C2×C4—102no—
730C2×C4—102no—
731C2×C4—202no—
732C2×C4—202no—
733C2×C4—404no—
734C2×C4—404no—
735C2×C4—404no—
736C2×C4D5×#4112yes—
737C2×C4D5×#4112yes—
738C2×C4C22×C22⋊D512yes—
739C2×C4C22×C22⋊D512yes—
740C2×C4C22×C22⋊D512yes—
741C2×C4C22×C22⋊D512yes—
742C2×C4C22×C22⋊D512yes—
743C2×C4C22×C22⋊D511yescharacteristic
744C2×C4C24×D511yescharacteristic
745C8—102no—
746C8—102no—
747C8—102no—
748C8—102no—
749C5C2×#311911yescharacteristic, complemented, Sylow
750C22—22no—
751C22—22no—
752C22—22no—
753C22—44no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—42no—
758C22—42no—
759C22—42no—
760C22—84no—
761C22—84no—
762C22—104no—
763C22—202no—
764C22—202no—
765C22—208no—
766C22#6616212yes—
767C22#6616912yes—
768C22#6617012yes—
769C22C23×C22⋊D511yescharacteristic
770C4—22no—
771C4—22no—
772C4—22no—
773C4—22no—
774C4—22no—
775C4—42no—
776C4—42no—
777C4—104no—
778C4—202no—
779C4—202no—
780C4#6616212yes—
781C4C2×D5×#4111yescharacteristic
782C4C2×D5×#4111yescharacteristic
783C2—42no—
784C2—82no—
785C2—82no—
786C2—204no—
787C2#1061516514yesdirect product factor
788C2C2×#6616211yescharacteristic
789C2C2×#6616911yescharacteristic
790C2C2×#6617011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×#540C2
socleC23×C5C22×D4
hypercenterC2×#540D5
hypocenterC5C2×#3119
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#540

Complements

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

NH ≅ G/Ntype
1. C2×C5×#540C2semidirect
2. C2×#65857C2semidirect
3. #10615165C2direct (N × H)
4. C2×#65364C2semidirect
5. C2×#65361C2semidirect
6. C2×#65352C2semidirect
7. C2×#65355C2semidirect
8. C2×#65326C2semidirect
9. C2×#65326C2semidirect
10. C2×#65323C2semidirect
11. C2×#65322C2semidirect
12. C2×C4×#687C2semidirect
13. C2×#65303C2semidirect
14. C2×#65307C2semidirect
15. C2×C4×#686C2semidirect
16. C2×#65289C2semidirect
19. C5×#540C22semidirect
37. #65857C22semidirect
52. #65364C22semidirect
53. #65361C22semidirect
54. #65355C22semidirect
55. #65352C22semidirect
56. #65326C22semidirect
57. #65326C22semidirect
58. #65323C22semidirect
59. #65322C22semidirect
60. #65307C22semidirect
61. C4×#687C22semidirect
62. #65303C22semidirect
63. C4×#686C22semidirect
64. #65289C22semidirect
183. C2×#540D5semidirect
306. #540C2×D5semidirect
673. C2×C5#3119semidirect
749. C5C2×#3119semidirect
787. C2#10615165direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#5402
C2×#658572
#106151652
C2×#653642
C2×#653612
C2×#653522
C2×#653552
C2×#653262
C2×#653232
C2×#653222
C2×C4×#6872
C2×#653032
C2×#653072
C2×C4×#6862
C2×#652892
C2×#31195