Finite Group Databasebeta

← C2×#10615447 #12980326

Subgroups — C2×#10615447 #12980326

Order 1280.

2066 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#559C211yesmaximal, characteristic, complemented
2C2×#65919C211yesmaximal, characteristic, complemented
3#10615447C2116yesmaximal, direct product factor
4C2×#65361C211yesmaximal, characteristic, complemented
5C2×#65363C211yesmaximal, characteristic, complemented
6C2×#65343C211yesmaximal, characteristic, complemented
7C2×#65346C211yesmaximal, characteristic, complemented
8C2×#65347C211yesmaximal, characteristic, complemented
9C2×#65348C211yesmaximal, characteristic, complemented
10C2×#65317C211yesmaximal, characteristic, complemented
11C2×#65315C211yesmaximal, characteristic, complemented
12C2×#65313C211yesmaximal, characteristic, complemented
13C2×#65305C211yesmaximal, characteristic, complemented
14C2×#65304C211yesmaximal, characteristic, complemented
15C2×#65307C211yesmaximal, characteristic, complemented
16C2×C4×#686C211yesmaximal, characteristic, complemented
17C5×#559—24no—
18C5×#559C2218yescomplemented
19C2×C5×#127C2211yescharacteristic
20C2×C5×#124—21no—
21C2×C5×#124C2211yescharacteristic
22C2×C5×#124C2211yescharacteristic
23C2×C5×#123—21no—
24C2×C5×#123—21no—
25C2×C4×C5×Q8C2211yescharacteristic
26C2×C4×C5×Q8C2211yescharacteristic
27C2×C4×C5×D4—21no—
28C2×C4×C5×D4C2211yescharacteristic
29C2×C4×C5×D4C2211yescharacteristic
30C2×#4093—21no—
31C22×#689C2211yescharacteristic
32C22×#688C2211yescharacteristic
33C22×#688C2211yescharacteristic
34C22×#687C2211yescharacteristic
35C22×#687C2211yescharacteristic
36C22×#686C2211yescharacteristic
37C22×#686C2211yescharacteristic
38C22×#686C2211yescharacteristic
39C22×#686C2211yescharacteristic
40#65919—24no—
41#65919C2218yescomplemented
42C2×#4040—21no—
43C2×#4040—21no—
44C2×#4039—21no—
45C2×#4021C2211yescharacteristic
46C2×#4021C2211yescharacteristic
47C2×#4020C2211yescharacteristic
48C2×C4×D20C2211yescharacteristic
49C2×C4×D20C2211yescharacteristic
50C2×C4×Dic10C2211yescharacteristic
51C2×#3967C2211yescharacteristic
52C2×#3964C2211yescharacteristic
53C2×#3964C2211yescharacteristic
54#65363C2218yescomplemented
55#65361C2218yescomplemented
56#65348C2218yescomplemented
57#65347C2218yescomplemented
58#65346C2218yescomplemented
59#65343C2218yescomplemented
60#65317C2218yescomplemented
61#65315C2218yescomplemented
62#65313C2218yescomplemented
63#65307C2218yescomplemented
64#65305C2218yescomplemented
65#65304C2218yescomplemented
66C4×#686C2218yescomplemented
67C2×#3942C2211yescharacteristic
68C2×#3941C2211yescharacteristic
69C2×#3941C2211yescharacteristic
70C2×#3939C2211yescharacteristic
71C2×C4⋊#168C2211yescharacteristic
72C2×C4⋊#168C2211yescharacteristic
73C2×C4⋊#168C2211yescharacteristic
74C2×#3935C2211yescharacteristic
75C2×#3935C2211yescharacteristic
76C2×C4×#168C2211yescharacteristic
77C2×#3403—51nomaximal, Sylow
78C22×C5×Q8D411yescharacteristic
79C22×C5×Q8C2311yescharacteristic
80C22×C5×D4—21no—
81C22×C5×D4—21no—
82C22×C5×D4C2311yescharacteristic
83C22×C5×D4C2311yescharacteristic
84C23×C4×C5—21no—
85C23×C4×C5—21no—
86C22×D20—21no—
87C22×D20—21no—
88C22×D20C2311yescharacteristic
89C22×D20C2311yescharacteristic
90C22×C4×D5—21no—
91C22×C4×D5—21no—
92C22×Dic10C2311yescharacteristic
93C5×#127—22no—
94C5×#127C2314yes—
95C5×#124—28no—
96C5×#124—22no—
97C5×#124—22no—
98C5×#124C2314yes—
99C5×#124C2314yes—
100C5×#123—28no—
101C5×#123—28no—
102C4×C5×Q8—22no—
103C4×C5×Q8D414yes—
104C4×C5×Q8C2314yes—
105C4×C5×Q8C2314yes—
106C4×C5×D4—28no—
107C4×C5×D4—22no—
108C4×C5×D4—22no—
109C4×C5×D4C2314yes—
110C4×C5×D4C2314yes—
111C2×C5×C4⋊C4—21no—
112C2×C5×C4⋊C4D411yescharacteristic
113C2×C5×C4⋊C4D411yescharacteristic
114C2×C5×C4⋊C4D411yescharacteristic
115C2×C5×C4⋊C4C2311yescharacteristic
116C2×C5×C22⋊C4—21no—
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×C5C2311yescharacteristic
124C2×C42×C5C2311yescharacteristic
125C2×C42×C5C2311yescharacteristic
126#4093—28no—
127C2×#689—42no—
128C2×#689C2314yes—
129C2×#688—24no—
130C2×#688—42no—
131C2×#688C2314yes—
132C2×#688C2314yes—
133C2×#687—24no—
134C2×#687—42no—
135C2×#687C2314yes—
136C2×#687C2314yes—
137C2×#686—24no—
138C2×#686—42no—
139C2×#686—42no—
140C2×#686—42no—
141C2×#686C2314yes—
142C2×#686C2314yes—
143C2×#686C2314yes—
144C2×#686C2314yes—
145C2×#685—21no—
146C2×#685—21no—
147C2×#685—21no—
148C2×#685—21no—
149C2×#685—21no—
150C2×#685—21no—
151C2×C4⋊Dic5C2311yescharacteristic
152C2×#683—21no—
153C2×C4×Dic5—21no—
154C22×#168C2311yescharacteristic
155C22×#168C2311yescharacteristic
156C22×#168C2311yescharacteristic
157C22×#168C2311yescharacteristic
158#4040—28no—
159#4040—28no—
160#4039—28no—
161#4021—22no—
162#4021—22no—
163#4021C2314yes—
164#4021C2314yes—
165#4020—22no—
166#4020C2314yes—
167C4×D20—22no—
168C4×D20—22no—
169C4×D20C2314yes—
170C4×D20C2314yes—
171C4×Dic10—22no—
172C4×Dic10C2314yes—
173#3967C2314yes—
174#3964C2314yes—
175#3964C2314yes—
176#3942C2314yes—
177#3941C2314yes—
178#3941C2314yes—
179#3939C2314yes—
180C4⋊#168C2314yes—
181C4⋊#168C2314yes—
182C4⋊#168C2314yes—
183#3935C2314yes—
184#3935C2314yes—
185C4×#168C2314yes—
186C2×#559—51no—
187C2×#559D511yescharacteristic, complemented
188#3403—516no—
189C2×#496—51no—
190C2×#496—51no—
191C2×#495—51no—
192C2×#464—51no—
193C2×#464—51no—
194C2×#463—51no—
195C2×#463—51no—
196C2×#459—51no—
197C2×#459—51no—
198C2×#446—51no—
199C2×#440—51no—
200C2×#440—51no—
201C2×C4×D8—51no—
202C24×C5—21no—
203C24×C5—21no—
204C23×D5—21no—
205C23×D5—21no—
206C2×C5×Q8—21no—
207C2×C5×Q8—22no—
208C2×C5×Q8—22no—
209C2×C5×Q8—42no—
210C2×C5×Q8C2×D414yes—
211C2×C5×Q8C2412yes—
212C2×C5×D4—21no—
213C2×C5×D4—21no—
214C2×C5×D4—24no—
215C2×C5×D4—24no—
216C2×C5×D4—22no—
217C2×C5×D4—22no—
218C2×C5×D4—22no—
219C2×C5×D4—22no—
220C2×C5×D4—44no—
221C2×C5×D4—82no—
222C2×C5×D4C2412yes—
223C2×C5×D4C2412yes—
224C22×C4×C5—21no—
225C22×C4×C5—21no—
226C22×C4×C5—24no—
227C22×C4×C5—24no—
228C22×C4×C5—82no—
229C22×C4×C5—82no—
230C22×C4×C5C2×D411yescharacteristic
231C22×C4×C5C2×D411yescharacteristic
232C22×C4×C5C2×D411yescharacteristic
233C22×C4×C5C2×D411yescharacteristic
234C22×C4×C5C2×D411yescharacteristic
235C22×C4×C5C2×D411yescharacteristic
236C22×C4×C5C2411yescharacteristic
237C22×Dic5—21no—
238C22×Dic5—21no—
239C2×D20—22no—
240C2×D20—22no—
241C2×D20—22no—
242C2×D20—22no—
243C2×D20—24no—
244C2×D20—21no—
245C2×D20—21no—
246C2×D20—24no—
247C2×D20—44no—
248C2×D20—82no—
249C2×D20C2412yes—
250C2×D20C2412yes—
251C2×C4×D5—24no—
252C2×C4×D5—24no—
253C2×C4×D5—82no—
254C2×C4×D5—82no—
255C2×Dic10—22no—
256C2×Dic10—22no—
257C2×Dic10—21no—
258C2×Dic10C2412yes—
259C5×C4⋊C4—24no—
260C5×C4⋊C4—21no—
261C5×C4⋊C4C2×D414yes—
262C5×C4⋊C4C2×D414yes—
263C5×C4⋊C4C2×D414yes—
264C5×C4⋊C4C2412yes—
265C5×C22⋊C4—24no—
266C5×C22⋊C4—24no—
267C5×C22⋊C4—24no—
268C5×C22⋊C4—24no—
269C5×C22⋊C4—24no—
270C5×C22⋊C4—24no—
271C42×C5—24no—
272C42×C5C2×D412yes—
273C42×C5C2×D412yes—
274C42×C5C2×D412yes—
275C42×C5C2412yes—
276C42×C5C2412yes—
277C42×C5C2412yes—
278#689—44no—
279#688—28no—
280#688—44no—
281#687—28no—
282#687—44no—
283#686—28no—
284#686—44no—
285#686—44no—
286#686—44no—
287#685—24no—
288#685—24no—
289#685—24no—
290#685—24no—
291#685—24no—
292#685—24no—
293C4⋊Dic5—21no—
294C4⋊Dic5C2412yes—
295#683—24no—
296C4×Dic5—24no—
297C2×#168—22no—
298C2×#168—22no—
299C2×#168—22no—
300C2×#168#4114yes—
301C2×#168C2412yes—
302C2×#168C2412yes—
303C2×#168C2412yes—
304C2×#168C2412yes—
305C22×Q16—51no—
306C22×SD16—51no—
307C22×SD16—51no—
308C22×SD16—51no—
309C22×SD16—51no—
310C22×D8—51no—
311C22×D8—51no—
312C22×D8—51no—
313C22×D8—51no—
314#559—24no—
315#559—58no—
316#559—104no—
317#559C2×D518yescomplemented
318C2×#127—51no—
319C2×#127C2×D511yescharacteristic
320C2×#124—21no—
321C2×#124—51no—
322C2×#124—51no—
323C2×#124—101no—
324C2×#124C2×D511yescharacteristic
325C2×#124C2×D511yescharacteristic
326C2×#123—21no—
327C2×#123—21no—
328C2×#123—101no—
329C2×#123—101no—
330C2×C4×Q8—51no—
331C2×C4×Q8C2×D511yescharacteristic
332C2×C4×Q8C2×D511yescharacteristic
333C2×C4×D4—21no—
334C2×C4×D4—51no—
335C2×C4×D4—51no—
336C2×C4×D4—101no—
337C2×C4×D4C2×D511yescharacteristic
338C2×C4×D4C2×D511yescharacteristic
339#496—58no—
340#496—58no—
341#495—58no—
342#464—58no—
343#464—58no—
344#463—58no—
345#463—58no—
346#459—58no—
347#459—58no—
348#446—58no—
349#440—58no—
350#440—58no—
351C4×D8—58no—
352C2×#107—51no—
353C2×C4⋊C8—51no—
354C2×C4⋊C8—51no—
355C2×C4⋊C8—51no—
356C2×#103—51no—
357C2×#103—51no—
358C2×#102—51no—
359C2×#102—51no—
360C2×#102—51no—
361C2×#102—51no—
362C2×#97—51no—
363C2×#97—51no—
364C2×C4×C8—51no—
365C23×C5—22no—
366C23×C5—22no—
367C23×C5—42no—
368C23×C5—42no—
369C23×C5—42no—
370C23×C5—42no—
371C23×C5—42no—
372C23×C5—42no—
373C23×C5C22×D411yescharacteristic
374C22×D5—22no—
375C22×D5—22no—
376C22×D5—42no—
377C22×D5—42no—
378C22×D5—42no—
379C22×D5—42no—
380C22×D5—42no—
381C22×D5—42no—
382C5×Q8—22no—
383C5×Q8—22no—
384C5×Q8—44no—
385C5×Q8—42no—
386C5×D4—22no—
387C5×D4—22no—
388C5×D4—22no—
389C5×D4—22no—
390C5×D4—48no—
391C5×D4—42no—
392C5×D4—42no—
393C5×D4—84no—
394C2×C4×C5—22no—
395C2×C4×C5—22no—
396C2×C4×C5—22no—
397C2×C4×C5—22no—
398C2×C4×C5—22no—
399C2×C4×C5—22no—
400C2×C4×C5—22no—
401C2×C4×C5—22no—
402C2×C4×C5—42no—
403C2×C4×C5—42no—
404C2×C4×C5—84no—
405C2×C4×C5—84no—
406C2×C4×C5C22×D412yes—
407C2×C4×C5C22×D412yes—
408C2×C4×C5C22×D412yes—
409C2×C4×C5C22×D412yes—
410C2×C4×C5C22×D412yes—
411C2×C4×C5C22×D412yes—
412C2×C4×C5C22×D411yescharacteristic
413C2×C4×C5C2×#4112yes—
414C2×C4×C5H(5,𝔽2)12yes—
415C2×C4×C5C2511yescharacteristic
416C2×Dic5—22no—
417C2×Dic5—22no—
418C2×Dic5—42no—
419C2×Dic5—42no—
420D20—22no—
421D20—22no—
422D20—22no—
423D20—22no—
424D20—48no—
425D20—42no—
426D20—42no—
427D20—84no—
428C4×D5—84no—
429C4×D5—84no—
430Dic10—22no—
431Dic10—22no—
432Dic10—42no—
433#168—22no—
434#168—22no—
435#168—22no—
436#168C2×#4114yes—
437C22×Q8—51no—
438C22×Q8C22⋊D511yescharacteristic
439C22×Q8C22×D511yescharacteristic
440C22×D4—21no—
441C22×D4—21no—
442C22×D4—51no—
443C22×D4—51no—
444C22×D4—101no—
445C22×D4—101no—
446C22×D4C22×D511yescharacteristic
447C22×D4C22×D511yescharacteristic
448C23×C4—21no—
449C23×C4—21no—
450C23×C4—101no—
451C23×C4—101no—
452C2×Q16—54no—
453C2×Q16—202no—
454C2×SD16—54no—
455C2×SD16—54no—
456C2×SD16—54no—
457C2×SD16—54no—
458C2×SD16—104no—
459C2×SD16—104no—
460C2×SD16—202no—
461C2×SD16—202no—
462C2×D8—54no—
463C2×D8—54no—
464C2×D8—54no—
465C2×D8—54no—
466C2×D8—104no—
467C2×D8—202no—
468C2×D8—202no—
469C2×D8—202no—
470C22×C8—51no—
471C22×C8—51no—
472C22×C8—51no—
473C22×C8—51no—
474#127—22no—
475#127—54no—
476#127—102no—
477#127C22×D514yes—
478#124—28no—
479#124—22no—
480#124—22no—
481#124—54no—
482#124—54no—
483#124—108no—
484#124—102no—
485#124—102no—
486#124C22×D514yes—
487#124C22×D514yes—
488#123—28no—
489#123—28no—
490#123—108no—
491#123—108no—
492C4×Q8—22no—
493C4×Q8—54no—
494C4×Q8—102no—
495C4×Q8C22⋊D514yes—
496C4×Q8C22×D514yes—
497C4×Q8C22×D514yes—
498C4×D4—28no—
499C4×D4—22no—
500C4×D4—22no—
501C4×D4—54no—
502C4×D4—54no—
503C4×D4—108no—
504C4×D4—102no—
505C4×D4—102no—
506C4×D4C22×D514yes—
507C4×D4C22×D514yes—
508C2×C4⋊C4—21no—
509C2×C4⋊C4—51no—
510C2×C4⋊C4—101no—
511C2×C4⋊C4C22⋊D511yescharacteristic
512C2×C4⋊C4C22⋊D511yescharacteristic
513C2×C4⋊C4C22⋊D511yescharacteristic
514C2×C4⋊C4C22×D511yescharacteristic
515C2×C22⋊C4—21no—
516C2×C22⋊C4—21no—
517C2×C22⋊C4—21no—
518C2×C22⋊C4—21no—
519C2×C22⋊C4—21no—
520C2×C22⋊C4—21no—
521C2×C22⋊C4—101no—
522C2×C22⋊C4—101no—
523C2×C22⋊C4—101no—
524C2×C22⋊C4—101no—
525C2×C22⋊C4—101no—
526C2×C22⋊C4—101no—
527C2×C42—21no—
528C2×C42—101no—
529C2×C42C22×D511yescharacteristic
530C2×C42C22×D511yescharacteristic
531C2×C42C22×D511yescharacteristic
532#107—54no—
533C4⋊C8—54no—
534C4⋊C8—54no—
535C4⋊C8—54no—
536#103—54no—
537#103—54no—
538#102—54no—
539#102—54no—
540#102—54no—
541#102—54no—
542#97—54no—
543#97—54no—
544C4×C8—54no—
545C22×C5—42no—
546C22×C5—42no—
547C22×C5—42no—
548C22×C5—42no—
549C22×C5—42no—
550C22×C5—42no—
551C22×C5—84no—
552C22×C5—84no—
553C22×C5#55012yes—
554C22×C5#57512yes—
555C22×C5#57612yes—
556C22×C5C23×D411yescharacteristic
557C2×D5—42no—
558C2×D5—42no—
559C2×D5—42no—
560C2×D5—42no—
561C2×D5—42no—
562C2×D5—42no—
563C2×D5—84no—
564C2×D5—84no—
565C4×C5—22no—
566C4×C5—22no—
567C4×C5—22no—
568C4×C5—22no—
569C4×C5—22no—
570C4×C5—22no—
571C4×C5—42no—
572C4×C5—42no—
573C4×C5#55012yes—
574C4×C5C22×#4111yescharacteristic
575C4×C5C2×H(5,𝔽2)11yescharacteristic
576Dic5—42no—
577Dic5—42no—
578C24—21no—
579C24—21no—
580C24—101no—
581C24—101no—
582C2×Q8—21no—
583C2×Q8—22no—
584C2×Q8—22no—
585C2×Q8—42no—
586C2×Q8—52no—
587C2×Q8—101no—
588C2×Q8—102no—
589C2×Q8—102no—
590C2×Q8C2×C22⋊D514yes—
591C2×Q8C23×D512yes—
592C2×D4—22no—
593C2×D4—22no—
594C2×D4—22no—
595C2×D4—22no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—24no—
599C2×D4—24no—
600C2×D4—44no—
601C2×D4—52no—
602C2×D4—52no—
603C2×D4—82no—
604C2×D4—102no—
605C2×D4—102no—
606C2×D4—102no—
607C2×D4—102no—
608C2×D4—104no—
609C2×D4—101no—
610C2×D4—101no—
611C2×D4—104no—
612C2×D4—204no—
613C2×D4—402no—
614C2×D4C23×D512yes—
615C2×D4C23×D512yes—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—24no—
619C22×C4—24no—
620C22×C4—82no—
621C22×C4—82no—
622C22×C4—101no—
623C22×C4—101no—
624C22×C4—104no—
625C22×C4—104no—
626C22×C4—402no—
627C22×C4—402no—
628C22×C4C2×C22⋊D511yescharacteristic
629C22×C4C2×C22⋊D511yescharacteristic
630C22×C4C2×C22⋊D511yescharacteristic
631C22×C4C2×C22⋊D511yescharacteristic
632C22×C4C2×C22⋊D511yescharacteristic
633C22×C4C2×C22⋊D511yescharacteristic
634C22×C4C23×D511yescharacteristic
635Q16—204no—
636SD16—108no—
637SD16—108no—
638SD16—204no—
639SD16—204no—
640D8—108no—
641D8—204no—
642D8—204no—
643D8—204no—
644C2×C8—54no—
645C2×C8—52no—
646C2×C8—52no—
647C2×C8—52no—
648C2×C8—52no—
649C2×C8—102no—
650C2×C8—102no—
651C2×C8—102no—
652C4⋊C4—24no—
653C4⋊C4—21no—
654C4⋊C4—52no—
655C4⋊C4—101no—
656C4⋊C4—104no—
657C4⋊C4C2×C22⋊D514yes—
658C4⋊C4C2×C22⋊D514yes—
659C4⋊C4C2×C22⋊D514yes—
660C4⋊C4C23×D512yes—
661C22⋊C4—24no—
662C22⋊C4—24no—
663C22⋊C4—24no—
664C22⋊C4—24no—
665C22⋊C4—24no—
666C22⋊C4—24no—
667C22⋊C4—104no—
668C22⋊C4—104no—
669C22⋊C4—104no—
670C22⋊C4—104no—
671C22⋊C4—104no—
672C22⋊C4—104no—
673C42—24no—
674C42—104no—
675C42C2×C22⋊D512yes—
676C42C2×C22⋊D512yes—
677C42C2×C22⋊D512yes—
678C42C23×D512yes—
679C42C23×D512yes—
680C42C23×D512yes—
681C2×C5—82no—
682C2×C5—82no—
683C2×C5#340314yescomplemented
684C2×C5C2×#55011yescharacteristic
685C2×C5C2×#57511yescharacteristic
686C2×C5C2×#57611yescharacteristic
687D5—82no—
688D5—82no—
689C23—22no—
690C23—22no—
691C23—42no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—102no—
698C23—102no—
699C23—202no—
700C23—202no—
701C23—202no—
702C23—202no—
703C23—202no—
704C23—202no—
705C23C22×C22⋊D511yescharacteristic
706Q8—22no—
707Q8—22no—
708Q8—44no—
709Q8—42no—
710Q8—102no—
711Q8—102no—
712Q8—202no—
713D4—22no—
714D4—22no—
715D4—22no—
716D4—22no—
717D4—48no—
718D4—42no—
719D4—42no—
720D4—84no—
721D4—102no—
722D4—102no—
723D4—102no—
724D4—102no—
725D4—208no—
726D4—202no—
727D4—202no—
728D4—404no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—84no—
740C2×C4—84no—
741C2×C4—102no—
742C2×C4—102no—
743C2×C4—202no—
744C2×C4—202no—
745C2×C4—404no—
746C2×C4—404no—
747C2×C4D5×#4112yes—
748C2×C4#414912yes—
749C2×C4C22×C22⋊D512yes—
750C2×C4C22×C22⋊D512yes—
751C2×C4C22×C22⋊D512yes—
752C2×C4C22×C22⋊D512yes—
753C2×C4C22×C22⋊D512yes—
754C2×C4C22×C22⋊D512yes—
755C2×C4C22×C22⋊D511yescharacteristic
756C2×C4C24×D511yescharacteristic
757C8—54no—
758C8—102no—
759C8—102no—
760C8—102no—
761C5C2×#340311yescharacteristic, complemented, Sylow
762C22—42no—
763C22—42no—
764C22—42no—
765C22—42no—
766C22—42no—
767C22—42no—
768C22—84no—
769C22—84no—
770C22—202no—
771C22—202no—
772C22—202no—
773C22—202no—
774C22—202no—
775C22—202no—
776C22—404no—
777C22—404no—
778C22#6615612yes—
779C22#6616812yes—
780C22#6616912yes—
781C22C23×C22⋊D511yescharacteristic
782C4—22no—
783C4—22no—
784C4—22no—
785C4—22no—
786C4—22no—
787C4—22no—
788C4—42no—
789C4—42no—
790C4—202no—
791C4—202no—
792C4#6616812yes—
793C4C2×D5×#4111yescharacteristic
794C4C2×#414911yescharacteristic
795C2—82no—
796C2—82no—
797C2—402no—
798C2—402no—
799C2#1061544714yesdirect product factor
800C2C2×#6615611yescharacteristic
801C2C2×#6616811yescharacteristic
802C2C2×#6616911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×#559C2
socleC23×C5C22×D4
hypercenterC2×#559D5
hypocenterC5C2×#3403
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#559

Complements

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

NH ≅ G/Ntype
1. C2×C5×#559C2semidirect
2. C2×#65919C2semidirect
3. #10615447C2direct (N × H)
4. C2×#65361C2semidirect
5. C2×#65363C2semidirect
6. C2×#65343C2semidirect
7. C2×#65346C2semidirect
8. C2×#65347C2semidirect
9. C2×#65348C2semidirect
10. C2×#65317C2semidirect
11. C2×#65315C2semidirect
12. C2×#65313C2semidirect
13. C2×#65305C2semidirect
14. C2×#65304C2semidirect
15. C2×#65307C2semidirect
16. C2×C4×#686C2semidirect
18. C5×#559C22semidirect
41. #65919C22semidirect
54. #65363C22semidirect
55. #65361C22semidirect
56. #65348C22semidirect
57. #65347C22semidirect
58. #65346C22semidirect
59. #65343C22semidirect
60. #65317C22semidirect
61. #65315C22semidirect
62. #65313C22semidirect
63. #65307C22semidirect
64. #65305C22semidirect
65. #65304C22semidirect
66. C4×#686C22semidirect
187. C2×#559D5semidirect
317. #559C2×D5semidirect
683. C2×C5#3403semidirect
761. C5C2×#3403semidirect
799. C2#10615447direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#5592
C2×#659192
#106154472
C2×#653612
C2×#653632
C2×#653432
C2×#653462
C2×#653472
C2×#653482
C2×#653172
C2×#653152
C2×#653132
C2×#653052
C2×#653042
C2×#653072
C2×C4×#6862
C2×#34035