Finite Group Databasebeta

← C2×#10613257 #12975973

Subgroups — C2×#10613257 #12975973

Order 1280.

2254 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65964C211yesmaximal, characteristic
2C2×#65867C211yesmaximal, characteristic, complemented
3C2×C5×#485C211yesmaximal, characteristic, complemented
4C2×#65341C211yesmaximal, characteristic, complemented
5C2×#65290C211yesmaximal, characteristic, complemented
6#10613257C2116yesmaximal, direct product factor
7C2×#65174C211yesmaximal, characteristic, complemented
8C2×#65178C211yesmaximal, characteristic, complemented
9C2×#65159C211yesmaximal, characteristic, complemented
10C2×#65153C211yesmaximal, characteristic, complemented
11C2×#65087C211yesmaximal, characteristic, complemented
12C2×#65099C211yesmaximal, characteristic, complemented
13C2×#65093C211yesmaximal, characteristic, complemented
14C2×#65084C211yesmaximal, characteristic, complemented
15C2×#65020C211yesmaximal, characteristic, complemented
16C2×#65017C211yesmaximal, characteristic, complemented
17C22×#713C2211yescharacteristic
18C23×D20C2211yescharacteristic
19C2×C5×C22⋊Q8C2211yescharacteristic
20C2×C5×#117C2211yescharacteristic
21C2×#4093C2211yescharacteristic
22C22×#689C2211yescharacteristic, complemented
23C2×C4×C22⋊D5C2211yescharacteristic
24C2×#4070C2211yescharacteristic
25C22×#681C2211yescharacteristic
26C22×#677C2211yescharacteristic
27C22×#677C2211yescharacteristic
28C22×C8×D5C2211yescharacteristic, complemented
29#65964—24no—
30#65964C2218yes—
31#65867—24no—
32#65867C2218yescomplemented
33C2×#4043C2211yescharacteristic, complemented
34C2×#4041—21no—
35C2×#4041C2211yescharacteristic
36C2×#4040—21no—
37C2×#4039C2211yescharacteristic
38C2×#4038C2211yescharacteristic, complemented
39C2×#4034C2211yescharacteristic, complemented
40C2×#4033C2211yescharacteristic, complemented
41C2×#4031—21no—
42C2×#4028—21no—
43C2×D5×C22⋊C4—21no—
44C2×#4025—21no—
45C2×#4022—21no—
46C2×C4×Dic10—21no—
47C5×#485C2218yescomplemented
48C2×C5×#107C2211yescharacteristic, complemented
49C2×C5×#106C2211yescharacteristic, complemented
50C2×C5×#103C2211yescharacteristic, complemented
51C2×C5×#103C2211yescharacteristic, complemented
52C2×C5×C22⋊C8C2211yescharacteristic
53C2×#3967C2211yescharacteristic, complemented
54C2×#3953C2211yescharacteristic
55C2×#3953C2211yescharacteristic
56C2×#3952C2211yescharacteristic, complemented
57C2×#3947C2211yescharacteristic, complemented
58C2×#3946C2211yescharacteristic, complemented
59#65341C2218yescomplemented
60#65290C2218yescomplemented
61C2×#3942C2211yescharacteristic, complemented
62C2×#3941C2211yescharacteristic
63C2×#3941C2211yescharacteristic
64C2×#3941C2211yescharacteristic
65C2×#3941C2211yescharacteristic
66C2×#3940C2211yescharacteristic, complemented
67#65178C2218yescomplemented
68#65174C2218yescomplemented
69#65159C2218yescomplemented
70#65153C2218yescomplemented
71#65099C2218yescomplemented
72#65093C2218yescomplemented
73#65087C2218yescomplemented
74#65084C2218yescomplemented
75#65020C2218yescomplemented
76#65017C2218yescomplemented
77C2×#3311—51nomaximal, Sylow
78C24×D5—21no—
79C22×C5×Q8C2311yescharacteristic
80C23×C4×C5C2311yescharacteristic
81C22×C22⋊D5D411yescharacteristic
82C2×#713—22no—
83C2×#713—24no—
84C2×#713—42no—
85C2×#713C2314yes—
86C22×D20—24no—
87C22×D20—21no—
88C22×D20—21no—
89C22×D20—22no—
90C22×D20—21no—
91C22×D20—42no—
92C22×D20C2311yescharacteristic
93C22×D20C2314yes—
94C22×D20C2311yescharacteristic
95C22×C4×D5—21no—
96C22×C4×D5—21no—
97C22×C4×D5C2311yescharacteristic
98C22×Dic10—21no—
99C22×Dic10C2311yescharacteristic
100C22×C5×C8C2311yescharacteristic
101C22×C5×C8C2311yescharacteristic
102C5×C22⋊Q8—22no—
103C5×C22⋊Q8C2314yes—
104C5×#117—22no—
105C5×#117C2314yes—
106C2×C5×C4⋊C4—21no—
107C2×C5×C4⋊C4C2311yescharacteristic
108C2×C5×C4⋊C4C2311yescharacteristic
109C2×C5×C4⋊C4C2311yescharacteristic
110C2×C5×C22⋊C4—21no—
111C2×C5×C22⋊C4—21no—
112C2×C42×C5—21no—
113C2×C22⋊Dic5—21no—
114C2×C22⋊Dic5D411yescharacteristic
115#4093—22no—
116#4093C2314yes—
117C2×#689—42no—
118C2×#689C2314yescomplemented
119C4×C22⋊D5D414yes—
120C4×C22⋊D5C2314yes—
121C2×#685—21no—
122C2×#685—21no—
123C2×#685—21no—
124C2×#685—21no—
125C2×#685—21no—
126C2×#685—21no—
127C2×#685D411yescharacteristic
128C2×C4⋊Dic5—21no—
129C2×C4⋊Dic5C2311yescharacteristic
130#4070—22no—
131#4070C2314yes—
132C2×#683—21no—
133C2×#683—21no—
134C2×#683—21no—
135C2×#683D411yescharacteristic
136C2×C4×Dic5—21no—
137C2×C4×Dic5—21no—
138C2×C4×Dic5C2311yescharacteristic
139C2×#681—42no—
140C2×#681C2314yes—
141C22×#168C2311yescharacteristic
142C22×#168C2311yescharacteristic
143C2×#677—24no—
144C2×#677—42no—
145C2×#677C2314yes—
146C2×#677C2314yes—
147C2×C8×D5—42no—
148C2×C8×D5C2314yescomplemented
149#4043—22no—
150#4043C2314yescomplemented
151#4041—22no—
152#4041—28no—
153#4041C2314yes—
154#4040—28no—
155#4039—22no—
156#4039C2314yes—
157#4038—22no—
158#4038C2314yescomplemented
159#4034—22no—
160#4034C2314yescomplemented
161#4033—22no—
162#4033C2314yescomplemented
163#4031—28no—
164#4028—28no—
165D5×C22⋊C4—28no—
166#4025—28no—
167#4022—28no—
168C4×Dic10—28no—
169C5×#107C2314yescomplemented
170C5×#106C2314yescomplemented
171C5×#103C2314yescomplemented
172C5×#103C2314yescomplemented
173C5×C22⋊C8C2314yes—
174#3967C2314yescomplemented
175#3953C2314yes—
176#3953C2314yes—
177#3952C2314yescomplemented
178#3947C2314yescomplemented
179#3946C2314yescomplemented
180#3942C2314yescomplemented
181#3941C2314yes—
182#3941C2314yes—
183#3941C2314yes—
184#3941C2314yes—
185#3940C2314yescomplemented
186C2×#556—51no—
187C2×#546—51no—
188#3311—516no—
189C2×#489—51no—
190C2×#485D511yescharacteristic, complemented
191C2×#482—51no—
192C2×#476—51no—
193C2×#470—51no—
194C2×#465—51no—
195C2×#464—51no—
196C2×#452—51no—
197C2×#450—51no—
198C2×#440—51no—
199C2×#435—51no—
200C2×#418—51no—
201C2×#416—51no—
202C24×C5C2×D411yescharacteristic
203C23×D5—21no—
204C23×D5—21no—
205C23×D5—24no—
206C23×D5—44no—
207C23×D5—44no—
208C23×D5—82no—
209C23×D5C2×D411yescharacteristic
210C2×C5×Q8—21no—
211C2×C5×Q8—22no—
212C2×C5×Q8—22no—
213C2×C5×Q8C2412yes—
214C22×C4×C5—22no—
215C22×C4×C5—22no—
216C22×C4×C5—21no—
217C22×C4×C5—21no—
218C22×C4×C5—21no—
219C22×C4×C5—21no—
220C22×C4×C5C2×D411yescharacteristic
221C22×C4×C5C2×D412yes—
222C22×C4×C5C2412yes—
223C22×C4×C5C2411yescharacteristic
224C2×C22⋊D5—42no—
225C2×C22⋊D5C2×D414yes—
226C22×Dic5—21no—
227C22×Dic5—21no—
228C22×Dic5C2×D411yescharacteristic
229C22×Dic5C2×D411yescharacteristic
230C22×Dic5C2×D411yescharacteristic
231#713—28no—
232#713—44no—
233#713—48no—
234C2×D20—21no—
235C2×D20—22no—
236C2×D20—22no—
237C2×D20—22no—
238C2×D20—28no—
239C2×D20—24no—
240C2×D20—24no—
241C2×D20—21no—
242C2×D20—24no—
243C2×D20—44no—
244C2×D20—48no—
245C2×D20—44no—
246C2×D20—44no—
247C2×D20—82no—
248C2×D20#4114yes—
249C2×D20C2412yes—
250C2×D20C2412yes—
251C2×C4×D5—22no—
252C2×C4×D5—22no—
253C2×C4×D5—24no—
254C2×C4×D5—24no—
255C2×C4×D5—44no—
256C2×C4×D5—82no—
257C2×C4×D5C2×D412yes—
258C2×C4×D5C2412yes—
259C2×Dic10—22no—
260C2×Dic10—22no—
261C2×Dic10—21no—
262C2×Dic10—24no—
263C2×Dic10—44no—
264C2×Dic10C2412yes—
265C2×C5×C8—22no—
266C2×C5×C8—22no—
267C2×C5×C8C2412yes—
268C2×C5×C8C2412yes—
269C5×C4⋊C4—24no—
270C5×C4⋊C4—21no—
271C5×C4⋊C4—21no—
272C5×C4⋊C4—21no—
273C5×C4⋊C4C2412yes—
274C5×C4⋊C4C2412yes—
275C5×C4⋊C4C2412yes—
276C5×C22⋊C4—24no—
277C5×C22⋊C4—24no—
278C42×C5—24no—
279C22⋊Dic5—24no—
280C22⋊Dic5C2×D414yes—
281#689—44no—
282#685—24no—
283#685—24no—
284#685—24no—
285#685—24no—
286#685—24no—
287#685—24no—
288#685C2×D414yes—
289C4⋊Dic5—21no—
290C4⋊Dic5—24no—
291C4⋊Dic5C2412yes—
292#683—24no—
293#683—24no—
294#683—24no—
295#683C2×D414yes—
296C4×Dic5—24no—
297C4×Dic5—24no—
298C4×Dic5C2×D412yes—
299C4×Dic5C2412yes—
300#681—44no—
301C2×#168—22no—
302C2×#168—22no—
303C2×#168C2412yes—
304C2×#168C2412yes—
305#677—28no—
306#677—44no—
307C8×D5—44no—
308C22×#41—51no—
309C23×D4—51no—
310C22×Q16—51no—
311C22×SD16—51no—
312C22×SD16—51no—
313C22×M16—51no—
314C23×C8—51no—
315#556—58no—
316#556—104no—
317#546—58no—
318#546—104no—
319C2×C4⋊Q8—51no—
320C2×#126—101no—
321C2×#126—101no—
322C2×#124—51no—
323C2×#124—101no—
324C2×#123—101no—
325C2×C22⋊Q8—51no—
326C2×C22⋊Q8—51no—
327C2×C22⋊Q8C2×D511yescharacteristic
328C2×#121—51no—
329C2×#121—101no—
330C2×#120—101no—
331C2×C4×Q8—51no—
332C2×C4×Q8—101no—
333C2×C4×D4—51no—
334C2×C4×D4—51no—
335C2×#117—51no—
336C2×#117C2×D511yescharacteristic
337C22×C22⋊C4—101no—
338#489—58no—
339#485C2×D518yescomplemented
340#482—58no—
341#476—58no—
342#470—58no—
343#465—58no—
344#464—58no—
345#452—58no—
346#450—58no—
347#440—58no—
348#435—58no—
349C2×#107C2×D511yescharacteristic, complemented
350C2×#106—51no—
351C2×#106C2×D511yescharacteristic, complemented
352C2×C4⋊C8—51no—
353#418—58no—
354#416—58no—
355C2×#103—51no—
356C2×#103—51no—
357C2×#103C2×D511yescharacteristic, complemented
358C2×#103C2×D511yescharacteristic, complemented
359C2×#102—51no—
360C2×#102—51no—
361C2×#102—51no—
362C2×#102—51no—
363C2×#102—51no—
364C2×#102—51no—
365C2×C22⋊C8—51no—
366C2×C22⋊C8C2×D511yescharacteristic
367C2×#97—51no—
368C23×C5—22no—
369C23×C5—22no—
370C23×C5—22no—
371C23×C5C22×D412yes—
372C23×C5C22×D411yescharacteristic
373C22×D5—22no—
374C22×D5—24no—
375C22×D5—22no—
376C22×D5—22no—
377C22×D5—22no—
378C22×D5—22no—
379C22×D5—48no—
380C22×D5—42no—
381C22×D5—42no—
382C22×D5—48no—
383C22×D5—42no—
384C22×D5—42no—
385C22×D5—42no—
386C22×D5—84no—
387C22×D5—816no—
388C22×D5C22×D412yes—
389C5×Q8—22no—
390C5×Q8—22no—
391C5×Q8—42no—
392C2×C4×C5—22no—
393C2×C4×C5—24no—
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—42no—
401C2×C4×C5—42no—
402C2×C4×C5—42no—
403C2×C4×C5—42no—
404C2×C4×C5C22×D412yes—
405C2×C4×C5C22×D411yescharacteristic
406C2×C4×C5C2×#4112yes—
407C2×C4×C5H(5,𝔽2)12yes—
408C2×C4×C5C2511yescharacteristic
409C22⋊D5—44no—
410C2×Dic5—22no—
411C2×Dic5—22no—
412C2×Dic5—22no—
413C2×Dic5—22no—
414C2×Dic5—22no—
415C2×Dic5—42no—
416C2×Dic5—42no—
417C2×Dic5C22×D412yes—
418C2×Dic5C22×D412yes—
419C2×Dic5C22×D412yes—
420D20—24no—
421D20—22no—
422D20—22no—
423D20—22no—
424D20—48no—
425D20—48no—
426D20—42no—
427D20—84no—
428D20C2×#4114yes—
429C4×D5—24no—
430C4×D5—22no—
431C4×D5—22no—
432C4×D5—48no—
433C4×D5—84no—
434Dic10—22no—
435Dic10—22no—
436Dic10—48no—
437Dic10—42no—
438C5×C8—22no—
439C5×C8—22no—
440#168—22no—
441#168—22no—
442C25—101no—
443C2×#41—54no—
444C2×#41—102no—
445C2×#41—104no—
446C2×#41—202no—
447C22×Q8—51no—
448C22×Q8—101no—
449C22×Q8C22×D511yescharacteristic
450C22×D4—51no—
451C22×D4—51no—
452C22×D4—51no—
453C22×D4—54no—
454C22×D4—104no—
455C22×D4—101no—
456C22×D4—101no—
457C22×D4—101no—
458C22×D4—102no—
459C22×D4—202no—
460C23×C4—51no—
461C23×C4—101no—
462C23×C4—101no—
463C23×C4C22×D511yescharacteristic
464C2×Q16—54no—
465C2×Q16—202no—
466C2×SD16—54no—
467C2×SD16—54no—
468C2×SD16—104no—
469C2×SD16—202no—
470C2×M16—54no—
471C2×M16—202no—
472C22×C8—51no—
473C22×C8—51no—
474C22×C8—54no—
475C22×C8—202no—
476C22×C8C22×D511yescharacteristic
477C22×C8C22×D511yescharacteristic
478C4⋊Q8—54no—
479C4⋊Q8—102no—
480#126—108no—
481#126—108no—
482#124—54no—
483#124—102no—
484#124—108no—
485#123—108no—
486C22⋊Q8—22no—
487C22⋊Q8—54no—
488C22⋊Q8—54no—
489C22⋊Q8—102no—
490C22⋊Q8—102no—
491C22⋊Q8C22×D514yes—
492#121—54no—
493#121—108no—
494#121—102no—
495#120—108no—
496C4×Q8—54no—
497C4×Q8—108no—
498C4×Q8—102no—
499C4×D4—54no—
500C4×D4—54no—
501C4×D4—54no—
502C4×D4—102no—
503#117—22no—
504#117—54no—
505#117—102no—
506#117C22×D514yes—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—51no—
509C2×C4⋊C4—51no—
510C2×C4⋊C4—101no—
511C2×C4⋊C4—101no—
512C2×C4⋊C4—101no—
513C2×C4⋊C4—101no—
514C2×C4⋊C4C22×D511yescharacteristic
515C2×C4⋊C4C22×D511yescharacteristic
516C2×C4⋊C4C22×D511yescharacteristic
517C2×C22⋊C4—21no—
518C2×C22⋊C4—21no—
519C2×C22⋊C4—51no—
520C2×C22⋊C4—51no—
521C2×C22⋊C4—108no—
522C2×C22⋊C4—101no—
523C2×C22⋊C4—101no—
524C2×C22⋊C4—101no—
525C2×C22⋊C4—101no—
526C2×C22⋊C4—101no—
527C2×C22⋊C4—101no—
528C2×C22⋊C4—101no—
529C2×C42—21no—
530C2×C42—51no—
531C2×C42—101no—
532C2×C42—101no—
533#107C22×D514yescomplemented
534#106—54no—
535#106C22×D514yescomplemented
536C4⋊C8—54no—
537#103—54no—
538#103—54no—
539#103C22×D514yescomplemented
540#103C22×D514yescomplemented
541#102—54no—
542#102—54no—
543#102—54no—
544#102—54no—
545#102—54no—
546#102—54no—
547C22⋊C8—54no—
548C22⋊C8C22×D514yes—
549#97—54no—
550C22×C5—22no—
551C22×C5—22no—
552C22×C5—22no—
553C22×C5—44no—
554C22×C5#54612yes—
555C22×C5#57512yes—
556C22×C5#57712yes—
557C22×C5C23×D411yescharacteristic
558C2×D5—22no—
559C2×D5—24no—
560C2×D5—22no—
561C2×D5—22no—
562C2×D5—44no—
563C2×D5—48no—
564C2×D5—42no—
565C2×D5—42no—
566C2×D5—42no—
567C2×D5—42no—
568C2×D5—42no—
569C2×D5—816no—
570C2×D5—84no—
571C4×C5—22no—
572C4×C5—42no—
573C4×C5—42no—
574C4×C5—42no—
575C4×C5—42no—
576C4×C5#54612yes—
577C4×C5C22×#4111yescharacteristic
578C4×C5C2×H(5,𝔽2)11yescharacteristic
579Dic5—22no—
580Dic5—22no—
581Dic5—22no—
582Dic5—42no—
583Dic5—42no—
584C24—51no—
585C24—101no—
586C24—101no—
587C24—104no—
588C24—204no—
589C24—204no—
590C24—402no—
591C24D4×D511yescharacteristic
592#41—108no—
593#41—204no—
594#41—208no—
595C2×Q8—21no—
596C2×Q8—22no—
597C2×Q8—22no—
598C2×Q8—52no—
599C2×Q8—104no—
600C2×Q8—101no—
601C2×Q8—102no—
602C2×Q8—102no—
603C2×Q8—204no—
604C2×Q8C23×D512yes—
605C2×D4—54no—
606C2×D4—54no—
607C2×D4—52no—
608C2×D4—52no—
609C2×D4—108no—
610C2×D4—104no—
611C2×D4—104no—
612C2×D4—101no—
613C2×D4—104no—
614C2×D4—101no—
615C2×D4—102no—
616C2×D4—102no—
617C2×D4—102no—
618C2×D4—204no—
619C2×D4—208no—
620C2×D4—204no—
621C2×D4—204no—
622C2×D4—202no—
623C2×D4—402no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—51no—
631C22×C4—51no—
632C22×C4—51no—
633C22×C4—52no—
634C22×C4—52no—
635C22×C4—104no—
636C22×C4—104no—
637C22×C4—102no—
638C22×C4—102no—
639C22×C4—101no—
640C22×C4—101no—
641C22×C4—204no—
642C22×C4—402no—
643C22×C4D4×D512yes—
644C22×C4D4×D511yescharacteristic
645C22×C4C23×D512yes—
646C22×C4C23×D511yescharacteristic
647Q16—204no—
648SD16—108no—
649SD16—204no—
650M16—204no—
651C2×C8—22no—
652C2×C8—22no—
653C2×C8—52no—
654C2×C8—52no—
655C2×C8—102no—
656C2×C8—102no—
657C2×C8—204no—
658C2×C8C23×D512yes—
659C2×C8C23×D512yes—
660C4⋊C4—24no—
661C4⋊C4—21no—
662C4⋊C4—21no—
663C4⋊C4—21no—
664C4⋊C4—54no—
665C4⋊C4—52no—
666C4⋊C4—104no—
667C4⋊C4—104no—
668C4⋊C4—104no—
669C4⋊C4—101no—
670C4⋊C4—104no—
671C4⋊C4C23×D512yes—
672C4⋊C4C23×D512yes—
673C4⋊C4C23×D512yes—
674C22⋊C4—24no—
675C22⋊C4—24no—
676C22⋊C4—54no—
677C22⋊C4—54no—
678C22⋊C4—104no—
679C22⋊C4—104no—
680C22⋊C4—104no—
681C22⋊C4—104no—
682C22⋊C4—104no—
683C22⋊C4—104no—
684C22⋊C4—104no—
685C42—24no—
686C42—52no—
687C42—52no—
688C42—104no—
689C42—104no—
690C2×C5—42no—
691C2×C5#331114yescomplemented
692C2×C5C2×#54611yescharacteristic
693C2×C5C2×#57511yescharacteristic
694C2×C5C2×#57711yescharacteristic
695D5—42no—
696D5—44no—
697D5—82no—
698C23—22no—
699C23—22no—
700C23—22no—
701C23—52no—
702C23—102no—
703C23—102no—
704C23—102no—
705C23—104no—
706C23—102no—
707C23—102no—
708C23—208no—
709C23—208no—
710C23—202no—
711C23—202no—
712C23—202no—
713C23—202no—
714C23—202no—
715C23—404no—
716C23—4016no—
717C23C2×D4×D512yes—
718C23C2×D4×D511yescharacteristic
719Q8—22no—
720Q8—22no—
721Q8—42no—
722Q8—102no—
723Q8—102no—
724Q8—208no—
725Q8—202no—
726D4—54no—
727D4—104no—
728D4—102no—
729D4—102no—
730D4—102no—
731D4—208no—
732D4—208no—
733D4—204no—
734D4—202no—
735D4—404no—
736C2×C4—22no—
737C2×C4—24no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—52no—
749C2×C4—52no—
750C2×C4—52no—
751C2×C4—102no—
752C2×C4—102no—
753C2×C4—102no—
754C2×C4—104no—
755C2×C4—102no—
756C2×C4—102no—
757C2×C4—102no—
758C2×C4—102no—
759C2×C4—208no—
760C2×C4—202no—
761C2×C4—202no—
762C2×C4—404no—
763C2×C4C2×D4×D512yes—
764C2×C4C2×D4×D511yescharacteristic
765C2×C4D5×#4112yes—
766C2×C4#414912yes—
767C2×C4C24×D511yescharacteristic
768C8—22no—
769C8—22no—
770C8—102no—
771C8—102no—
772C5C2×#331111yescharacteristic, complemented, Sylow
773C22—22no—
774C22—22no—
775C22—22no—
776C22—44no—
777C22—102no—
778C22—104no—
779C22—102no—
780C22—102no—
781C22—204no—
782C22—208no—
783C22—202no—
784C22—202no—
785C22—202no—
786C22—202no—
787C22—202no—
788C22—4016no—
789C22—404no—
790C22#6598812yes—
791C22#6610412yes—
792C22#6611112yes—
793C22C22×D4×D511yescharacteristic
794C4—22no—
795C4—42no—
796C4—42no—
797C4—42no—
798C4—42no—
799C4—102no—
800C4—102no—
801C4—102no—
802C4—202no—
803C4—202no—
804C4#6598812yes—
805C4C2×D5×#4111yescharacteristic
806C4C2×#414911yescharacteristic
807C2—42no—
808C2—202no—
809C2—204no—
810C2—402no—
811C2#1061325714yesdirect product factor
812C2C2×#6598811yescharacteristic
813C2C2×#6610411yescharacteristic
814C2C2×#6611111yescharacteristic
subgroupG/H
centerC23C2×D4×D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×#485C2
socleC23×C5C22×D4
prime radicalC2×#65964C2
hypercenterC2×#485D5
hypocenterC5C2×#3311
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#485

Complements

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

NH ≅ G/Ntype
2. C2×#65867C2semidirect
3. C2×C5×#485C2semidirect
4. C2×#65341C2semidirect
5. C2×#65290C2semidirect
6. #10613257C2direct (N × H)
7. C2×#65174C2semidirect
8. C2×#65178C2semidirect
9. C2×#65159C2semidirect
10. C2×#65153C2semidirect
11. C2×#65087C2semidirect
12. C2×#65099C2semidirect
13. C2×#65093C2semidirect
14. C2×#65084C2semidirect
15. C2×#65020C2semidirect
16. C2×#65017C2semidirect
22. C22×#689C22semidirect
28. C22×C8×D5C22semidirect
32. #65867C22semidirect
33. C2×#4043C22semidirect
38. C2×#4038C22semidirect
39. C2×#4034C22semidirect
40. C2×#4033C22semidirect
47. C5×#485C22semidirect
48. C2×C5×#107C22semidirect
49. C2×C5×#106C22semidirect
50. C2×C5×#103C22semidirect
51. C2×C5×#103C22semidirect
53. C2×#3967C22semidirect
56. C2×#3952C22semidirect
57. C2×#3947C22semidirect
58. C2×#3946C22semidirect
59. #65341C22semidirect
60. #65290C22semidirect
61. C2×#3942C22semidirect
66. C2×#3940C22semidirect
67. #65178C22semidirect
68. #65174C22semidirect
69. #65159C22semidirect
70. #65153C22semidirect
71. #65099C22semidirect
72. #65093C22semidirect
73. #65087C22semidirect
74. #65084C22semidirect
75. #65020C22semidirect
76. #65017C22semidirect
118. C2×#689C23semidirect
148. C2×C8×D5C23semidirect
150. #4043C23semidirect
158. #4038C23semidirect
160. #4034C23semidirect
162. #4033C23semidirect
169. C5×#107C23semidirect
170. C5×#106C23semidirect
171. C5×#103C23semidirect
172. C5×#103C23semidirect
174. #3967C23semidirect
177. #3952C23semidirect
178. #3947C23semidirect
179. #3946C23semidirect
180. #3942C23semidirect
185. #3940C23semidirect
190. C2×#485D5semidirect
339. #485C2×D5semidirect
349. C2×#107C2×D5semidirect
351. C2×#106C2×D5semidirect
357. C2×#103C2×D5semidirect
358. C2×#103C2×D5semidirect
533. #107C22×D5semidirect
535. #106C22×D5semidirect
539. #103C22×D5semidirect
540. #103C22×D5semidirect
691. C2×C5#3311semidirect
772. C5C2×#3311semidirect
811. C2#10613257direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#659642
C2×#658672
C2×C5×#4852
C2×#653412
C2×#652902
#106132572
C2×#651742
C2×#651782
C2×#651592
C2×#651532
C2×#650872
C2×#650992
C2×#650932
C2×#650842
C2×#650202
C2×#650172
C2×#33115