Finite Group Databasebeta

← C2×#10611850 #12970653

Subgroups — C2×#10611850 #12970653

Order 1280.

2278 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#66164C211yesmaximal, characteristic, complemented
2C2×#65937C211yesmaximal, characteristic, complemented
3C2×C5×#449C211yesmaximal, characteristic, complemented
4C2×#65528C211yesmaximal, characteristic, complemented
5C2×#65457C211yesmaximal, characteristic, complemented
6C2×#65454C211yesmaximal, characteristic, complemented
7C2×#65443C211yesmaximal, characteristic, complemented
8C2×#65439C211yesmaximal, characteristic, complemented
9C2×#65325C211yesmaximal, characteristic, complemented
10#10611850C2116yesmaximal, direct product factor
11C2×#65087C211yesmaximal, characteristic, complemented
12C2×#65084C211yesmaximal, characteristic, complemented
13C2×#65051C211yesmaximal, characteristic, complemented
14C2×#65049C211yesmaximal, characteristic, complemented
15C2×#65020C211yesmaximal, characteristic, complemented
16C2×#65009C211yesmaximal, characteristic, complemented
17C22×C5×#41C2211yescharacteristic
18C23×D20C2211yescharacteristic
19C22×C5×SD16C2211yescharacteristic, complemented
20C22×C5×D8C2211yescharacteristic, complemented
21C2×C5×#121C2211yescharacteristic
22#66164—24no—
23#66164C2218yescomplemented
24C2×#4093C2211yescharacteristic
25C2×#4093C2211yescharacteristic
26C22×#689C2211yescharacteristic, complemented
27C2×#4086C2211yescharacteristic
28C2×#4086C2211yescharacteristic
29C2×#4083—21no—
30C2×#4083—21no—
31C2×#4082—21no—
32C2×#4082C2211yescharacteristic, complemented
33C2×#4081—21no—
34C2×D4×Dic5C2211yescharacteristic, complemented
35C22×#687C2211yescharacteristic, complemented
36C22×#686C2211yescharacteristic
37C22×#686C2211yescharacteristic
38C2×#4076—21no—
39C2×#4076—21no—
40C2×#4072C2211yescharacteristic
41C2×#4070C2211yescharacteristic
42C22×#677C2211yescharacteristic
43C22×#677C2211yescharacteristic
44#65937—24no—
45#65937C2218yescomplemented
46C2×#4034C2211yescharacteristic, complemented
47C2×#4033C2211yescharacteristic, complemented
48C2×#4025—21no—
49C2×#4024—21no—
50C5×#449C2218yescomplemented
51C2×C5×#103C2211yescharacteristic, complemented
52C2×C5×#102C2211yescharacteristic, complemented
53C2×C5×C22⋊C8C2211yescharacteristic
54#65528C2218yescomplemented
55C2×#3967C2211yescharacteristic, complemented
56C2×#3964C2211yescharacteristic, complemented
57C2×C22⋊#168C2211yescharacteristic
58#65457C2218yescomplemented
59#65454C2218yescomplemented
60#65443C2218yescomplemented
61#65439C2218yescomplemented
62C2×#3953C2211yescharacteristic
63C2×#3953C2211yescharacteristic
64C2×#3947C2211yescharacteristic, complemented
65C2×#3946C2211yescharacteristic, complemented
66C2×#3946C2211yescharacteristic, complemented
67C2×C8×Dic5C2211yescharacteristic, complemented
68#65325C2218yescomplemented
69C2×#3941C2211yescharacteristic
70C2×#3941C2211yescharacteristic
71#65087C2218yescomplemented
72#65084C2218yescomplemented
73#65051C2218yescomplemented
74#65049C2218yescomplemented
75#65020C2218yescomplemented
76#65009C2218yescomplemented
77C2×#3224—51nomaximal, Sylow
78C24×D5—21no—
79C2×C5×#41—22no—
80C2×C5×#41—42no—
81C2×C5×#41—42no—
82C2×C5×#41C2314yes—
83C22×C5×Q8C2311yescharacteristic
84C22×C5×D4—21no—
85C22×C5×D4—21no—
86C22×C5×D4C2311yescharacteristic
87C22×C5×D4C2311yescharacteristic
88C23×C4×C5—21no—
89C23×C4×C5C2311yescharacteristic
90C22×C22⋊D5—21no—
91C22×C22⋊D5—21no—
92C22×C22⋊D5—21no—
93C22×C22⋊D5—21no—
94C23×Dic5—21no—
95C22×D20—21no—
96C22×D20—22no—
97C22×D20—42no—
98C22×D20—42no—
99C22×D20C2311yescharacteristic
100C22×D20C2311yescharacteristic
101C22×D20C2314yes—
102C22×Dic10—21no—
103C22×Dic10C2311yescharacteristic
104C2×C5×SD16—42no—
105C2×C5×SD16C2314yescomplemented
106C2×C5×D8—42no—
107C2×C5×D8C2314yescomplemented
108C22×C5×C8C2311yescharacteristic
109C22×C5×C8C2311yescharacteristic
110C5×#121—22no—
111C5×#121C2314yes—
112C2×C5×C4⋊C4C2311yescharacteristic
113C2×C5×C22⋊C4—21no—
114C2×C22⋊Dic5—21no—
115C2×C22⋊Dic5—21no—
116C2×C22⋊Dic5—21no—
117C2×C22⋊Dic5—21no—
118C2×C22⋊Dic5D411yescharacteristic
119C2×C22⋊Dic5D411yescharacteristic
120#4093—22no—
121#4093—22no—
122#4093C2314yes—
123#4093C2314yes—
124C2×#689—42no—
125C2×#689C2314yescomplemented
126#4086—22no—
127#4086—22no—
128#4086C2314yes—
129#4086C2314yes—
130#4083—28no—
131#4083—28no—
132#4082—28no—
133#4082—22no—
134#4082C2314yescomplemented
135#4081—28no—
136D4×Dic5—22no—
137D4×Dic5C2314yescomplemented
138C2×#687—42no—
139C2×#687C2314yescomplemented
140C2×#686—42no—
141C2×#686—42no—
142C2×#686C2314yes—
143C2×#686C2314yes—
144#4076—28no—
145#4076—28no—
146C2×#685—21no—
147C2×#685—21no—
148C2×#685—21no—
149C2×#685—21no—
150#4072D414yes—
151#4072C2314yes—
152C2×C4⋊Dic5D411yescharacteristic
153C2×C4⋊Dic5D411yescharacteristic
154C2×C4⋊Dic5C2311yescharacteristic
155#4070—22no—
156#4070C2314yes—
157C2×#683—21no—
158C2×#683—21no—
159C2×#683—21no—
160C2×C4×Dic5—21no—
161C2×C4×Dic5C2311yescharacteristic
162C2×C4×Dic5C2311yescharacteristic
163C22×#168C2311yescharacteristic
164C22×#168C2311yescharacteristic
165C2×#677—42no—
166C2×#677—42no—
167C2×#677C2314yes—
168C2×#677C2314yes—
169#4034—22no—
170#4034C2314yescomplemented
171#4033—22no—
172#4033C2314yescomplemented
173#4025—28no—
174#4024—28no—
175C5×#103C2314yescomplemented
176C5×#102C2314yescomplemented
177C5×C22⋊C8C2314yes—
178#3967C2314yescomplemented
179#3964C2314yescomplemented
180C22⋊#168C2314yes—
181#3953C2314yes—
182#3953C2314yes—
183#3947C2314yescomplemented
184#3946C2314yescomplemented
185#3946C2314yescomplemented
186C8×Dic5C2314yescomplemented
187#3941C2314yes—
188#3941C2314yes—
189C2×#542—51no—
190C2×#535—51no—
191#3224—516no—
192C2×#496—51no—
193C2×#495—51no—
194C2×#489—51no—
195C2×#486—51no—
196C2×#464—51no—
197C2×#460—51no—
198C2×#463—51no—
199C2×#459—51no—
200C2×#452—51no—
201C2×#449D511yescharacteristic, complemented
202C2×#450—51no—
203C2×#447—51no—
204C2×#433—51no—
205C24×C5—21no—
206C24×C5—21no—
207C24×C5C2×D411yescharacteristic
208C23×D5—21no—
209C23×D5—21no—
210C23×D5—24no—
211C23×D5—44no—
212C23×D5—82no—
213C23×D5—82no—
214C5×#41—44no—
215C5×#41—44no—
216C5×#41—48no—
217C2×C5×Q8—21no—
218C2×C5×Q8—22no—
219C2×C5×Q8—22no—
220C2×C5×Q8C2412yes—
221C2×C5×D4—24no—
222C2×C5×D4—24no—
223C2×C5×D4—21no—
224C2×C5×D4—21no—
225C2×C5×D4—22no—
226C2×C5×D4—22no—
227C2×C5×D4—22no—
228C2×C5×D4—22no—
229C2×C5×D4—44no—
230C2×C5×D4—82no—
231C2×C5×D4C2412yes—
232C2×C5×D4C2412yes—
233C22×C4×C5—22no—
234C22×C4×C5—22no—
235C22×C4×C5—21no—
236C22×C4×C5—21no—
237C22×C4×C5—24no—
238C22×C4×C5—44no—
239C22×C4×C5C2×D411yescharacteristic
240C22×C4×C5C2×D412yes—
241C22×C4×C5C2412yes—
242C22×C4×C5C2411yescharacteristic
243C2×C22⋊D5—24no—
244C2×C22⋊D5—24no—
245C2×C22⋊D5—24no—
246C2×C22⋊D5—24no—
247C2×C22⋊D5—82no—
248C2×C22⋊D5—82no—
249C2×C22⋊D5—82no—
250C2×C22⋊D5—82no—
251C22×Dic5—21no—
252C22×Dic5—21no—
253C22×Dic5—24no—
254C22×Dic5—82no—
255C22×Dic5C2×D411yescharacteristic
256C22×Dic5C2×D411yescharacteristic
257C22×Dic5C2×D411yescharacteristic
258C22×Dic5C2×D411yescharacteristic
259C2×D20—22no—
260C2×D20—22no—
261C2×D20—22no—
262C2×D20—22no—
263C2×D20—24no—
264C2×D20—21no—
265C2×D20—21no—
266C2×D20—44no—
267C2×D20—44no—
268C2×D20—44no—
269C2×D20—48no—
270C2×D20C2412yes—
271C2×D20C2412yes—
272C2×Dic10—22no—
273C2×Dic10—22no—
274C2×Dic10—21no—
275C2×Dic10—24no—
276C2×Dic10—82no—
277C2×Dic10C2412yes—
278C5×SD16—44no—
279C5×D8—44no—
280C2×C5×C8—22no—
281C2×C5×C8—22no—
282C2×C5×C8C2412yes—
283C2×C5×C8C2412yes—
284C5×C4⋊C4—21no—
285C5×C4⋊C4C2412yes—
286C5×C22⋊C4—24no—
287C22⋊Dic5—24no—
288C22⋊Dic5—24no—
289C22⋊Dic5—24no—
290C22⋊Dic5—24no—
291C22⋊Dic5C2×D414yes—
292C22⋊Dic5C2×D414yes—
293#689—44no—
294#687—44no—
295#686—44no—
296#686—44no—
297#685—24no—
298#685—24no—
299#685—24no—
300#685—24no—
301C4⋊Dic5—21no—
302C4⋊Dic5C2×D414yes—
303C4⋊Dic5C2×D414yes—
304C4⋊Dic5C2412yes—
305#683—24no—
306#683—24no—
307#683—24no—
308C4×Dic5—24no—
309C4×Dic5C2×D412yes—
310C4×Dic5C2×D412yes—
311C4×Dic5C2412yes—
312C4×Dic5C2412yes—
313C2×#168—22no—
314C2×#168—22no—
315C2×#168C2412yes—
316C2×#168C2412yes—
317#677—44no—
318#677—44no—
319C22×#41C2×D511yescharacteristic
320C23×D4—51no—
321C22×Q16—51no—
322C22×SD16—51no—
323C22×SD16—51no—
324C22×SD16—51no—
325C22×SD16C2×D511yescharacteristic, complemented
326C22×D8—51no—
327C22×D8—51no—
328C22×D8C2×D511yescharacteristic, complemented
329#542—58no—
330#542—104no—
331#535—58no—
332#535—104no—
333C2×C4⋊Q8—51no—
334C2×#127—51no—
335C2×#127—51no—
336C2×#126—101no—
337C2×#124—51no—
338C2×#124—51no—
339C2×#124—51no—
340C2×#124—101no—
341C2×#123—101no—
342C2×C22⋊Q8—51no—
343C2×C22⋊Q8—101no—
344C2×#121—101no—
345C2×#121—101no—
346C2×#121C2×D511yescharacteristic
347C2×#120—101no—
348C2×#120—101no—
349C2×C4×Q8—51no—
350C2×C4×D4—51no—
351C2×#117—51no—
352#496—58no—
353#495—58no—
354#489—58no—
355#486—58no—
356#464—58no—
357#463—58no—
358#460—58no—
359#459—58no—
360#452—58no—
361#450—58no—
362#449C2×D518yescomplemented
363#447—58no—
364#433—58no—
365C2×C4⋊C8—51no—
366C2×C4⋊C8—51no—
367C2×#103—51no—
368C2×#103C2×D511yescharacteristic, complemented
369C2×#102—51no—
370C2×#102—51no—
371C2×#102—51no—
372C2×#102—51no—
373C2×#102—51no—
374C2×#102C2×D511yescharacteristic, complemented
375C2×C22⋊C8—51no—
376C2×C22⋊C8C2×D511yescharacteristic
377C2×#97—51no—
378C2×C4×C8—51no—
379C23×C5—22no—
380C23×C5—22no—
381C23×C5—22no—
382C23×C5—22no—
383C23×C5—22no—
384C23×C5—42no—
385C23×C5—42no—
386C23×C5—42no—
387C23×C5—42no—
388C23×C5—42no—
389C23×C5—42no—
390C23×C5C22×D412yes—
391C23×C5C22×D411yescharacteristic
392C22×D5—22no—
393C22×D5—22no—
394C22×D5—48no—
395C22×D5—42no—
396C22×D5—42no—
397C22×D5—42no—
398C22×D5—42no—
399C22×D5—42no—
400C22×D5—42no—
401C22×D5—84no—
402C22×D5—84no—
403C22×D5—816no—
404C5×Q8—22no—
405C5×Q8—22no—
406C5×Q8—42no—
407C5×D4—22no—
408C5×D4—22no—
409C5×D4—22no—
410C5×D4—22no—
411C5×D4—48no—
412C5×D4—42no—
413C5×D4—42no—
414C5×D4—84no—
415C2×C4×C5—22no—
416C2×C4×C5—24no—
417C2×C4×C5—22no—
418C2×C4×C5—22no—
419C2×C4×C5—22no—
420C2×C4×C5—22no—
421C2×C4×C5—48no—
422C2×C4×C5—42no—
423C2×C4×C5—42no—
424C2×C4×C5C22×D412yes—
425C2×C4×C5C22×D411yescharacteristic
426C2×C4×C5H(5,𝔽2)12yes—
427C2×C4×C5H(5,𝔽2)12yes—
428C2×C4×C5C2511yescharacteristic
429C22⋊D5—84no—
430C22⋊D5—84no—
431C22⋊D5—84no—
432C22⋊D5—84no—
433C2×Dic5—22no—
434C2×Dic5—22no—
435C2×Dic5—22no—
436C2×Dic5—22no—
437C2×Dic5—22no—
438C2×Dic5—22no—
439C2×Dic5—42no—
440C2×Dic5—42no—
441C2×Dic5—84no—
442C2×Dic5C22×D412yes—
443C2×Dic5C22×D412yes—
444C2×Dic5C22×D412yes—
445C2×Dic5C22×D412yes—
446D20—22no—
447D20—22no—
448D20—22no—
449D20—22no—
450D20—48no—
451D20—42no—
452D20—42no—
453Dic10—22no—
454Dic10—22no—
455Dic10—42no—
456Dic10—84no—
457C5×C8—22no—
458C5×C8—22no—
459#168—22no—
460#168—22no—
461C25—101no—
462C2×#41—22no—
463C2×#41—42no—
464C2×#41—42no—
465C2×#41C22×D514yes—
466C22×Q8—51no—
467C22×Q8—101no—
468C22×Q8C22×D511yescharacteristic
469C22×D4—21no—
470C22×D4—21no—
471C22×D4—51no—
472C22×D4—51no—
473C22×D4—54no—
474C22×D4—101no—
475C22×D4—101no—
476C22×D4—101no—
477C22×D4—101no—
478C22×D4—101no—
479C22×D4—102no—
480C22×D4—202no—
481C22×D4—202no—
482C22×D4C22×D511yescharacteristic
483C22×D4C22×D511yescharacteristic
484C23×C4—21no—
485C23×C4—101no—
486C23×C4C22×D511yescharacteristic
487C2×Q16—54no—
488C2×Q16—202no—
489C2×SD16—42no—
490C2×SD16—54no—
491C2×SD16—54no—
492C2×SD16—54no—
493C2×SD16—202no—
494C2×SD16—202no—
495C2×SD16—202no—
496C2×SD16C22×D514yescomplemented
497C2×D8—42no—
498C2×D8—54no—
499C2×D8—54no—
500C2×D8—202no—
501C2×D8—202no—
502C2×D8C22×D514yescomplemented
503C22×C8—51no—
504C22×C8—51no—
505C22×C8C22×D511yescharacteristic
506C22×C8C22×D511yescharacteristic
507C4⋊Q8—54no—
508C4⋊Q8—102no—
509#127—54no—
510#127—54no—
511#127—102no—
512#127—102no—
513#126—108no—
514#124—54no—
515#124—54no—
516#124—54no—
517#124—102no—
518#124—102no—
519#124—102no—
520#124—108no—
521#123—108no—
522C22⋊Q8—54no—
523C22⋊Q8—108no—
524C22⋊Q8—102no—
525#121—22no—
526#121—108no—
527#121—108no—
528#121C22×D514yes—
529#120—108no—
530#120—108no—
531C4×Q8—54no—
532C4×Q8—102no—
533C4×D4—54no—
534C4×D4—102no—
535#117—54no—
536#117—54no—
537C2×C4⋊C4—51no—
538C2×C4⋊C4—51no—
539C2×C4⋊C4—51no—
540C2×C4⋊C4—101no—
541C2×C4⋊C4—101no—
542C2×C4⋊C4—101no—
543C2×C4⋊C4C22×D511yescharacteristic
544C2×C22⋊C4—21no—
545C2×C22⋊C4—51no—
546C2×C22⋊C4—51no—
547C2×C22⋊C4—101no—
548C2×C22⋊C4—101no—
549C2×C22⋊C4—101no—
550C2×C22⋊C4—101no—
551C2×C22⋊C4—101no—
552C2×C22⋊C4—101no—
553C2×C22⋊C4—101no—
554C2×C22⋊C4—101no—
555C2×C42—51no—
556C2×C42—51no—
557C2×C42—101no—
558C4⋊C8—54no—
559C4⋊C8—54no—
560#103—54no—
561#103C22×D514yescomplemented
562#102—54no—
563#102—54no—
564#102—54no—
565#102—54no—
566#102—54no—
567#102C22×D514yescomplemented
568C22⋊C8—54no—
569C22⋊C8C22×D514yes—
570#97—54no—
571C4×C8—54no—
572C22×C5—22no—
573C22×C5—22no—
574C22×C5—22no—
575C22×C5—44no—
576C22×C5—42no—
577C22×C5—42no—
578C22×C5—42no—
579C22×C5—42no—
580C22×C5—42no—
581C22×C5—42no—
582C22×C5—84no—
583C22×C5—84no—
584C22×C5#53512yes—
585C22×C5#57612yes—
586C22×C5#57712yes—
587C22×C5C23×D411yescharacteristic
588C2×D5—42no—
589C2×D5—42no—
590C2×D5—42no—
591C2×D5—42no—
592C2×D5—42no—
593C2×D5—42no—
594C2×D5—816no—
595C2×D5—84no—
596C2×D5—84no—
597C4×C5—22no—
598C4×C5—42no—
599C4×C5—42no—
600C4×C5#53512yes—
601C4×C5C2×H(5,𝔽2)11yescharacteristic
602C4×C5C2×H(5,𝔽2)11yescharacteristic
603Dic5—22no—
604Dic5—22no—
605Dic5—22no—
606Dic5—22no—
607Dic5—42no—
608Dic5—42no—
609C24—21no—
610C24—21no—
611C24—101no—
612C24—101no—
613C24—104no—
614C24—204no—
615C24—402no—
616C24—402no—
617C24D4×D511yescharacteristic
618#41—44no—
619#41—44no—
620#41—48no—
621C2×Q8—21no—
622C2×Q8—22no—
623C2×Q8—22no—
624C2×Q8—52no—
625C2×Q8—104no—
626C2×Q8—101no—
627C2×Q8—102no—
628C2×Q8—102no—
629C2×Q8—402no—
630C2×Q8C23×D512yes—
631C2×D4—24no—
632C2×D4—24no—
633C2×D4—21no—
634C2×D4—21no—
635C2×D4—22no—
636C2×D4—22no—
637C2×D4—22no—
638C2×D4—22no—
639C2×D4—44no—
640C2×D4—52no—
641C2×D4—52no—
642C2×D4—82no—
643C2×D4—104no—
644C2×D4—104no—
645C2×D4—104no—
646C2×D4—104no—
647C2×D4—104no—
648C2×D4—101no—
649C2×D4—101no—
650C2×D4—102no—
651C2×D4—102no—
652C2×D4—102no—
653C2×D4—102no—
654C2×D4—204no—
655C2×D4—204no—
656C2×D4—204no—
657C2×D4—208no—
658C2×D4—402no—
659C2×D4—402no—
660C2×D4—402no—
661C2×D4—402no—
662C2×D4C23×D512yes—
663C2×D4C23×D512yes—
664C22×C4—22no—
665C22×C4—22no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—24no—
669C22×C4—44no—
670C22×C4—51no—
671C22×C4—51no—
672C22×C4—51no—
673C22×C4—51no—
674C22×C4—104no—
675C22×C4—101no—
676C22×C4—101no—
677C22×C4—402no—
678C22×C4D4×D512yes—
679C22×C4D4×D511yescharacteristic
680C22×C4C23×D512yes—
681C22×C4C23×D511yescharacteristic
682Q16—204no—
683SD16—44no—
684SD16—204no—
685SD16—204no—
686SD16—204no—
687D8—44no—
688D8—204no—
689D8—204no—
690C2×C8—22no—
691C2×C8—22no—
692C2×C8—52no—
693C2×C8—52no—
694C2×C8—102no—
695C2×C8—102no—
696C2×C8C23×D512yes—
697C2×C8C23×D512yes—
698C4⋊C4—21no—
699C4⋊C4—54no—
700C4⋊C4—54no—
701C4⋊C4—52no—
702C4⋊C4—104no—
703C4⋊C4—104no—
704C4⋊C4—101no—
705C4⋊C4—104no—
706C4⋊C4C23×D512yes—
707C22⋊C4—24no—
708C22⋊C4—54no—
709C22⋊C4—54no—
710C22⋊C4—104no—
711C22⋊C4—104no—
712C22⋊C4—104no—
713C22⋊C4—104no—
714C22⋊C4—104no—
715C22⋊C4—104no—
716C22⋊C4—104no—
717C22⋊C4—104no—
718C42—52no—
719C42—52no—
720C42—52no—
721C42—52no—
722C42—104no—
723C2×C5—42no—
724C2×C5—82no—
725C2×C5—82no—
726C2×C5#322414yescomplemented
727C2×C5C2×#53511yescharacteristic
728C2×C5C2×#57611yescharacteristic
729C2×C5C2×#57711yescharacteristic
730D5—82no—
731D5—82no—
732C23—22no—
733C23—22no—
734C23—22no—
735C23—22no—
736C23—22no—
737C23—42no—
738C23—42no—
739C23—42no—
740C23—42no—
741C23—42no—
742C23—42no—
743C23—102no—
744C23—102no—
745C23—208no—
746C23—202no—
747C23—202no—
748C23—202no—
749C23—202no—
750C23—202no—
751C23—202no—
752C23—404no—
753C23—404no—
754C23—4016no—
755C23C2×D4×D512yes—
756C23C2×D4×D511yescharacteristic
757Q8—22no—
758Q8—22no—
759Q8—42no—
760Q8—102no—
761Q8—102no—
762Q8—202no—
763Q8—404no—
764D4—22no—
765D4—22no—
766D4—22no—
767D4—22no—
768D4—48no—
769D4—42no—
770D4—42no—
771D4—84no—
772D4—102no—
773D4—102no—
774D4—102no—
775D4—102no—
776D4—208no—
777D4—202no—
778D4—202no—
779D4—404no—
780D4—404no—
781D4—404no—
782D4—404no—
783C2×C4—22no—
784C2×C4—24no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—48no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—52no—
793C2×C4—52no—
794C2×C4—52no—
795C2×C4—52no—
796C2×C4—102no—
797C2×C4—102no—
798C2×C4—102no—
799C2×C4—102no—
800C2×C4—102no—
801C2×C4—102no—
802C2×C4—202no—
803C2×C4—202no—
804C2×C4—404no—
805C2×C4C2×D4×D512yes—
806C2×C4C2×D4×D511yescharacteristic
807C2×C4#414412yes—
808C2×C4#414412yes—
809C2×C4C24×D511yescharacteristic
810C8—22no—
811C8—22no—
812C8—102no—
813C8—102no—
814C5C2×#322411yescharacteristic, complemented, Sylow
815C22—22no—
816C22—22no—
817C22—22no—
818C22—44no—
819C22—42no—
820C22—42no—
821C22—42no—
822C22—42no—
823C22—42no—
824C22—42no—
825C22—84no—
826C22—84no—
827C22—202no—
828C22—202no—
829C22—202no—
830C22—202no—
831C22—202no—
832C22—202no—
833C22—4016no—
834C22—404no—
835C22—404no—
836C22#6592612yes—
837C22#6610412yes—
838C22#6610812yes—
839C22C22×D4×D511yescharacteristic
840C4—22no—
841C4—42no—
842C4—42no—
843C4—102no—
844C4—102no—
845C4—102no—
846C4—102no—
847C4—202no—
848C4—202no—
849C4#6592612yes—
850C4C2×#414411yescharacteristic
851C4C2×#414411yescharacteristic
852C2—42no—
853C2—82no—
854C2—82no—
855C2—402no—
856C2—402no—
857C2#1061185014yesdirect product factor
858C2C2×#6592611yescharacteristic
859C2C2×#6610411yescharacteristic
860C2C2×#6610811yescharacteristic
subgroupG/H
centerC23C2×D4×D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×#449C2
socleC23×C5C22×D4
hypercenterC2×#449D5
hypocenterC5C2×#3224
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#449

Complements

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

NH ≅ G/Ntype
1. C2×#66164C2semidirect
2. C2×#65937C2semidirect
3. C2×C5×#449C2semidirect
4. C2×#65528C2semidirect
5. C2×#65457C2semidirect
6. C2×#65454C2semidirect
7. C2×#65443C2semidirect
8. C2×#65439C2semidirect
9. C2×#65325C2semidirect
10. #10611850C2direct (N × H)
11. C2×#65087C2semidirect
12. C2×#65084C2semidirect
13. C2×#65051C2semidirect
14. C2×#65049C2semidirect
15. C2×#65020C2semidirect
16. C2×#65009C2semidirect
19. C22×C5×SD16C22semidirect
20. C22×C5×D8C22semidirect
23. #66164C22semidirect
26. C22×#689C22semidirect
32. C2×#4082C22semidirect
34. C2×D4×Dic5C22semidirect
35. C22×#687C22semidirect
45. #65937C22semidirect
46. C2×#4034C22semidirect
47. C2×#4033C22semidirect
50. C5×#449C22semidirect
51. C2×C5×#103C22semidirect
52. C2×C5×#102C22semidirect
54. #65528C22semidirect
55. C2×#3967C22semidirect
56. C2×#3964C22semidirect
58. #65457C22semidirect
59. #65454C22semidirect
60. #65443C22semidirect
61. #65439C22semidirect
64. C2×#3947C22semidirect
65. C2×#3946C22semidirect
66. C2×#3946C22semidirect
67. C2×C8×Dic5C22semidirect
68. #65325C22semidirect
71. #65087C22semidirect
72. #65084C22semidirect
73. #65051C22semidirect
74. #65049C22semidirect
75. #65020C22semidirect
76. #65009C22semidirect
105. C2×C5×SD16C23semidirect
107. C2×C5×D8C23semidirect
125. C2×#689C23semidirect
134. #4082C23semidirect
137. D4×Dic5C23semidirect
139. C2×#687C23semidirect
170. #4034C23semidirect
172. #4033C23semidirect
175. C5×#103C23semidirect
176. C5×#102C23semidirect
178. #3967C23semidirect
179. #3964C23semidirect
183. #3947C23semidirect
184. #3946C23semidirect
185. #3946C23semidirect
186. C8×Dic5C23semidirect
201. C2×#449D5semidirect
325. C22×SD16C2×D5semidirect
328. C22×D8C2×D5semidirect
362. #449C2×D5semidirect
368. C2×#103C2×D5semidirect
374. C2×#102C2×D5semidirect
496. C2×SD16C22×D5semidirect
502. C2×D8C22×D5semidirect
561. #103C22×D5semidirect
567. #102C22×D5semidirect
726. C2×C5#3224semidirect
814. C5C2×#3224semidirect
857. C2#10611850direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#661642
C2×#659372
C2×C5×#4492
C2×#655282
C2×#654572
C2×#654542
C2×#654432
C2×#654392
C2×#653252
#106118502
C2×#650872
C2×#650842
C2×#650512
C2×#650492
C2×#650202
C2×#650092
C2×#32245