Finite Group Databasebeta

← C2×#10613177 #12975808

Subgroups — C2×#10613177 #12975808

Order 1280.

2514 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65964C211yesmaximal, characteristic, complemented
2C2×#65841C211yesmaximal, characteristic, complemented
3C2×C5×#483C211yesmaximal, characteristic, complemented
4C2×#65337C211yesmaximal, characteristic, complemented
5C22×#3941C211yesmaximal, characteristic, complemented
6#10613177C2116yesmaximal, direct product factor
7C2×#65159C211yesmaximal, characteristic, complemented
8C2×#65152C211yesmaximal, characteristic, complemented
9C2×#65154C211yesmaximal, characteristic, complemented
10C2×#65158C211yesmaximal, characteristic, complemented
11C2×#65108C211yesmaximal, characteristic, complemented
12C2×#65100C211yesmaximal, characteristic, complemented
13C2×#65092C211yesmaximal, characteristic, complemented
14C2×#65084C211yesmaximal, characteristic, complemented
15C2×#65021C211yesmaximal, characteristic, complemented
16C2×#65019C211yesmaximal, characteristic, complemented
17C22×#713C2211yescharacteristic
18C22×#709—21no—
19C23×D20C2211yescharacteristic
20C2×C5×C22⋊Q8C2211yescharacteristic
21C22×C5×C4⋊C4C2211yescharacteristic
22C2×#4093C2211yescharacteristic
23C22×#688C2211yescharacteristic, complemented
24C2×#4076C2211yescharacteristic
25C2×#4075—21no—
26C2×C4×C22⋊D5C2211yescharacteristic
27C23×#168C2211yescharacteristic
28C22×D40C2211yescharacteristic
29C22×D40C2211yescharacteristic
30C22×#676C2211yescharacteristic, complemented
31#65964—24no—
32#65964C2218yescomplemented
33C2×#4042—21no—
34#65841—24no—
35#65841C2218yescomplemented
36C2×#4041—21no—
37C2×#4041C2211yescharacteristic
38C2×#4041C2211yescharacteristic, complemented
39C2×#4040—21no—
40C2×#4040—21no—
41C2×#4039C2211yescharacteristic
42C2×#4039C2211yescharacteristic, complemented
43C2×D5×C4⋊C4C2211yescharacteristic, complemented
44C2×#4034C2211yescharacteristic, complemented
45C2×#4028—21no—
46C2×D5×C22⋊C4—21no—
47C5×#483C2218yescomplemented
48C2×C5×#106C2211yescharacteristic, 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#65337C2218yescomplemented
60C2×#3941C2211yescharacteristic
61C2×#3941C2211yescharacteristic
62C2×#3941C2211yescharacteristic
63C2×#3941C2211yescharacteristic
64C2×#3941C2218yescomplemented
65C2×#3941C2211yescharacteristic, complemented
66C2×#3940C2211yescharacteristic, complemented
67#65159C2218yescomplemented
68#65158C2218yescomplemented
69#65154C2218yescomplemented
70#65152C2218yescomplemented
71#65108C2218yescomplemented
72#65100C2218yescomplemented
73#65092C2218yescomplemented
74#65084C2218yescomplemented
75#65021C2218yescomplemented
76#65019C2218yescomplemented
77C2×#3306—51nomaximal, Sylow
78C24×D5—21no—
79C22×C5×Q8C2311yescharacteristic
80C23×C4×C5—21no—
81C23×C4×C5C2311yescharacteristic
82C22×C22⋊D5—21no—
83C22×C22⋊D5D411yescharacteristic
84C2×#713—22no—
85C2×#713—24no—
86C2×#713—42no—
87C2×#713C2314yes—
88C2×#709—28no—
89C2×#709—48no—
90C22×D20—24no—
91C22×D20—21no—
92C22×D20—21no—
93C22×D20—21no—
94C22×D20—22no—
95C22×D20—21no—
96C22×D20—42no—
97C22×D20C2311yescharacteristic
98C22×D20C2311yescharacteristic
99C22×D20C2314yes—
100C22×D20C2311yescharacteristic
101C22×C4×D5—21no—
102C22×C4×D5—21no—
103C22×C4×D5—21no—
104C22×C4×D5—21no—
105C22×C4×D5C2311yescharacteristic
106C22×Dic10—21no—
107C22×C5×C8C2311yescharacteristic
108C22×C5×C8C2311yescharacteristic
109C5×C22⋊Q8—22no—
110C5×C22⋊Q8C2314yes—
111C2×C5×C4⋊C4—21no—
112C2×C5×C4⋊C4—21no—
113C2×C5×C4⋊C4—22no—
114C2×C5×C4⋊C4C2311yescharacteristic
115C2×C5×C4⋊C4C2311yescharacteristic
116C2×C5×C4⋊C4C2311yescharacteristic
117C2×C5×C4⋊C4C2314yes—
118C2×C5×C22⋊C4—21no—
119C2×C22⋊Dic5D411yescharacteristic
120#4093—22no—
121#4093C2314yes—
122C2×#688—42no—
123C2×#688C2314yescomplemented
124#4076—22no—
125#4076C2314yes—
126#4075—28no—
127C4×C22⋊D5D414yes—
128C4×C22⋊D5C2314yes—
129C2×#685—21no—
130C2×#685—21no—
131C2×#685—21no—
132C2×#685—21no—
133C2×#685—21no—
134C2×#685—21no—
135C2×#685—21no—
136C2×#685D411yescharacteristic
137C2×C4⋊Dic5C2311yescharacteristic
138C2×#683—21no—
139C2×#683—21no—
140C2×#683D411yescharacteristic
141C2×C4×Dic5C2311yescharacteristic
142C22×#168—42no—
143C22×#168C2311yescharacteristic
144C22×#168C2311yescharacteristic
145C22×#168C2314yes—
146C2×D40—24no—
147C2×D40—42no—
148C2×D40C2314yes—
149C2×D40C2314yes—
150C2×#676—42no—
151C2×#676C2314yescomplemented
152#4042—28no—
153#4041—22no—
154#4041—22no—
155#4041—28no—
156#4041C2314yes—
157#4041C2314yescomplemented
158#4040—28no—
159#4040—28no—
160#4039—22no—
161#4039—22no—
162#4039C2314yes—
163#4039C2314yescomplemented
164D5×C4⋊C4—22no—
165D5×C4⋊C4C2314yescomplemented
166#4034—22no—
167#4034C2314yescomplemented
168#4028—28no—
169D5×C22⋊C4—28no—
170C5×#106C2314yescomplemented
171C5×#106C2314yescomplemented
172C5×#103C2314yescomplemented
173C5×#103C2314yescomplemented
174C5×C22⋊C8C2314yes—
175#3967C2314yescomplemented
176#3953C2314yes—
177#3953C2314yes—
178#3952C2314yescomplemented
179#3947C2314yescomplemented
180#3946C2314yescomplemented
181#3941C2314yes—
182#3941C2314yes—
183#3941C2314yes—
184#3941C2314yes—
185#3941C2314yescomplemented
186#3940C2314yescomplemented
187C2×#547—51no—
188C2×#546—51no—
189#3306—516no—
190C2×#489—51no—
191C2×#481—51no—
192C2×#483D511yescharacteristic, complemented
193C2×#476—51no—
194C2×#469—51no—
195C2×#465—51no—
196C2×#463—51no—
197C2×#449—51no—
198C2×#447—51no—
199C2×#442—51no—
200C2×#435—51no—
201C2×#417—51no—
202C22×#102—51no—
203C24×C5C2×D411yescharacteristic
204C23×D5—21no—
205C23×D5—21no—
206C23×D5—21no—
207C23×D5—24no—
208C23×D5—44no—
209C23×D5—44no—
210C23×D5—82no—
211C23×D5C2×D411yescharacteristic
212C2×C5×Q8—21no—
213C2×C5×Q8—22no—
214C2×C5×Q8—22no—
215C2×C5×Q8C2412yes—
216C22×C4×C5—22no—
217C22×C4×C5—22no—
218C22×C4×C5—21no—
219C22×C4×C5—21no—
220C22×C4×C5—21no—
221C22×C4×C5—21no—
222C22×C4×C5—24no—
223C22×C4×C5—44no—
224C22×C4×C5C2×D411yescharacteristic
225C22×C4×C5C2×D412yes—
226C22×C4×C5C2412yes—
227C22×C4×C5C2411yescharacteristic
228C2×C22⋊D5—24no—
229C2×C22⋊D5—24no—
230C2×C22⋊D5—44no—
231C2×C22⋊D5C2×D414yes—
232C22×Dic5—21no—
233C22×Dic5C2×D411yescharacteristic
234C22×Dic5C2×D411yescharacteristic
235C22×Dic5C2×D411yescharacteristic
236#713—28no—
237#713—44no—
238#713—48no—
239#709—432no—
240C2×D20—21no—
241C2×D20—22no—
242C2×D20—22no—
243C2×D20—22no—
244C2×D20—22no—
245C2×D20—22no—
246C2×D20—28no—
247C2×D20—24no—
248C2×D20—24no—
249C2×D20—24no—
250C2×D20—21no—
251C2×D20—21no—
252C2×D20—24no—
253C2×D20—44no—
254C2×D20—48no—
255C2×D20—44no—
256C2×D20—44no—
257C2×D20—44no—
258C2×D20—82no—
259C2×D20#4114yescomplemented
260C2×D20C2412yes—
261C2×D20C2412yes—
262C2×D20C2412yes—
263C2×C4×D5—22no—
264C2×C4×D5—22no—
265C2×C4×D5—24no—
266C2×C4×D5—24no—
267C2×C4×D5—24no—
268C2×C4×D5—24no—
269C2×C4×D5—44no—
270C2×C4×D5—44no—
271C2×C4×D5—44no—
272C2×C4×D5—82no—
273C2×C4×D5C2×D412yes—
274C2×C4×D5C2412yes—
275C2×Dic10—24no—
276C2×Dic10—44no—
277C2×C5×C8—22no—
278C2×C5×C8—22no—
279C2×C5×C8C2412yes—
280C2×C5×C8C2412yes—
281C5×C4⋊C4—21no—
282C5×C4⋊C4—21no—
283C5×C4⋊C4—24no—
284C5×C4⋊C4—24no—
285C5×C4⋊C4—21no—
286C5×C4⋊C4C2412yes—
287C5×C4⋊C4C2412yes—
288C5×C4⋊C4C2412yes—
289C5×C22⋊C4—24no—
290C22⋊Dic5C2×D414yes—
291#688—44no—
292#685—24no—
293#685—24no—
294#685—24no—
295#685—24no—
296#685—24no—
297#685—24no—
298#685—24no—
299#685C2×D414yes—
300C4⋊Dic5—21no—
301C4⋊Dic5C2412yes—
302#683—24no—
303#683—24no—
304#683C2×D414yes—
305C4×Dic5C2×D412yes—
306C4×Dic5C2412yes—
307C2×#168—22no—
308C2×#168—22no—
309C2×#168—44no—
310C2×#168C2412yes—
311C2×#168C2412yes—
312D40—28no—
313D40—44no—
314#676—44no—
315C22×#41—51no—
316C22×#41—101no—
317C23×D4—51no—
318C22×SD16—51no—
319C22×D8—51no—
320C22×D8—51no—
321C22×M16—51no—
322C23×C8—51no—
323#547—58no—
324#547—104no—
325#546—58no—
326#546—104no—
327C2×C4⋊Q8—51no—
328C2×#124—51no—
329C2×#123—101no—
330C2×#123—101no—
331C2×#123—101no—
332C2×C22⋊Q8—101no—
333C2×C22⋊Q8C2×D511yescharacteristic
334C2×#121—51no—
335C2×#121—51no—
336C2×#121—51no—
337C2×#121—101no—
338C2×#120—101no—
339C2×C4×D4—51no—
340C2×C4×D4—51no—
341C2×C4×D4—51no—
342C22×C4⋊C4—51no—
343C22×C4⋊C4C2×D511yescharacteristic
344C22×C22⋊C4—101no—
345#489—58no—
346#483C2×D518yescomplemented
347#481—58no—
348#476—58no—
349#469—58no—
350#465—58no—
351#463—58no—
352#449—58no—
353#447—58no—
354#442—58no—
355#435—58no—
356C2×#106—51no—
357C2×#106C2×D511yescharacteristic, complemented
358C2×#106C2×D511yescharacteristic, complemented
359C2×C4⋊C8—51no—
360#417—58no—
361C2×#103—51no—
362C2×#103C2×D511yescharacteristic, complemented
363C2×#103C2×D511yescharacteristic, complemented
364C2×#102—51no—
365C2×#102—51no—
366C2×#102—51no—
367C2×#102—51no—
368C2×#102—51no—
369C2×#102—51no—
370C2×#102—58no—
371C2×#102—51no—
372C2×C22⋊C8—51no—
373C2×C22⋊C8C2×D511yescharacteristic
374C2×#97—51no—
375C23×C5—22no—
376C23×C5—22no—
377C23×C5AGL(1,ℤ/8)14yes—
378C23×C5C22×D412yes—
379C23×C5C22×D411yescharacteristic
380C22×D5—22no—
381C22×D5—24no—
382C22×D5—22no—
383C22×D5—22no—
384C22×D5—22no—
385C22×D5—22no—
386C22×D5—22no—
387C22×D5—48no—
388C22×D5—42no—
389C22×D5—42no—
390C22×D5—42no—
391C22×D5—42no—
392C22×D5—42no—
393C22×D5—48no—
394C22×D5—42no—
395C22×D5—42no—
396C22×D5—42no—
397C22×D5—84no—
398C22×D5—816no—
399C22×D5C22×D412yes—
400C5×Q8—22no—
401C5×Q8—22no—
402C5×Q8—42no—
403C2×C4×C5—22no—
404C2×C4×C5—24no—
405C2×C4×C5—22no—
406C2×C4×C5—22no—
407C2×C4×C5—22no—
408C2×C4×C5—22no—
409C2×C4×C5—22no—
410C2×C4×C5—22no—
411C2×C4×C5—42no—
412C2×C4×C5—42no—
413C2×C4×C5—42no—
414C2×C4×C5—48no—
415C2×C4×C5—42no—
416C2×C4×C5C22×D412yes—
417C2×C4×C5C22×D411yescharacteristic
418C2×C4×C5C2×#4112yes—
419C2×C4×C5H(5,𝔽2)12yes—
420C2×C4×C5C2511yescharacteristic
421C22⋊D5—28no—
422C22⋊D5—48no—
423C2×Dic5—22no—
424C2×Dic5—22no—
425C2×Dic5—22no—
426C2×Dic5—22no—
427C2×Dic5—42no—
428C2×Dic5C22×D412yes—
429C2×Dic5C22×D412yes—
430C2×Dic5C22×D412yes—
431D20—24no—
432D20—22no—
433D20—22no—
434D20—22no—
435D20—22no—
436D20—22no—
437D20—48no—
438D20—48no—
439D20—48no—
440D20—42no—
441D20—42no—
442D20—84no—
443D20C2×#4114yescomplemented
444C4×D5—24no—
445C4×D5—22no—
446C4×D5—22no—
447C4×D5—48no—
448C4×D5—48no—
449C4×D5—48no—
450C4×D5—84no—
451Dic10—48no—
452C5×C8—22no—
453C5×C8—22no—
454#168—22no—
455#168—22no—
456C25—101no—
457C2×#41—54no—
458C2×#41—108no—
459C2×#41—102no—
460C2×#41—104no—
461C2×#41—208no—
462C2×#41—202no—
463C22×Q8—101no—
464C22×Q8C22×D511yescharacteristic
465C22×D4—51no—
466C22×D4—51no—
467C22×D4—51no—
468C22×D4—51no—
469C22×D4—54no—
470C22×D4—104no—
471C22×D4—101no—
472C22×D4—101no—
473C22×D4—101no—
474C22×D4—101no—
475C22×D4—101no—
476C22×D4—102no—
477C22×D4—202no—
478C23×C4—21no—
479C23×C4—51no—
480C23×C4—101no—
481C23×C4—101no—
482C23×C4—101no—
483C23×C4—101no—
484C23×C4C22×D511yescharacteristic
485C2×SD16—54no—
486C2×SD16—202no—
487C2×D8—54no—
488C2×D8—54no—
489C2×D8—104no—
490C2×D8—202no—
491C2×M16—54no—
492C2×M16—202no—
493C22×C8—51no—
494C22×C8—51no—
495C22×C8—54no—
496C22×C8—202no—
497C22×C8C22×D511yescharacteristic
498C22×C8C22×D511yescharacteristic
499C4⋊Q8—54no—
500C4⋊Q8—102no—
501#124—54no—
502#124—102no—
503#123—108no—
504#123—108no—
505#123—108no—
506C22⋊Q8—22no—
507C22⋊Q8—108no—
508C22⋊Q8C22×D514yes—
509#121—54no—
510#121—54no—
511#121—54no—
512#121—108no—
513#121—102no—
514#121—102no—
515#121—102no—
516#120—108no—
517C4×D4—54no—
518C4×D4—54no—
519C4×D4—54no—
520C4×D4—54no—
521C4×D4—102no—
522C4×D4—102no—
523C2×C4⋊C4—21no—
524C2×C4⋊C4—22no—
525C2×C4⋊C4—21no—
526C2×C4⋊C4—51no—
527C2×C4⋊C4—51no—
528C2×C4⋊C4—54no—
529C2×C4⋊C4—102no—
530C2×C4⋊C4—101no—
531C2×C4⋊C4—101no—
532C2×C4⋊C4C22×D511yescharacteristic
533C2×C4⋊C4C22×D511yescharacteristic
534C2×C4⋊C4C22×D514yes—
535C2×C4⋊C4C22×D511yescharacteristic
536C2×C22⋊C4—21no—
537C2×C22⋊C4—51no—
538C2×C22⋊C4—51no—
539C2×C22⋊C4—108no—
540C2×C22⋊C4—101no—
541C2×C22⋊C4—101no—
542C2×C22⋊C4—101no—
543C2×C22⋊C4—101no—
544C2×C22⋊C4—101no—
545C2×C22⋊C4—101no—
546C2×C22⋊C4—101no—
547C2×C42—51no—
548#106—54no—
549#106C22×D514yescomplemented
550#106C22×D514yescomplemented
551C4⋊C8—54no—
552#103—54no—
553#103C22×D514yescomplemented
554#103C22×D514yescomplemented
555#102—54no—
556#102—54no—
557#102—54no—
558#102—54no—
559#102—54no—
560#102—54no—
561#102—54no—
562C22⋊C8—54no—
563C22⋊C8C22×D514yes—
564#97—54no—
565C22×C5—22no—
566C22×C5—28no—
567C22×C5—22no—
568C22×C5#54612yes—
569C22×C5C2×AGL(1,ℤ/8)14yes—
570C22×C5C2×AGL(1,ℤ/8)12yes—
571C22×C5#57712yes—
572C22×C5C23×D411yescharacteristic
573C2×D5—22no—
574C2×D5—24no—
575C2×D5—22no—
576C2×D5—22no—
577C2×D5—44no—
578C2×D5—48no—
579C2×D5—42no—
580C2×D5—42no—
581C2×D5—42no—
582C2×D5—42no—
583C2×D5—42no—
584C2×D5—42no—
585C2×D5—42no—
586C2×D5—42no—
587C2×D5—816no—
588C2×D5—84no—
589C2×D5—84no—
590C4×C5—22no—
591C4×C5—42no—
592C4×C5—42no—
593C4×C5—42no—
594C4×C5—42no—
595C4×C5#54612yes—
596C4×C5C22×#4111yescharacteristic
597C4×C5C2×H(5,𝔽2)11yescharacteristic
598Dic5—22no—
599Dic5—22no—
600Dic5—22no—
601Dic5—42no—
602C24—51no—
603C24—101no—
604C24—101no—
605C24—101no—
606C24—104no—
607C24—204no—
608C24—204no—
609C24—402no—
610C24D4×D511yescharacteristic
611#41—108no—
612#41—2032no—
613#41—204no—
614#41—208no—
615C2×Q8—21no—
616C2×Q8—22no—
617C2×Q8—22no—
618C2×Q8—104no—
619C2×Q8—204no—
620C2×Q8C23×D512yes—
621C2×D4—54no—
622C2×D4—54no—
623C2×D4—52no—
624C2×D4—52no—
625C2×D4—52no—
626C2×D4—108no—
627C2×D4—104no—
628C2×D4—104no—
629C2×D4—104no—
630C2×D4—104no—
631C2×D4—104no—
632C2×D4—101no—
633C2×D4—101no—
634C2×D4—104no—
635C2×D4—101no—
636C2×D4—102no—
637C2×D4—102no—
638C2×D4—102no—
639C2×D4—102no—
640C2×D4—102no—
641C2×D4—204no—
642C2×D4—208no—
643C2×D4—204no—
644C2×D4—204no—
645C2×D4—204no—
646C2×D4—204no—
647C2×D4—402no—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—24no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—44no—
656C22×C4—51no—
657C22×C4—51no—
658C22×C4—51no—
659C22×C4—52no—
660C22×C4—52no—
661C22×C4—104no—
662C22×C4—104no—
663C22×C4—104no—
664C22×C4—104no—
665C22×C4—102no—
666C22×C4—102no—
667C22×C4—101no—
668C22×C4—204no—
669C22×C4—204no—
670C22×C4—204no—
671C22×C4—402no—
672C22×C4D4×D512yes—
673C22×C4D4×D511yescharacteristic
674C22×C4C23×D512yes—
675C22×C4C23×D511yescharacteristic
676SD16—204no—
677D8—108no—
678D8—204no—
679M16—204no—
680C2×C8—22no—
681C2×C8—22no—
682C2×C8—52no—
683C2×C8—52no—
684C2×C8—102no—
685C2×C8—102no—
686C2×C8—204no—
687C2×C8C23×D512yes—
688C2×C8C23×D512yes—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—24no—
692C4⋊C4—24no—
693C4⋊C4—21no—
694C4⋊C4—54no—
695C4⋊C4—52no—
696C4⋊C4—104no—
697C4⋊C4—104no—
698C4⋊C4—101no—
699C4⋊C4C23×D512yes—
700C4⋊C4C23×D512yes—
701C4⋊C4C23×D512yes—
702C22⋊C4—24no—
703C22⋊C4—54no—
704C22⋊C4—54no—
705C22⋊C4—104no—
706C22⋊C4—104no—
707C22⋊C4—104no—
708C22⋊C4—104no—
709C22⋊C4—104no—
710C22⋊C4—104no—
711C22⋊C4—104no—
712C42—52no—
713C42—52no—
714C2×C5—24no—
715C2×C5#330614yescomplemented
716C2×C5C2×#54611yescharacteristic
717C2×C5C22×AGL(1,ℤ/8)11yescharacteristic
718C2×C5C2×#57711yescharacteristic
719D5—42no—
720D5—44no—
721D5—82no—
722D5—82no—
723C23—22no—
724C23—22no—
725C23—52no—
726C23—102no—
727C23—102no—
728C23—102no—
729C23—104no—
730C23—102no—
731C23—102no—
732C23—102no—
733C23—208no—
734C23—202no—
735C23—202no—
736C23—202no—
737C23—208no—
738C23—202no—
739C23—202no—
740C23—202no—
741C23—202no—
742C23—202no—
743C23—404no—
744C23—4016no—
745C23#406014yes—
746C23C2×D4×D512yes—
747C23C2×D4×D511yescharacteristic
748Q8—22no—
749Q8—22no—
750Q8—42no—
751Q8—208no—
752D4—54no—
753D4—108no—
754D4—104no—
755D4—102no—
756D4—102no—
757D4—102no—
758D4—102no—
759D4—102no—
760D4—208no—
761D4—208no—
762D4—208no—
763D4—208no—
764D4—202no—
765D4—202no—
766D4—404no—
767C2×C4—22no—
768C2×C4—24no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—48no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—52no—
781C2×C4—52no—
782C2×C4—52no—
783C2×C4—102no—
784C2×C4—102no—
785C2×C4—102no—
786C2×C4—104no—
787C2×C4—102no—
788C2×C4—102no—
789C2×C4—102no—
790C2×C4—208no—
791C2×C4—208no—
792C2×C4—208no—
793C2×C4—202no—
794C2×C4—404no—
795C2×C4C2×D4×D512yes—
796C2×C4C2×D4×D511yescharacteristic
797C2×C4D5×#4112yes—
798C2×C4#414912yes—
799C2×C4C24×D511yescharacteristic
800C8—22no—
801C8—22no—
802C8—102no—
803C8—102no—
804C5C2×#330611yescharacteristic, complemented, Sylow
805C22—22no—
806C22—28no—
807C22—22no—
808C22—102no—
809C22—104no—
810C22—102no—
811C22—102no—
812C22—204no—
813C22—208no—
814C22—202no—
815C22—202no—
816C22—202no—
817C22—202no—
818C22—202no—
819C22—202no—
820C22—202no—
821C22—202no—
822C22—4016no—
823C22—404no—
824C22—404no—
825C22#6598812yes—
826C22C2×#406014yes—
827C22C2×#406012yes—
828C22#6611212yes—
829C22C22×D4×D511yescharacteristic
830C4—22no—
831C4—42no—
832C4—42no—
833C4—42no—
834C4—42no—
835C4—102no—
836C4—102no—
837C4—102no—
838C4—202no—
839C4#6598812yes—
840C4C2×D5×#4111yescharacteristic
841C4C2×#414911yescharacteristic
842C2—24no—
843C2—202no—
844C2—204no—
845C2—402no—
846C2—402no—
847C2#1061317714yesdirect product factor
848C2C2×#6598811yescharacteristic
849C2C22×#406011yescharacteristic
850C2C2×#6611211yescharacteristic
subgroupG/H
centerC23C2×D4×D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×#483C2
socleC23×C5C22×D4
hypercenterC2×#483D5
hypocenterC5C2×#3306
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#483

Complements

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

NH ≅ G/Ntype
1. C2×#65964C2semidirect
2. C2×#65841C2semidirect
3. C2×C5×#483C2semidirect
4. C2×#65337C2semidirect
5. C22×#3941C2semidirect
6. #10613177C2direct (N × H)
7. C2×#65159C2semidirect
8. C2×#65152C2semidirect
9. C2×#65154C2semidirect
10. C2×#65158C2semidirect
11. C2×#65108C2semidirect
12. C2×#65100C2semidirect
13. C2×#65092C2semidirect
14. C2×#65084C2semidirect
15. C2×#65021C2semidirect
16. C2×#65019C2semidirect
23. C22×#688C22semidirect
30. C22×#676C22semidirect
32. #65964C22semidirect
35. #65841C22semidirect
38. C2×#4041C22semidirect
42. C2×#4039C22semidirect
43. C2×D5×C4⋊C4C22semidirect
44. C2×#4034C22semidirect
47. C5×#483C22semidirect
48. C2×C5×#106C22semidirect
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. #65337C22semidirect
64. C2×#3941C22semidirect
65. C2×#3941C22semidirect
66. C2×#3940C22semidirect
67. #65159C22semidirect
68. #65158C22semidirect
69. #65154C22semidirect
70. #65152C22semidirect
71. #65108C22semidirect
72. #65100C22semidirect
73. #65092C22semidirect
74. #65084C22semidirect
75. #65021C22semidirect
76. #65019C22semidirect
123. C2×#688C23semidirect
151. C2×#676C23semidirect
157. #4041C23semidirect
163. #4039C23semidirect
165. D5×C4⋊C4C23semidirect
167. #4034C23semidirect
170. C5×#106C23semidirect
171. C5×#106C23semidirect
172. C5×#103C23semidirect
173. C5×#103C23semidirect
175. #3967C23semidirect
178. #3952C23semidirect
179. #3947C23semidirect
180. #3946C23semidirect
185. #3941C23semidirect
186. #3940C23semidirect
192. C2×#483D5semidirect
259. C2×D20#41semidirect
346. #483C2×D5semidirect
357. C2×#106C2×D5semidirect
358. C2×#106C2×D5semidirect
362. C2×#103C2×D5semidirect
363. C2×#103C2×D5semidirect
443. D20C2×#41semidirect
549. #106C22×D5semidirect
550. #106C22×D5semidirect
553. #103C22×D5semidirect
554. #103C22×D5semidirect
715. C2×C5#3306semidirect
804. C5C2×#3306semidirect
847. C2#10613177direct (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×#658412
C2×C5×#4832
C2×#653372
C22×#39412
#106131772
C2×#651592
C2×#651522
C2×#651542
C2×#651582
C2×#651082
C2×#651002
C2×#650922
C2×#650842
C2×#650212
C2×#650192
C2×#33065