Finite Group Databasebeta

← C2×#10611123 #12970657

Subgroups — C2×#10611123 #12970657

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×#65868C211yesmaximal, characteristic, complemented
2C2×#65859C211yesmaximal, characteristic, complemented
3C2×C5×#433C211yesmaximal, characteristic, complemented
4#10611123C2116yesmaximal, direct product factor
5C2×#65134C211yesmaximal, characteristic, complemented
6C2×#65137C211yesmaximal, characteristic, complemented
7C2×#65133C211yesmaximal, characteristic, complemented
8C2×#65132C211yesmaximal, characteristic, complemented
9C2×#65022C211yesmaximal, characteristic, complemented
10C2×#65023C211yesmaximal, characteristic, complemented
11C2×#65020C211yesmaximal, characteristic, complemented
12C2×#65021C211yesmaximal, characteristic, complemented
13C2×#65001C211yesmaximal, characteristic, complemented
14C2×#65003C211yesmaximal, characteristic, complemented
15C2×#64985C211yesmaximal, characteristic, complemented
16C2×#64983C211yesmaximal, characteristic, complemented
17C22×#709C2211yescharacteristic
18C23×D20C2211yescharacteristic
19C2×C5×#117C2211yescharacteristic
20C2×#4076C2211yescharacteristic
21C2×#4070C2211yescharacteristic
22C22×Dic20C2211yescharacteristic, complemented
23C22×D40C2211yescharacteristic
24C22×D40C2211yescharacteristic
25C22×D40C2211yescharacteristic, complemented
26C22×#677C2211yescharacteristic
27C22×#677C2211yescharacteristic
28C22×#677C2211yescharacteristic, complemented
29C22×#677C2211yescharacteristic, complemented
30#65868—24no—
31#65868C2218yescomplemented
32#65859—24no—
33#65859C2218yescomplemented
34C2×#4044—21no—
35C2×#4042—21no—
36C2×#4041—21no—
37C2×#4041—21no—
38C2×#4031—21no—
39C2×#4029—21no—
40C2×#4028—21no—
41C2×#4028—21no—
42C2×#4021C2211yescharacteristic
43C2×#4021C2211yescharacteristic
44C2×#4021C2211yescharacteristic, complemented
45C2×#4020C2211yescharacteristic
46C2×#4020C2211yescharacteristic
47C2×C4×D20C2211yescharacteristic, complemented
48C2×#4015C2211yescharacteristic, complemented
49C2×C4×Dic10C2211yescharacteristic, complemented
50C5×#433C2218yescomplemented
51C2×C5×C4⋊C8C2211yescharacteristic, complemented
52C2×C5×C4⋊C8C2211yescharacteristic, complemented
53C2×C5×C22⋊C8C2211yescharacteristic
54C2×C5×C22⋊C8C2211yescharacteristic
55C2×C5×#97C2211yescharacteristic, complemented
56C2×C4×C5×C8C2211yescharacteristic, complemented
57C2×#3953C2211yescharacteristic
58C2×#3953C2211yescharacteristic
59C2×#3953C2211yescharacteristic
60C2×#3953C2211yescharacteristic
61C2×#3953C2211yescharacteristic, complemented
62C2×#3953C2211yescharacteristic, complemented
63C2×#3948C2211yescharacteristic, complemented
64C2×#3948C2211yescharacteristic, complemented
65#65137C2218yescomplemented
66#65134C2218yescomplemented
67#65133C2218yescomplemented
68#65132C2218yescomplemented
69#65023C2218yescomplemented
70#65022C2218yescomplemented
71#65021C2218yescomplemented
72#65020C2218yescomplemented
73#65003C2218yescomplemented
74#65001C2218yescomplemented
75#64985C2218yescomplemented
76#64983C2218yescomplemented
77C2×#3224—51nomaximal, Sylow
78C24×D5—21no—
79C23×C4×C5C2311yescharacteristic
80C22×C22⋊D5—21no—
81C22×C22⋊D5—21no—
82C2×#709—22no—
83C2×#709—42no—
84C2×#709—42no—
85C2×#709C2314yes—
86C22×D20—21no—
87C22×D20—22no—
88C22×D20—21no—
89C22×D20—21no—
90C22×D20—21no—
91C22×D20—21no—
92C22×D20—42no—
93C22×D20—42no—
94C22×D20C2311yescharacteristic
95C22×D20C2311yescharacteristic
96C22×D20C2311yescharacteristic
97C22×D20C2311yescharacteristic
98C22×D20C2314yes—
99C22×C4×D5—21no—
100C22×C4×D5—21no—
101C22×Dic10—21no—
102C22×Dic10C2311yescharacteristic
103C22×Dic10C2311yescharacteristic
104C22×C5×C8C2311yescharacteristic
105C22×C5×C8C2311yescharacteristic
106C22×C5×C8C2311yescharacteristic
107C22×C5×C8C2311yescharacteristic
108C5×#117D414yes—
109C5×#117C2314yes—
110C2×C5×C4⋊C4D411yescharacteristic
111C2×C5×C4⋊C4D411yescharacteristic
112C2×C5×C22⋊C4D411yescharacteristic
113C2×C5×C22⋊C4D411yescharacteristic
114C2×C42×C5C2311yescharacteristic
115C2×C42×C5C2311yescharacteristic
116C2×C22⋊Dic5—21no—
117#4076—22no—
118#4076C2314yes—
119C2×#685—21no—
120C2×#685—21no—
121C2×#685—21no—
122C2×#685—21no—
123C2×#685—21no—
124C2×#685—21no—
125C2×#685—21no—
126C2×#685—21no—
127C2×C4⋊Dic5—21no—
128C2×C4⋊Dic5C2311yescharacteristic
129C2×C4⋊Dic5C2311yescharacteristic
130#4070—22no—
131#4070C2314yes—
132C2×#683—21no—
133C2×#683—21no—
134C2×C4×Dic5—21no—
135C2×Dic20—42no—
136C2×Dic20C2314yescomplemented
137C2×D40—42no—
138C2×D40—42no—
139C2×D40—42no—
140C2×D40C2314yes—
141C2×D40C2314yes—
142C2×D40C2314yescomplemented
143C2×#677—42no—
144C2×#677—42no—
145C2×#677—42no—
146C2×#677—42no—
147C2×#677C2314yes—
148C2×#677C2314yes—
149C2×#677C2314yescomplemented
150C2×#677C2314yescomplemented
151#4044—28no—
152#4042—28no—
153#4041—28no—
154#4041—28no—
155#4031—28no—
156#4029—28no—
157#4028—28no—
158#4028—28no—
159#4021—22no—
160#4021—22no—
161#4021—22no—
162#4021C2314yes—
163#4021C2314yes—
164#4021C2314yescomplemented
165#4020—22no—
166#4020—22no—
167#4020C2314yes—
168#4020C2314yes—
169C4×D20—22no—
170C4×D20C2314yescomplemented
171#4015—22no—
172#4015C2314yescomplemented
173C4×Dic10—22no—
174C4×Dic10C2314yescomplemented
175C5×C4⋊C8C2314yescomplemented
176C5×C4⋊C8C2314yescomplemented
177C5×C22⋊C8C2314yes—
178C5×C22⋊C8C2314yes—
179C5×#97C2314yescomplemented
180C4×C5×C8C2314yescomplemented
181#3953C2314yes—
182#3953C2314yes—
183#3953C2314yes—
184#3953C2314yes—
185#3953C2314yescomplemented
186#3953C2314yescomplemented
187#3948C2314yescomplemented
188#3948C2314yescomplemented
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×#449—51no—
202C2×#450—51no—
203C2×#447—51no—
204C2×#433D511yescharacteristic, complemented
205C24×C5C2×D411yescharacteristic
206C23×D5—21no—
207C23×D5—21no—
208C23×D5—21no—
209C23×D5—21no—
210C23×D5—24no—
211C23×D5—44no—
212C23×D5—82no—
213C23×D5—82no—
214C22×C4×C5—22no—
215C22×C4×C5—22no—
216C22×C4×C5C2×D411yescharacteristic
217C22×C4×C5C2×D411yescharacteristic
218C22×C4×C5C2×D411yescharacteristic
219C22×C4×C5C2×D411yescharacteristic
220C22×C4×C5C2×D411yescharacteristic
221C22×C4×C5C2×D412yes—
222C22×C4×C5C2412yes—
223C22×C4×C5C2411yescharacteristic
224C2×C22⋊D5—24no—
225C2×C22⋊D5—24no—
226C2×C22⋊D5—44no—
227C2×C22⋊D5—82no—
228C22×Dic5—21no—
229C22×Dic5—21no—
230C22×Dic5—21no—
231C22×Dic5—21no—
232#709—44no—
233#709—44no—
234#709—48no—
235C2×D20—22no—
236C2×D20—22no—
237C2×D20—22no—
238C2×D20—22no—
239C2×D20—22no—
240C2×D20—22no—
241C2×D20—22no—
242C2×D20—22no—
243C2×D20—21no—
244C2×D20—21no—
245C2×D20—24no—
246C2×D20—21no—
247C2×D20—21no—
248C2×D20—24no—
249C2×D20—24no—
250C2×D20—24no—
251C2×D20—24no—
252C2×D20—44no—
253C2×D20—44no—
254C2×D20—44no—
255C2×D20—48no—
256C2×D20—82no—
257C2×D20—82no—
258C2×D20—82no—
259C2×D20—82no—
260C2×D20C2412yes—
261C2×D20C2412yes—
262C2×D20C2412yes—
263C2×D20C2412yes—
264C2×C4×D5—24no—
265C2×C4×D5—24no—
266C2×C4×D5—44no—
267C2×C4×D5—82no—
268C2×Dic10—22no—
269C2×Dic10—22no—
270C2×Dic10—22no—
271C2×Dic10—22no—
272C2×Dic10—21no—
273C2×Dic10—21no—
274C2×Dic10—24no—
275C2×Dic10—82no—
276C2×Dic10C2412yes—
277C2×Dic10C2412yes—
278C2×C5×C8—22no—
279C2×C5×C8—22no—
280C2×C5×C8—22no—
281C2×C5×C8—22no—
282C2×C5×C8C2412yes—
283C2×C5×C8C2412yes—
284C2×C5×C8C2412yes—
285C2×C5×C8C2412yes—
286C5×C4⋊C4C2×D414yes—
287C5×C4⋊C4C2×D414yes—
288C5×C22⋊C4C2×D414yes—
289C5×C22⋊C4C2×D414yes—
290C42×C5C2×D412yes—
291C42×C5C2×D412yes—
292C42×C5C2412yes—
293C42×C5C2412yes—
294C22⋊Dic5—24no—
295#685—24no—
296#685—24no—
297#685—24no—
298#685—24no—
299#685—24no—
300#685—24no—
301#685—24no—
302#685—24no—
303C4⋊Dic5—21no—
304C4⋊Dic5—21no—
305C4⋊Dic5—24no—
306C4⋊Dic5C2412yes—
307C4⋊Dic5C2412yes—
308#683—24no—
309#683—24no—
310C4×Dic5—24no—
311Dic20—44no—
312D40—44no—
313D40—44no—
314D40—44no—
315#677—44no—
316#677—44no—
317#677—44no—
318#677—44no—
319C22×#41—51no—
320C23×D4—51no—
321C22×Q16—51no—
322C22×SD16—51no—
323C22×SD16—51no—
324C22×SD16—51no—
325C22×SD16—51no—
326C22×D8—51no—
327C22×D8—51no—
328C22×D8—51no—
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—51no—
345C2×#121—101no—
346C2×#121—101no—
347C2×#120—101no—
348C2×#120—101no—
349C2×C4×Q8—51no—
350C2×C4×D4—51no—
351C2×#117C2×D511yescharacteristic
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#449—58no—
363#447—58no—
364#433C2×D518yescomplemented
365C2×C4⋊C8C2×D511yescharacteristic, complemented
366C2×C4⋊C8C2×D511yescharacteristic, complemented
367C2×#103—51no—
368C2×#103—51no—
369C2×#102—51no—
370C2×#102—51no—
371C2×#102—51no—
372C2×#102—51no—
373C2×#102—51no—
374C2×#102—51no—
375C2×C22⋊C8C2×D511yescharacteristic
376C2×C22⋊C8C2×D511yescharacteristic
377C2×#97C2×D511yescharacteristic, complemented
378C2×C4×C8C2×D511yescharacteristic, complemented
379C23×C5—22no—
380C23×C5—22no—
381C23×C5—22no—
382C23×C5C22×D412yes—
383C23×C5C22×D411yescharacteristic
384C22×D5—22no—
385C22×D5—22no—
386C22×D5—22no—
387C22×D5—22no—
388C22×D5—48no—
389C22×D5—42no—
390C22×D5—42no—
391C22×D5—42no—
392C22×D5—42no—
393C22×D5—42no—
394C22×D5—42no—
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—
404C2×C4×C5—22no—
405C2×C4×C5—22no—
406C2×C4×C5—22no—
407C2×C4×C5—22no—
408C2×C4×C5—22no—
409C2×C4×C5—24no—
410C2×C4×C5—22no—
411C2×C4×C5—22no—
412C2×C4×C5C22×D412yes—
413C2×C4×C5C22×D412yes—
414C2×C4×C5C22×D412yes—
415C2×C4×C5C22×D412yes—
416C2×C4×C5C22×D412yes—
417C2×C4×C5C22×D411yescharacteristic
418C2×C4×C5H(5,𝔽2)12yes—
419C2×C4×C5H(5,𝔽2)12yes—
420C2×C4×C5C2511yescharacteristic
421C22⋊D5—48no—
422C22⋊D5—84no—
423C2×Dic5—22no—
424C2×Dic5—22no—
425C2×Dic5—22no—
426C2×Dic5—22no—
427C2×Dic5—42no—
428C2×Dic5—42no—
429C2×Dic5—42no—
430C2×Dic5—42no—
431D20—22no—
432D20—22no—
433D20—22no—
434D20—22no—
435D20—22no—
436D20—22no—
437D20—22no—
438D20—22no—
439D20—48no—
440D20—42no—
441D20—42no—
442D20—42no—
443D20—42no—
444D20—84no—
445D20—84no—
446D20—84no—
447D20—84no—
448C4×D5—48no—
449C4×D5—84no—
450Dic10—22no—
451Dic10—22no—
452Dic10—22no—
453Dic10—22no—
454Dic10—42no—
455Dic10—42no—
456Dic10—84no—
457C5×C8—22no—
458C5×C8—22no—
459C5×C8—22no—
460C5×C8—22no—
461C25—101no—
462C2×#41—54no—
463C2×#41—102no—
464C2×#41—202no—
465C2×#41—202no—
466C22×Q8—51no—
467C22×Q8—51no—
468C22×Q8—101no—
469C22×D4—51no—
470C22×D4—51no—
471C22×D4—51no—
472C22×D4—51no—
473C22×D4—54no—
474C22×D4—101no—
475C22×D4—101no—
476C22×D4—101no—
477C22×D4—102no—
478C22×D4—101no—
479C22×D4—101no—
480C22×D4—101no—
481C22×D4—101no—
482C22×D4—202no—
483C22×D4—202no—
484C23×C4—101no—
485C23×C4—101no—
486C23×C4C22×D511yescharacteristic
487C2×Q16—54no—
488C2×Q16—202no—
489C2×SD16—54no—
490C2×SD16—54no—
491C2×SD16—54no—
492C2×SD16—54no—
493C2×SD16—202no—
494C2×SD16—202no—
495C2×SD16—202no—
496C2×SD16—202no—
497C2×D8—54no—
498C2×D8—54no—
499C2×D8—54no—
500C2×D8—202no—
501C2×D8—202no—
502C2×D8—202no—
503C22×C8C22×D511yescharacteristic
504C22×C8C22×D511yescharacteristic
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—108no—
518#124—102no—
519#124—102no—
520#124—102no—
521#123—108no—
522C22⋊Q8—54no—
523C22⋊Q8—102no—
524C22⋊Q8—108no—
525#121—54no—
526#121—102no—
527#121—108no—
528#121—108no—
529#120—108no—
530#120—108no—
531C4×Q8—54no—
532C4×Q8—102no—
533C4×D4—54no—
534C4×D4—102no—
535#117D2014yes—
536#117C22×D514yes—
537C2×C4⋊C4—51no—
538C2×C4⋊C4—51no—
539C2×C4⋊C4—101no—
540C2×C4⋊C4—101no—
541C2×C4⋊C4—101no—
542C2×C4⋊C4D2011yescharacteristic
543C2×C4⋊C4D2011yescharacteristic
544C2×C22⋊C4—101no—
545C2×C22⋊C4—101no—
546C2×C22⋊C4—101no—
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⋊C4D2011yescharacteristic
554C2×C22⋊C4D2011yescharacteristic
555C2×C42—101no—
556C2×C42C22×D511yescharacteristic
557C2×C42C22×D511yescharacteristic
558C4⋊C8C22×D514yescomplemented
559C4⋊C8C22×D514yescomplemented
560#103—54no—
561#103—54no—
562#102—54no—
563#102—54no—
564#102—54no—
565#102—54no—
566#102—54no—
567#102—54no—
568C22⋊C8C22×D514yes—
569C22⋊C8C22×D514yes—
570#97C22×D514yescomplemented
571C4×C8C22×D514yescomplemented
572C22×C5—22no—
573C22×C5—22no—
574C22×C5—22no—
575C22×C5—44no—
576C22×C5#53512yes—
577C22×C5#57612yes—
578C22×C5#57712yes—
579C22×C5C23×D411yescharacteristic
580C2×D5—42no—
581C2×D5—42no—
582C2×D5—42no—
583C2×D5—42no—
584C2×D5—42no—
585C2×D5—42no—
586C2×D5—42no—
587C2×D5—42no—
588C2×D5—42no—
589C2×D5—42no—
590C2×D5—42no—
591C2×D5—42no—
592C2×D5—816no—
593C2×D5—84no—
594C2×D5—84no—
595C2×D5—84no—
596C2×D5—84no—
597C4×C5—22no—
598C4×C5—22no—
599C4×C5—22no—
600C4×C5—22no—
601C4×C5—22no—
602C4×C5#53512yes—
603C4×C5C2×H(5,𝔽2)11yescharacteristic
604C4×C5C2×H(5,𝔽2)11yescharacteristic
605Dic5—42no—
606Dic5—42no—
607Dic5—42no—
608Dic5—42no—
609C24—101no—
610C24—101no—
611C24—101no—
612C24—101no—
613C24—104no—
614C24—204no—
615C24—402no—
616C24—402no—
617C24C2×D2011yescharacteristic
618#41—204no—
619#41—204no—
620#41—208no—
621C2×Q8—52no—
622C2×Q8—52no—
623C2×Q8—101no—
624C2×Q8—101no—
625C2×Q8—104no—
626C2×Q8—102no—
627C2×Q8—102no—
628C2×Q8—102no—
629C2×Q8—102no—
630C2×Q8—402no—
631C2×D4—52no—
632C2×D4—52no—
633C2×D4—52no—
634C2×D4—52no—
635C2×D4—104no—
636C2×D4—104no—
637C2×D4—101no—
638C2×D4—104no—
639C2×D4—101no—
640C2×D4—101no—
641C2×D4—101no—
642C2×D4—104no—
643C2×D4—104no—
644C2×D4—104no—
645C2×D4—104no—
646C2×D4—102no—
647C2×D4—102no—
648C2×D4—102no—
649C2×D4—102no—
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—204no—
659C2×D4—402no—
660C2×D4—402no—
661C2×D4—402no—
662C2×D4—402no—
663C2×D4—402no—
664C22×C4—22no—
665C22×C4—22no—
666C22×C4—101no—
667C22×C4—101no—
668C22×C4—101no—
669C22×C4—101no—
670C22×C4—104no—
671C22×C4—104no—
672C22×C4—204no—
673C22×C4—402no—
674C22×C4C2×D2012yes—
675C22×C4C2×D2011yescharacteristic
676C22×C4C2×D2011yescharacteristic
677C22×C4C2×D2011yescharacteristic
678C22×C4C2×D2011yescharacteristic
679C22×C4C2×D2011yescharacteristic
680C22×C4C23×D512yes—
681C22×C4C23×D511yescharacteristic
682Q16—204no—
683SD16—204no—
684SD16—204no—
685SD16—204no—
686SD16—204no—
687D8—204no—
688D8—204no—
689D8—204no—
690C2×C8—22no—
691C2×C8—22no—
692C2×C8—22no—
693C2×C8—22no—
694C2×C8C23×D512yes—
695C2×C8C23×D512yes—
696C2×C8C23×D512yes—
697C2×C8C23×D512yes—
698C4⋊C4—52no—
699C4⋊C4—52no—
700C4⋊C4—101no—
701C4⋊C4—101no—
702C4⋊C4—104no—
703C4⋊C4—104no—
704C4⋊C4—104no—
705C4⋊C4C2×D2014yes—
706C4⋊C4C2×D2014yes—
707C22⋊C4—104no—
708C22⋊C4—104no—
709C22⋊C4—104no—
710C22⋊C4—104no—
711C22⋊C4—104no—
712C22⋊C4—104no—
713C22⋊C4—104no—
714C22⋊C4—104no—
715C22⋊C4—104no—
716C22⋊C4C2×D2014yes—
717C22⋊C4C2×D2014yes—
718C42—104no—
719C42C2×D2012yes—
720C42C2×D2012yes—
721C42C23×D512yes—
722C42C23×D512yes—
723C2×C5—42no—
724C2×C5#322414yescomplemented
725C2×C5C2×#53511yescharacteristic
726C2×C5C2×#57611yescharacteristic
727C2×C5C2×#57711yescharacteristic
728D5—82no—
729D5—82no—
730D5—82no—
731D5—82no—
732C23—22no—
733C23—22no—
734C23—22no—
735C23—102no—
736C23—102no—
737C23—102no—
738C23—102no—
739C23—208no—
740C23—202no—
741C23—202no—
742C23—202no—
743C23—202no—
744C23—202no—
745C23—202no—
746C23—202no—
747C23—202no—
748C23—202no—
749C23—202no—
750C23—202no—
751C23—202no—
752C23—404no—
753C23—404no—
754C23—4016no—
755C23C22×D2012yes—
756C23C22×D2011yescharacteristic
757Q8—102no—
758Q8—102no—
759Q8—102no—
760Q8—102no—
761Q8—202no—
762Q8—202no—
763Q8—404no—
764D4—102no—
765D4—102no—
766D4—102no—
767D4—102no—
768D4—102no—
769D4—102no—
770D4—102no—
771D4—102no—
772D4—208no—
773D4—208no—
774D4—202no—
775D4—202no—
776D4—202no—
777D4—202no—
778D4—404no—
779D4—404no—
780D4—404no—
781D4—404no—
782D4—404no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—24no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—102no—
792C2×C4—102no—
793C2×C4—102no—
794C2×C4—102no—
795C2×C4—208no—
796C2×C4—202no—
797C2×C4—202no—
798C2×C4—202no—
799C2×C4—202no—
800C2×C4—404no—
801C2×C4C22×D2012yes—
802C2×C4C22×D2012yes—
803C2×C4C22×D2012yes—
804C2×C4C22×D2012yes—
805C2×C4C22×D2012yes—
806C2×C4C22×D2011yescharacteristic
807C2×C4#414912yes—
808C2×C4#414912yes—
809C2×C4C24×D511yescharacteristic
810C8—22no—
811C8—22no—
812C8—22no—
813C8—22no—
814C5C2×#322411yescharacteristic, complemented, Sylow
815C22—22no—
816C22—22no—
817C22—22no—
818C22—44no—
819C22—202no—
820C22—202no—
821C22—202no—
822C22—202no—
823C22—202no—
824C22—202no—
825C22—202no—
826C22—202no—
827C22—202no—
828C22—202no—
829C22—202no—
830C22—202no—
831C22—4016no—
832C22—404no—
833C22—404no—
834C22—404no—
835C22—404no—
836C22#6585912yes—
837C22#6608512yes—
838C22#6608612yes—
839C22C23×D2011yescharacteristic
840C4—22no—
841C4—22no—
842C4—22no—
843C4—22no—
844C4—22no—
845C4—202no—
846C4—202no—
847C4—202no—
848C4—202no—
849C4#6585912yes—
850C4C2×#414911yescharacteristic
851C4C2×#414911yescharacteristic
852C2—42no—
853C2—402no—
854C2—402no—
855C2—402no—
856C2—402no—
857C2#1061112314yesdirect product factor
858C2C2×#6585911yescharacteristic
859C2C2×#6608611yescharacteristic
860C2C2×#6608511yescharacteristic
subgroupG/H
centerC23C22×D20
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×#433C2
socleC23×C5C22×D4
hypercenterC2×#433D5
hypocenterC5C2×#3224
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#433

Complements

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

NH ≅ G/Ntype
1. C2×#65868C2semidirect
2. C2×#65859C2semidirect
3. C2×C5×#433C2semidirect
4. #10611123C2direct (N × H)
5. C2×#65134C2semidirect
6. C2×#65137C2semidirect
7. C2×#65133C2semidirect
8. C2×#65132C2semidirect
9. C2×#65022C2semidirect
10. C2×#65023C2semidirect
11. C2×#65020C2semidirect
12. C2×#65021C2semidirect
13. C2×#65001C2semidirect
14. C2×#65003C2semidirect
15. C2×#64985C2semidirect
16. C2×#64983C2semidirect
22. C22×Dic20C22semidirect
25. C22×D40C22semidirect
28. C22×#677C22semidirect
29. C22×#677C22semidirect
31. #65868C22semidirect
33. #65859C22semidirect
44. C2×#4021C22semidirect
47. C2×C4×D20C22semidirect
48. C2×#4015C22semidirect
49. C2×C4×Dic10C22semidirect
50. C5×#433C22semidirect
51. C2×C5×C4⋊C8C22semidirect
52. C2×C5×C4⋊C8C22semidirect
55. C2×C5×#97C22semidirect
56. C2×C4×C5×C8C22semidirect
61. C2×#3953C22semidirect
62. C2×#3953C22semidirect
63. C2×#3948C22semidirect
64. C2×#3948C22semidirect
65. #65137C22semidirect
66. #65134C22semidirect
67. #65133C22semidirect
68. #65132C22semidirect
69. #65023C22semidirect
70. #65022C22semidirect
71. #65021C22semidirect
72. #65020C22semidirect
73. #65003C22semidirect
74. #65001C22semidirect
75. #64985C22semidirect
76. #64983C22semidirect
136. C2×Dic20C23semidirect
142. C2×D40C23semidirect
149. C2×#677C23semidirect
150. C2×#677C23semidirect
164. #4021C23semidirect
170. C4×D20C23semidirect
172. #4015C23semidirect
174. C4×Dic10C23semidirect
175. C5×C4⋊C8C23semidirect
176. C5×C4⋊C8C23semidirect
179. C5×#97C23semidirect
180. C4×C5×C8C23semidirect
185. #3953C23semidirect
186. #3953C23semidirect
187. #3948C23semidirect
188. #3948C23semidirect
204. C2×#433D5semidirect
364. #433C2×D5semidirect
365. C2×C4⋊C8C2×D5semidirect
366. C2×C4⋊C8C2×D5semidirect
377. C2×#97C2×D5semidirect
378. C2×C4×C8C2×D5semidirect
558. C4⋊C8C22×D5semidirect
559. C4⋊C8C22×D5semidirect
570. #97C22×D5semidirect
571. C4×C8C22×D5semidirect
724. C2×C5#3224semidirect
814. C5C2×#3224semidirect
857. C2#10611123direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#658682
C2×#658592
C2×C5×#4332
#106111232
C2×#651342
C2×#651372
C2×#651332
C2×#651322
C2×#650222
C2×#650232
C2×#650202
C2×#650212
C2×#650012
C2×#650032
C2×#649852
C2×#649832
C2×#32245