Finite Group Databasebeta

← C2×#10611584 #12978988

Subgroups — C2×#10611584 #12978988

Order 1280.

2134 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65893C211yesmaximal, characteristic, complemented
2C2×D4×Dic10C211yesmaximal, characteristic, complemented
3C2×C5×#442C211yesmaximal, characteristic, complemented
4C2×#65442C211yesmaximal, characteristic, complemented
5C2×#65439C211yesmaximal, characteristic
6C2×#65305C211yesmaximal, characteristic, complemented
7C2×#65297C211yesmaximal, characteristic, complemented
8#10611584C2116yesmaximal, direct product factor
9C2×#65143C211yesmaximal, characteristic, complemented
10C2×#65159C211yesmaximal, characteristic, complemented
11C2×#65054C211yesmaximal, characteristic, complemented
12C2×#65049C211yesmaximal, characteristic, complemented
13C2×#65074C211yesmaximal, characteristic, complemented
14C2×#65047C211yesmaximal, characteristic, complemented
15C2×#65003C211yesmaximal, characteristic, complemented
16C2×#64990C211yesmaximal, characteristic, complemented
17C23×Dic10—21no—
18C22×C5×D8C2211yescharacteristic
19C2×C4×C5×D4C2211yescharacteristic
20C2×C4×C5×D4C2211yescharacteristic
21C2×#4086C2211yescharacteristic
22C2×#4082C2211yescharacteristic
23C2×D4×Dic5C2211yescharacteristic
24C2×D4×Dic5C2211yescharacteristic
25C22×#687C2211yescharacteristic
26C22×#686C2211yescharacteristic
27C2×#4075—21no—
28C2×C4×C22⋊D5—21no—
29C2×#4070—21no—
30#65893—24no—
31#65893C2218yescomplemented
32D4×Dic10—24no—
33D4×Dic10C2218yescomplemented
34C2×#4039C2211yescharacteristic
35C2×#4034C2211yescharacteristic
36C2×#4034C2211yescharacteristic
37C2×#4033C2211yescharacteristic
38C2×#4031—21no—
39C2×#4029—21no—
40C2×#4024—21no—
41C2×#4024—21no—
42C2×#4021C2211yescharacteristic
43C2×#4015C2211yescharacteristic
44C2×C4×Dic10C2211yescharacteristic
45C5×#442C2218yescomplemented
46C2×C5×#106C2211yescharacteristic
47C2×C5×#102C2211yescharacteristic
48C2×C5×#102C2211yescharacteristic
49C2×C5×#97C2211yescharacteristic
50C2×#3964C2211yescharacteristic
51C2×#3964C2211yescharacteristic
52#65442C2218yescomplemented
53#65439C2218yes—
54C2×#3953C2211yescharacteristic
55C2×#3953C2211yescharacteristic
56C2×#3948C2211yescharacteristic
57C2×#3948C2211yescharacteristic
58C2×#3947C2211yescharacteristic
59C2×#3946C2211yescharacteristic
60C2×#3946C2211yescharacteristic
61C2×C8×Dic5C2211yescharacteristic
62#65305C2218yescomplemented
63#65297C2218yescomplemented
64C2×#3942C2211yescharacteristic
65C2×#3941C2211yescharacteristic
66C2×#3940C2211yescharacteristic
67C2×#3940C2211yescharacteristic
68C2×C4⋊#168C2211yescharacteristic
69#65159C2218yescomplemented
70#65143C2218yescomplemented
71#65074C2218yescomplemented
72#65054C2218yescomplemented
73#65049C2218yescomplemented
74#65047C2218yescomplemented
75#65003C2218yescomplemented
76#64990C2218yescomplemented
77C2×#3373—51nomaximal, Sylow
78C22×C5×D4C2311yescharacteristic
79C22×C5×D4C2311yescharacteristic
80C23×C4×C5—21no—
81C23×C4×C5—21no—
82C22×C22⋊D5—21no—
83C22×C22⋊D5—21no—
84C23×Dic5—21no—
85C23×Dic5—21no—
86C22×D20C2311yescharacteristic
87C22×C4×D5—21no—
88C22×Dic10—21no—
89C22×Dic10—21no—
90C22×Dic10—21no—
91C22×Dic10—28no—
92C22×Dic10—48no—
93C22×Dic10D411yescharacteristic
94C22×Dic10C2311yescharacteristic
95C2×C5×D8—24no—
96C2×C5×D8C2314yes—
97C22×C5×C8C2311yescharacteristic
98C22×C5×C8C2311yescharacteristic
99C4×C5×D4—22no—
100C4×C5×D4—22no—
101C4×C5×D4C2314yes—
102C4×C5×D4C2314yes—
103C2×C5×C4⋊C4C2311yescharacteristic
104C2×C5×C4⋊C4C2311yescharacteristic
105C2×C5×C22⋊C4—21no—
106C2×C5×C22⋊C4—21no—
107C2×C42×C5C2311yescharacteristic
108C2×C22⋊Dic5—21no—
109C2×C22⋊Dic5—21no—
110C2×C22⋊Dic5—21no—
111C2×C22⋊Dic5—21no—
112#4086—22no—
113#4086C2314yes—
114#4082—22no—
115#4082C2314yes—
116D4×Dic5—22no—
117D4×Dic5—22no—
118D4×Dic5C2314yes—
119D4×Dic5C2314yes—
120C2×#687—24no—
121C2×#687C2314yes—
122C2×#686—24no—
123C2×#686C2314yes—
124#4075—28no—
125C4×C22⋊D5—28no—
126C2×#685—21no—
127C2×#685—21no—
128C2×#685—21no—
129C2×C4⋊Dic5—21no—
130C2×C4⋊Dic5D411yescharacteristic
131C2×C4⋊Dic5C2311yescharacteristic
132C2×C4⋊Dic5C2311yescharacteristic
133#4070—28no—
134C2×#683—21no—
135C2×#683—21no—
136C2×#683—21no—
137C2×#683D411yescharacteristic
138C2×#683D411yescharacteristic
139C2×C4×Dic5—21no—
140C2×C4×Dic5C2311yescharacteristic
141C2×C4×Dic5C2311yescharacteristic
142C22×#168C2311yescharacteristic
143C22×#168C2311yescharacteristic
144#4039—22no—
145#4039C2314yes—
146#4034—22no—
147#4034—22no—
148#4034C2314yes—
149#4034C2314yes—
150#4033—22no—
151#4033C2314yes—
152#4031—28no—
153#4029—28no—
154#4024—28no—
155#4024—28no—
156#4021—22no—
157#4021C2314yes—
158#4015—22no—
159#4015C2314yes—
160C4×Dic10D414yes—
161C4×Dic10C2314yes—
162C5×#106C2314yes—
163C5×#102C2314yes—
164C5×#102C2314yes—
165C5×#97C2314yes—
166#3964C2314yes—
167#3964C2314yes—
168#3953C2314yes—
169#3953C2314yes—
170#3948C2314yes—
171#3948C2314yes—
172#3947C2314yes—
173#3946C2314yes—
174#3946C2314yes—
175C8×Dic5C2314yes—
176#3942C2314yes—
177#3941C2314yes—
178#3940C2314yes—
179#3940C2314yes—
180C4⋊#168C2314yes—
181C2×#559—51no—
182C2×D4×Q8—51no—
183#3373—516no—
184C2×#489—51no—
185C2×#489—51no—
186C2×#486—51no—
187C2×#475—51no—
188C2×#476—51no—
189C2×#476—51no—
190C2×#463—51no—
191C2×#463—51no—
192C2×#459—51no—
193C2×#446—51no—
194C2×#442—51no—
195C2×#442D511yescharacteristic, complemented
196C2×C4×SD16—51no—
197C24×C5—21no—
198C24×C5—21no—
199C23×D5—21no—
200C2×C5×D4—21no—
201C2×C5×D4—21no—
202C2×C5×D4—22no—
203C2×C5×D4—22no—
204C2×C5×D4—22no—
205C2×C5×D4#4114yes—
206C2×C5×D4C2412yes—
207C2×C5×D4C2412yes—
208C22×C4×C5—21no—
209C22×C4×C5—21no—
210C22×C4×C5—24no—
211C22×C4×C5—24no—
212C22×C4×C5—44no—
213C22×C4×C5—82no—
214C22×C4×C5C2×D411yescharacteristic
215C22×C4×C5C2×D411yescharacteristic
216C22×C4×C5C2411yescharacteristic
217C2×C22⋊D5—24no—
218C2×C22⋊D5—24no—
219C2×C22⋊D5—44no—
220C2×C22⋊D5—82no—
221C22×Dic5—21no—
222C22×Dic5—21no—
223C22×Dic5—21no—
224C22×Dic5—24no—
225C22×Dic5—24no—
226C22×Dic5—44no—
227C22×Dic5—44no—
228C22×Dic5C2×D411yescharacteristic
229C22×Dic5C2×D411yescharacteristic
230C22×Dic5C2×D411yescharacteristic
231C22×Dic5C2×D411yescharacteristic
232C2×D20—22no—
233C2×D20—22no—
234C2×D20—21no—
235C2×D20C2412yes—
236C2×C4×D5—24no—
237C2×C4×D5—82no—
238C2×Dic10—24no—
239C2×Dic10—22no—
240C2×Dic10—22no—
241C2×Dic10—24no—
242C2×Dic10—21no—
243C2×Dic10—24no—
244C2×Dic10—24no—
245C2×Dic10—432no—
246C2×Dic10—44no—
247C2×Dic10—44no—
248C2×Dic10—44no—
249C2×Dic10C2×D414yes—
250C2×Dic10C2412yes—
251C5×D8—28no—
252C2×C5×C8—22no—
253C2×C5×C8—22no—
254C2×C5×C8C2412yes—
255C2×C5×C8C2412yes—
256C5×C4⋊C4—21no—
257C5×C4⋊C4—21no—
258C5×C4⋊C4C2412yes—
259C5×C4⋊C4C2412yes—
260C5×C22⋊C4—24no—
261C5×C22⋊C4—24no—
262C42×C5C2×D412yes—
263C42×C5C2412yes—
264C22⋊Dic5—24no—
265C22⋊Dic5—24no—
266C22⋊Dic5—24no—
267C22⋊Dic5—24no—
268#687—28no—
269#686—28no—
270#685—24no—
271#685—24no—
272#685—24no—
273C4⋊Dic5—21no—
274C4⋊Dic5—21no—
275C4⋊Dic5—24no—
276C4⋊Dic5C2×D414yes—
277C4⋊Dic5C2412yes—
278C4⋊Dic5C2412yes—
279#683—24no—
280#683—24no—
281#683—24no—
282#683C2×D414yes—
283#683C2×D414yes—
284C4×Dic5—24no—
285C4×Dic5C2×D412yes—
286C4×Dic5C2×D412yes—
287C4×Dic5C2412yes—
288C4×Dic5C2412yes—
289C2×#168—22no—
290C2×#168—22no—
291C2×#168C2412yes—
292C2×#168C2412yes—
293C23×Q8—101no—
294C22×SD16—51no—
295C22×D8—51no—
296C22×D8C2×D511yescharacteristic
297#559—58no—
298#559—104no—
299D4×Q8—58no—
300D4×Q8—104no—
301C2×C4⋊Q8—51no—
302C2×C4⋊Q8—51no—
303C2×C4⋊Q8—51no—
304C2×#127—51no—
305C2×#124—51no—
306C2×#124—51no—
307C2×#124—101no—
308C2×#123—101no—
309C2×#123—101no—
310C2×C22⋊Q8—101no—
311C2×C22⋊Q8—101no—
312C2×C22⋊Q8—101no—
313C2×C4×Q8—51no—
314C2×C4×Q8—51no—
315C2×C4×D4—51no—
316C2×C4×D4—51no—
317C2×C4×D4—51no—
318C2×C4×D4—101no—
319C2×C4×D4C2×D511yescharacteristic
320C2×C4×D4C2×D511yescharacteristic
321#489—58no—
322#489—58no—
323#486—58no—
324#476—58no—
325#476—58no—
326#475—58no—
327#463—58no—
328#463—58no—
329#459—58no—
330#446—58no—
331#442—58no—
332#442C2×D518yescomplemented
333C4×SD16—58no—
334C2×#106—51no—
335C2×#106—51no—
336C2×#106C2×D511yescharacteristic
337C2×C4⋊C8—51no—
338C2×C4⋊C8—51no—
339C2×C4⋊C8—51no—
340C2×#103—51no—
341C2×#103—51no—
342C2×#103—51no—
343C2×#102—51no—
344C2×#102—51no—
345C2×#102—51no—
346C2×#102—51no—
347C2×#102—51no—
348C2×#102C2×D511yescharacteristic
349C2×#102C2×D511yescharacteristic
350C2×#97—51no—
351C2×#97C2×D511yescharacteristic
352C2×C4×C8—51no—
353C23×C5—24no—
354C23×C5—22no—
355C23×C5—22no—
356C23×C5—42no—
357C23×C5—42no—
358C23×C5—42no—
359C23×C5—42no—
360C23×C5—42no—
361C23×C5C22×D411yescharacteristic
362C22×D5—22no—
363C22×D5—42no—
364C22×D5—42no—
365C22×D5—42no—
366C5×D4—24no—
367C5×D4—22no—
368C5×D4—22no—
369C5×D4—22no—
370C5×D4—42no—
371C5×D4C2×#4114yes—
372C2×C4×C5—22no—
373C2×C4×C5—22no—
374C2×C4×C5—22no—
375C2×C4×C5—22no—
376C2×C4×C5—48no—
377C2×C4×C5—42no—
378C2×C4×C5—42no—
379C2×C4×C5—84no—
380C2×C4×C5C22×D412yes—
381C2×C4×C5C22×D412yes—
382C2×C4×C5C22×D411yescharacteristic
383C2×C4×C5C2×#4112yes—
384C2×C4×C52−1+412yes—
385C2×C4×C5C2511yescharacteristic
386C22⋊D5—48no—
387C22⋊D5—84no—
388C2×Dic5—22no—
389C2×Dic5—22no—
390C2×Dic5—22no—
391C2×Dic5—22no—
392C2×Dic5—22no—
393C2×Dic5—22no—
394C2×Dic5—48no—
395C2×Dic5—42no—
396C2×Dic5—42no—
397C2×Dic5—42no—
398C2×Dic5—48no—
399C2×Dic5AGL(1,ℤ/8)14yes—
400C2×Dic5C22×D412yes—
401C2×Dic5C22×D412yes—
402C2×Dic5C22×D412yes—
403C2×Dic5C22×D412yes—
404D20—22no—
405D20—22no—
406D20—42no—
407C4×D5—84no—
408Dic10—28no—
409Dic10—22no—
410Dic10—22no—
411Dic10—48no—
412Dic10—48no—
413Dic10—42no—
414Dic10—48no—
415C5×C8—22no—
416C5×C8—22no—
417#168—22no—
418#168—22no—
419C22×Q8—51no—
420C22×Q8—51no—
421C22×Q8—101no—
422C22×Q8—101no—
423C22×Q8—108no—
424C22×Q8—101no—
425C22×Q8—208no—
426C22×D4—51no—
427C22×D4—101no—
428C22×D4—101no—
429C22×D4C22×D511yescharacteristic
430C22×D4C22×D511yescharacteristic
431C23×C4—21no—
432C23×C4—21no—
433C23×C4—101no—
434C23×C4—101no—
435C23×C4—101no—
436C2×SD16—54no—
437C2×SD16—104no—
438C2×D8—24no—
439C2×D8—54no—
440C2×D8—104no—
441C2×D8C22×D514yes—
442C22×C8—51no—
443C22×C8—51no—
444C22×C8C22×D511yescharacteristic
445C22×C8C22×D511yescharacteristic
446C4⋊Q8—54no—
447C4⋊Q8—54no—
448C4⋊Q8—54no—
449C4⋊Q8—102no—
450C4⋊Q8—102no—
451C4⋊Q8—102no—
452#127—54no—
453#127—102no—
454#124—54no—
455#124—54no—
456#124—102no—
457#124—108no—
458#124—102no—
459#123—108no—
460#123—108no—
461C22⋊Q8—108no—
462C22⋊Q8—108no—
463C22⋊Q8—108no—
464C4×Q8—54no—
465C4×Q8—54no—
466C4×Q8—54no—
467C4×Q8—102no—
468C4×D4—22no—
469C4×D4—22no—
470C4×D4—54no—
471C4×D4—54no—
472C4×D4—54no—
473C4×D4—102no—
474C4×D4—102no—
475C4×D4—102no—
476C4×D4—108no—
477C4×D4C22×D514yes—
478C4×D4C22×D514yes—
479C2×C4⋊C4—51no—
480C2×C4⋊C4—51no—
481C2×C4⋊C4—51no—
482C2×C4⋊C4—51no—
483C2×C4⋊C4—51no—
484C2×C4⋊C4—101no—
485C2×C4⋊C4—101no—
486C2×C4⋊C4—101no—
487C2×C4⋊C4—101no—
488C2×C4⋊C4C22×D511yescharacteristic
489C2×C4⋊C4C22×D511yescharacteristic
490C2×C22⋊C4—21no—
491C2×C22⋊C4—21no—
492C2×C22⋊C4—101no—
493C2×C22⋊C4—101no—
494C2×C22⋊C4—101no—
495C2×C22⋊C4—101no—
496C2×C22⋊C4—101no—
497C2×C22⋊C4—101no—
498C2×C22⋊C4—101no—
499C2×C42—51no—
500C2×C42—51no—
501C2×C42—101no—
502C2×C42C22×D511yescharacteristic
503#106—54no—
504#106—54no—
505#106C22×D514yes—
506C4⋊C8—54no—
507C4⋊C8—54no—
508C4⋊C8—54no—
509#103—54no—
510#103—54no—
511#103—54no—
512#102—54no—
513#102—54no—
514#102—54no—
515#102—54no—
516#102—54no—
517#102C22×D514yes—
518#102C22×D514yes—
519#97—54no—
520#97C22×D514yes—
521C4×C8—54no—
522C22×C5—24no—
523C22×C5—48no—
524C22×C5—42no—
525C22×C5—42no—
526C22×C5—42no—
527C22×C5—42no—
528C22×C5—42no—
529C22×C5—84no—
530C22×C5#54812yes—
531C22×C5C2×AGL(1,ℤ/8)12yes—
532C22×C5#57712yes—
533C22×C5C23×D411yescharacteristic
534C2×D5—42no—
535C2×D5—42no—
536C2×D5—42no—
537C2×D5—84no—
538C4×C5—22no—
539C4×C5—22no—
540C4×C5—42no—
541C4×C5—42no—
542C4×C5#54812yes—
543C4×C5C22×#4111yescharacteristic
544C4×C5C2×2−1+411yescharacteristic
545Dic5—22no—
546Dic5—22no—
547Dic5—22no—
548Dic5—42no—
549Dic5—42no—
550Dic5—42no—
551Dic5C2×AGL(1,ℤ/8)14yes—
552C24—21no—
553C24—21no—
554C24—101no—
555C2×Q8—54no—
556C2×Q8—52no—
557C2×Q8—104no—
558C2×Q8—104no—
559C2×Q8—104no—
560C2×Q8—101no—
561C2×Q8—104no—
562C2×Q8—102no—
563C2×Q8—102no—
564C2×Q8—204no—
565C2×Q8—204no—
566C2×Q8—204no—
567C2×Q8—2032no—
568C2×D4—22no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—22no—
572C2×D4—22no—
573C2×D4—52no—
574C2×D4—104no—
575C2×D4—104no—
576C2×D4—102no—
577C2×D4—101no—
578C2×D4—102no—
579C2×D4—204no—
580C2×D4—402no—
581C2×D4#70914yes—
582C2×D4C23×D512yes—
583C2×D4C23×D512yes—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—24no—
587C22×C4—24no—
588C22×C4—44no—
589C22×C4—51no—
590C22×C4—51no—
591C22×C4—51no—
592C22×C4—51no—
593C22×C4—82no—
594C22×C4—104no—
595C22×C4—104no—
596C22×C4—104no—
597C22×C4—101no—
598C22×C4—101no—
599C22×C4—101no—
600C22×C4—204no—
601C22×C4—204no—
602C22×C4—402no—
603C22×C4D4×D511yescharacteristic
604C22×C4D4×D511yescharacteristic
605C22×C4C23×D511yescharacteristic
606SD16—108no—
607D8—28no—
608D8—108no—
609C2×C8—22no—
610C2×C8—22no—
611C2×C8—52no—
612C2×C8—52no—
613C2×C8—102no—
614C2×C8—102no—
615C2×C8C23×D512yes—
616C2×C8C23×D512yes—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—54no—
620C4⋊C4—54no—
621C4⋊C4—54no—
622C4⋊C4—52no—
623C4⋊C4—52no—
624C4⋊C4—104no—
625C4⋊C4—104no—
626C4⋊C4—104no—
627C4⋊C4—101no—
628C4⋊C4—101no—
629C4⋊C4—104no—
630C4⋊C4C23×D512yes—
631C4⋊C4C23×D512yes—
632C22⋊C4—24no—
633C22⋊C4—24no—
634C22⋊C4—104no—
635C22⋊C4—104no—
636C22⋊C4—104no—
637C22⋊C4—104no—
638C22⋊C4—104no—
639C22⋊C4—104no—
640C22⋊C4—104no—
641C42—52no—
642C42—52no—
643C42—52no—
644C42—52no—
645C42—104no—
646C42D4×D512yes—
647C42C23×D512yes—
648C2×C5—44no—
649C2×C5—82no—
650C2×C5#337314yescomplemented
651C2×C5C2×#54811yescharacteristic
652C2×C5C22×AGL(1,ℤ/8)11yescharacteristic
653C2×C5C2×#57711yescharacteristic
654D5—82no—
655C23—24no—
656C23—22no—
657C23—22no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—102no—
664C23—202no—
665C23—202no—
666C23—202no—
667C23C2×D4×D511yescharacteristic
668Q8—108no—
669Q8—102no—
670Q8—102no—
671Q8—208no—
672Q8—208no—
673Q8—208no—
674Q8—202no—
675D4—24no—
676D4—22no—
677D4—22no—
678D4—22no—
679D4—42no—
680D4—102no—
681D4—102no—
682D4—208no—
683D4—202no—
684D4—404no—
685D4C2×#70914yes—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—48no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—54no—
694C2×C4—52no—
695C2×C4—52no—
696C2×C4—52no—
697C2×C4—52no—
698C2×C4—84no—
699C2×C4—102no—
700C2×C4—102no—
701C2×C4—102no—
702C2×C4—102no—
703C2×C4—102no—
704C2×C4—102no—
705C2×C4—208no—
706C2×C4—208no—
707C2×C4—202no—
708C2×C4—202no—
709C2×C4—202no—
710C2×C4—404no—
711C2×C4C2×#70912yes—
712C2×C4C2×D4×D512yes—
713C2×C4C2×D4×D512yes—
714C2×C4C2×D4×D511yescharacteristic
715C2×C4#415012yes—
716C2×C4C24×D511yescharacteristic
717C8—22no—
718C8—22no—
719C8—102no—
720C8—102no—
721C5C2×#337311yescharacteristic, complemented, Sylow
722C22—24no—
723C22—48no—
724C22—42no—
725C22—42no—
726C22—42no—
727C22—42no—
728C22—42no—
729C22—84no—
730C22—202no—
731C22—202no—
732C22—202no—
733C22—404no—
734C22#6588612yes—
735C22D5×AGL(1,ℤ/8)12yes—
736C22#6610912yes—
737C22C22×D4×D511yescharacteristic
738C4—22no—
739C4—22no—
740C4—42no—
741C4—42no—
742C4—54no—
743C4—102no—
744C4—102no—
745C4—102no—
746C4—202no—
747C4—202no—
748C4—202no—
749C4#6588612yes—
750C4C22×#70911yescharacteristic
751C4C2×#415011yescharacteristic
752C2—44no—
753C2—82no—
754C2—402no—
755C2#1061158414yesdirect product factor
756C2C2×#6588611yescharacteristic
757C2C2×D5×AGL(1,ℤ/8)11yescharacteristic
758C2C2×#6610911yescharacteristic
subgroupG/H
centerC23C2×D4×D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×#442C2
socleC23×C5C22×D4
prime radicalC2×#65439C2
hypercenterC2×#442D5
hypocenterC5C2×#3373
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#442

Complements

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

NH ≅ G/Ntype
1. C2×#65893C2semidirect
2. C2×D4×Dic10C2semidirect
3. C2×C5×#442C2semidirect
4. C2×#65442C2semidirect
6. C2×#65305C2semidirect
7. C2×#65297C2semidirect
8. #10611584C2direct (N × H)
9. C2×#65143C2semidirect
10. C2×#65159C2semidirect
11. C2×#65054C2semidirect
12. C2×#65049C2semidirect
13. C2×#65074C2semidirect
14. C2×#65047C2semidirect
15. C2×#65003C2semidirect
16. C2×#64990C2semidirect
31. #65893C22semidirect
33. D4×Dic10C22semidirect
45. C5×#442C22semidirect
52. #65442C22semidirect
62. #65305C22semidirect
63. #65297C22semidirect
69. #65159C22semidirect
70. #65143C22semidirect
71. #65074C22semidirect
72. #65054C22semidirect
73. #65049C22semidirect
74. #65047C22semidirect
75. #65003C22semidirect
76. #64990C22semidirect
195. C2×#442D5semidirect
332. #442C2×D5semidirect
650. C2×C5#3373semidirect
721. C5C2×#3373semidirect
755. C2#10611584direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#658932
C2×D4×Dic102
C2×C5×#4422
C2×#654422
C2×#654392
C2×#653052
C2×#652972
#106115842
C2×#651432
C2×#651592
C2×#650542
C2×#650492
C2×#650742
C2×#650472
C2×#650032
C2×#649902
C2×#33735