Finite Group Databasebeta

← C2×#10611947 #12967556

Subgroups — C2×#10611947 #12967556

Order 1280.

2070 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#66161C211yesmaximal, characteristic
2C2×#65959C211yesmaximal, characteristic, complemented
3C2×C5×#452C211yesmaximal, characteristic
4C2×#65528C211yesmaximal, characteristic
5C2×#65471C211yesmaximal, characteristic, complemented
6C2×#65473C211yesmaximal, characteristic, complemented
7C2×#65451C211yesmaximal, characteristic, complemented
8C2×SD16×Dic5C211yesmaximal, characteristic, complemented
9C2×#65333C211yesmaximal, characteristic, complemented
10#10611947C2116yesmaximal, direct product factor
11C2×#65088C211yesmaximal, characteristic, complemented
12C2×#65079C211yesmaximal, characteristic, complemented
13C2×#65052C211yesmaximal, characteristic, complemented
14C2×#65046C211yesmaximal, characteristic, complemented
15C2×#65010C211yesmaximal, characteristic, complemented
16C2×#65009C211yesmaximal, characteristic, complemented
17C22×C5×#41C2211yescharacteristic
18C22×C5×Q16C2211yescharacteristic
19C22×C5×SD16C2211yescharacteristic
20C2×C5×C22⋊Q8C2211yescharacteristic
21#66161—24no—
22#66161C2218yes—
23C2×Q8×Dic5C2211yescharacteristic
24C2×Q8×Dic5C2211yescharacteristic
25C2×Q8×Dic5C2211yescharacteristic
26C2×#4090C2211yescharacteristic
27C22×#689C2211yescharacteristic
28C2×D4×Dic5—21no—
29C2×D4×Dic5—21no—
30C2×D4×Dic5C2211yescharacteristic
31C2×D4×Dic5C2211yescharacteristic
32C22×#687C2211yescharacteristic
33C2×#4072—21no—
34C2×#4072C2211yescharacteristic
35C22×C4⋊Dic5—21no—
36C22×C4⋊Dic5C2211yescharacteristic
37C2×#4070C2211yescharacteristic
38#65959—24no—
39#65959C2218yescomplemented
40C2×#4036—21no—
41C2×#4036C2211yescharacteristic
42C2×#4035—21no—
43C2×#4033C2211yescharacteristic
44C2×#4025—21no—
45C2×#4025—21no—
46C5×#452C2218yes—
47C2×C5×#103C2211yescharacteristic
48C2×C5×#102C2211yescharacteristic
49C2×C5×C22⋊C8C2211yescharacteristic
50#65528C2218yes—
51C2×#3967C2211yescharacteristic
52C2×#3967C2211yescharacteristic
53C2×#3967C2211yescharacteristic
54C2×#3964C2211yescharacteristic
55C2×C22⋊#168C2211yescharacteristic
56#65473C2218yescomplemented
57#65471C2218yescomplemented
58#65451C2218yescomplemented
59SD16×Dic5C2218yescomplemented
60C2×#3949C2211yescharacteristic
61C2×#3949C2211yescharacteristic
62C2×#3948C2211yescharacteristic
63C2×#3948C2211yescharacteristic
64C2×#3947C2211yescharacteristic
65C2×#3946C2211yescharacteristic
66C2×#3946C2211yescharacteristic
67C2×C8×Dic5C2211yescharacteristic
68#65333C2218yescomplemented
69C2×#3939C2211yescharacteristic
70C2×#3939C2211yescharacteristic
71#65088C2218yescomplemented
72#65079C2218yescomplemented
73#65052C2218yescomplemented
74#65046C2218yescomplemented
75#65010C2218yescomplemented
76#65009C2218yescomplemented
77C2×#3120—51nomaximal, Sylow
78C2×C5×#41—24no—
79C2×C5×#41—24no—
80C2×C5×#41—22no—
81C2×C5×#41C2314yes—
82C22×C5×Q8C2311yescharacteristic
83C22×C5×Q8C2311yescharacteristic
84C22×C5×D4—21no—
85C22×C5×D4C2311yescharacteristic
86C23×C4×C5—21no—
87C23×C4×C5C2311yescharacteristic
88C23×Dic5—21no—
89C23×Dic5—21no—
90C23×Dic5—21no—
91C22×Dic10C2311yescharacteristic
92C2×C5×Q16—24no—
93C2×C5×Q16C2314yes—
94C2×C5×SD16—24no—
95C2×C5×SD16C2314yes—
96C22×C5×C8C2311yescharacteristic
97C22×C5×C8C2311yescharacteristic
98C5×C22⋊Q8—22no—
99C5×C22⋊Q8C2314yes—
100C2×C5×C4⋊C4—21no—
101C2×C5×C4⋊C4C2311yescharacteristic
102C2×C5×C22⋊C4—21no—
103C2×C22⋊Dic5—21no—
104C2×C22⋊Dic5—21no—
105C2×C22⋊Dic5—21no—
106C2×C22⋊Dic5D411yescharacteristic
107C2×C22⋊Dic5D411yescharacteristic
108Q8×Dic5—22no—
109Q8×Dic5—22no—
110Q8×Dic5—22no—
111Q8×Dic5C2314yes—
112Q8×Dic5C2314yes—
113Q8×Dic5C2314yes—
114#4090—22no—
115#4090C2314yes—
116C2×#689—24no—
117C2×#689C2314yes—
118D4×Dic5—28no—
119D4×Dic5—28no—
120D4×Dic5—22no—
121D4×Dic5—22no—
122D4×Dic5C2314yes—
123D4×Dic5C2314yes—
124C2×#687—24no—
125C2×#687C2314yes—
126#4072—28no—
127#4072D414yes—
128#4072C2314yes—
129C2×C4⋊Dic5—21no—
130C2×C4⋊Dic5—22no—
131C2×C4⋊Dic5—21no—
132C2×C4⋊Dic5—21no—
133C2×C4⋊Dic5—21no—
134C2×C4⋊Dic5—21no—
135C2×C4⋊Dic5—28no—
136C2×C4⋊Dic5D411yescharacteristic
137C2×C4⋊Dic5D411yescharacteristic
138C2×C4⋊Dic5C2311yescharacteristic
139C2×C4⋊Dic5C2314yes—
140C2×C4⋊Dic5C2311yescharacteristic
141C2×C4⋊Dic5C2311yescharacteristic
142#4070—22no—
143#4070C2314yes—
144C2×#683—21no—
145C2×#683—21no—
146C2×#683—21no—
147C2×#683—21no—
148C2×#683—21no—
149C2×C4×Dic5—21no—
150C2×C4×Dic5—21no—
151C2×C4×Dic5—21no—
152C2×C4×Dic5—21no—
153C2×C4×Dic5C2311yescharacteristic
154C2×C4×Dic5C2311yescharacteristic
155C22×#168C2311yescharacteristic
156C22×#168C2311yescharacteristic
157#4036—28no—
158#4036—22no—
159#4036C2314yes—
160#4035—28no—
161#4033—22no—
162#4033C2314yes—
163#4025—28no—
164#4025—28no—
165C5×#103C2314yes—
166C5×#102C2314yes—
167C5×C22⋊C8C2314yes—
168#3967C2314yes—
169#3967C2314yes—
170#3967C2314yes—
171#3964C2314yes—
172C22⋊#168C2314yes—
173#3949C2314yes—
174#3949C2314yes—
175#3948C2314yes—
176#3948C2314yes—
177#3947C2314yes—
178#3946C2314yes—
179#3946C2314yes—
180C8×Dic5C2314yes—
181#3939C2314yes—
182#3939C2314yes—
183C2×#541—51no—
184C2×#520—51no—
185#3120—516no—
186C2×#484—51no—
187C2×#483—51no—
188C2×#479—51no—
189C2×#478—51no—
190C2×#462—51no—
191C2×#461—51no—
192C2×#452—51no—
193C2×#452D511yescharacteristic
194C2×#441—51no—
195C2×#440—51no—
196C2×C4×Q16—51no—
197C2×C4×SD16—51no—
198C2×#433—51no—
199C24×C5—21no—
200C24×C5C2×D411yescharacteristic
201C5×#41—216no—
202C5×#41—28no—
203C5×#41—28no—
204C2×C5×Q8—21no—
205C2×C5×Q8—21no—
206C2×C5×Q8—22no—
207C2×C5×Q8—22no—
208C2×C5×Q8—22no—
209C2×C5×Q8#4114yes—
210C2×C5×Q8C2412yes—
211C2×C5×Q8C2412yes—
212C2×C5×D4—28no—
213C2×C5×D4—24no—
214C2×C5×D4—21no—
215C2×C5×D4—22no—
216C2×C5×D4#4114yes—
217C2×C5×D4C2412yes—
218C22×C4×C5—28no—
219C22×C4×C5—21no—
220C22×C4×C5—24no—
221C22×C4×C5—22no—
222C22×C4×C5—22no—
223C22×C4×C5—21no—
224C22×C4×C5—21no—
225C22×C4×C5C2×D411yescharacteristic
226C22×C4×C5C2×D412yes—
227C22×C4×C5C2412yes—
228C22×C4×C5C2411yescharacteristic
229C22×Dic5—21no—
230C22×Dic5—21no—
231C22×Dic5—21no—
232C22×Dic5—21no—
233C22×Dic5—24no—
234C22×Dic5—24no—
235C22×Dic5—24no—
236C22×Dic5—82no—
237C22×Dic5—82no—
238C22×Dic5—82no—
239C22×Dic5C2×D411yescharacteristic
240C22×Dic5C2×D411yescharacteristic
241C22×Dic5C2×D411yescharacteristic
242C22×Dic5C2×D411yescharacteristic
243C2×Dic10—22no—
244C2×Dic10—22no—
245C2×Dic10—21no—
246C2×Dic10C2412yes—
247C5×Q16—28no—
248C5×SD16—28no—
249C2×C5×C8—22no—
250C2×C5×C8—22no—
251C2×C5×C8C2412yes—
252C2×C5×C8C2412yes—
253C5×C4⋊C4—24no—
254C5×C4⋊C4—21no—
255C5×C4⋊C4C2412yes—
256C5×C22⋊C4—24no—
257C22⋊Dic5—24no—
258C22⋊Dic5—24no—
259C22⋊Dic5—24no—
260C22⋊Dic5C2×D414yes—
261C22⋊Dic5C2×D414yes—
262#689—28no—
263#687—28no—
264C4⋊Dic5—21no—
265C4⋊Dic5—24no—
266C4⋊Dic5—21no—
267C4⋊Dic5—21no—
268C4⋊Dic5—24no—
269C4⋊Dic5—24no—
270C4⋊Dic5—24no—
271C4⋊Dic5—24no—
272C4⋊Dic5C2×D414yes—
273C4⋊Dic5C2×D414yes—
274C4⋊Dic5C2412yes—
275C4⋊Dic5C2412yes—
276C4⋊Dic5C2412yes—
277#683—24no—
278#683—24no—
279#683—24no—
280#683—24no—
281#683—24no—
282C4×Dic5—24no—
283C4×Dic5—24no—
284C4×Dic5—24no—
285C4×Dic5—24no—
286C4×Dic5C2×D412yes—
287C4×Dic5C2×D412yes—
288C4×Dic5C2412yes—
289C4×Dic5C2412yes—
290C2×#168—22no—
291C2×#168—22no—
292C2×#168C2412yes—
293C2×#168C2412yes—
294C22×#41C2×D511yescharacteristic
295C22×Q16—51no—
296C22×Q16C2×D511yescharacteristic
297C22×SD16—51no—
298C22×SD16C2×D511yescharacteristic
299#541—58no—
300#541—104no—
301C2×C4⋊Q8—51no—
302C2×#126—101no—
303C2×#126—101no—
304C2×#125—51no—
305C2×#125—101no—
306C2×#125—101no—
307C2×C22⋊Q8—51no—
308C2×C22⋊Q8C2×D511yescharacteristic
309#520—58no—
310#520—104no—
311C2×C4×Q8—51no—
312C2×C4×Q8—51no—
313C2×C4×Q8—51no—
314C2×C4×Q8—51no—
315C2×C4×D4—51no—
316C2×C4×D4—51no—
317C2×C4×D4—101no—
318C2×C4×D4—101no—
319C2×#117—51no—
320C2×#117—101no—
321C22×C4⋊C4—51no—
322C22×C4⋊C4—101no—
323#484—58no—
324#483—58no—
325#479—58no—
326#478—58no—
327#462—58no—
328#461—58no—
329#452—58no—
330#452C2×D518yes—
331#441—58no—
332#440—58no—
333C4×Q16—58no—
334C4×SD16—58no—
335#433—58no—
336C2×#107—51no—
337C2×#107—51no—
338C2×#106—51no—
339C2×#106—51no—
340C2×C4⋊C8—51no—
341C2×C4⋊C8—51no—
342C2×#103—51no—
343C2×#103—51no—
344C2×#103—51no—
345C2×#103—51no—
346C2×#103—51no—
347C2×#103C2×D511yescharacteristic
348C2×#102—51no—
349C2×#102C2×D511yescharacteristic
350C2×C22⋊C8—51no—
351C2×C22⋊C8C2×D511yescharacteristic
352C2×#97—51no—
353C2×C4×C8—51no—
354C23×C5—22no—
355C23×C5—24no—
356C23×C5—22no—
357C23×C5—22no—
358C23×C5—22no—
359C23×C5—42no—
360C23×C5—42no—
361C23×C5C22×D412yes—
362C23×C5C22×D411yescharacteristic
363C5×Q8—24no—
364C5×Q8—22no—
365C5×Q8—22no—
366C5×Q8—22no—
367C5×Q8—42no—
368C5×Q8C2×#4114yes—
369C5×D4—216no—
370C5×D4—24no—
371C5×D4—22no—
372C5×D4C2×#4114yes—
373C2×C4×C5—216no—
374C2×C4×C5—22no—
375C2×C4×C5—24no—
376C2×C4×C5—22no—
377C2×C4×C5—24no—
378C2×C4×C5—22no—
379C2×C4×C5—22no—
380C2×C4×C5—22no—
381C2×C4×C5—22no—
382C2×C4×C5—42no—
383C2×C4×C5—42no—
384C2×C4×C5C22×D412yes—
385C2×C4×C5C22×D411yescharacteristic
386C2×C4×C5C2×#4112yes—
387C2×C4×C5C2×#4112yes—
388C2×C4×C5C2511yescharacteristic
389C2×Dic5—22no—
390C2×Dic5—22no—
391C2×Dic5—22no—
392C2×Dic5—22no—
393C2×Dic5—22no—
394C2×Dic5—22no—
395C2×Dic5—22no—
396C2×Dic5—22no—
397C2×Dic5—42no—
398C2×Dic5—42no—
399C2×Dic5—42no—
400C2×Dic5—42no—
401C2×Dic5—84no—
402C2×Dic5—84no—
403C2×Dic5—84no—
404C2×Dic5C22×D412yes—
405C2×Dic5C22×D412yes—
406C2×Dic5C22×D412yes—
407C2×Dic5C22×D412yes—
408Dic10—22no—
409Dic10—22no—
410Dic10—42no—
411C5×C8—22no—
412C5×C8—22no—
413#168—22no—
414#168—22no—
415C2×#41—24no—
416C2×#41—24no—
417C2×#41—22no—
418C2×#41C22×D514yes—
419C22×Q8—51no—
420C22×Q8C22×D511yescharacteristic
421C22×Q8C22×D511yescharacteristic
422C22×D4—21no—
423C22×D4C22×D511yescharacteristic
424C23×C4—21no—
425C23×C4—101no—
426C23×C4—101no—
427C23×C4—101no—
428C23×C4C22×D511yescharacteristic
429C2×Q16—24no—
430C2×Q16—54no—
431C2×Q16—104no—
432C2×Q16C22×D514yes—
433C2×SD16—24no—
434C2×SD16—54no—
435C2×SD16—104no—
436C2×SD16C22×D514yes—
437C22×C8—51no—
438C22×C8—51no—
439C22×C8C22×D511yescharacteristic
440C22×C8C22×D511yescharacteristic
441C4⋊Q8—54no—
442C4⋊Q8—102no—
443#126—108no—
444#126—108no—
445#125—54no—
446#125—102no—
447#125—108no—
448#125—108no—
449C22⋊Q8—22no—
450C22⋊Q8—54no—
451C22⋊Q8—102no—
452C22⋊Q8C22×D514yes—
453C4×Q8—54no—
454C4×Q8—54no—
455C4×Q8—54no—
456C4×Q8—54no—
457C4×Q8—102no—
458C4×Q8—102no—
459C4×Q8—102no—
460C4×Q8—102no—
461C4×D4—54no—
462C4×D4—54no—
463C4×D4—102no—
464C4×D4—102no—
465C4×D4—108no—
466C4×D4—108no—
467#117—54no—
468#117—54no—
469#117—108no—
470C2×C4⋊C4—21no—
471C2×C4⋊C4—51no—
472C2×C4⋊C4—51no—
473C2×C4⋊C4—51no—
474C2×C4⋊C4—51no—
475C2×C4⋊C4—54no—
476C2×C4⋊C4—51no—
477C2×C4⋊C4—108no—
478C2×C4⋊C4—101no—
479C2×C4⋊C4—101no—
480C2×C4⋊C4—101no—
481C2×C4⋊C4—101no—
482C2×C4⋊C4—101no—
483C2×C4⋊C4—101no—
484C2×C4⋊C4—101no—
485C2×C4⋊C4—101no—
486C2×C4⋊C4—101no—
487C2×C4⋊C4—102no—
488C2×C4⋊C4—101no—
489C2×C4⋊C4C22×D511yescharacteristic
490C2×C22⋊C4—21no—
491C2×C22⋊C4—51no—
492C2×C22⋊C4—51no—
493C2×C22⋊C4—101no—
494C2×C22⋊C4—101no—
495C2×C22⋊C4—101no—
496C2×C42—51no—
497C2×C42—51no—
498C2×C42—101no—
499C2×C42—101no—
500C2×C42—101no—
501C2×C42—101no—
502#107—54no—
503#107—54no—
504#106—54no—
505#106—54no—
506C4⋊C8—54no—
507C4⋊C8—54no—
508#103—54no—
509#103—54no—
510#103—54no—
511#103—54no—
512#103—54no—
513#103C22×D514yes—
514#102—54no—
515#102C22×D514yes—
516C22⋊C8—54no—
517C22⋊C8C22×D514yes—
518#97—54no—
519C4×C8—54no—
520C22×C5—22no—
521C22×C5—24no—
522C22×C5—22no—
523C22×C5—22no—
524C22×C5—44no—
525C22×C5—48no—
526C22×C5—42no—
527C22×C5—42no—
528C22×C5#52512yes—
529C22×C5#57712yes—
530C22×C5#57812yes—
531C22×C5C23×D411yescharacteristic
532C4×C5—22no—
533C4×C5—24no—
534C4×C5—42no—
535C4×C5—42no—
536C4×C5#52512yes—
537C4×C5C22×#4111yescharacteristic
538C4×C5C22×#4111yescharacteristic
539Dic5—22no—
540Dic5—22no—
541Dic5—22no—
542Dic5—22no—
543Dic5—42no—
544Dic5—42no—
545Dic5—42no—
546Dic5—42no—
547C24—21no—
548C24D4×D511yescharacteristic
549#41—216no—
550#41—28no—
551#41—28no—
552C2×Q8—21no—
553C2×Q8—21no—
554C2×Q8—22no—
555C2×Q8—22no—
556C2×Q8—22no—
557C2×Q8—52no—
558C2×Q8—101no—
559C2×Q8—102no—
560C2×Q8—102no—
561C2×Q8#71114yes—
562C2×Q8C23×D512yes—
563C2×Q8C23×D512yes—
564C2×D4—28no—
565C2×D4—24no—
566C2×D4—21no—
567C2×D4—22no—
568C2×D4#71114yes—
569C2×D4C23×D512yes—
570C22×C4—28no—
571C22×C4—21no—
572C22×C4—24no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—51no—
578C22×C4—51no—
579C22×C4—51no—
580C22×C4—51no—
581C22×C4—104no—
582C22×C4—104no—
583C22×C4—101no—
584C22×C4—101no—
585C22×C4—101no—
586C22×C4—101no—
587C22×C4—104no—
588C22×C4—402no—
589C22×C4—402no—
590C22×C4—402no—
591C22×C4D4×D512yes—
592C22×C4D4×D511yescharacteristic
593C22×C4C23×D512yes—
594C22×C4C23×D511yescharacteristic
595Q16—28no—
596Q16—108no—
597SD16—28no—
598SD16—108no—
599C2×C8—22no—
600C2×C8—22no—
601C2×C8—52no—
602C2×C8—52no—
603C2×C8—102no—
604C2×C8—102no—
605C2×C8C23×D512yes—
606C2×C8C23×D512yes—
607C4⋊C4—24no—
608C4⋊C4—21no—
609C4⋊C4—54no—
610C4⋊C4—54no—
611C4⋊C4—52no—
612C4⋊C4—52no—
613C4⋊C4—52no—
614C4⋊C4—104no—
615C4⋊C4—104no—
616C4⋊C4—104no—
617C4⋊C4—104no—
618C4⋊C4—104no—
619C4⋊C4—104no—
620C4⋊C4—104no—
621C4⋊C4—104no—
622C4⋊C4—104no—
623C4⋊C4—101no—
624C4⋊C4—101no—
625C4⋊C4—101no—
626C4⋊C4—104no—
627C4⋊C4C23×D512yes—
628C22⋊C4—24no—
629C22⋊C4—54no—
630C22⋊C4—54no—
631C22⋊C4—104no—
632C22⋊C4—104no—
633C22⋊C4—104no—
634C42—52no—
635C42—52no—
636C42—52no—
637C42—52no—
638C42—104no—
639C42—104no—
640C42—104no—
641C42—104no—
642C2×C5—42no—
643C2×C5—44no—
644C2×C5#312014yescomplemented
645C2×C5C2×#52511yescharacteristic
646C2×C5C2×#57711yescharacteristic
647C2×C5C2×#57811yescharacteristic
648C23—22no—
649C23—22no—
650C23—22no—
651C23—24no—
652C23—22no—
653C23—42no—
654C23—42no—
655C23C2×D4×D512yes—
656C23C2×D4×D511yescharacteristic
657Q8—24no—
658Q8—22no—
659Q8—22no—
660Q8—22no—
661Q8—42no—
662Q8—102no—
663Q8—102no—
664Q8—202no—
665Q8C2×#71114yes—
666D4—216no—
667D4—24no—
668D4—22no—
669D4C2×#71114yes—
670C2×C4—216no—
671C2×C4—22no—
672C2×C4—24no—
673C2×C4—22no—
674C2×C4—24no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—52no—
682C2×C4—52no—
683C2×C4—52no—
684C2×C4—52no—
685C2×C4—102no—
686C2×C4—102no—
687C2×C4—102no—
688C2×C4—102no—
689C2×C4—102no—
690C2×C4—102no—
691C2×C4—102no—
692C2×C4—102no—
693C2×C4—202no—
694C2×C4—202no—
695C2×C4—202no—
696C2×C4—202no—
697C2×C4—404no—
698C2×C4—404no—
699C2×C4—404no—
700C2×C4C2×D4×D512yes—
701C2×C4C2×D4×D511yescharacteristic
702C2×C4C2×#71112yes—
703C2×C4C2×#71112yes—
704C2×C4C24×D511yescharacteristic
705C8—22no—
706C8—22no—
707C8—102no—
708C8—102no—
709C5C2×#312011yescharacteristic, complemented, Sylow
710C22—22no—
711C22—22no—
712C22—24no—
713C22—22no—
714C22—42no—
715C22—42no—
716C22—44no—
717C22—48no—
718C22#6592012yes—
719C22#6610412yes—
720C22#6611312yes—
721C22C22×D4×D511yescharacteristic
722C4—22no—
723C4—24no—
724C4—42no—
725C4—42no—
726C4—102no—
727C4—102no—
728C4—102no—
729C4—102no—
730C4—202no—
731C4—202no—
732C4—202no—
733C4—202no—
734C4#6592012yes—
735C4C22×#71111yescharacteristic
736C4C22×#71111yescharacteristic
737C2—42no—
738C2—44no—
739C2#1061194714yesdirect product factor
740C2C2×#6592011yescharacteristic
741C2C2×#6610411yescharacteristic
742C2C2×#6611311yescharacteristic
subgroupG/H
centerC23C2×D4×D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×#452C2
socleC23×C5C22×D4
prime radicalC22×C5×#41C22
hypercenterC2×#452D5
hypocenterC5C2×#3120
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#452

Complements

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

NH ≅ G/Ntype
2. C2×#65959C2semidirect
5. C2×#65471C2semidirect
6. C2×#65473C2semidirect
7. C2×#65451C2semidirect
8. C2×SD16×Dic5C2semidirect
9. C2×#65333C2semidirect
10. #10611947C2direct (N × H)
11. C2×#65088C2semidirect
12. C2×#65079C2semidirect
13. C2×#65052C2semidirect
14. C2×#65046C2semidirect
15. C2×#65010C2semidirect
16. C2×#65009C2semidirect
39. #65959C22semidirect
56. #65473C22semidirect
57. #65471C22semidirect
58. #65451C22semidirect
59. SD16×Dic5C22semidirect
68. #65333C22semidirect
71. #65088C22semidirect
72. #65079C22semidirect
73. #65052C22semidirect
74. #65046C22semidirect
75. #65010C22semidirect
76. #65009C22semidirect
644. C2×C5#3120semidirect
709. C5C2×#3120semidirect
739. C2#10611947direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#661612
C2×#659592
C2×C5×#4522
C2×#655282
C2×#654712
C2×#654732
C2×#654512
C2×SD16×Dic52
C2×#653332
#106119472
C2×#650882
C2×#650792
C2×#650522
C2×#650462
C2×#650102
C2×#650092
C2×#31205