Finite Group Databasebeta

← C2×#10612532 #12977999

Subgroups — C2×#10612532 #12977999

Order 1280.

2082 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65975C211yesmaximal, characteristic, complemented
2C2×#65945C211yesmaximal, characteristic
3C2×C5×#468C211yesmaximal, characteristic, complemented
4C2×#65463C211yesmaximal, characteristic, complemented
5C2×SD16×Dic5C211yesmaximal, characteristic, complemented
6C2×#65417C211yesmaximal, characteristic, complemented
7C2×#65410C211yesmaximal, characteristic, complemented
8C2×#65333C211yesmaximal, characteristic, complemented
9C2×#65324C211yesmaximal, characteristic, complemented
10#10612532C2116yesmaximal, direct product factor
11C2×#65170C211yesmaximal, characteristic, complemented
12C2×#65163C211yesmaximal, characteristic, complemented
13C2×#65098C211yesmaximal, characteristic, complemented
14C2×#65080C211yesmaximal, characteristic, complemented
15C2×#65068C211yesmaximal, characteristic, complemented
16C2×#65048C211yesmaximal, characteristic, complemented
17C22×#711—21no—
18C22×C5×SD16C2211yescharacteristic
19C22×C5×M16C2211yescharacteristic
20C2×C5×C22⋊Q8C2211yescharacteristic
21C2×C5×#121C2211yescharacteristic
22C2×#4092C2211yescharacteristic
23C2×Q8×Dic5C2211yescharacteristic
24C2×#4084C2211yescharacteristic
25C2×#4081—21no—
26C2×D4×Dic5C2211yescharacteristic
27C2×C4×C22⋊D5C2211yescharacteristic
28C2×#4072C2211yescharacteristic
29C22×C4⋊Dic5C2211yescharacteristic
30C22×#676C2211yescharacteristic
31#65975—24no—
32#65975C2218yescomplemented
33#65945—24no—
34#65945C2218yes—
35C2×#4044—21no—
36C2×#4038C2211yescharacteristic
37C2×D5×C4⋊C4C2211yescharacteristic
38C2×#4034C2211yescharacteristic
39C2×#4034C2211yescharacteristic
40C2×#4033—21no—
41C2×#4031—21no—
42C2×#4029—21no—
43C2×#4025—21no—
44C2×#4024—21no—
45C5×#468C2218yescomplemented
46C2×C5×#107C2211yescharacteristic
47C2×C5×#103C2211yescharacteristic
48C2×C5×#102C2211yescharacteristic
49C2×#3967C2211yescharacteristic
50C2×#3967C2211yescharacteristic
51C2×#3964C2211yescharacteristic
52C2×#3964C2211yescharacteristic
53C2×C22⋊#168C2211yescharacteristic
54#65463C2218yescomplemented
55SD16×Dic5C2218yescomplemented
56#65417C2218yescomplemented
57#65410C2218yescomplemented
58C2×#3952C2211yescharacteristic
59C2×#3950C2211yescharacteristic
60C2×#3950C2211yescharacteristic
61C2×#3949C2211yescharacteristic
62C2×#3949C2211yescharacteristic
63C2×#3946C2211yescharacteristic
64C2×C8×Dic5C2211yescharacteristic
65#65333C2218yescomplemented
66#65324C2218yescomplemented
67C2×#3940C2211yescharacteristic
68C2×#3939C2211yescharacteristic
69C2×#3939C2211yescharacteristic
70C2×#3939C2211yescharacteristic
71#65170C2218yescomplemented
72#65163C2218yescomplemented
73#65098C2218yescomplemented
74#65080C2218yescomplemented
75#65068C2218yescomplemented
76#65048C2218yescomplemented
77C2×#3353—51nomaximal, Sylow
78C22×C5×Q8C2311yescharacteristic
79C22×C5×D4—21no—
80C22×C5×D4C2311yescharacteristic
81C23×C4×C5C2311yescharacteristic
82C22×C22⋊D5—21no—
83C22×C22⋊D5D411yescharacteristic
84C23×Dic5—21no—
85C23×Dic5—21no—
86C2×#711—28no—
87C2×#711—48no—
88C22×C4×D5—21no—
89C22×C4×D5C2311yescharacteristic
90C22×Dic10—21no—
91C22×Dic10—21no—
92C2×C5×SD16—24no—
93C2×C5×SD16C2314yes—
94C2×C5×M16—24no—
95C2×C5×M16C2314yes—
96C22×C5×C8C2311yescharacteristic
97C22×C5×C8C2311yescharacteristic
98C5×C22⋊Q8—22no—
99C5×C22⋊Q8C2314yes—
100C5×#121—22no—
101C5×#121C2314yes—
102C2×C5×C4⋊C4—21no—
103C2×C5×C4⋊C4C2311yescharacteristic
104C2×C5×C4⋊C4C2311yescharacteristic
105C2×C5×C22⋊C4—21no—
106C2×C5×C22⋊C4—21no—
107C2×C22⋊Dic5—21no—
108C2×C22⋊Dic5—21no—
109C2×C22⋊Dic5—21no—
110C2×C22⋊Dic5D411yescharacteristic
111#4092—22no—
112#4092C2314yes—
113Q8×Dic5—22no—
114Q8×Dic5C2314yes—
115#4084—22no—
116#4084C2314yes—
117#4081—28no—
118D4×Dic5—22no—
119D4×Dic5C2314yes—
120C4×C22⋊D5D414yes—
121C4×C22⋊D5C2314yes—
122C2×#685—21no—
123C2×#685—21no—
124C2×#685D411yescharacteristic
125#4072—22no—
126#4072C2314yes—
127C2×C4⋊Dic5—21no—
128C2×C4⋊Dic5—22no—
129C2×C4⋊Dic5—21no—
130C2×C4⋊Dic5C2311yescharacteristic
131C2×C4⋊Dic5C2311yescharacteristic
132C2×C4⋊Dic5C2311yescharacteristic
133C2×C4⋊Dic5C2311yescharacteristic
134C2×C4⋊Dic5C2314yes—
135C2×#683—21no—
136C2×#683—21no—
137C2×#683—21no—
138C2×#683—21no—
139C2×#683D411yescharacteristic
140C2×C4×Dic5—21no—
141C2×C4×Dic5—21no—
142C2×C4×Dic5—21no—
143C2×C4×Dic5C2311yescharacteristic
144C22×#168C2311yescharacteristic
145C22×#168C2311yescharacteristic
146C2×#676—24no—
147C2×#676C2314yes—
148#4044—28no—
149#4038—22no—
150#4038C2314yes—
151D5×C4⋊C4—22no—
152D5×C4⋊C4C2314yes—
153#4034—22no—
154#4034—22no—
155#4034C2314yes—
156#4034C2314yes—
157#4033—28no—
158#4031—28no—
159#4029—28no—
160#4025—28no—
161#4024—28no—
162C5×#107C2314yes—
163C5×#103C2314yes—
164C5×#102C2314yes—
165#3967C2314yes—
166#3967C2314yes—
167#3964C2314yes—
168#3964C2314yes—
169C22⋊#168C2314yes—
170#3952C2314yes—
171#3950C2314yes—
172#3950C2314yes—
173#3949C2314yes—
174#3949C2314yes—
175#3946C2314yes—
176C8×Dic5C2314yes—
177#3940C2314yes—
178#3939C2314yes—
179#3939C2314yes—
180#3939C2314yes—
181C2×#556—51no—
182C2×#547—51no—
183#3353—516no—
184C2×#500—51no—
185C2×#484—51no—
186C2×#484—51no—
187C2×#482—51no—
188C2×#482—51no—
189C2×#475—51no—
190C2×#474—51no—
191C2×#468—51no—
192C2×#468D511yescharacteristic, complemented
193C2×C4×SD16—51no—
194C2×#436—51no—
195C2×#428—51no—
196C2×#428—51no—
197C24×C5—21no—
198C24×C5C2×D411yescharacteristic
199C23×D5C2×D411yescharacteristic
200C2×C5×Q8—21no—
201C2×C5×Q8—22no—
202C2×C5×Q8—22no—
203C2×C5×Q8C2412yes—
204C2×C5×D4—24no—
205C2×C5×D4—21no—
206C2×C5×D4—22no—
207C2×C5×D4—22no—
208C2×C5×D4—44no—
209C2×C5×D4C2412yes—
210C22×C4×C5—22no—
211C22×C4×C5—22no—
212C22×C4×C5—21no—
213C22×C4×C5—21no—
214C22×C4×C5—21no—
215C22×C4×C5C2×D411yescharacteristic
216C22×C4×C5C2×D412yes—
217C22×C4×C5C2412yes—
218C22×C4×C5C2411yescharacteristic
219C2×C22⋊D5—24no—
220C2×C22⋊D5—24no—
221C2×C22⋊D5—44no—
222C2×C22⋊D5C2×D414yes—
223C22×Dic5—21no—
224C22×Dic5—21no—
225C22×Dic5—21no—
226C22×Dic5—21no—
227C22×Dic5—24no—
228C22×Dic5—24no—
229C22×Dic5—44no—
230C22×Dic5—44no—
231C22×Dic5C2×D411yescharacteristic
232C22×Dic5C2×D411yescharacteristic
233C22×Dic5C2×D411yescharacteristic
234#711—432no—
235C2×C4×D5—22no—
236C2×C4×D5—22no—
237C2×C4×D5—24no—
238C2×C4×D5—44no—
239C2×C4×D5C2×D412yes—
240C2×C4×D5C2412yes—
241C2×Dic10—24no—
242C2×Dic10—24no—
243C2×Dic10—44no—
244C2×Dic10—44no—
245C5×SD16—28no—
246C5×M16—28no—
247C2×C5×C8—22no—
248C2×C5×C8#4114yescomplemented
249C2×C5×C8C2412yes—
250C2×C5×C8C2412yes—
251C5×C4⋊C4—24no—
252C5×C4⋊C4—21no—
253C5×C4⋊C4—21no—
254C5×C4⋊C4C2412yes—
255C5×C4⋊C4C2412yes—
256C5×C22⋊C4—24no—
257C5×C22⋊C4—24no—
258C22⋊Dic5—24no—
259C22⋊Dic5—24no—
260C22⋊Dic5—24no—
261C22⋊Dic5C2×D414yes—
262#685—24no—
263#685—24no—
264#685C2×D414yes—
265C4⋊Dic5—24no—
266C4⋊Dic5—21no—
267C4⋊Dic5—21no—
268C4⋊Dic5—21no—
269C4⋊Dic5—21no—
270C4⋊Dic5—24no—
271C4⋊Dic5C2412yes—
272C4⋊Dic5C2412yes—
273C4⋊Dic5C2412yes—
274C4⋊Dic5C2412yes—
275#683—24no—
276#683—24no—
277#683—24no—
278#683—24no—
279#683C2×D414yes—
280C4×Dic5—24no—
281C4×Dic5—24no—
282C4×Dic5—24no—
283C4×Dic5C2×D412yes—
284C4×Dic5C2412yes—
285C2×#168—22no—
286C2×#168—22no—
287C2×#168C2412yes—
288C2×#168C2412yes—
289#676—28no—
290C22×#41—101no—
291C22×SD16C2×D511yescharacteristic
292C22×M16—51no—
293C22×M16C2×D511yescharacteristic
294#556—58no—
295#556—104no—
296#547—58no—
297#547—104no—
298C2×C4⋊Q8—51no—
299C2×C4⋊Q8—51no—
300C2×#126—101no—
301C2×#126—101no—
302C2×#124—101no—
303C2×#123—101no—
304C2×#123—101no—
305C2×C22⋊Q8—51no—
306C2×C22⋊Q8—101no—
307C2×C22⋊Q8C2×D511yescharacteristic
308C2×#121—51no—
309C2×#121C2×D511yescharacteristic
310C2×C4×Q8—51no—
311C2×C4×Q8—101no—
312C2×C4×D4—51no—
313C2×C4×D4—51no—
314C2×#117—51no—
315C2×#117—51no—
316C22×C4⋊C4—51no—
317C22×C4⋊C4—51no—
318#500—58no—
319#484—58no—
320#484—58no—
321#482—58no—
322#482—58no—
323#475—58no—
324#474—58no—
325#468—58no—
326#468C2×D518yescomplemented
327C4×SD16—58no—
328#436—58no—
329#428—58no—
330#428—58no—
331C2×#107—51no—
332C2×#107—51no—
333C2×#107—51no—
334C2×#107—51no—
335C2×#107—51no—
336C2×#107C2×D511yescharacteristic
337C2×#106—51no—
338C2×#106—51no—
339C2×#106—51no—
340C2×C4⋊C8—51no—
341C2×#103—51no—
342C2×#103—51no—
343C2×#103C2×D511yescharacteristic
344C2×#102—51no—
345C2×#102—51no—
346C2×#102C2×D511yescharacteristic
347C2×C22⋊C8—51no—
348C2×C22⋊C8—51no—
349C2×C4×C8—51no—
350C23×C5—22no—
351C23×C5—22no—
352C23×C5—22no—
353C23×C5—22no—
354C23×C5—42no—
355C23×C5—42no—
356C23×C5—42no—
357C23×C5C22×D412yes—
358C23×C5C22×D411yescharacteristic
359C22×D5—22no—
360C22×D5—22no—
361C22×D5—22no—
362C22×D5C22×D412yes—
363C5×Q8—22no—
364C5×Q8—22no—
365C5×Q8—42no—
366C5×D4—22no—
367C5×D4—22no—
368C5×D4—48no—
369C5×D4—42no—
370C2×C4×C5—22no—
371C2×C4×C5—24no—
372C2×C4×C5—22no—
373C2×C4×C5—22no—
374C2×C4×C5—22no—
375C2×C4×C5—22no—
376C2×C4×C5—22no—
377C2×C4×C5—42no—
378C2×C4×C5—42no—
379C2×C4×C5—42no—
380C2×C4×C5C22×D412yes—
381C2×C4×C5C22×D411yescharacteristic
382C2×C4×C5C2×#4112yes—
383C2×C4×C52−1+412yes—
384C2×C4×C5C2511yescharacteristic
385C22⋊D5—28no—
386C22⋊D5—48no—
387C2×Dic5—22no—
388C2×Dic5—22no—
389C2×Dic5—22no—
390C2×Dic5—22no—
391C2×Dic5—22no—
392C2×Dic5—22no—
393C2×Dic5—48no—
394C2×Dic5—42no—
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—
403C4×D5—24no—
404C4×D5—22no—
405C4×D5—22no—
406C4×D5—48no—
407Dic10—48no—
408Dic10—48no—
409C5×C8—22no—
410C5×C8C2×#4114yescomplemented
411#168—22no—
412#168—22no—
413C2×#41—108no—
414C2×#41—208no—
415C22×Q8—101no—
416C22×Q8—101no—
417C22×Q8C22×D511yescharacteristic
418C22×D4—21no—
419C22×D4—51no—
420C22×D4—101no—
421C22×D4C22×D511yescharacteristic
422C23×C4—51no—
423C23×C4—101no—
424C23×C4—101no—
425C23×C4—101no—
426C23×C4C22×D511yescharacteristic
427C2×SD16—24no—
428C2×SD16C22×D514yes—
429C2×M16—24no—
430C2×M16—54no—
431C2×M16—104no—
432C2×M16C22×D514yes—
433C22×C8—51no—
434C22×C8—51no—
435C22×C8C22×D511yescharacteristic
436C22×C8C22×D511yescharacteristic
437C4⋊Q8—54no—
438C4⋊Q8—54no—
439C4⋊Q8—102no—
440C4⋊Q8—102no—
441#126—108no—
442#126—108no—
443#124—108no—
444#123—108no—
445#123—108no—
446C22⋊Q8—22no—
447C22⋊Q8—54no—
448C22⋊Q8—108no—
449C22⋊Q8—102no—
450C22⋊Q8C22×D514yes—
451#121—22no—
452#121—54no—
453#121—102no—
454#121C22×D514yes—
455C4×Q8—54no—
456C4×Q8—102no—
457C4×Q8—108no—
458C4×D4—54no—
459C4×D4—54no—
460C4×D4—54no—
461C4×D4—102no—
462#117—54no—
463#117—54no—
464#117—102no—
465#117—102no—
466C2×C4⋊C4—21no—
467C2×C4⋊C4—51no—
468C2×C4⋊C4—51no—
469C2×C4⋊C4—51no—
470C2×C4⋊C4—54no—
471C2×C4⋊C4—51no—
472C2×C4⋊C4—51no—
473C2×C4⋊C4—54no—
474C2×C4⋊C4—102no—
475C2×C4⋊C4—101no—
476C2×C4⋊C4—101no—
477C2×C4⋊C4—101no—
478C2×C4⋊C4—101no—
479C2×C4⋊C4—101no—
480C2×C4⋊C4—101no—
481C2×C4⋊C4—102no—
482C2×C4⋊C4C22×D511yescharacteristic
483C2×C4⋊C4C22×D511yescharacteristic
484C2×C22⋊C4—21no—
485C2×C22⋊C4—21no—
486C2×C22⋊C4—51no—
487C2×C22⋊C4—51no—
488C2×C22⋊C4—101no—
489C2×C22⋊C4—101no—
490C2×C22⋊C4—101no—
491C2×C22⋊C4—101no—
492C2×C22⋊C4—101no—
493C2×C42—51no—
494C2×C42—101no—
495C2×C42—101no—
496C2×C42—101no—
497#107—54no—
498#107—54no—
499#107—54no—
500#107—54no—
501#107—54no—
502#107C22×D514yes—
503#106—54no—
504#106—54no—
505#106—54no—
506C4⋊C8—54no—
507#103—54no—
508#103—54no—
509#103C22×D514yes—
510#102—54no—
511#102—54no—
512#102C22×D514yes—
513C22⋊C8—54no—
514C22⋊C8—54no—
515C4×C8—54no—
516C22×C5—22no—
517C22×C5—22no—
518C22×C5—22no—
519C22×C5—44no—
520C22×C5—42no—
521C22×C5—42no—
522C22×C5—42no—
523C22×C5—84no—
524C22×C5#54712yes—
525C22×C5C2×AGL(1,ℤ/8)12yes—
526C22×C5#57812yes—
527C22×C5C23×D411yescharacteristic
528C2×D5—22no—
529C2×D5—22no—
530C2×D5—22no—
531C2×D5—44no—
532C4×C5—22no—
533C4×C5—42no—
534C4×C5—42no—
535C4×C5—42no—
536C4×C5#54712yes—
537C4×C5C22×#4111yescharacteristic
538C4×C5C2×2−1+411yescharacteristic
539Dic5—22no—
540Dic5—22no—
541Dic5—42no—
542Dic5—42no—
543Dic5—42no—
544Dic5—42no—
545Dic5C2×AGL(1,ℤ/8)14yes—
546C24—21no—
547C24—51no—
548C24D4×D511yescharacteristic
549#41—2032no—
550C2×Q8—21no—
551C2×Q8—22no—
552C2×Q8—22no—
553C2×Q8—104no—
554C2×Q8—104no—
555C2×Q8—204no—
556C2×Q8—204no—
557C2×Q8C23×D512yes—
558C2×D4—24no—
559C2×D4—21no—
560C2×D4—22no—
561C2×D4—22no—
562C2×D4—44no—
563C2×D4—54no—
564C2×D4—104no—
565C2×D4—104no—
566C2×D4—204no—
567C2×D4C23×D512yes—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—51no—
574C22×C4—51no—
575C22×C4—51no—
576C22×C4—52no—
577C22×C4—52no—
578C22×C4—104no—
579C22×C4—104no—
580C22×C4—102no—
581C22×C4—102no—
582C22×C4—104no—
583C22×C4—101no—
584C22×C4—101no—
585C22×C4—101no—
586C22×C4—101no—
587C22×C4—204no—
588C22×C4—204no—
589C22×C4—204no—
590C22×C4D4×D512yes—
591C22×C4D4×D511yescharacteristic
592C22×C4C23×D512yes—
593C22×C4C23×D511yescharacteristic
594SD16—28no—
595M16—28no—
596M16—108no—
597C2×C8—22no—
598C2×C8—52no—
599C2×C8—52no—
600C2×C8—102no—
601C2×C8—102no—
602C2×C8#71114yescomplemented
603C2×C8C23×D512yes—
604C2×C8C23×D512yes—
605C4⋊C4—24no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—54no—
609C4⋊C4—52no—
610C4⋊C4—52no—
611C4⋊C4—52no—
612C4⋊C4—52no—
613C4⋊C4—104no—
614C4⋊C4—104no—
615C4⋊C4—104no—
616C4⋊C4—104no—
617C4⋊C4—104no—
618C4⋊C4—101no—
619C4⋊C4—101no—
620C4⋊C4—104no—
621C4⋊C4—101no—
622C4⋊C4—101no—
623C4⋊C4C23×D512yes—
624C4⋊C4C23×D512yes—
625C22⋊C4—24no—
626C22⋊C4—24no—
627C22⋊C4—54no—
628C22⋊C4—54no—
629C22⋊C4—104no—
630C22⋊C4—104no—
631C22⋊C4—104no—
632C22⋊C4—104no—
633C22⋊C4—104no—
634C42—52no—
635C42—52no—
636C42—104no—
637C42—104no—
638C42—104no—
639C2×C5—42no—
640C2×C5—82no—
641C2×C5#335314yescomplemented
642C2×C5C2×#54711yescharacteristic
643C2×C5C22×AGL(1,ℤ/8)11yescharacteristic
644C2×C5C2×#57811yescharacteristic
645D5—42no—
646C23—22no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—52no—
654C23—102no—
655C23—102no—
656C23—102no—
657C23C2×D4×D512yes—
658C23C2×D4×D511yescharacteristic
659Q8—22no—
660Q8—22no—
661Q8—42no—
662Q8—208no—
663Q8—208no—
664D4—22no—
665D4—22no—
666D4—48no—
667D4—42no—
668D4—108no—
669D4—208no—
670C2×C4—22no—
671C2×C4—24no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—54no—
681C2×C4—52no—
682C2×C4—52no—
683C2×C4—52no—
684C2×C4—102no—
685C2×C4—102no—
686C2×C4—104no—
687C2×C4—102no—
688C2×C4—102no—
689C2×C4—102no—
690C2×C4—102no—
691C2×C4—102no—
692C2×C4—102no—
693C2×C4—208no—
694C2×C4—208no—
695C2×C4—208no—
696C2×C4—202no—
697C2×C4—202no—
698C2×C4—202no—
699C2×C4—202no—
700C2×C4C2×D4×D512yes—
701C2×C4C2×D4×D511yescharacteristic
702C2×C4C2×#71112yes—
703C2×C4#415012yes—
704C2×C4C24×D511yescharacteristic
705C8—22no—
706C8—102no—
707C8—102no—
708C8C2×#71114yescomplemented
709C5C2×#335311yescharacteristic, complemented, Sylow
710C22—22no—
711C22—22no—
712C22—22no—
713C22—44no—
714C22—42no—
715C22—42no—
716C22—42no—
717C22—84no—
718C22—102no—
719C22—102no—
720C22—102no—
721C22—204no—
722C22#6594512yes—
723C22D5×AGL(1,ℤ/8)12yes—
724C22#6611312yes—
725C22C22×D4×D511yescharacteristic
726C4—22no—
727C4—42no—
728C4—42no—
729C4—42no—
730C4—54no—
731C4—102no—
732C4—102no—
733C4—202no—
734C4—202no—
735C4—202no—
736C4—202no—
737C4#6594512yes—
738C4C22×#71111yescharacteristic
739C4C2×#415011yescharacteristic
740C2—42no—
741C2—82no—
742C2—202no—
743C2#1061253214yesdirect product factor
744C2C2×#6594511yescharacteristic
745C2C2×D5×AGL(1,ℤ/8)11yescharacteristic
746C2C2×#6611311yescharacteristic
subgroupG/H
centerC23C2×D4×D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×#468C2
socleC23×C5C22×D4
prime radicalC2×#65945C2
hypercenterC2×#468D5
hypocenterC5C2×#3353
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#468

Complements

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

NH ≅ G/Ntype
1. C2×#65975C2semidirect
3. C2×C5×#468C2semidirect
4. C2×#65463C2semidirect
5. C2×SD16×Dic5C2semidirect
6. C2×#65417C2semidirect
7. C2×#65410C2semidirect
8. C2×#65333C2semidirect
9. C2×#65324C2semidirect
10. #10612532C2direct (N × H)
11. C2×#65170C2semidirect
12. C2×#65163C2semidirect
13. C2×#65098C2semidirect
14. C2×#65080C2semidirect
15. C2×#65068C2semidirect
16. C2×#65048C2semidirect
32. #65975C22semidirect
45. C5×#468C22semidirect
54. #65463C22semidirect
55. SD16×Dic5C22semidirect
56. #65417C22semidirect
57. #65410C22semidirect
65. #65333C22semidirect
66. #65324C22semidirect
71. #65170C22semidirect
72. #65163C22semidirect
73. #65098C22semidirect
74. #65080C22semidirect
75. #65068C22semidirect
76. #65048C22semidirect
192. C2×#468D5semidirect
248. C2×C5×C8#41semidirect
326. #468C2×D5semidirect
410. C5×C8C2×#41semidirect
602. C2×C8#711semidirect
641. C2×C5#3353semidirect
708. C8C2×#711semidirect
709. C5C2×#3353semidirect
743. C2#10612532direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#659752
C2×#659452
C2×C5×#4682
C2×#654632
C2×SD16×Dic52
C2×#654172
C2×#654102
C2×#653332
C2×#653242
#106125322
C2×#651702
C2×#651632
C2×#650982
C2×#650802
C2×#650682
C2×#650482
C2×#33535