Finite Group Databasebeta

← C2×#10615445 #12979043

Subgroups — C2×#10615445 #12979043

Order 1280.

1950 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×C5×#559C211yesmaximal, characteristic, complemented
2C2×#65913C211yesmaximal, characteristic, complemented
3#10615445C2116yesmaximal, direct product factor
4C2×#65361C211yesmaximal, characteristic
5C2×#65360C211yesmaximal, characteristic, complemented
6C2×#65346C211yesmaximal, characteristic, complemented
7C2×#65346C211yesmaximal, characteristic, complemented
8C2×#65344C211yesmaximal, characteristic, complemented
9C2×#65345C211yesmaximal, characteristic, complemented
10C2×#65315C211yesmaximal, characteristic, complemented
11C2×#65313C211yesmaximal, characteristic, complemented
12C2×#65311C211yesmaximal, characteristic, complemented
13C2×#65298C211yesmaximal, characteristic, complemented
14C2×#65296C211yesmaximal, characteristic, complemented
15C2×#65303C211yesmaximal, characteristic, complemented
16C2×C4×#686C211yesmaximal, characteristic, complemented
17C5×#559—24no—
18C5×#559C2218yescomplemented
19C2×C5×#127C2211yescharacteristic
20C2×C5×#124—21no—
21C2×C5×#124C2211yescharacteristic
22C2×C5×#124C2211yescharacteristic
23C2×C5×#123—21no—
24C2×C5×#123—21no—
25C2×C4×C5×Q8C2211yescharacteristic
26C2×C4×C5×Q8C2211yescharacteristic
27C2×C4×C5×D4—21no—
28C2×C4×C5×D4C2211yescharacteristic
29C2×C4×C5×D4C2211yescharacteristic
30C2×#4092—21no—
31C22×#688C2211yescharacteristic
32C22×#686C2211yescharacteristic
33C22×#686C2211yescharacteristic
34#65913—24no—
35#65913C2218yescomplemented
36C2×#4042—21no—
37C2×#4042—21no—
38C2×D5×C4⋊C4—21no—
39C2×C4×D20C2211yescharacteristic
40C2×C4×D20C2211yescharacteristic
41C2×C4×D20C2211yescharacteristic
42C2×#4016C2211yescharacteristic
43C2×#4016C2211yescharacteristic
44C2×#4015C2211yescharacteristic
45C2×#3967C2211yescharacteristic
46C2×#3967C2211yescharacteristic
47C2×#3967C2211yescharacteristic
48C2×#3964C2211yescharacteristic
49C2×#3964C2211yescharacteristic
50C2×#3964C2211yescharacteristic
51C2×#3964C2211yescharacteristic
52C2×#3964C2211yescharacteristic
53C2×#3964C2211yescharacteristic
54#65361C2218yes—
55#65360C2218yescomplemented
56#65346C2218yescomplemented
57#65346C2218yescomplemented
58#65345C2218yescomplemented
59#65344C2218yescomplemented
60#65315C2218yescomplemented
61#65313C2218yescomplemented
62#65311C2218yescomplemented
63#65303C2218yescomplemented
64C4×#686C2218yescomplemented
65#65298C2218yescomplemented
66#65296C2218yescomplemented
67C2×#3941C2211yescharacteristic
68C2×#3940C2211yescharacteristic
69C2×#3939C2211yescharacteristic
70C2×#3939C2211yescharacteristic
71C2×C4⋊#168C2211yescharacteristic
72C2×C4⋊#168C2211yescharacteristic
73C2×C4⋊#168C2211yescharacteristic
74C2×#3935C2211yescharacteristic
75C2×#3935C2211yescharacteristic
76C2×C4×#168C2211yescharacteristic
77C2×#3370—51nomaximal, Sylow
78C22×C5×Q8D411yescharacteristic
79C22×C5×Q8C2311yescharacteristic
80C22×C5×D4—21no—
81C22×C5×D4—21no—
82C22×C5×D4C2311yescharacteristic
83C22×C5×D4C2311yescharacteristic
84C23×C4×C5—21no—
85C23×C4×C5—21no—
86C22×D20C2311yescharacteristic
87C22×C4×D5—21no—
88C22×C4×D5—21no—
89C22×C4×D5—21no—
90C22×Dic10—21no—
91C5×#127—22no—
92C5×#127C2314yes—
93C5×#124—28no—
94C5×#124—22no—
95C5×#124—22no—
96C5×#124C2314yes—
97C5×#124C2314yes—
98C5×#123—28no—
99C5×#123—28no—
100C4×C5×Q8—22no—
101C4×C5×Q8D414yes—
102C4×C5×Q8C2314yes—
103C4×C5×Q8C2314yes—
104C4×C5×D4—28no—
105C4×C5×D4—22no—
106C4×C5×D4—22no—
107C4×C5×D4C2314yes—
108C4×C5×D4C2314yes—
109C2×C5×C4⋊C4—21no—
110C2×C5×C4⋊C4D411yescharacteristic
111C2×C5×C4⋊C4D411yescharacteristic
112C2×C5×C4⋊C4D411yescharacteristic
113C2×C5×C4⋊C4C2311yescharacteristic
114C2×C5×C22⋊C4—21no—
115C2×C5×C22⋊C4—21no—
116C2×C5×C22⋊C4—21no—
117C2×C5×C22⋊C4—21no—
118C2×C5×C22⋊C4—21no—
119C2×C5×C22⋊C4—21no—
120C2×C42×C5—21no—
121C2×C42×C5C2311yescharacteristic
122C2×C42×C5C2311yescharacteristic
123C2×C42×C5C2311yescharacteristic
124#4092—28no—
125C2×#688—24no—
126C2×#688C2314yes—
127C2×#686—24no—
128C2×#686—24no—
129C2×#686C2314yes—
130C2×#686C2314yes—
131C2×#685—21no—
132C2×#685—21no—
133C2×#685—21no—
134C2×C4⋊Dic5—21no—
135C2×C4⋊Dic5C2311yescharacteristic
136C2×C4⋊Dic5C2311yescharacteristic
137C2×C4⋊Dic5C2311yescharacteristic
138C2×#683—21no—
139C2×#683—21no—
140C2×#683—21no—
141C2×#683—21no—
142C22×#168C2311yescharacteristic
143C22×#168C2311yescharacteristic
144C22×#168C2311yescharacteristic
145C22×#168C2311yescharacteristic
146#4042—28no—
147#4042—28no—
148D5×C4⋊C4—28no—
149C4×D20—22no—
150C4×D20—22no—
151C4×D20—22no—
152C4×D20C2314yes—
153C4×D20C2314yes—
154C4×D20C2314yes—
155#4016—22no—
156#4016—22no—
157#4016C2314yes—
158#4016C2314yes—
159#4015—22no—
160#4015C2314yes—
161#3967C2314yes—
162#3967C2314yes—
163#3967C2314yes—
164#3964C2314yes—
165#3964C2314yes—
166#3964C2314yes—
167#3964C2314yes—
168#3964C2314yes—
169#3964C2314yes—
170#3941C2314yes—
171#3940C2314yes—
172#3939C2314yes—
173#3939C2314yes—
174C4⋊#168C2314yes—
175C4⋊#168C2314yes—
176C4⋊#168C2314yes—
177#3935C2314yes—
178#3935C2314yes—
179C4×#168C2314yes—
180C2×#559D511yescharacteristic, complemented
181C2×#554—51no—
182#3370—516no—
183C2×#490—51no—
184C2×#489—51no—
185C2×#488—51no—
186C2×#479—51no—
187C2×#478—51no—
188C2×#474—51no—
189C2×#463—51no—
190C2×#463—51no—
191C2×#459—51no—
192C2×#446—51no—
193C2×#442—51no—
194C2×#440—51no—
195C2×C4×D8—51no—
196C24×C5—21no—
197C24×C5—21no—
198C23×D5—21no—
199C2×C5×Q8—21no—
200C2×C5×Q8—22no—
201C2×C5×Q8—22no—
202C2×C5×Q8—42no—
203C2×C5×Q8C2×D414yes—
204C2×C5×Q8C2412yes—
205C2×C5×D4—21no—
206C2×C5×D4—21no—
207C2×C5×D4—24no—
208C2×C5×D4—24no—
209C2×C5×D4—22no—
210C2×C5×D4—22no—
211C2×C5×D4—22no—
212C2×C5×D4—22no—
213C2×C5×D4—44no—
214C2×C5×D4—82no—
215C2×C5×D4C2412yes—
216C2×C5×D4C2412yes—
217C22×C4×C5—21no—
218C22×C4×C5—21no—
219C22×C4×C5—24no—
220C22×C4×C5—24no—
221C22×C4×C5—82no—
222C22×C4×C5—82no—
223C22×C4×C5C2×D411yescharacteristic
224C22×C4×C5C2×D411yescharacteristic
225C22×C4×C5C2×D411yescharacteristic
226C22×C4×C5C2×D411yescharacteristic
227C22×C4×C5C2×D411yescharacteristic
228C22×C4×C5C2×D411yescharacteristic
229C22×C4×C5C2411yescharacteristic
230C22×Dic5—21no—
231C22×Dic5—21no—
232C22×Dic5—21no—
233C2×D20—21no—
234C2×D20—22no—
235C2×D20#4114yes—
236C2×D20C2412yes—
237C2×C4×D5—24no—
238C2×C4×D5—24no—
239C2×C4×D5—24no—
240C2×C4×D5—44no—
241C2×C4×D5—82no—
242C2×C4×D5—82no—
243C2×Dic10—24no—
244C2×Dic10—82no—
245C5×C4⋊C4—24no—
246C5×C4⋊C4—21no—
247C5×C4⋊C4C2×D414yes—
248C5×C4⋊C4C2×D414yes—
249C5×C4⋊C4C2×D414yes—
250C5×C4⋊C4C2412yes—
251C5×C22⋊C4—24no—
252C5×C22⋊C4—24no—
253C5×C22⋊C4—24no—
254C5×C22⋊C4—24no—
255C5×C22⋊C4—24no—
256C5×C22⋊C4—24no—
257C42×C5—24no—
258C42×C5C2×D412yes—
259C42×C5C2×D412yes—
260C42×C5C2×D412yes—
261C42×C5C2412yes—
262C42×C5C2412yes—
263C42×C5C2412yes—
264#688—28no—
265#686—28no—
266#686—28no—
267#685—24no—
268#685—24no—
269#685—24no—
270C4⋊Dic5—21no—
271C4⋊Dic5—21no—
272C4⋊Dic5—24no—
273C4⋊Dic5—21no—
274C4⋊Dic5C2412yes—
275C4⋊Dic5C2412yes—
276C4⋊Dic5C2412yes—
277#683—24no—
278#683—24no—
279#683—24no—
280#683—24no—
281C2×#168—22no—
282C2×#168—22no—
283C2×#168—22no—
284C2×#168—22no—
285C2×#168C2412yes—
286C2×#168C2412yes—
287C2×#168C2412yes—
288C2×#168C2412yes—
289C22×SD16—51no—
290C22×D8—51no—
291C22×D8—51no—
292#559—24no—
293#559C2×D518yescomplemented
294#554—58no—
295#554—104no—
296C2×C4⋊Q8—51no—
297C2×#127C2×D511yescharacteristic
298C2×#125—51no—
299C2×#125—51no—
300C2×#124—21no—
301C2×#124C2×D511yescharacteristic
302C2×#124C2×D511yescharacteristic
303C2×#123—21no—
304C2×#123—21no—
305C2×C22⋊Q8—101no—
306C2×C22⋊Q8—101no—
307C2×C22⋊Q8—101no—
308C2×C4×Q8C2×D511yescharacteristic
309C2×C4×Q8C2×D511yescharacteristic
310C2×C4×D4—21no—
311C2×C4×D4—51no—
312C2×C4×D4—51no—
313C2×C4×D4—51no—
314C2×C4×D4C2×D511yescharacteristic
315C2×C4×D4C2×D511yescharacteristic
316C22×C4⋊C4—101no—
317#490—58no—
318#489—58no—
319#488—58no—
320#479—58no—
321#478—58no—
322#474—58no—
323#463—58no—
324#463—58no—
325#459—58no—
326#446—58no—
327#442—58no—
328#440—58no—
329C4×D8—58no—
330C2×#107—51no—
331C2×#107—51no—
332C2×#106—51no—
333C2×C4⋊C8—51no—
334C2×C4⋊C8—51no—
335C2×C4⋊C8—51no—
336C2×#103—51no—
337C2×#103—51no—
338C2×#103—51no—
339C2×#102—51no—
340C2×#102—51no—
341C2×#102—51no—
342C2×#102—51no—
343C2×#102—51no—
344C2×#102—51no—
345C2×#102—51no—
346C2×#97—51no—
347C2×#97—51no—
348C2×C4×C8—51no—
349C23×C5—22no—
350C23×C5—22no—
351C23×C5—42no—
352C23×C5—42no—
353C23×C5—42no—
354C23×C5—42no—
355C23×C5—42no—
356C23×C5—42no—
357C23×C5C22×D411yescharacteristic
358C22×D5—24no—
359C22×D5—22no—
360C22×D5—42no—
361C22×D5—42no—
362C5×Q8—22no—
363C5×Q8—22no—
364C5×Q8—44no—
365C5×Q8—42no—
366C5×D4—22no—
367C5×D4—22no—
368C5×D4—22no—
369C5×D4—22no—
370C5×D4—48no—
371C5×D4—42no—
372C5×D4—42no—
373C5×D4—84no—
374C2×C4×C5—22no—
375C2×C4×C5—22no—
376C2×C4×C5—22no—
377C2×C4×C5—22no—
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×C5—84no—
385C2×C4×C5—84no—
386C2×C4×C5C22×D412yes—
387C2×C4×C5C22×D412yes—
388C2×C4×C5C22×D412yes—
389C2×C4×C5C22×D412yes—
390C2×C4×C5C22×D412yes—
391C2×C4×C5C22×D412yes—
392C2×C4×C5C22×D411yescharacteristic
393C2×C4×C5C2×#4112yes—
394C2×C4×C52−1+412yes—
395C2×C4×C5C2511yescharacteristic
396C2×Dic5—22no—
397C2×Dic5—22no—
398C2×Dic5—22no—
399C2×Dic5—42no—
400C2×Dic5—42no—
401C2×Dic5—42no—
402D20—24no—
403D20—22no—
404D20C2×#4114yes—
405C4×D5—48no—
406C4×D5—84no—
407C4×D5—84no—
408Dic10—84no—
409#168—22no—
410#168—22no—
411#168—22no—
412#168—22no—
413C22×Q8—101no—
414C22×Q8C22⋊D511yescharacteristic
415C22×Q8C22×D511yescharacteristic
416C22×D4—21no—
417C22×D4—21no—
418C22×D4—51no—
419C22×D4C22×D511yescharacteristic
420C22×D4C22×D511yescharacteristic
421C23×C4—21no—
422C23×C4—21no—
423C23×C4—101no—
424C23×C4—101no—
425C23×C4—101no—
426C2×SD16—54no—
427C2×SD16—104no—
428C2×D8—54no—
429C2×D8—54no—
430C2×D8—104no—
431C2×D8—104no—
432C22×C8—51no—
433C22×C8—51no—
434C22×C8—51no—
435C22×C8—51no—
436C4⋊Q8—54no—
437C4⋊Q8—102no—
438#127—22no—
439#127C22×D514yes—
440#125—54no—
441#125—54no—
442#125—102no—
443#125—102no—
444#124—28no—
445#124—22no—
446#124—22no—
447#124C22×D514yes—
448#124C22×D514yes—
449#123—28no—
450#123—28no—
451C22⋊Q8—108no—
452C22⋊Q8—108no—
453C22⋊Q8—108no—
454C4×Q8—22no—
455C4×Q8C22⋊D514yes—
456C4×Q8C22×D514yes—
457C4×Q8C22×D514yes—
458C4×D4—28no—
459C4×D4—22no—
460C4×D4—22no—
461C4×D4—54no—
462C4×D4—54no—
463C4×D4—54no—
464C4×D4—102no—
465C4×D4—102no—
466C4×D4—102no—
467C4×D4C22×D514yes—
468C4×D4C22×D514yes—
469C2×C4⋊C4—21no—
470C2×C4⋊C4—51no—
471C2×C4⋊C4—51no—
472C2×C4⋊C4—51no—
473C2×C4⋊C4—101no—
474C2×C4⋊C4—101no—
475C2×C4⋊C4—101no—
476C2×C4⋊C4—101no—
477C2×C4⋊C4—101no—
478C2×C4⋊C4—108no—
479C2×C4⋊C4C22⋊D511yescharacteristic
480C2×C4⋊C4C22⋊D511yescharacteristic
481C2×C4⋊C4C22⋊D511yescharacteristic
482C2×C4⋊C4C22×D511yescharacteristic
483C2×C22⋊C4—21no—
484C2×C22⋊C4—21no—
485C2×C22⋊C4—21no—
486C2×C22⋊C4—21no—
487C2×C22⋊C4—21no—
488C2×C22⋊C4—21no—
489C2×C22⋊C4—101no—
490C2×C22⋊C4—101no—
491C2×C22⋊C4—101no—
492C2×C42—21no—
493C2×C42C22×D511yescharacteristic
494C2×C42C22×D511yescharacteristic
495C2×C42C22×D511yescharacteristic
496#107—54no—
497#107—54no—
498#106—54no—
499C4⋊C8—54no—
500C4⋊C8—54no—
501C4⋊C8—54no—
502#103—54no—
503#103—54no—
504#103—54no—
505#102—54no—
506#102—54no—
507#102—54no—
508#102—54no—
509#102—54no—
510#102—54no—
511#102—54no—
512#97—54no—
513#97—54no—
514C4×C8—54no—
515C22×C5—42no—
516C22×C5—42no—
517C22×C5—42no—
518C22×C5—42no—
519C22×C5—42no—
520C22×C5—42no—
521C22×C5—84no—
522C22×C5—84no—
523C22×C5#54812yes—
524C22×C5#57512yes—
525C22×C5#57612yes—
526C22×C5C23×D411yescharacteristic
527C2×D5—24no—
528C2×D5—48no—
529C2×D5—42no—
530C2×D5—42no—
531C4×C5—22no—
532C4×C5—22no—
533C4×C5—22no—
534C4×C5—22no—
535C4×C5—22no—
536C4×C5—22no—
537C4×C5—42no—
538C4×C5—42no—
539C4×C5#54812yes—
540C4×C5C22×#4111yescharacteristic
541C4×C5C2×2−1+411yescharacteristic
542Dic5—42no—
543Dic5—42no—
544Dic5—42no—
545C24—21no—
546C24—21no—
547C24—101no—
548C2×Q8—21no—
549C2×Q8—22no—
550C2×Q8—22no—
551C2×Q8—42no—
552C2×Q8—104no—
553C2×Q8—402no—
554C2×Q8C2×C22⋊D514yes—
555C2×Q8C23×D512yes—
556C2×D4—22no—
557C2×D4—22no—
558C2×D4—22no—
559C2×D4—22no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—24no—
563C2×D4—24no—
564C2×D4—44no—
565C2×D4—54no—
566C2×D4—52no—
567C2×D4—82no—
568C2×D4—102no—
569C2×D4—101no—
570C2×D4C23×D512yes—
571C2×D4C23×D512yes—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—24no—
575C22×C4—24no—
576C22×C4—82no—
577C22×C4—82no—
578C22×C4—101no—
579C22×C4—101no—
580C22×C4—101no—
581C22×C4—104no—
582C22×C4—104no—
583C22×C4—104no—
584C22×C4—204no—
585C22×C4—402no—
586C22×C4—402no—
587C22×C4C2×C22⋊D511yescharacteristic
588C22×C4C2×C22⋊D511yescharacteristic
589C22×C4C2×C22⋊D511yescharacteristic
590C22×C4C2×C22⋊D511yescharacteristic
591C22×C4C2×C22⋊D511yescharacteristic
592C22×C4C2×C22⋊D511yescharacteristic
593C22×C4C23×D511yescharacteristic
594SD16—108no—
595D8—108no—
596D8—108no—
597C2×C8—52no—
598C2×C8—52no—
599C2×C8—52no—
600C2×C8—52no—
601C2×C8—102no—
602C2×C8—102no—
603C2×C8—102no—
604C2×C8—102no—
605C4⋊C4—24no—
606C4⋊C4—21no—
607C4⋊C4—52no—
608C4⋊C4—52no—
609C4⋊C4—52no—
610C4⋊C4—101no—
611C4⋊C4—101no—
612C4⋊C4—101no—
613C4⋊C4—104no—
614C4⋊C4—104no—
615C4⋊C4—104no—
616C4⋊C4—104no—
617C4⋊C4—104no—
618C4⋊C4C2×C22⋊D514yes—
619C4⋊C4C2×C22⋊D514yes—
620C4⋊C4C2×C22⋊D514yes—
621C4⋊C4C23×D512yes—
622C22⋊C4—24no—
623C22⋊C4—24no—
624C22⋊C4—24no—
625C22⋊C4—24no—
626C22⋊C4—24no—
627C22⋊C4—24no—
628C22⋊C4—104no—
629C22⋊C4—104no—
630C22⋊C4—104no—
631C42—24no—
632C42C2×C22⋊D512yes—
633C42C2×C22⋊D512yes—
634C42C2×C22⋊D512yes—
635C42C23×D512yes—
636C42C23×D512yes—
637C42C23×D512yes—
638C2×C5—82no—
639C2×C5—82no—
640C2×C5#337014yescomplemented
641C2×C5C2×#54811yescharacteristic
642C2×C5C2×#57511yescharacteristic
643C2×C5C2×#57611yescharacteristic
644D5—44no—
645C23—22no—
646C23—22no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—104no—
654C23—102no—
655C23—202no—
656C23—202no—
657C23C22×C22⋊D511yescharacteristic
658Q8—22no—
659Q8—22no—
660Q8—44no—
661Q8—42no—
662Q8—404no—
663D4—22no—
664D4—22no—
665D4—22no—
666D4—22no—
667D4—48no—
668D4—42no—
669D4—42no—
670D4—54no—
671D4—84no—
672D4—104no—
673D4—102no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—84no—
685C2×C4—84no—
686C2×C4—102no—
687C2×C4—102no—
688C2×C4—102no—
689C2×C4—208no—
690C2×C4—202no—
691C2×C4—202no—
692C2×C4—202no—
693C2×C4—404no—
694C2×C4—404no—
695C2×C4D5×#4112yes—
696C2×C4#415012yes—
697C2×C4C22×C22⋊D512yes—
698C2×C4C22×C22⋊D512yes—
699C2×C4C22×C22⋊D512yes—
700C2×C4C22×C22⋊D512yes—
701C2×C4C22×C22⋊D512yes—
702C2×C4C22×C22⋊D512yes—
703C2×C4C22×C22⋊D511yescharacteristic
704C2×C4C24×D511yescharacteristic
705C8—102no—
706C8—102no—
707C8—102no—
708C8—102no—
709C5C2×#337011yescharacteristic, complemented, Sylow
710C22—42no—
711C22—42no—
712C22—42no—
713C22—42no—
714C22—42no—
715C22—42no—
716C22—84no—
717C22—84no—
718C22—104no—
719C22—202no—
720C22—202no—
721C22—208no—
722C22#6615612yes—
723C22#6616512yes—
724C22#6616912yes—
725C22C23×C22⋊D511yescharacteristic
726C4—22no—
727C4—22no—
728C4—22no—
729C4—22no—
730C4—22no—
731C4—22no—
732C4—42no—
733C4—42no—
734C4—202no—
735C4—202no—
736C4—202no—
737C4#6616512yes—
738C4C2×D5×#4111yescharacteristic
739C4C2×#415011yescharacteristic
740C2—82no—
741C2—82no—
742C2—204no—
743C2#1061544514yesdirect product factor
744C2C2×#6615611yescharacteristic
745C2C2×#6616511yescharacteristic
746C2C2×#6616911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×#559C2
socleC23×C5C22×D4
prime radicalC2×#65361C2
hypercenterC2×#559D5
hypocenterC5C2×#3370
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#559

Complements

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

NH ≅ G/Ntype
1. C2×C5×#559C2semidirect
2. C2×#65913C2semidirect
3. #10615445C2direct (N × H)
5. C2×#65360C2semidirect
6. C2×#65346C2semidirect
7. C2×#65346C2semidirect
8. C2×#65344C2semidirect
9. C2×#65345C2semidirect
10. C2×#65315C2semidirect
11. C2×#65313C2semidirect
12. C2×#65311C2semidirect
13. C2×#65298C2semidirect
14. C2×#65296C2semidirect
15. C2×#65303C2semidirect
16. C2×C4×#686C2semidirect
18. C5×#559C22semidirect
35. #65913C22semidirect
55. #65360C22semidirect
56. #65346C22semidirect
57. #65346C22semidirect
58. #65345C22semidirect
59. #65344C22semidirect
60. #65315C22semidirect
61. #65313C22semidirect
62. #65311C22semidirect
63. #65303C22semidirect
64. C4×#686C22semidirect
65. #65298C22semidirect
66. #65296C22semidirect
180. C2×#559D5semidirect
293. #559C2×D5semidirect
640. C2×C5#3370semidirect
709. C5C2×#3370semidirect
743. C2#10615445direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#5592
C2×#659132
#106154452
C2×#653612
C2×#653602
C2×#653462
C2×#653442
C2×#653452
C2×#653152
C2×#653132
C2×#653112
C2×#652982
C2×#652962
C2×#653032
C2×C4×#6862
C2×#33705