Finite Group Databasebeta

← C2×#10615176 #12969170

Subgroups — C2×#10615176 #12969170

Order 1280.

1906 conjugacy classes of subgroups.

The subgroup lattice has 734 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#541C211yesmaximal, characteristic, complemented
2C2×#65868C211yesmaximal, characteristic
3#10615176C2116yesmaximal, direct product factor
4C2×#65375C211yesmaximal, characteristic, complemented
5C2×#65370C211yesmaximal, characteristic, complemented
6C2×#65354C211yesmaximal, characteristic, complemented
7C2×#65357C211yesmaximal, characteristic, complemented
8C2×#65341C211yesmaximal, characteristic, complemented
9C2×#65338C211yesmaximal, characteristic
10C2×#65340C211yesmaximal, characteristic, complemented
11C2×#65337C211yesmaximal, characteristic
12C2×#65315C211yesmaximal, characteristic, complemented
13C2×#65319C211yesmaximal, characteristic, complemented
14C2×C4×#689C211yesmaximal, characteristic, complemented
15C2×C4×#688C211yesmaximal, characteristic, complemented
16C2×#65286C211yesmaximal, characteristic, complemented
17C5×#541—24no—
18C5×#541C2218yescomplemented
19C2×C5×C4⋊Q8C2211yescharacteristic
20C2×C5×#126—21no—
21C2×C5×#126—21no—
22C2×C5×#125—21no—
23C2×C5×#125—21no—
24C2×C5×#125C2211yescharacteristic
25C2×C5×C22⋊Q8C2211yescharacteristic
26C2×C5×C22⋊Q8C2211yescharacteristic
27C2×C4×C5×Q8C2211yescharacteristic
28C2×C4×C5×Q8C2211yescharacteristic
29C2×C5×#117C2211yescharacteristic
30C22×#689C2211yescharacteristic
31C22×#689C2211yescharacteristic
32C22×#688C2211yescharacteristic
33C22×#688C2211yescharacteristic
34C2×#4076C2211yescharacteristic
35C2×#4070C2211yescharacteristic
36C22×#681C2211yescharacteristic
37C23×#168C2211yescharacteristic
38#65868—24no—
39#65868C2218yes—
40C2×#4044—21no—
41C2×#4042—21no—
42C2×#4031—21no—
43C2×#4029—21no—
44C2×#4021C2211yescharacteristic
45C2×C4×D20C2211yescharacteristic
46C2×#4015C2211yescharacteristic
47C2×C4×Dic10C2211yescharacteristic
48C2×#3967C2211yescharacteristic
49C2×#3967C2211yescharacteristic
50C2×#3967C2211yescharacteristic
51C2×#3967C2211yescharacteristic
52#65375C2218yescomplemented
53#65370C2218yescomplemented
54#65357C2218yescomplemented
55#65354C2218yescomplemented
56#65341C2218yescomplemented
57#65340C2218yescomplemented
58#65338C2218yes—
59#65337C2218yes—
60#65319C2218yescomplemented
61C4×#689C2218yescomplemented
62#65315C2218yescomplemented
63C4×#688C2218yescomplemented
64#65286C2218yescomplemented
65C2×#3942C2211yescharacteristic
66C2×#3942C2211yescharacteristic
67C2×#3941C2211yescharacteristic
68C2×#3941C2211yescharacteristic
69C2×#3940C2211yescharacteristic
70C2×#3940C2211yescharacteristic
71C2×#3939C2211yescharacteristic
72C2×#3939C2211yescharacteristic
73C2×#3935C2211yescharacteristic
74C2×#3935C2211yescharacteristic
75C2×C4×#168C2211yescharacteristic
76C2×C4×#168C2211yescharacteristic
77C2×#3178—51nomaximal, Sylow
78C22×C5×Q8C2311yescharacteristic
79C22×C5×Q8C2311yescharacteristic
80C23×C4×C5C2311yescharacteristic
81C22×C22⋊D5—21no—
82C22×D20C2311yescharacteristic
83C22×C4×D5—21no—
84C22×Dic10—21no—
85C22×Dic10C2311yescharacteristic
86C5×C4⋊Q8—22no—
87C5×C4⋊Q8C2314yes—
88C5×#126—28no—
89C5×#126—28no—
90C5×#125—28no—
91C5×#125—28no—
92C5×#125—22no—
93C5×#125C2314yes—
94C5×C22⋊Q8—22no—
95C5×C22⋊Q8—22no—
96C5×C22⋊Q8C2314yes—
97C5×C22⋊Q8C2314yes—
98C4×C5×Q8—22no—
99C4×C5×Q8—22no—
100C4×C5×Q8C2314yes—
101C4×C5×Q8C2314yes—
102C5×#117D414yes—
103C5×#117C2314yes—
104C2×C5×C4⋊C4—21no—
105C2×C5×C4⋊C4—21no—
106C2×C5×C4⋊C4—21no—
107C2×C5×C4⋊C4—21no—
108C2×C5×C4⋊C4—21no—
109C2×C5×C4⋊C4—21no—
110C2×C5×C4⋊C4—21no—
111C2×C5×C4⋊C4—21no—
112C2×C5×C4⋊C4D411yescharacteristic
113C2×C5×C4⋊C4D411yescharacteristic
114C2×C5×C4⋊C4C2311yescharacteristic
115C2×C5×C4⋊C4C2311yescharacteristic
116C2×C5×C22⋊C4—21no—
117C2×C5×C22⋊C4—21no—
118C2×C5×C22⋊C4D411yescharacteristic
119C2×C5×C22⋊C4D411yescharacteristic
120C2×C42×C5—21no—
121C2×C42×C5—21no—
122C2×C42×C5C2311yescharacteristic
123C2×C42×C5C2311yescharacteristic
124C2×C22⋊Dic5—21no—
125C2×#689—24no—
126C2×#689—24no—
127C2×#689C2314yes—
128C2×#689C2314yes—
129C2×#688—24no—
130C2×#688—24no—
131C2×#688C2314yes—
132C2×#688C2314yes—
133#4076—22no—
134#4076C2314yes—
135C2×#685—21no—
136C2×#685—21no—
137C2×#685—21no—
138C2×#685—21no—
139C2×C4⋊Dic5—21no—
140C2×C4⋊Dic5C2311yescharacteristic
141C2×C4⋊Dic5C2311yescharacteristic
142#4070—22no—
143#4070C2314yes—
144C2×#683—21no—
145C2×#683—21no—
146C2×C4×Dic5—21no—
147C2×#681—24no—
148C2×#681C2314yes—
149C22×#168—24no—
150C22×#168C2314yes—
151C22×#168C2311yescharacteristic
152C22×#168C2311yescharacteristic
153C22×#168C2311yescharacteristic
154C22×#168C2311yescharacteristic
155#4044—28no—
156#4042—28no—
157#4031—28no—
158#4029—28no—
159#4021—22no—
160#4021C2314yes—
161C4×D20—22no—
162C4×D20C2314yes—
163#4015—22no—
164#4015C2314yes—
165C4×Dic10—22no—
166C4×Dic10C2314yes—
167#3967C2314yes—
168#3967C2314yes—
169#3967C2314yes—
170#3967C2314yes—
171#3942C2314yes—
172#3942C2314yes—
173#3941C2314yes—
174#3941C2314yes—
175#3940C2314yes—
176#3940C2314yes—
177#3939C2314yes—
178#3939C2314yes—
179#3935C2314yes—
180#3935C2314yes—
181C4×#168C2314yes—
182C4×#168C2314yes—
183C2×#542—51no—
184C2×#541D511yescharacteristic, complemented
185#3178—516no—
186C2×#501—51no—
187C2×#497—51no—
188C2×#488—51no—
189C2×#487—51no—
190C2×#470—51no—
191C2×#468—51no—
192C2×#467—51no—
193C2×#465—51no—
194C2×#441—51no—
195C2×#440—51no—
196C2×C4×Q16—51no—
197C2×C4×SD16—51no—
198C2×#405—51no—
199C24×C5C2×D411yescharacteristic
200C23×D5—21no—
201C2×C5×Q8—21no—
202C2×C5×Q8—21no—
203C2×C5×Q8—22no—
204C2×C5×Q8—22no—
205C2×C5×Q8—22no—
206C2×C5×Q8—22no—
207C2×C5×Q8C2412yes—
208C2×C5×Q8C2412yes—
209C22×C4×C5—22no—
210C22×C4×C5—22no—
211C22×C4×C5—21no—
212C22×C4×C5—21no—
213C22×C4×C5—21no—
214C22×C4×C5—21no—
215C22×C4×C5C2×D411yescharacteristic
216C22×C4×C5C2×D411yescharacteristic
217C22×C4×C5C2×D411yescharacteristic
218C22×C4×C5C2×D411yescharacteristic
219C22×C4×C5C2×D411yescharacteristic
220C22×C4×C5C2×D412yes—
221C22×C4×C5C2412yes—
222C22×C4×C5C2411yescharacteristic
223C2×C22⋊D5—24no—
224C2×C22⋊D5—82no—
225C22×Dic5—21no—
226C22×Dic5—21no—
227C22×Dic5—21no—
228C2×D20—22no—
229C2×D20—22no—
230C2×D20—21no—
231C2×D20C2412yes—
232C2×C4×D5—24no—
233C2×C4×D5—82no—
234C2×Dic10—22no—
235C2×Dic10—22no—
236C2×Dic10—21no—
237C2×Dic10—24no—
238C2×Dic10—82no—
239C2×Dic10C2412yes—
240C5×C4⋊C4—24no—
241C5×C4⋊C4—24no—
242C5×C4⋊C4—24no—
243C5×C4⋊C4—24no—
244C5×C4⋊C4—24no—
245C5×C4⋊C4—24no—
246C5×C4⋊C4—24no—
247C5×C4⋊C4—24no—
248C5×C4⋊C4—21no—
249C5×C4⋊C4—21no—
250C5×C4⋊C4C2×D414yes—
251C5×C4⋊C4C2×D414yes—
252C5×C4⋊C4C2412yes—
253C5×C4⋊C4C2412yes—
254C5×C22⋊C4—24no—
255C5×C22⋊C4—24no—
256C5×C22⋊C4C2×D414yes—
257C5×C22⋊C4C2×D414yes—
258C42×C5—24no—
259C42×C5—24no—
260C42×C5C2×D412yes—
261C42×C5C2×D412yes—
262C42×C5C2412yes—
263C42×C5C2412yes—
264C22⋊Dic5—24no—
265#689—28no—
266#689—28no—
267#688—28no—
268#688—28no—
269#685—24no—
270#685—24no—
271#685—24no—
272#685—24no—
273C4⋊Dic5—21no—
274C4⋊Dic5—21no—
275C4⋊Dic5—24no—
276C4⋊Dic5C2412yes—
277C4⋊Dic5C2412yes—
278#683—24no—
279#683—24no—
280C4×Dic5—24no—
281#681—28no—
282C2×#168—22no—
283C2×#168—22no—
284C2×#168—28no—
285C2×#168#4114yes—
286C2×#168#4114yes—
287C2×#168C2412yes—
288C2×#168C2412yes—
289C2×#168C2412yes—
290C2×#168C2412yes—
291C22×Q16—51no—
292C22×Q16—51no—
293C22×SD16—51no—
294C22×SD16—51no—
295C22×M16—51no—
296C23×C8—51no—
297#542—58no—
298#542—104no—
299#541—24no—
300#541C2×D518yescomplemented
301C2×C4⋊Q8—51no—
302C2×C4⋊Q8C2×D511yescharacteristic
303C2×#126—21no—
304C2×#126—21no—
305C2×#126—101no—
306C2×#125—21no—
307C2×#125—21no—
308C2×#125C2×D511yescharacteristic
309C2×#124—51no—
310C2×#124—101no—
311C2×#123—101no—
312C2×C22⋊Q8—51no—
313C2×C22⋊Q8—101no—
314C2×C22⋊Q8C2×D511yescharacteristic
315C2×C22⋊Q8C2×D511yescharacteristic
316C2×#121—51no—
317C2×C4×Q8—51no—
318C2×C4×Q8C2×D511yescharacteristic
319C2×C4×Q8C2×D511yescharacteristic
320C2×C4×D4—51no—
321C2×#117C2×D511yescharacteristic
322#501—58no—
323#497—58no—
324#488—58no—
325#487—58no—
326#470—58no—
327#468—58no—
328#467—58no—
329#465—58no—
330#441—58no—
331#440—58no—
332C4×Q16—58no—
333C4×SD16—58no—
334C2×#107—51no—
335C2×#107—51no—
336C2×#106—51no—
337C2×#106—51no—
338C2×#103—51no—
339C2×#103—51no—
340C2×#103—51no—
341C2×#103—51no—
342C2×#103—51no—
343C2×#103—51no—
344C2×#102—51no—
345C2×#102—51no—
346#405—58no—
347C2×#97—51no—
348C2×#97—51no—
349C2×C4×C8—51no—
350C2×C4×C8—51no—
351C23×C5—22no—
352C23×C5—22no—
353C23×C5—22no—
354C23×C5C22×D412yes—
355C23×C5C22×D411yescharacteristic
356C22×D5—22no—
357C22×D5—42no—
358C22×D5—42no—
359C22×D5—42no—
360C5×Q8—22no—
361C5×Q8—22no—
362C5×Q8—22no—
363C5×Q8—22no—
364C5×Q8—42no—
365C5×Q8—42no—
366C2×C4×C5—22no—
367C2×C4×C5—22no—
368C2×C4×C5—22no—
369C2×C4×C5—22no—
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—22no—
378C2×C4×C5—42no—
379C2×C4×C5—42no—
380C2×C4×C5—42no—
381C2×C4×C5—42no—
382C2×C4×C5C22×D412yes—
383C2×C4×C5C22×D412yes—
384C2×C4×C5C22×D412yes—
385C2×C4×C5C22×D412yes—
386C2×C4×C5C22×D412yes—
387C2×C4×C5C22×D411yescharacteristic
388C2×C4×C5C2×#4112yes—
389C2×C4×C5C2×#4112yes—
390C2×C4×C5C2511yescharacteristic
391C22⋊D5—84no—
392C2×Dic5—22no—
393C2×Dic5—22no—
394C2×Dic5—22no—
395C2×Dic5—42no—
396C2×Dic5—42no—
397C2×Dic5—42no—
398D20—22no—
399D20—22no—
400D20—42no—
401C4×D5—84no—
402Dic10—22no—
403Dic10—22no—
404Dic10—42no—
405Dic10—84no—
406#168—22no—
407#168—22no—
408#168C2×#4114yes—
409#168C2×#4114yes—
410C22×Q8—51no—
411C22×Q8—101no—
412C22×Q8C22×D511yescharacteristic
413C22×Q8C22×D511yescharacteristic
414C22×D4—51no—
415C22×D4—101no—
416C23×C4—101no—
417C23×C4C22×D511yescharacteristic
418C2×Q16—54no—
419C2×Q16—54no—
420C2×Q16—104no—
421C2×Q16—104no—
422C2×SD16—54no—
423C2×SD16—54no—
424C2×SD16—104no—
425C2×SD16—104no—
426C2×M16—54no—
427C2×M16—104no—
428C22×C8—51no—
429C22×C8—51no—
430C22×C8—51no—
431C22×C8—54no—
432C22×C8—51no—
433C22×C8—104no—
434C4⋊Q8—22no—
435C4⋊Q8—54no—
436C4⋊Q8—102no—
437C4⋊Q8C22×D514yes—
438#126—28no—
439#126—28no—
440#126—108no—
441#125—28no—
442#125—28no—
443#125—22no—
444#125C22×D514yes—
445#124—54no—
446#124—108no—
447#124—102no—
448#123—108no—
449C22⋊Q8—22no—
450C22⋊Q8—22no—
451C22⋊Q8—54no—
452C22⋊Q8—102no—
453C22⋊Q8—108no—
454C22⋊Q8C22×D514yes—
455C22⋊Q8C22×D514yes—
456#121—54no—
457#121—102no—
458C4×Q8—22no—
459C4×Q8—22no—
460C4×Q8—54no—
461C4×Q8—102no—
462C4×Q8C22×D514yes—
463C4×Q8C22×D514yes—
464C4×D4—54no—
465C4×D4—102no—
466#117C22⋊D514yes—
467#117C22×D514yes—
468C2×C4⋊C4—21no—
469C2×C4⋊C4—21no—
470C2×C4⋊C4—21no—
471C2×C4⋊C4—21no—
472C2×C4⋊C4—21no—
473C2×C4⋊C4—21no—
474C2×C4⋊C4—21no—
475C2×C4⋊C4—21no—
476C2×C4⋊C4—51no—
477C2×C4⋊C4—51no—
478C2×C4⋊C4—101no—
479C2×C4⋊C4—101no—
480C2×C4⋊C4—101no—
481C2×C4⋊C4C22⋊D511yescharacteristic
482C2×C4⋊C4C22⋊D511yescharacteristic
483C2×C4⋊C4C22×D511yescharacteristic
484C2×C4⋊C4C22×D511yescharacteristic
485C2×C22⋊C4—21no—
486C2×C22⋊C4—21no—
487C2×C22⋊C4—101no—
488C2×C22⋊C4—101no—
489C2×C22⋊C4—101no—
490C2×C22⋊C4—101no—
491C2×C22⋊C4—101no—
492C2×C22⋊C4C22⋊D511yescharacteristic
493C2×C22⋊C4C22⋊D511yescharacteristic
494C2×C42—21no—
495C2×C42—21no—
496C2×C42—101no—
497C2×C42C22×D511yescharacteristic
498C2×C42C22×D511yescharacteristic
499#107—54no—
500#107—54no—
501#106—54no—
502#106—54no—
503#103—54no—
504#103—54no—
505#103—54no—
506#103—54no—
507#103—54no—
508#103—54no—
509#102—54no—
510#102—54no—
511#97—54no—
512#97—54no—
513C4×C8—54no—
514C4×C8—54no—
515C22×C5—22no—
516C22×C5—22no—
517C22×C5—22no—
518C22×C5—44no—
519C22×C5#53212yes—
520C22×C5#57712yes—
521C22×C5#57812yes—
522C22×C5C23×D411yescharacteristic
523C2×D5—42no—
524C2×D5—42no—
525C2×D5—42no—
526C2×D5—84no—
527C4×C5—22no—
528C4×C5—22no—
529C4×C5—22no—
530C4×C5—22no—
531C4×C5—22no—
532C4×C5—42no—
533C4×C5—42no—
534C4×C5—42no—
535C4×C5—42no—
536C4×C5#53212yes—
537C4×C5C22×#4111yescharacteristic
538C4×C5C22×#4111yescharacteristic
539Dic5—42no—
540Dic5—42no—
541Dic5—42no—
542C24—101no—
543C24C2×C22⋊D511yescharacteristic
544C2×Q8—21no—
545C2×Q8—21no—
546C2×Q8—22no—
547C2×Q8—22no—
548C2×Q8—22no—
549C2×Q8—22no—
550C2×Q8—52no—
551C2×Q8—101no—
552C2×Q8—104no—
553C2×Q8—102no—
554C2×Q8—102no—
555C2×Q8—402no—
556C2×Q8C23×D512yes—
557C2×Q8C23×D512yes—
558C2×D4—52no—
559C2×D4—104no—
560C2×D4—102no—
561C2×D4—102no—
562C2×D4—101no—
563C2×D4—402no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—101no—
571C22×C4—101no—
572C22×C4—101no—
573C22×C4—104no—
574C22×C4—402no—
575C22×C4C2×C22⋊D512yes—
576C22×C4C2×C22⋊D511yescharacteristic
577C22×C4C2×C22⋊D511yescharacteristic
578C22×C4C2×C22⋊D511yescharacteristic
579C22×C4C2×C22⋊D511yescharacteristic
580C22×C4C2×C22⋊D511yescharacteristic
581C22×C4C23×D512yes—
582C22×C4C23×D511yescharacteristic
583Q16—108no—
584Q16—108no—
585SD16—108no—
586SD16—108no—
587M16—108no—
588C2×C8—54no—
589C2×C8—54no—
590C2×C8—52no—
591C2×C8—52no—
592C2×C8—52no—
593C2×C8—52no—
594C2×C8—108no—
595C2×C8—102no—
596C2×C8—102no—
597C4⋊C4—24no—
598C4⋊C4—24no—
599C4⋊C4—24no—
600C4⋊C4—24no—
601C4⋊C4—24no—
602C4⋊C4—24no—
603C4⋊C4—24no—
604C4⋊C4—24no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—52no—
608C4⋊C4—52no—
609C4⋊C4—101no—
610C4⋊C4—101no—
611C4⋊C4—104no—
612C4⋊C4—104no—
613C4⋊C4—104no—
614C4⋊C4C2×C22⋊D514yes—
615C4⋊C4C2×C22⋊D514yes—
616C4⋊C4C23×D512yes—
617C4⋊C4C23×D512yes—
618C22⋊C4—24no—
619C22⋊C4—24no—
620C22⋊C4—104no—
621C22⋊C4—104no—
622C22⋊C4—104no—
623C22⋊C4—104no—
624C22⋊C4—104no—
625C22⋊C4C2×C22⋊D514yes—
626C22⋊C4C2×C22⋊D514yes—
627C42—24no—
628C42—24no—
629C42—104no—
630C42C2×C22⋊D512yes—
631C42C2×C22⋊D512yes—
632C42C23×D512yes—
633C42C23×D512yes—
634C2×C5—42no—
635C2×C5#317814yescomplemented
636C2×C5C2×#53211yescharacteristic
637C2×C5C2×#57711yescharacteristic
638C2×C5C2×#57811yescharacteristic
639D5—82no—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—102no—
644C23—202no—
645C23—202no—
646C23—202no—
647C23C22×C22⋊D512yes—
648C23C22×C22⋊D511yescharacteristic
649Q8—22no—
650Q8—22no—
651Q8—22no—
652Q8—22no—
653Q8—42no—
654Q8—42no—
655Q8—102no—
656Q8—102no—
657Q8—202no—
658Q8—404no—
659D4—102no—
660D4—102no—
661D4—202no—
662D4—404no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—24no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—102no—
680C2×C4—102no—
681C2×C4—102no—
682C2×C4—202no—
683C2×C4—202no—
684C2×C4—202no—
685C2×C4—404no—
686C2×C4D5×#4112yes—
687C2×C4D5×#4112yes—
688C2×C4C22×C22⋊D512yes—
689C2×C4C22×C22⋊D512yes—
690C2×C4C22×C22⋊D512yes—
691C2×C4C22×C22⋊D512yes—
692C2×C4C22×C22⋊D512yes—
693C2×C4C22×C22⋊D511yescharacteristic
694C2×C4C24×D511yescharacteristic
695C8—54no—
696C8—54no—
697C8—102no—
698C8—102no—
699C5C2×#317811yescharacteristic, complemented, Sylow
700C22—22no—
701C22—22no—
702C22—22no—
703C22—44no—
704C22—202no—
705C22—202no—
706C22—202no—
707C22—404no—
708C22#6616612yes—
709C22#6617112yes—
710C22#6617212yes—
711C22C23×C22⋊D511yescharacteristic
712C4—22no—
713C4—22no—
714C4—22no—
715C4—22no—
716C4—22no—
717C4—42no—
718C4—42no—
719C4—42no—
720C4—42no—
721C4—202no—
722C4—202no—
723C4—202no—
724C4#6616612yes—
725C4C2×D5×#4111yescharacteristic
726C4C2×D5×#4111yescharacteristic
727C2—42no—
728C2—402no—
729C2#1061517614yesdirect product factor
730C2C2×#6616611yescharacteristic
731C2C2×#6617111yescharacteristic
732C2C2×#6617211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×#541C2
socleC23×C5C22×D4
prime radicalC2×#4076C22
hypercenterC2×#541D5
hypocenterC5C2×#3178
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#541

Complements

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

NH ≅ G/Ntype
1. C2×C5×#541C2semidirect
3. #10615176C2direct (N × H)
4. C2×#65375C2semidirect
5. C2×#65370C2semidirect
6. C2×#65354C2semidirect
7. C2×#65357C2semidirect
8. C2×#65341C2semidirect
10. C2×#65340C2semidirect
12. C2×#65315C2semidirect
13. C2×#65319C2semidirect
14. C2×C4×#689C2semidirect
15. C2×C4×#688C2semidirect
16. C2×#65286C2semidirect
18. C5×#541C22semidirect
52. #65375C22semidirect
53. #65370C22semidirect
54. #65357C22semidirect
55. #65354C22semidirect
56. #65341C22semidirect
57. #65340C22semidirect
60. #65319C22semidirect
61. C4×#689C22semidirect
62. #65315C22semidirect
63. C4×#688C22semidirect
64. #65286C22semidirect
184. C2×#541D5semidirect
300. #541C2×D5semidirect
635. C2×C5#3178semidirect
699. C5C2×#3178semidirect
729. C2#10615176direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#5412
C2×#658682
#106151762
C2×#653752
C2×#653702
C2×#653542
C2×#653572
C2×#653412
C2×#653382
C2×#653402
C2×#653372
C2×#653152
C2×#653192
C2×C4×#6892
C2×C4×#6882
C2×#652862
C2×#31785