Finite Group Databasebeta

← C2×#10611515 #12967446

Subgroups — C2×#10611515 #12967446

Order 1280.

2150 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×Q8×D5C211yesmaximal, characteristic, complemented
2C2×#65891C211yesmaximal, characteristic
3C2×C5×#440C211yesmaximal, characteristic, complemented
4C2×#65459C211yesmaximal, characteristic
5C2×#65455C211yesmaximal, characteristic, complemented
6C2×#65319C211yesmaximal, characteristic, complemented
7C2×#65307C211yesmaximal, characteristic, complemented
8#10611515C2116yesmaximal, direct product factor
9C2×#65166C211yesmaximal, characteristic, complemented
10C2×#65173C211yesmaximal, characteristic, complemented
11C2×#65097C211yesmaximal, characteristic, complemented
12C2×#65088C211yesmaximal, characteristic, complemented
13C2×#65056C211yesmaximal, characteristic, complemented
14C2×#65066C211yesmaximal, characteristic
15C2×#65005C211yesmaximal, characteristic, complemented
16C2×#64994C211yesmaximal, characteristic, complemented
17C22×Q8×D5C2211yescharacteristic
18C22×C5×SD16C2211yescharacteristic
19C2×C4×C5×Q8C2211yescharacteristic
20C2×C4×C5×D4C2211yescharacteristic
21C2×Q8×Dic5C2211yescharacteristic
22C22×#689C2211yescharacteristic
23C2×#4084C2211yescharacteristic
24C2×#4082C2211yescharacteristic
25C22×#687C2211yescharacteristic
26C2×C4×C22⋊D5—21no—
27C2×#4072—21no—
28C22×Dic20C2211yescharacteristic
29C4×Q8×D5—24no—
30C4×Q8×D5C2218yescomplemented
31#65891—24no—
32#65891C2218yes—
33C2×#4043C2211yescharacteristic
34C2×D5×C4⋊C4—21no—
35C2×D5×C4⋊C4C2211yescharacteristic
36C2×#4036C2211yescharacteristic
37C2×#4033—21no—
38C2×#4033C2211yescharacteristic
39C2×#4029—21no—
40C2×#4025—21no—
41C2×C42×D5—21no—
42C2×C42×D5C2211yescharacteristic
43C2×C4×Dic10—21no—
44C2×C4×Dic10C2211yescharacteristic
45C2×C4×Dic10C2211yescharacteristic
46C5×#440C2218yescomplemented
47C2×C5×#107C2211yescharacteristic
48C2×C5×#103C2211yescharacteristic
49C2×C5×#102C2211yescharacteristic
50C2×C5×#97C2211yescharacteristic
51C2×#3967C2211yescharacteristic
52C2×#3964C2211yescharacteristic
53#65459C2218yes—
54#65455C2218yescomplemented
55C2×#3952C2211yescharacteristic
56C2×#3952C2211yescharacteristic
57C2×#3949C2211yescharacteristic
58C2×#3948C2211yescharacteristic
59C2×#3948C2211yescharacteristic
60C2×#3946C2211yescharacteristic
61C2×#3946C2211yescharacteristic
62#65319C2218yescomplemented
63#65307C2218yescomplemented
64C2×#3942C2211yescharacteristic
65C2×#3942C2211yescharacteristic
66C2×#3940C2211yescharacteristic
67C2×#3939C2211yescharacteristic
68C2×#3935C2211yescharacteristic
69#65173C2218yescomplemented
70#65166C2218yescomplemented
71#65097C2218yescomplemented
72#65088C2218yescomplemented
73#65066C2218yes—
74#65056C2218yescomplemented
75#65005C2218yescomplemented
76#64994C2218yescomplemented
77C2×#3117—51nomaximal, Sylow
78C22×C5×Q8C2311yescharacteristic
79C22×C5×D4C2311yescharacteristic
80C23×C4×C5—21no—
81C22×C22⋊D5—21no—
82C2×Q8×D5—24no—
83C2×Q8×D5—22no—
84C2×Q8×D5—24no—
85C2×Q8×D5C2314yes—
86C22×C4×D5—21no—
87C22×C4×D5—21no—
88C22×C4×D5D411yescharacteristic
89C22×C4×D5D411yescharacteristic
90C22×C4×D5C2311yescharacteristic
91C22×Dic10—21no—
92C22×Dic10C2311yescharacteristic
93C22×Dic10C2311yescharacteristic
94C2×C5×SD16—24no—
95C2×C5×SD16C2314yes—
96C22×C5×C8C2311yescharacteristic
97C22×C5×C8C2311yescharacteristic
98C4×C5×Q8—22no—
99C4×C5×Q8C2314yes—
100C4×C5×D4—22no—
101C4×C5×D4C2314yes—
102C2×C5×C4⋊C4—21no—
103C2×C5×C4⋊C4C2311yescharacteristic
104C2×C5×C4⋊C4C2311yescharacteristic
105C2×C5×C22⋊C4—21no—
106C2×C42×C5—21no—
107C2×C42×C5C2311yescharacteristic
108C2×C22⋊Dic5—21no—
109C2×C22⋊Dic5—21no—
110C2×C22⋊Dic5—21no—
111Q8×Dic5—22no—
112Q8×Dic5C2314yes—
113C2×#689—24no—
114C2×#689C2314yes—
115#4084—22no—
116#4084C2314yes—
117#4082—22no—
118#4082C2314yes—
119C2×#687—24no—
120C2×#687C2314yes—
121C4×C22⋊D5—28no—
122C2×#685—21no—
123#4072—28no—
124C2×C4⋊Dic5—21no—
125C2×C4⋊Dic5—21no—
126C2×C4⋊Dic5—21no—
127C2×C4⋊Dic5C2311yescharacteristic
128C2×C4⋊Dic5C2311yescharacteristic
129C2×#683—21no—
130C2×#683—21no—
131C2×#683—21no—
132C2×#683—21no—
133C2×#683—21no—
134C2×C4×Dic5—21no—
135C2×C4×Dic5—21no—
136C2×C4×Dic5—21no—
137C2×C4×Dic5—21no—
138C2×C4×Dic5D411yescharacteristic
139C2×C4×Dic5D411yescharacteristic
140C2×C4×Dic5C2311yescharacteristic
141C22×#168C2311yescharacteristic
142C22×#168C2311yescharacteristic
143C2×Dic20—24no—
144C2×Dic20C2314yes—
145#4043—22no—
146#4043C2314yes—
147D5×C4⋊C4—28no—
148D5×C4⋊C4—22no—
149D5×C4⋊C4C2314yes—
150#4036—22no—
151#4036C2314yes—
152#4033—28no—
153#4033—22no—
154#4033C2314yes—
155#4029—28no—
156#4025—28no—
157C42×D5—28no—
158C42×D5D414yes—
159C42×D5C2314yes—
160C4×Dic10—22no—
161C4×Dic10—22no—
162C4×Dic10—28no—
163C4×Dic10C2314yes—
164C4×Dic10C2314yes—
165C5×#107C2314yes—
166C5×#103C2314yes—
167C5×#102C2314yes—
168C5×#97C2314yes—
169#3967C2314yes—
170#3964C2314yes—
171#3952C2314yes—
172#3952C2314yes—
173#3949C2314yes—
174#3948C2314yes—
175#3948C2314yes—
176#3946C2314yes—
177#3946C2314yes—
178#3942C2314yes—
179#3942C2314yes—
180#3940C2314yes—
181#3939C2314yes—
182#3935C2314yes—
183C2×#529—51no—
184C22×C4×Q8—51no—
185#3117—516no—
186C2×#484—51no—
187C2×#481—51no—
188C2×#479—51no—
189C2×#479—51no—
190C2×#464—51no—
191C2×#464—51no—
192C2×#451—51no—
193C2×#448—51no—
194C2×#441—51no—
195C2×#441—51no—
196C2×#440—51no—
197C2×#440D511yescharacteristic, complemented
198C2×#432—51no—
199C24×C5—21no—
200C23×D5C2×D411yescharacteristic
201C2×C5×Q8—21no—
202C2×C5×Q8—22no—
203C2×C5×Q8#4114yes—
204C2×C5×Q8C2412yes—
205C2×C5×D4—21no—
206C2×C5×D4—22no—
207C2×C5×D4—22no—
208C2×C5×D4C2412yes—
209C22×C4×C5—21no—
210C22×C4×C5—21no—
211C22×C4×C5—21no—
212C22×C4×C5—24no—
213C22×C4×C5—44no—
214C22×C4×C5C2×D411yescharacteristic
215C22×C4×C5C2×D411yescharacteristic
216C22×C4×C5C2411yescharacteristic
217C2×C22⋊D5—24no—
218C2×C22⋊D5—44no—
219C22×Dic5—21no—
220C22×Dic5—21no—
221C22×Dic5—21no—
222C22×Dic5—21no—
223C22×Dic5C2×D411yescharacteristic
224C22×Dic5C2×D411yescharacteristic
225C22×Dic5C2×D411yescharacteristic
226Q8×D5—216no—
227Q8×D5—28no—
228Q8×D5—28no—
229C2×C4×D5—28no—
230C2×C4×D5—24no—
231C2×C4×D5—24no—
232C2×C4×D5—22no—
233C2×C4×D5—22no—
234C2×C4×D5—24no—
235C2×C4×D5—42no—
236C2×C4×D5—44no—
237C2×C4×D5C2×D414yes—
238C2×C4×D5C2×D412yes—
239C2×C4×D5C2×D414yes—
240C2×C4×D5C2412yes—
241C2×Dic10—28no—
242C2×Dic10—21no—
243C2×Dic10—22no—
244C2×Dic10—24no—
245C2×Dic10—22no—
246C2×Dic10—22no—
247C2×Dic10—21no—
248C2×Dic10#4114yes—
249C2×Dic10C2412yes—
250C2×Dic10C2412yes—
251C5×SD16—28no—
252C2×C5×C8—22no—
253C2×C5×C8—22no—
254C2×C5×C8C2412yes—
255C2×C5×C8C2412yes—
256C5×C4⋊C4—24no—
257C5×C4⋊C4—21no—
258C5×C4⋊C4—21no—
259C5×C4⋊C4C2412yes—
260C5×C4⋊C4C2412yes—
261C5×C22⋊C4—24no—
262C42×C5—24no—
263C42×C5C2×D412yes—
264C42×C5C2412yes—
265C22⋊Dic5—24no—
266C22⋊Dic5—24no—
267C22⋊Dic5—24no—
268#689—28no—
269#687—28no—
270#685—24no—
271C4⋊Dic5—21no—
272C4⋊Dic5—21no—
273C4⋊Dic5—24no—
274C4⋊Dic5—24no—
275C4⋊Dic5—24no—
276C4⋊Dic5C2412yes—
277C4⋊Dic5C2412yes—
278#683—24no—
279#683—24no—
280#683—24no—
281#683—24no—
282#683—24no—
283C4×Dic5—24no—
284C4×Dic5—24no—
285C4×Dic5—24no—
286C4×Dic5—24no—
287C4×Dic5C2×D414yes—
288C4×Dic5C2×D412yes—
289C4×Dic5C2×D414yes—
290C4×Dic5C2412yes—
291C2×#168—22no—
292C2×#168—22no—
293C2×#168C2412yes—
294C2×#168C2412yes—
295Dic20—28no—
296C23×Q8—51no—
297C22×Q16—51no—
298C22×Q16—51no—
299C22×SD16—51no—
300C22×SD16C2×D511yescharacteristic
301#529—58no—
302#529—104no—
303C2×#126—101no—
304C2×#125—51no—
305C2×#124—51no—
306C2×#123—101no—
307C2×C22⋊Q8—51no—
308C2×#121—51no—
309C2×C4×Q8—51no—
310C2×C4×Q8—58no—
311C2×C4×Q8—51no—
312C2×C4×Q8—51no—
313C2×C4×Q8—51no—
314C2×C4×Q8—101no—
315C2×C4×Q8—101no—
316C2×C4×Q8—104no—
317C2×C4×Q8C2×D511yescharacteristic
318C2×C4×D4—101no—
319C2×C4×D4C2×D511yescharacteristic
320C2×#117—101no—
321C22×C4⋊C4—51no—
322C22×C4⋊C4—101no—
323C22×C42—51no—
324C22×C42—101no—
325#484—58no—
326#481—58no—
327#479—58no—
328#479—58no—
329#464—58no—
330#464—58no—
331#451—58no—
332#448—58no—
333#441—58no—
334#441—58no—
335#440—58no—
336#440C2×D518yescomplemented
337#432—58no—
338C2×#107—51no—
339C2×#107C2×D511yescharacteristic
340C2×#106—51no—
341C2×#106—51no—
342C2×C4⋊C8—51no—
343C2×C4⋊C8—51no—
344C2×#103—51no—
345C2×#103—51no—
346C2×#103—51no—
347C2×#103—51no—
348C2×#103—51no—
349C2×#103C2×D511yescharacteristic
350C2×#102—51no—
351C2×#102C2×D511yescharacteristic
352C2×C22⋊C8—51no—
353C2×C22⋊C8—51no—
354C2×#97—51no—
355C2×#97C2×D511yescharacteristic
356C23×C5—22no—
357C23×C5—42no—
358C23×C5—42no—
359C23×C5—42no—
360C23×C5C22×D411yescharacteristic
361C22×D5—22no—
362C22×D5—22no—
363C22×D5#13714yes—
364C22×D5C22×D412yes—
365C5×Q8—24no—
366C5×Q8—22no—
367C5×Q8C2×#4114yes—
368C5×D4—22no—
369C5×D4—22no—
370C5×D4—42no—
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—48no—
378C2×C4×C5—42no—
379C2×C4×C5—42no—
380C2×C4×C5C22×D412yes—
381C2×C4×C5C22×D412yes—
382C2×C4×C5C22×D411yescharacteristic
383C2×C4×C5C2×#4112yes—
384C2×C4×C5C2×#4112yes—
385C2×C4×C5C2511yescharacteristic
386C22⋊D5—48no—
387C2×Dic5—22no—
388C2×Dic5—24no—
389C2×Dic5—22no—
390C2×Dic5—22no—
391C2×Dic5—22no—
392C2×Dic5—22no—
393C2×Dic5—22no—
394C2×Dic5—22no—
395C2×Dic5—42no—
396C2×Dic5—42no—
397C2×Dic5—42no—
398C2×Dic5C22×D412yes—
399C2×Dic5C22×D412yes—
400C2×Dic5C22×D412yes—
401C4×D5—216no—
402C4×D5—28no—
403C4×D5—24no—
404C4×D5—22no—
405C4×D5—22no—
406C4×D5—44no—
407C4×D5—48no—
408Dic10—216no—
409Dic10—24no—
410Dic10—22no—
411Dic10—22no—
412Dic10—22no—
413Dic10—42no—
414Dic10C2×#4114yes—
415C5×C8—22no—
416C5×C8—22no—
417#168—22no—
418#168—22no—
419C22×Q8—54no—
420C22×Q8—51no—
421C22×Q8—51no—
422C22×Q8—101no—
423C22×Q8—102no—
424C22×Q8—104no—
425C22×Q8—104no—
426C22×Q8C22×D511yescharacteristic
427C22×D4—101no—
428C22×D4C22×D511yescharacteristic
429C23×C4—21no—
430C23×C4—51no—
431C23×C4—51no—
432C23×C4—51no—
433C23×C4—101no—
434C23×C4—101no—
435C2×Q16—54no—
436C2×Q16—54no—
437C2×Q16—104no—
438C2×Q16—104no—
439C2×SD16—24no—
440C2×SD16—54no—
441C2×SD16—104no—
442C2×SD16C22×D514yes—
443C22×C8—51no—
444C22×C8—51no—
445C22×C8C22×D511yescharacteristic
446C22×C8C22×D511yescharacteristic
447#126—108no—
448#125—54no—
449#125—102no—
450#124—54no—
451#124—102no—
452#123—108no—
453C22⋊Q8—54no—
454C22⋊Q8—102no—
455#121—54no—
456#121—102no—
457C4×Q8—22no—
458C4×Q8—54no—
459C4×Q8—54no—
460C4×Q8—54no—
461C4×Q8—54no—
462C4×Q8—108no—
463C4×Q8—108no—
464C4×Q8—102no—
465C4×Q8—102no—
466C4×Q8—102no—
467C4×Q8—102no—
468C4×Q8C22×D514yes—
469C4×D4—22no—
470C4×D4—108no—
471C4×D4C22×D514yes—
472#117—108no—
473C2×C4⋊C4—21no—
474C2×C4⋊C4—51no—
475C2×C4⋊C4—51no—
476C2×C4⋊C4—54no—
477C2×C4⋊C4—102no—
478C2×C4⋊C4—108no—
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⋊C4C22×D511yescharacteristic
488C2×C4⋊C4C22×D511yescharacteristic
489C2×C22⋊C4—21no—
490C2×C22⋊C4—101no—
491C2×C22⋊C4—101no—
492C2×C22⋊C4—101no—
493C2×C22⋊C4—101no—
494C2×C42—21no—
495C2×C42—51no—
496C2×C42—51no—
497C2×C42—51no—
498C2×C42—54no—
499C2×C42—54no—
500C2×C42—108no—
501C2×C42—101no—
502C2×C42—101no—
503C2×C42—101no—
504C2×C42—101no—
505C2×C42C22×D511yescharacteristic
506#107—54no—
507#107C22×D514yes—
508#106—54no—
509#106—54no—
510C4⋊C8—54no—
511C4⋊C8—54no—
512#103—54no—
513#103—54no—
514#103—54no—
515#103—54no—
516#103—54no—
517#103C22×D514yes—
518#102—54no—
519#102C22×D514yes—
520C22⋊C8—54no—
521C22⋊C8—54no—
522#97—54no—
523#97C22×D514yes—
524C22×C5—42no—
525C22×C5—42no—
526C22×C5—42no—
527C22×C5—84no—
528C22×C5#52512yes—
529C22×C5C2×#13712yes—
530C22×C5#57512yes—
531C22×C5C23×D411yescharacteristic
532C2×D5—28no—
533C2×D5—22no—
534C2×D5—22no—
535C2×D5C2×#13714yes—
536C4×C5—24no—
537C4×C5—22no—
538C4×C5—22no—
539C4×C5—42no—
540C4×C5—42no—
541C4×C5#52512yes—
542C4×C5C22×#4111yescharacteristic
543C4×C5C22×#4111yescharacteristic
544Dic5—22no—
545Dic5—24no—
546Dic5—22no—
547Dic5—22no—
548Dic5—42no—
549Dic5—42no—
550Dic5—42no—
551C24—21no—
552C24—51no—
553C2×Q8—21no—
554C2×Q8—22no—
555C2×Q8—54no—
556C2×Q8—52no—
557C2×Q8—52no—
558C2×Q8—104no—
559C2×Q8—108no—
560C2×Q8—108no—
561C2×Q8—1016no—
562C2×Q8—108no—
563C2×Q8—102no—
564C2×Q8—101no—
565C2×Q8—101no—
566C2×Q8—102no—
567C2×Q8—102no—
568C2×Q8#70914yes—
569C2×Q8C23×D512yes—
570C2×D4—22no—
571C2×D4—21no—
572C2×D4—22no—
573C2×D4—104no—
574C2×D4—204no—
575C2×D4C23×D512yes—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—24no—
580C22×C4—44no—
581C22×C4—51no—
582C22×C4—51no—
583C22×C4—51no—
584C22×C4—54no—
585C22×C4—52no—
586C22×C4—52no—
587C22×C4—54no—
588C22×C4—104no—
589C22×C4—104no—
590C22×C4—108no—
591C22×C4—104no—
592C22×C4—101no—
593C22×C4—102no—
594C22×C4—102no—
595C22×C4—101no—
596C22×C4—101no—
597C22×C4—101no—
598C22×C4—202no—
599C22×C4—204no—
600C22×C4D4×D511yescharacteristic
601C22×C4D4×D511yescharacteristic
602C22×C4C23×D511yescharacteristic
603Q16—108no—
604Q16—108no—
605SD16—28no—
606SD16—108no—
607C2×C8—22no—
608C2×C8—22no—
609C2×C8—52no—
610C2×C8—52no—
611C2×C8—102no—
612C2×C8—102no—
613C2×C8C23×D512yes—
614C2×C8C23×D512yes—
615C4⋊C4—24no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—52no—
619C4⋊C4—52no—
620C4⋊C4—104no—
621C4⋊C4—104no—
622C4⋊C4—104no—
623C4⋊C4—104no—
624C4⋊C4—104no—
625C4⋊C4—104no—
626C4⋊C4—101no—
627C4⋊C4—101no—
628C4⋊C4—104no—
629C4⋊C4—104no—
630C4⋊C4C23×D512yes—
631C4⋊C4C23×D512yes—
632C22⋊C4—24no—
633C22⋊C4—104no—
634C22⋊C4—104no—
635C22⋊C4—104no—
636C22⋊C4—104no—
637C42—24no—
638C42—54no—
639C42—52no—
640C42—54no—
641C42—52no—
642C42—104no—
643C42—104no—
644C42—104no—
645C42—104no—
646C42D4×D512yes—
647C42C23×D512yes—
648C2×C5—82no—
649C2×C5#311714yescomplemented
650C2×C5C2×#52511yescharacteristic
651C2×C5C22×#13711yescharacteristic
652C2×C5C2×#57511yescharacteristic
653D5—24no—
654C23—22no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—54no—
659C23—52no—
660C23—102no—
661C23—102no—
662C23C2×D4×D511yescharacteristic
663Q8—24no—
664Q8—22no—
665Q8—54no—
666Q8—1016no—
667Q8—104no—
668Q8—102no—
669Q8—102no—
670Q8—102no—
671Q8—202no—
672Q8C2×#70914yes—
673D4—22no—
674D4—22no—
675D4—42no—
676D4—208no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—24no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—48no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—52no—
687C2×C4—52no—
688C2×C4—52no—
689C2×C4—108no—
690C2×C4—1016no—
691C2×C4—102no—
692C2×C4—102no—
693C2×C4—102no—
694C2×C4—104no—
695C2×C4—102no—
696C2×C4—104no—
697C2×C4—102no—
698C2×C4—102no—
699C2×C4—102no—
700C2×C4—102no—
701C2×C4—102no—
702C2×C4—204no—
703C2×C4—208no—
704C2×C4—202no—
705C2×C4—202no—
706C2×C4—202no—
707C2×C4C2×#70912yes—
708C2×C4C2×D4×D512yes—
709C2×C4C2×D4×D512yes—
710C2×C4C2×D4×D511yescharacteristic
711C2×C4D5×#4112yes—
712C2×C4C24×D511yescharacteristic
713C8—22no—
714C8—22no—
715C8—102no—
716C8—102no—
717C5C2×#311711yescharacteristic, complemented, Sylow
718C22—42no—
719C22—42no—
720C22—42no—
721C22—54no—
722C22—84no—
723C22—108no—
724C22—102no—
725C22—102no—
726C22#6588112yes—
727C22#6610712yes—
728C22D5×#13712yes—
729C22C22×D4×D511yescharacteristic
730C4—24no—
731C4—22no—
732C4—22no—
733C4—42no—
734C4—42no—
735C4—102no—
736C4—104no—
737C4—102no—
738C4—102no—
739C4—202no—
740C4—202no—
741C4—202no—
742C4#6588112yes—
743C4C22×#70911yescharacteristic
744C4C2×D5×#4111yescharacteristic
745C2—82no—
746C2—104no—
747C2#1061151514yesdirect product factor
748C2C2×#6588111yescharacteristic
749C2C2×#6610711yescharacteristic
750C2C2×D5×#13711yescharacteristic
subgroupG/H
centerC23C2×D4×D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×#440C2
socleC23×C5C22×D4
prime radicalC2×#4084C22
hypercenterC2×#440D5
hypocenterC5C2×#3117
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#440

Complements

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

NH ≅ G/Ntype
1. C2×C4×Q8×D5C2semidirect
3. C2×C5×#440C2semidirect
5. C2×#65455C2semidirect
6. C2×#65319C2semidirect
7. C2×#65307C2semidirect
8. #10611515C2direct (N × H)
9. C2×#65166C2semidirect
10. C2×#65173C2semidirect
11. C2×#65097C2semidirect
12. C2×#65088C2semidirect
13. C2×#65056C2semidirect
15. C2×#65005C2semidirect
16. C2×#64994C2semidirect
30. C4×Q8×D5C22semidirect
46. C5×#440C22semidirect
54. #65455C22semidirect
62. #65319C22semidirect
63. #65307C22semidirect
69. #65173C22semidirect
70. #65166C22semidirect
71. #65097C22semidirect
72. #65088C22semidirect
74. #65056C22semidirect
75. #65005C22semidirect
76. #64994C22semidirect
197. C2×#440D5semidirect
336. #440C2×D5semidirect
649. C2×C5#3117semidirect
717. C5C2×#3117semidirect
747. C2#10611515direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×Q8×D52
C2×#658912
C2×C5×#4402
C2×#654592
C2×#654552
C2×#653192
C2×#653072
#106115152
C2×#651662
C2×#651732
C2×#650972
C2×#650882
C2×#650562
C2×#650662
C2×#650052
C2×#649942
C2×#31175