Finite Group Databasebeta

← C2×#10611520 #12967645

Subgroups — C2×#10611520 #12967645

Order 1280.

2122 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65906C211yesmaximal, characteristic, complemented
2C2×#65896C211yesmaximal, characteristic
3C2×C5×#440C211yesmaximal, characteristic, complemented
4C2×#65459C211yesmaximal, characteristic, complemented
5C2×#65452C211yesmaximal, characteristic, complemented
6C2×C4×#688C211yesmaximal, characteristic, complemented
7C2×C4×#687C211yesmaximal, characteristic, complemented
8#10611520C2116yesmaximal, direct product factor
9C2×#65166C211yesmaximal, characteristic, complemented
10C2×#65174C211yesmaximal, characteristic, complemented
11C2×#65095C211yesmaximal, characteristic, complemented
12C2×#65085C211yesmaximal, characteristic, complemented
13C2×#65051C211yesmaximal, characteristic, complemented
14C2×#65073C211yesmaximal, characteristic, complemented
15C2×#64999C211yesmaximal, characteristic, complemented
16C2×#64998C211yesmaximal, characteristic, complemented
17C22×Q8×D5C2211yescharacteristic
18C22×C5×SD16C2211yescharacteristic
19C2×C4×C5×Q8C2211yescharacteristic
20C2×C4×C5×D4C2211yescharacteristic
21C2×Q8×Dic5C2211yescharacteristic
22C22×#688C2211yescharacteristic
23C2×#4086C2211yescharacteristic
24C2×#4084C2211yescharacteristic
25C22×#687C2211yescharacteristic
26C2×#4076—21no—
27C2×#4075—21no—
28C22×#677C2211yescharacteristic
29#65906—24no—
30#65906C2218yescomplemented
31#65896—24no—
32#65896C2218yes—
33C2×#4041C2211yescharacteristic
34C2×#4038—21no—
35C2×#4038C2211yescharacteristic
36C2×#4036C2211yescharacteristic
37C2×#4033—21no—
38C2×#4033C2211yescharacteristic
39C2×#4030—21no—
40C2×#4029—21no—
41C2×C4×D20C2211yescharacteristic
42C2×#4018—21no—
43C2×#4018C2211yescharacteristic
44C2×C4×Dic10—21no—
45C2×C4×Dic10C2211yescharacteristic
46C5×#440C2218yescomplemented
47C2×C5×#107C2211yescharacteristic
48C2×C5×#103C2211yescharacteristic
49C2×C5×#102C2211yescharacteristic
50C2×C5×#97C2211yescharacteristic
51C2×#3967C2211yescharacteristic
52C2×#3964C2211yescharacteristic
53#65459C2218yescomplemented
54#65452C2218yescomplemented
55C2×#3953C2211yescharacteristic
56C2×#3952C2211yescharacteristic
57C2×#3952C2211yescharacteristic
58C2×#3950C2211yescharacteristic
59C2×#3948C2211yescharacteristic
60C2×#3946C2211yescharacteristic
61C2×#3946C2211yescharacteristic
62C4×#688C2218yescomplemented
63C4×#687C2218yescomplemented
64C2×#3942C2211yescharacteristic
65C2×#3941C2211yescharacteristic
66C2×#3940C2211yescharacteristic
67C2×#3940C2211yescharacteristic
68C2×C4×#168C2211yescharacteristic
69#65174C2218yescomplemented
70#65166C2218yescomplemented
71#65095C2218yescomplemented
72#65085C2218yescomplemented
73#65073C2218yescomplemented
74#65051C2218yescomplemented
75#64999C2218yescomplemented
76#64998C2218yescomplemented
77C2×#3126—51nomaximal, Sylow
78C22×C5×Q8C2311yescharacteristic
79C22×C5×D4C2311yescharacteristic
80C23×C4×C5—21no—
81C22×C22⋊D5—21no—
82C22×C22⋊D5—21no—
83C22×C22⋊D5—21no—
84C2×Q8×D5—24no—
85C2×Q8×D5—22no—
86C2×Q8×D5—24no—
87C2×Q8×D5C2314yes—
88C22×D20—21no—
89C22×D20C2311yescharacteristic
90C22×C4×D5—21no—
91C22×C4×D5—21no—
92C22×C4×D5C2311yescharacteristic
93C22×Dic10—21no—
94C22×Dic10C2311yescharacteristic
95C2×C5×SD16—24no—
96C2×C5×SD16C2314yes—
97C22×C5×C8C2311yescharacteristic
98C22×C5×C8C2311yescharacteristic
99C4×C5×Q8—22no—
100C4×C5×Q8C2314yes—
101C4×C5×D4—22no—
102C4×C5×D4C2314yes—
103C2×C5×C4⋊C4—21no—
104C2×C5×C4⋊C4C2311yescharacteristic
105C2×C5×C4⋊C4C2311yescharacteristic
106C2×C5×C22⋊C4—21no—
107C2×C42×C5—21no—
108C2×C42×C5C2311yescharacteristic
109C2×C22⋊Dic5—21no—
110Q8×Dic5—22no—
111Q8×Dic5C2314yes—
112C2×#688—24no—
113C2×#688C2314yes—
114#4086—22no—
115#4086C2314yes—
116#4084—22no—
117#4084C2314yes—
118C2×#687—24no—
119C2×#687C2314yes—
120#4076—28no—
121#4075—28no—
122C2×#685—21no—
123C2×#685—21no—
124C2×#685—21no—
125C2×#685D411yescharacteristic
126C2×#685D411yescharacteristic
127C2×C4⋊Dic5—21no—
128C2×C4⋊Dic5—21no—
129C2×C4⋊Dic5C2311yescharacteristic
130C2×C4⋊Dic5C2311yescharacteristic
131C2×#683—21no—
132C2×#683—21no—
133C2×#683—21no—
134C2×#683D411yescharacteristic
135C2×#683D411yescharacteristic
136C2×C4×Dic5—21no—
137C2×C4×Dic5—21no—
138C2×C4×Dic5—21no—
139C2×C4×Dic5—21no—
140C2×C4×Dic5C2311yescharacteristic
141C22×#168C2311yescharacteristic
142C22×#168C2311yescharacteristic
143C2×#677—24no—
144C2×#677C2314yes—
145#4041—22no—
146#4041C2314yes—
147#4038—22no—
148#4038—28no—
149#4038C2314yes—
150#4036—22no—
151#4036C2314yes—
152#4033—28no—
153#4033—22no—
154#4033C2314yes—
155#4030—28no—
156#4029—28no—
157C4×D20—22no—
158C4×D20C2314yes—
159#4018—28no—
160#4018D414yes—
161#4018C2314yes—
162C4×Dic10—22no—
163C4×Dic10—28no—
164C4×Dic10C2314yes—
165C5×#107C2314yes—
166C5×#103C2314yes—
167C5×#102C2314yes—
168C5×#97C2314yes—
169#3967C2314yes—
170#3964C2314yes—
171#3953C2314yes—
172#3952C2314yes—
173#3952C2314yes—
174#3950C2314yes—
175#3948C2314yes—
176#3946C2314yes—
177#3946C2314yes—
178#3942C2314yes—
179#3941C2314yes—
180#3940C2314yes—
181#3940C2314yes—
182C4×#168C2314yes—
183C2×#540—51no—
184C2×#519—51no—
185#3126—516no—
186C2×#482—51no—
187C2×#482—51no—
188C2×#479—51no—
189C2×#479—51no—
190C2×#460—51no—
191C2×#460—51no—
192C2×#448—51no—
193C2×#448—51no—
194C2×#440—51no—
195C2×#440D511yescharacteristic, complemented
196C2×C4×SD16—51no—
197C2×C4×SD16—51no—
198C2×#433—51no—
199C24×C5—21no—
200C23×D5—21no—
201C23×D5C2×D411yescharacteristic
202C2×C5×Q8—21no—
203C2×C5×Q8—22no—
204C2×C5×Q8#4114yes—
205C2×C5×Q8C2412yes—
206C2×C5×D4—21no—
207C2×C5×D4—22no—
208C2×C5×D4—22no—
209C2×C5×D4C2412yes—
210C22×C4×C5—21no—
211C22×C4×C5—21no—
212C22×C4×C5—21no—
213C22×C4×C5—24no—
214C22×C4×C5—82no—
215C22×C4×C5C2×D411yescharacteristic
216C22×C4×C5C2×D411yescharacteristic
217C22×C4×C5C2411yescharacteristic
218C2×C22⋊D5—24no—
219C2×C22⋊D5—24no—
220C2×C22⋊D5—24no—
221C2×C22⋊D5—82no—
222C2×C22⋊D5—82no—
223C2×C22⋊D5—82no—
224C22×Dic5—21no—
225C22×Dic5—21no—
226C22×Dic5—21no—
227C22×Dic5C2×D411yescharacteristic
228C22×Dic5C2×D411yescharacteristic
229C22×Dic5C2×D411yescharacteristic
230Q8×D5—216no—
231Q8×D5—28no—
232Q8×D5—28no—
233C2×D20—22no—
234C2×D20—22no—
235C2×D20—21no—
236C2×D20—24no—
237C2×D20—82no—
238C2×D20C2412yes—
239C2×C4×D5—28no—
240C2×C4×D5—24no—
241C2×C4×D5—22no—
242C2×C4×D5—22no—
243C2×C4×D5—24no—
244C2×C4×D5—82no—
245C2×C4×D5C2×D412yes—
246C2×C4×D5C2412yes—
247C2×Dic10—28no—
248C2×Dic10—21no—
249C2×Dic10—22no—
250C2×Dic10—24no—
251C2×Dic10#4114yes—
252C2×Dic10C2412yes—
253C5×SD16—28no—
254C2×C5×C8—22no—
255C2×C5×C8—22no—
256C2×C5×C8C2412yes—
257C2×C5×C8C2412yes—
258C5×C4⋊C4—24no—
259C5×C4⋊C4—21no—
260C5×C4⋊C4—21no—
261C5×C4⋊C4C2412yes—
262C5×C4⋊C4C2412yes—
263C5×C22⋊C4—24no—
264C42×C5—24no—
265C42×C5C2×D412yes—
266C42×C5C2412yes—
267C22⋊Dic5—24no—
268#688—28no—
269#687—28no—
270#685—24no—
271#685—24no—
272#685—24no—
273#685C2×D414yes—
274#685C2×D414yes—
275C4⋊Dic5—21no—
276C4⋊Dic5—21no—
277C4⋊Dic5—24no—
278C4⋊Dic5—24no—
279C4⋊Dic5C2412yes—
280C4⋊Dic5C2412yes—
281#683—24no—
282#683—24no—
283#683—24no—
284#683C2×D414yes—
285#683C2×D414yes—
286C4×Dic5—24no—
287C4×Dic5—24no—
288C4×Dic5—24no—
289C4×Dic5—24no—
290C4×Dic5C2×D412yes—
291C4×Dic5C2412yes—
292C2×#168—22no—
293C2×#168—22no—
294C2×#168C2412yes—
295C2×#168C2412yes—
296#677—28no—
297C23×Q8—51no—
298C22×SD16—51no—
299C22×SD16—51no—
300C22×SD16—51no—
301C22×SD16C2×D511yescharacteristic
302#540—58no—
303#540—104no—
304C2×#127—51no—
305C2×#125—51no—
306C2×#123—101no—
307C2×#123—101no—
308C2×#121—51no—
309C2×#121—51no—
310C2×#121—101no—
311C2×#121—101no—
312#519—58no—
313#519—104no—
314C2×C4×Q8—51no—
315C2×C4×Q8—51no—
316C2×C4×Q8—51no—
317C2×C4×Q8—101no—
318C2×C4×Q8—101no—
319C2×C4×Q8C2×D511yescharacteristic
320C2×C4×D4—51no—
321C2×C4×D4C2×D511yescharacteristic
322C2×#117—51no—
323C2×#117—51no—
324C2×#117—101no—
325C2×#117—101no—
326#482—58no—
327#482—58no—
328#479—58no—
329#479—58no—
330#460—58no—
331#460—58no—
332#448—58no—
333#448—58no—
334#440—58no—
335#440C2×D518yescomplemented
336C4×SD16—58no—
337C4×SD16—58no—
338#433—58no—
339C2×#107—51no—
340C2×#107C2×D511yescharacteristic
341C2×#106—51no—
342C2×#106—51no—
343C2×C4⋊C8—51no—
344C2×C4⋊C8—51no—
345C2×#103—51no—
346C2×#103—51no—
347C2×#103—51no—
348C2×#103C2×D511yescharacteristic
349C2×#102—51no—
350C2×#102—51no—
351C2×#102—51no—
352C2×#102C2×D511yescharacteristic
353C2×C22⋊C8—51no—
354C2×C22⋊C8—51no—
355C2×#97C2×D511yescharacteristic
356C2×C4×C8—51no—
357C23×C5—22no—
358C23×C5—42no—
359C23×C5—42no—
360C23×C5—42no—
361C23×C5C22×D411yescharacteristic
362C22×D5—22no—
363C22×D5—22no—
364C22×D5—22no—
365C22×D5—22no—
366C22×D5—42no—
367C22×D5—42no—
368C22×D5—42no—
369C22×D5C22×D412yes—
370C5×Q8—24no—
371C5×Q8—22no—
372C5×Q8C2×#4114yes—
373C5×D4—22no—
374C5×D4—22no—
375C5×D4—42no—
376C2×C4×C5—24no—
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×C5C22×D412yes—
386C2×C4×C5C22×D412yes—
387C2×C4×C5C22×D411yescharacteristic
388C2×C4×C5C2×#4112yes—
389C2×C4×C5C2×#4112yes—
390C2×C4×C5C2511yescharacteristic
391C22⋊D5—84no—
392C22⋊D5—84no—
393C22⋊D5—84no—
394C2×Dic5—22no—
395C2×Dic5—24no—
396C2×Dic5—22no—
397C2×Dic5—22no—
398C2×Dic5—22no—
399C2×Dic5—22no—
400C2×Dic5—22no—
401C2×Dic5—42no—
402C2×Dic5—42no—
403C2×Dic5C22×D412yes—
404C2×Dic5C22×D412yes—
405C2×Dic5C22×D412yes—
406D20—22no—
407D20—22no—
408D20—42no—
409D20—84no—
410C4×D5—216no—
411C4×D5—24no—
412C4×D5—22no—
413C4×D5—22no—
414C4×D5—84no—
415Dic10—216no—
416Dic10—24no—
417Dic10—22no—
418Dic10C2×#4114yes—
419C5×C8—22no—
420C5×C8—22no—
421#168—22no—
422#168—22no—
423C22×Q8—54no—
424C22×Q8—51no—
425C22×Q8—101no—
426C22×Q8—102no—
427C22×Q8—104no—
428C22×Q8—104no—
429C22×Q8C22×D511yescharacteristic
430C22×D4—51no—
431C22×D4—101no—
432C22×D4—101no—
433C22×D4—101no—
434C22×D4—101no—
435C22×D4C22×D511yescharacteristic
436C23×C4—21no—
437C23×C4—51no—
438C23×C4—101no—
439C23×C4—101no—
440C2×SD16—24no—
441C2×SD16—54no—
442C2×SD16—54no—
443C2×SD16—54no—
444C2×SD16—104no—
445C2×SD16—104no—
446C2×SD16—104no—
447C2×SD16C22×D514yes—
448C22×C8—51no—
449C22×C8—51no—
450C22×C8C22×D511yescharacteristic
451C22×C8C22×D511yescharacteristic
452#127—54no—
453#127—102no—
454#125—54no—
455#125—102no—
456#123—108no—
457#123—108no—
458#121—54no—
459#121—54no—
460#121—108no—
461#121—108no—
462#121—102no—
463#121—102no—
464C4×Q8—22no—
465C4×Q8—54no—
466C4×Q8—54no—
467C4×Q8—54no—
468C4×Q8—108no—
469C4×Q8—102no—
470C4×Q8—102no—
471C4×Q8—108no—
472C4×Q8—102no—
473C4×Q8C22×D514yes—
474C4×D4—22no—
475C4×D4—54no—
476C4×D4—102no—
477C4×D4C22×D514yes—
478#117—54no—
479#117—54no—
480#117—54no—
481#117—108no—
482#117—108no—
483#117—102no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—51no—
486C2×C4⋊C4—51no—
487C2×C4⋊C4—51no—
488C2×C4⋊C4—51no—
489C2×C4⋊C4—101no—
490C2×C4⋊C4—101no—
491C2×C4⋊C4—101no—
492C2×C4⋊C4—101no—
493C2×C4⋊C4—101no—
494C2×C4⋊C4C22×D511yescharacteristic
495C2×C4⋊C4C22×D511yescharacteristic
496C2×C22⋊C4—21no—
497C2×C22⋊C4—51no—
498C2×C22⋊C4—51no—
499C2×C22⋊C4—101no—
500C2×C22⋊C4—101no—
501C2×C22⋊C4—101no—
502C2×C22⋊C4—101no—
503C2×C42—21no—
504C2×C42—51no—
505C2×C42—101no—
506C2×C42—101no—
507C2×C42—101no—
508C2×C42—101no—
509C2×C42C22×D511yescharacteristic
510#107—54no—
511#107C22×D514yes—
512#106—54no—
513#106—54no—
514C4⋊C8—54no—
515C4⋊C8—54no—
516#103—54no—
517#103—54no—
518#103—54no—
519#103C22×D514yes—
520#102—54no—
521#102—54no—
522#102—54no—
523#102C22×D514yes—
524C22⋊C8—54no—
525C22⋊C8—54no—
526#97C22×D514yes—
527C4×C8—54no—
528C22×C5—42no—
529C22×C5—42no—
530C22×C5—42no—
531C22×C5—84no—
532C22×C5#52512yes—
533C22×C5#57712yes—
534C22×C5#57712yes—
535C22×C5C23×D411yescharacteristic
536C2×D5—22no—
537C2×D5—22no—
538C2×D5—22no—
539C2×D5—44no—
540C2×D5—42no—
541C2×D5—42no—
542C2×D5—42no—
543C2×D5—84no—
544C4×C5—24no—
545C4×C5—22no—
546C4×C5—22no—
547C4×C5—42no—
548C4×C5—42no—
549C4×C5#52512yes—
550C4×C5C22×#4111yescharacteristic
551C4×C5C22×#4111yescharacteristic
552Dic5—22no—
553Dic5—24no—
554Dic5—22no—
555Dic5—22no—
556Dic5—42no—
557Dic5—42no—
558C24—21no—
559C24—51no—
560C24—101no—
561C2×Q8—21no—
562C2×Q8—22no—
563C2×Q8—54no—
564C2×Q8—52no—
565C2×Q8—104no—
566C2×Q8—108no—
567C2×Q8—108no—
568C2×Q8—1016no—
569C2×Q8—108no—
570C2×Q8—102no—
571C2×Q8—101no—
572C2×Q8#70914yes—
573C2×Q8C23×D512yes—
574C2×D4—22no—
575C2×D4—21no—
576C2×D4—22no—
577C2×D4—52no—
578C2×D4—104no—
579C2×D4—104no—
580C2×D4—104no—
581C2×D4—104no—
582C2×D4—102no—
583C2×D4—101no—
584C2×D4—102no—
585C2×D4—402no—
586C2×D4—402no—
587C2×D4—402no—
588C2×D4—402no—
589C2×D4C23×D512yes—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—24no—
594C22×C4—51no—
595C22×C4—51no—
596C22×C4—51no—
597C22×C4—52no—
598C22×C4—52no—
599C22×C4—82no—
600C22×C4—104no—
601C22×C4—108no—
602C22×C4—101no—
603C22×C4—102no—
604C22×C4—102no—
605C22×C4—101no—
606C22×C4—101no—
607C22×C4—104no—
608C22×C4—402no—
609C22×C4D4×D511yescharacteristic
610C22×C4D4×D511yescharacteristic
611C22×C4C23×D511yescharacteristic
612SD16—28no—
613SD16—108no—
614SD16—108no—
615SD16—108no—
616C2×C8—22no—
617C2×C8—22no—
618C2×C8—52no—
619C2×C8—52no—
620C2×C8—102no—
621C2×C8—102no—
622C2×C8C23×D512yes—
623C2×C8C23×D512yes—
624C4⋊C4—24no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—54no—
628C4⋊C4—54no—
629C4⋊C4—52no—
630C4⋊C4—52no—
631C4⋊C4—104no—
632C4⋊C4—104no—
633C4⋊C4—104no—
634C4⋊C4—104no—
635C4⋊C4—101no—
636C4⋊C4—101no—
637C4⋊C4—104no—
638C4⋊C4C23×D512yes—
639C4⋊C4C23×D512yes—
640C22⋊C4—24no—
641C22⋊C4—54no—
642C22⋊C4—54no—
643C22⋊C4—104no—
644C22⋊C4—104no—
645C22⋊C4—104no—
646C22⋊C4—104no—
647C42—24no—
648C42—52no—
649C42—52no—
650C42—104no—
651C42—104no—
652C42—104no—
653C42—104no—
654C42D4×D512yes—
655C42C23×D512yes—
656C2×C5—82no—
657C2×C5#312614yescomplemented
658C2×C5C2×#52511yescharacteristic
659C2×C5C2×#57711yescharacteristic
660C2×C5C2×#57711yescharacteristic
661D5—42no—
662D5—82no—
663C23—22no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—52no—
668C23—102no—
669C23—102no—
670C23—102no—
671C23—102no—
672C23—202no—
673C23—202no—
674C23—202no—
675C23C2×D4×D511yescharacteristic
676Q8—24no—
677Q8—22no—
678Q8—54no—
679Q8—1016no—
680Q8—104no—
681Q8—102no—
682Q8C2×#70914yes—
683D4—22no—
684D4—22no—
685D4—42no—
686D4—102no—
687D4—102no—
688D4—202no—
689D4—404no—
690D4—404no—
691D4—404no—
692D4—404no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—24no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—52no—
702C2×C4—52no—
703C2×C4—52no—
704C2×C4—84no—
705C2×C4—1016no—
706C2×C4—102no—
707C2×C4—102no—
708C2×C4—102no—
709C2×C4—104no—
710C2×C4—102no—
711C2×C4—104no—
712C2×C4—102no—
713C2×C4—102no—
714C2×C4—102no—
715C2×C4—102no—
716C2×C4—202no—
717C2×C4—202no—
718C2×C4—404no—
719C2×C4C2×#70912yes—
720C2×C4C2×D4×D512yes—
721C2×C4C2×D4×D512yes—
722C2×C4C2×D4×D511yescharacteristic
723C2×C4D5×#4112yes—
724C2×C4C24×D511yescharacteristic
725C8—22no—
726C8—22no—
727C8—102no—
728C8—102no—
729C5C2×#312611yescharacteristic, complemented, Sylow
730C22—42no—
731C22—42no—
732C22—42no—
733C22—84no—
734C22—102no—
735C22—102no—
736C22—102no—
737C22—204no—
738C22—202no—
739C22—202no—
740C22—202no—
741C22—404no—
742C22#6588112yes—
743C22#6610912yes—
744C22#6611212yes—
745C22C22×D4×D511yescharacteristic
746C4—24no—
747C4—22no—
748C4—22no—
749C4—42no—
750C4—42no—
751C4—102no—
752C4—104no—
753C4—102no—
754C4—102no—
755C4—202no—
756C4—202no—
757C4#6588112yes—
758C4C22×#70911yescharacteristic
759C4C2×D5×#4111yescharacteristic
760C2—82no—
761C2—202no—
762C2—402no—
763C2#1061152014yesdirect product factor
764C2C2×#6588111yescharacteristic
765C2C2×#6610911yescharacteristic
766C2C2×#6611211yescharacteristic
subgroupG/H
centerC23C2×D4×D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×#440C2
socleC23×C5C22×D4
prime radicalC2×#65896C2
hypercenterC2×#440D5
hypocenterC5C2×#3126
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×#65906C2semidirect
3. C2×C5×#440C2semidirect
4. C2×#65459C2semidirect
5. C2×#65452C2semidirect
6. C2×C4×#688C2semidirect
7. C2×C4×#687C2semidirect
8. #10611520C2direct (N × H)
9. C2×#65166C2semidirect
10. C2×#65174C2semidirect
11. C2×#65095C2semidirect
12. C2×#65085C2semidirect
13. C2×#65051C2semidirect
14. C2×#65073C2semidirect
15. C2×#64999C2semidirect
16. C2×#64998C2semidirect
30. #65906C22semidirect
46. C5×#440C22semidirect
53. #65459C22semidirect
54. #65452C22semidirect
62. C4×#688C22semidirect
63. C4×#687C22semidirect
69. #65174C22semidirect
70. #65166C22semidirect
71. #65095C22semidirect
72. #65085C22semidirect
73. #65073C22semidirect
74. #65051C22semidirect
75. #64999C22semidirect
76. #64998C22semidirect
195. C2×#440D5semidirect
335. #440C2×D5semidirect
657. C2×C5#3126semidirect
729. C5C2×#3126semidirect
763. C2#10611520direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#659062
C2×#658962
C2×C5×#4402
C2×#654592
C2×#654522
C2×C4×#6882
C2×C4×#6872
#106115202
C2×#651662
C2×#651742
C2×#650952
C2×#650852
C2×#650512
C2×#650732
C2×#649992
C2×#649982
C2×#31265