Finite Group Databasebeta

← C2×#10611495 #12980293

Subgroups — C2×#10611495 #12980293

Order 1280.

1970 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65901C211yesmaximal, characteristic, complemented
2C2×#65893C211yesmaximal, characteristic
3C2×C5×#440C211yesmaximal, characteristic, complemented
4C2×#65456C211yesmaximal, characteristic, complemented
5C2×#65464C211yesmaximal, characteristic
6C2×#65317C211yesmaximal, characteristic, complemented
7C2×#65308C211yesmaximal, characteristic, complemented
8#10611495C2116yesmaximal, direct product factor
9C2×#65178C211yesmaximal, characteristic, complemented
10C2×#65162C211yesmaximal, characteristic, complemented
11C2×#65082C211yesmaximal, characteristic, complemented
12C2×#65107C211yesmaximal, characteristic, complemented
13C2×#65056C211yesmaximal, characteristic, complemented
14C2×#65051C211yesmaximal, characteristic
15C2×#65004C211yesmaximal, characteristic, complemented
16C2×#64990C211yesmaximal, characteristic, complemented
17C22×C5×SD16C2211yescharacteristic
18C2×C4×C5×Q8C2211yescharacteristic
19C2×C4×C5×D4C2211yescharacteristic
20C2×#4090C2211yescharacteristic
21C2×#4090C2211yescharacteristic
22C22×#689C2211yescharacteristic
23C22×#688C2211yescharacteristic
24C2×#4086C2211yescharacteristic
25C2×#4082C2211yescharacteristic
26C22×#687C2211yescharacteristic
27C22×#687C2211yescharacteristic
28C2×#4075—21no—
29C2×C4×C22⋊D5—21no—
30C22×Dic20C2211yescharacteristic
31C22×Dic20C2211yescharacteristic
32C22×#677C2211yescharacteristic
33C22×#677C2211yescharacteristic
34#65901—24no—
35#65901C2218yescomplemented
36#65893—24no—
37#65893C2218yes—
38C2×#4039C2211yescharacteristic
39C2×#4035—21no—
40C2×#4035—21no—
41C2×#4033C2211yescharacteristic
42C2×#4033C2211yescharacteristic
43C2×#4033C2211yescharacteristic
44C2×#4031—21no—
45C2×#4029—21no—
46C2×#4021C2211yescharacteristic
47C2×#4016—21no—
48C2×#4015C2211yescharacteristic
49C2×C4×Dic10—21no—
50C2×C4×Dic10C2211yescharacteristic
51C5×#440C2218yescomplemented
52C2×C5×#107C2211yescharacteristic
53C2×C5×#103C2211yescharacteristic
54C2×C5×#102C2211yescharacteristic
55C2×C5×#97C2211yescharacteristic
56#65464C2218yes—
57#65456C2218yescomplemented
58C2×#3947C2211yescharacteristic
59C2×#3946C2211yescharacteristic
60C2×#3946C2211yescharacteristic
61C2×C8×Dic5C2211yescharacteristic
62#65317C2218yescomplemented
63#65308C2218yescomplemented
64C2×#3942C2211yescharacteristic
65C2×#3942C2211yescharacteristic
66C2×#3942C2211yescharacteristic
67C2×#3941C2211yescharacteristic
68C2×C4⋊#168C2211yescharacteristic
69#65178C2218yescomplemented
70#65162C2218yescomplemented
71#65107C2218yescomplemented
72#65082C2218yescomplemented
73#65056C2218yescomplemented
74#65051C2218yes—
75#65004C2218yescomplemented
76#64990C2218yescomplemented
77C2×#3400—51nomaximal, Sylow
78C22×C5×Q8C2311yescharacteristic
79C22×C5×D4C2311yescharacteristic
80C23×C4×C5—21no—
81C22×C22⋊D5—21no—
82C22×C22⋊D5—21no—
83C22×D20C2311yescharacteristic
84C22×C4×D5—21no—
85C22×Dic10D411yescharacteristic
86C22×Dic10C2311yescharacteristic
87C22×Dic10C2311yescharacteristic
88C22×Dic10C2311yescharacteristic
89C2×C5×SD16—24no—
90C2×C5×SD16C2314yes—
91C22×C5×C8C2311yescharacteristic
92C22×C5×C8C2311yescharacteristic
93C4×C5×Q8—22no—
94C4×C5×Q8C2314yes—
95C4×C5×D4—22no—
96C4×C5×D4C2314yes—
97C2×C5×C4⋊C4—21no—
98C2×C5×C4⋊C4C2311yescharacteristic
99C2×C5×C4⋊C4C2311yescharacteristic
100C2×C5×C22⋊C4—21no—
101C2×C42×C5—21no—
102C2×C42×C5C2311yescharacteristic
103C2×C22⋊Dic5—21no—
104C2×C22⋊Dic5—21no—
105#4090—22no—
106#4090—22no—
107#4090C2314yes—
108#4090C2314yes—
109C2×#689—42no—
110C2×#689C2314yes—
111C2×#688—42no—
112C2×#688C2314yes—
113#4086—22no—
114#4086C2314yes—
115#4082—22no—
116#4082C2314yes—
117C2×#687—42no—
118C2×#687—42no—
119C2×#687C2314yes—
120C2×#687C2314yes—
121#4075—28no—
122C4×C22⋊D5—28no—
123C2×#685—21no—
124C2×#685—21no—
125C2×#685—21no—
126C2×C4⋊Dic5—21no—
127C2×C4⋊Dic5—21no—
128C2×C4⋊Dic5D411yescharacteristic
129C2×#683—21no—
130C2×#683—21no—
131C2×#683—21no—
132C2×#683—21no—
133C2×#683—21no—
134C2×#683—21no—
135C2×#683—21no—
136C2×#683D411yescharacteristic
137C2×#683D411yescharacteristic
138C2×C4×Dic5—21no—
139C2×C4×Dic5—21no—
140C2×C4×Dic5—21no—
141C2×C4×Dic5C2311yescharacteristic
142C2×C4×Dic5C2311yescharacteristic
143C22×#168C2311yescharacteristic
144C22×#168C2311yescharacteristic
145C2×Dic20—24no—
146C2×Dic20—42no—
147C2×Dic20C2314yes—
148C2×Dic20C2314yes—
149C2×#677—24no—
150C2×#677—42no—
151C2×#677C2314yes—
152C2×#677C2314yes—
153#4039—22no—
154#4039C2314yes—
155#4035—28no—
156#4035—28no—
157#4033—22no—
158#4033—22no—
159#4033—22no—
160#4033C2314yes—
161#4033C2314yes—
162#4033C2314yes—
163#4031—28no—
164#4029—28no—
165#4021—22no—
166#4021C2314yes—
167#4016—28no—
168#4015—22no—
169#4015C2314yes—
170C4×Dic10—28no—
171C4×Dic10D414yes—
172C4×Dic10C2314yes—
173C5×#107C2314yes—
174C5×#103C2314yes—
175C5×#102C2314yes—
176C5×#97C2314yes—
177#3947C2314yes—
178#3946C2314yes—
179#3946C2314yes—
180C8×Dic5C2314yes—
181#3942C2314yes—
182#3942C2314yes—
183#3942C2314yes—
184#3941C2314yes—
185C4⋊#168C2314yes—
186C2×#559—51no—
187C2×#557—51no—
188#3400—516no—
189C2×#497—51no—
190C2×#497—51no—
191C2×#492—51no—
192C2×#464—51no—
193C2×#464—51no—
194C2×#462—51no—
195C2×#460—51no—
196C2×#461—51no—
197C2×#461—51no—
198C2×#446—51no—
199C2×#440—51no—
200C2×#440D511yescharacteristic, complemented
201C2×C4×Q16—51no—
202C24×C5—21no—
203C23×D5—21no—
204C2×C5×Q8—21no—
205C2×C5×Q8—22no—
206C2×C5×Q8—22no—
207C2×C5×Q8C2412yes—
208C2×C5×D4—21no—
209C2×C5×D4—22no—
210C2×C5×D4—22no—
211C2×C5×D4C2412yes—
212C22×C4×C5—21no—
213C22×C4×C5—21no—
214C22×C4×C5—21no—
215C22×C4×C5—24no—
216C22×C4×C5—82no—
217C22×C4×C5C2×D411yescharacteristic
218C22×C4×C5C2×D411yescharacteristic
219C22×C4×C5C2411yescharacteristic
220C2×C22⋊D5—24no—
221C2×C22⋊D5—24no—
222C2×C22⋊D5—44no—
223C2×C22⋊D5—82no—
224C22×Dic5—21no—
225C22×Dic5—21no—
226C22×Dic5—21no—
227C22×Dic5C2×D411yescharacteristic
228C22×Dic5C2×D411yescharacteristic
229C22×Dic5C2×D411yescharacteristic
230C22×Dic5C2×D411yescharacteristic
231C2×D20—22no—
232C2×D20—22no—
233C2×D20—21no—
234C2×D20C2412yes—
235C2×C4×D5—24no—
236C2×C4×D5—82no—
237C2×Dic10—24no—
238C2×Dic10—22no—
239C2×Dic10—22no—
240C2×Dic10—22no—
241C2×Dic10—22no—
242C2×Dic10—22no—
243C2×Dic10—22no—
244C2×Dic10—21no—
245C2×Dic10—21no—
246C2×Dic10—21no—
247C2×Dic10C2×D414yes—
248C2×Dic10C2412yes—
249C2×Dic10C2412yes—
250C2×Dic10C2412yes—
251C5×SD16—28no—
252C2×C5×C8—22no—
253C2×C5×C8#4114yes—
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—
267#689—44no—
268#688—44no—
269#687—44no—
270#687—44no—
271#685—24no—
272#685—24no—
273#685—24no—
274C4⋊Dic5—24no—
275C4⋊Dic5—24no—
276C4⋊Dic5C2×D414yes—
277#683—24no—
278#683—24no—
279#683—24no—
280#683—24no—
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×Dic5C2×D412yes—
290C4×Dic5C2×D412yes—
291C4×Dic5C2412yes—
292C4×Dic5C2412yes—
293C2×#168—22no—
294C2×#168—22no—
295C2×#168C2412yes—
296C2×#168C2412yes—
297Dic20—28no—
298Dic20—44no—
299#677—28no—
300#677—44no—
301C22×Q16—51no—
302C22×Q16—51no—
303C22×Q16—51no—
304C22×SD16—51no—
305C22×SD16—51no—
306C22×SD16—51no—
307C22×SD16—51no—
308C22×SD16—51no—
309C22×SD16C2×D511yescharacteristic
310#559—58no—
311#559—104no—
312#557—58no—
313#557—104no—
314C2×C4⋊Q8—51no—
315C2×C4⋊Q8—51no—
316C2×C4⋊Q8—51no—
317C2×#127—51no—
318C2×#125—101no—
319C2×#125—101no—
320C2×#125—101no—
321C2×#124—51no—
322C2×#124—51no—
323C2×#124—101no—
324C2×#123—101no—
325C2×#123—101no—
326C2×C4×Q8—51no—
327C2×C4×Q8—51no—
328C2×C4×Q8—51no—
329C2×C4×Q8—51no—
330C2×C4×Q8—101no—
331C2×C4×Q8C2×D511yescharacteristic
332C2×C4×D4—51no—
333C2×C4×D4—101no—
334C2×C4×D4C2×D511yescharacteristic
335#497—58no—
336#497—58no—
337#492—58no—
338#464—58no—
339#464—58no—
340#462—58no—
341#461—58no—
342#461—58no—
343#460—58no—
344#446—58no—
345#440—58no—
346#440C2×D518yescomplemented
347C4×Q16—58no—
348C2×#107C2×D511yescharacteristic
349C2×C4⋊C8—51no—
350C2×C4⋊C8—51no—
351C2×C4⋊C8—51no—
352C2×#103—51no—
353C2×#103—51no—
354C2×#103—51no—
355C2×#103C2×D511yescharacteristic
356C2×#102—51no—
357C2×#102C2×D511yescharacteristic
358C2×#97—51no—
359C2×#97C2×D511yescharacteristic
360C2×C4×C8—51no—
361C23×C5—22no—
362C23×C5—42no—
363C23×C5—42no—
364C23×C5—42no—
365C23×C5C22×D411yescharacteristic
366C22×D5—22no—
367C22×D5—42no—
368C22×D5—42no—
369C22×D5—42no—
370C5×Q8—22no—
371C5×Q8—22no—
372C5×Q8—42no—
373C5×D4—22no—
374C5×D4—22no—
375C5×D4—42no—
376C2×C4×C5—22no—
377C2×C4×C5—22no—
378C2×C4×C5—22no—
379C2×C4×C5—22no—
380C2×C4×C5—22no—
381C2×C4×C5—42no—
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×C5H(5,𝔽2)12yes—
390C2×C4×C5C2511yescharacteristic
391C22⋊D5—48no—
392C22⋊D5—84no—
393C2×Dic5—22no—
394C2×Dic5—22no—
395C2×Dic5—22no—
396C2×Dic5—22no—
397C2×Dic5—22no—
398C2×Dic5—22no—
399C2×Dic5—42no—
400C2×Dic5—42no—
401C2×Dic5—42no—
402C2×Dic5#13714yes—
403C2×Dic5C22×D412yes—
404C2×Dic5C22×D412yes—
405C2×Dic5C22×D412yes—
406C2×Dic5C22×D412yes—
407D20—22no—
408D20—22no—
409D20—42no—
410C4×D5—84no—
411Dic10—28no—
412Dic10—22no—
413Dic10—22no—
414Dic10—22no—
415Dic10—22no—
416Dic10—22no—
417Dic10—22no—
418Dic10—42no—
419Dic10—42no—
420Dic10—42no—
421C5×C8—22no—
422C5×C8C2×#4114yes—
423#168—22no—
424#168—22no—
425C22×Q8—51no—
426C22×Q8—51no—
427C22×Q8—51no—
428C22×Q8—51no—
429C22×Q8C22×D511yescharacteristic
430C22×D4—51no—
431C22×D4—101no—
432C22×D4—101no—
433C22×D4C22×D511yescharacteristic
434C23×C4—21no—
435C23×C4—101no—
436C2×Q16—54no—
437C2×Q16—54no—
438C2×Q16—54no—
439C2×Q16—104no—
440C2×Q16—202no—
441C2×Q16—202no—
442C2×SD16—24no—
443C2×SD16—54no—
444C2×SD16—54no—
445C2×SD16—54no—
446C2×SD16—54no—
447C2×SD16—54no—
448C2×SD16—104no—
449C2×SD16—202no—
450C2×SD16—202no—
451C2×SD16—202no—
452C2×SD16—202no—
453C2×SD16C22×D514yes—
454C22×C8—51no—
455C22×C8—51no—
456C22×C8C22×D511yescharacteristic
457C22×C8C22×D511yescharacteristic
458C4⋊Q8—54no—
459C4⋊Q8—54no—
460C4⋊Q8—54no—
461C4⋊Q8—102no—
462C4⋊Q8—102no—
463C4⋊Q8—102no—
464#127—54no—
465#127—102no—
466#125—108no—
467#125—108no—
468#125—108no—
469#124—54no—
470#124—54no—
471#124—102no—
472#124—108no—
473#124—102no—
474#123—108no—
475#123—108no—
476C4×Q8—22no—
477C4×Q8—54no—
478C4×Q8—54no—
479C4×Q8—54no—
480C4×Q8—54no—
481C4×Q8—54no—
482C4×Q8—108no—
483C4×Q8—102no—
484C4×Q8—102no—
485C4×Q8—102no—
486C4×Q8C22×D514yes—
487C4×D4—22no—
488C4×D4—54no—
489C4×D4—102no—
490C4×D4—108no—
491C4×D4C22×D514yes—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—51no—
494C2×C4⋊C4—51no—
495C2×C4⋊C4—51no—
496C2×C4⋊C4—101no—
497C2×C4⋊C4—101no—
498C2×C4⋊C4—101no—
499C2×C4⋊C4—101no—
500C2×C4⋊C4—101no—
501C2×C4⋊C4—101no—
502C2×C4⋊C4—101no—
503C2×C4⋊C4—101no—
504C2×C4⋊C4—101no—
505C2×C4⋊C4C22×D511yescharacteristic
506C2×C4⋊C4C22×D511yescharacteristic
507C2×C22⋊C4—21no—
508C2×C22⋊C4—101no—
509C2×C22⋊C4—101no—
510C2×C22⋊C4—101no—
511C2×C22⋊C4—101no—
512C2×C22⋊C4—101no—
513C2×C42—21no—
514C2×C42—51no—
515C2×C42—51no—
516C2×C42—101no—
517C2×C42—101no—
518C2×C42—101no—
519C2×C42C22×D511yescharacteristic
520#107C22×D514yes—
521C4⋊C8—54no—
522C4⋊C8—54no—
523C4⋊C8—54no—
524#103—54no—
525#103—54no—
526#103—54no—
527#103C22×D514yes—
528#102—54no—
529#102C22×D514yes—
530#97—54no—
531#97C22×D514yes—
532C4×C8—54no—
533C22×C5—42no—
534C22×C5—42no—
535C22×C5—42no—
536C22×C5—84no—
537C22×C5#55012yes—
538C22×C5C2×#13712yes—
539C22×C5#57712yes—
540C22×C5C23×D411yescharacteristic
541C2×D5—42no—
542C2×D5—42no—
543C2×D5—42no—
544C2×D5—84no—
545C4×C5—22no—
546C4×C5—22no—
547C4×C5—42no—
548C4×C5—42no—
549C4×C5—42no—
550C4×C5#55012yes—
551C4×C5C22×#4111yescharacteristic
552C4×C5C2×H(5,𝔽2)11yescharacteristic
553Dic5—22no—
554Dic5—22no—
555Dic5—22no—
556Dic5—42no—
557Dic5—42no—
558Dic5—42no—
559Dic5C2×#13714yes—
560C24—21no—
561C24—101no—
562C2×Q8—21no—
563C2×Q8—22no—
564C2×Q8—22no—
565C2×Q8—54no—
566C2×Q8—52no—
567C2×Q8—52no—
568C2×Q8—52no—
569C2×Q8—104no—
570C2×Q8—101no—
571C2×Q8—101no—
572C2×Q8—101no—
573C2×Q8—102no—
574C2×Q8—102no—
575C2×Q8—102no—
576C2×Q8—102no—
577C2×Q8—102no—
578C2×Q8—102no—
579C2×Q8C23×D512yes—
580C2×D4—22no—
581C2×D4—21no—
582C2×D4—22no—
583C2×D4—52no—
584C2×D4—104no—
585C2×D4—104no—
586C2×D4—102no—
587C2×D4—101no—
588C2×D4—102no—
589C2×D4—204no—
590C2×D4—402no—
591C2×D4C23×D512yes—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—24no—
596C22×C4—51no—
597C22×C4—51no—
598C22×C4—51no—
599C22×C4—51no—
600C22×C4—82no—
601C22×C4—104no—
602C22×C4—101no—
603C22×C4—101no—
604C22×C4—101no—
605C22×C4—402no—
606C22×C4D4×D511yescharacteristic
607C22×C4D4×D511yescharacteristic
608C22×C4C23×D511yescharacteristic
609Q16—108no—
610Q16—204no—
611Q16—204no—
612SD16—28no—
613SD16—108no—
614SD16—204no—
615SD16—204no—
616SD16—204no—
617SD16—204no—
618C2×C8—22no—
619C2×C8—52no—
620C2×C8—52no—
621C2×C8—102no—
622C2×C8—102no—
623C2×C8#70914yes—
624C2×C8C23×D512yes—
625C2×C8C23×D512yes—
626C4⋊C4—24no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—54no—
630C4⋊C4—54no—
631C4⋊C4—54no—
632C4⋊C4—104no—
633C4⋊C4—104no—
634C4⋊C4—104no—
635C4⋊C4—104no—
636C4⋊C4—104no—
637C4⋊C4—104no—
638C4⋊C4—104no—
639C4⋊C4—104no—
640C4⋊C4—104no—
641C4⋊C4C23×D512yes—
642C4⋊C4C23×D512yes—
643C22⋊C4—24no—
644C22⋊C4—104no—
645C22⋊C4—104no—
646C22⋊C4—104no—
647C22⋊C4—104no—
648C22⋊C4—104no—
649C42—24no—
650C42—52no—
651C42—52no—
652C42—52no—
653C42—52no—
654C42—104no—
655C42—104no—
656C42—104no—
657C42D4×D512yes—
658C42C23×D512yes—
659C2×C5—82no—
660C2×C5#340014yescomplemented
661C2×C5C2×#55011yescharacteristic
662C2×C5C22×#13711yescharacteristic
663C2×C5C2×#57711yescharacteristic
664D5—82no—
665C23—22no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—102no—
670C23—202no—
671C23—202no—
672C23—202no—
673C23C2×D4×D511yescharacteristic
674Q8—22no—
675Q8—22no—
676Q8—42no—
677Q8—108no—
678Q8—102no—
679Q8—102no—
680Q8—102no—
681Q8—102no—
682Q8—102no—
683Q8—102no—
684Q8—202no—
685Q8—202no—
686Q8—202no—
687D4—22no—
688D4—22no—
689D4—42no—
690D4—102no—
691D4—102no—
692D4—208no—
693D4—202no—
694D4—404no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—54no—
704C2×C4—52no—
705C2×C4—52no—
706C2×C4—52no—
707C2×C4—52no—
708C2×C4—84no—
709C2×C4—102no—
710C2×C4—102no—
711C2×C4—102no—
712C2×C4—102no—
713C2×C4—102no—
714C2×C4—102no—
715C2×C4—202no—
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×C4#414912yes—
724C2×C4C24×D511yescharacteristic
725C8—22no—
726C8—102no—
727C8—102no—
728C8C2×#70914yes—
729C5C2×#340011yescharacteristic, complemented, Sylow
730C22—42no—
731C22—42no—
732C22—42no—
733C22—84no—
734C22—202no—
735C22—202no—
736C22—202no—
737C22—404no—
738C22#6588712yes—
739C22#6610912yes—
740C22D5×#13712yes—
741C22C22×D4×D511yescharacteristic
742C4—22no—
743C4—22no—
744C4—42no—
745C4—42no—
746C4—42no—
747C4—54no—
748C4—102no—
749C4—102no—
750C4—102no—
751C4—202no—
752C4—202no—
753C4—202no—
754C4#6588712yes—
755C4C22×#70911yescharacteristic
756C4C2×#414911yescharacteristic
757C2—82no—
758C2—402no—
759C2#1061149514yesdirect product factor
760C2C2×#6588711yescharacteristic
761C2C2×#6610911yescharacteristic
762C2C2×D5×#13711yescharacteristic
subgroupG/H
centerC23C2×D4×D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×#440C2
socleC23×C5C22×D4
prime radicalC2×#4086C22
hypercenterC2×#440D5
hypocenterC5C2×#3400
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×#65901C2semidirect
3. C2×C5×#440C2semidirect
4. C2×#65456C2semidirect
6. C2×#65317C2semidirect
7. C2×#65308C2semidirect
8. #10611495C2direct (N × H)
9. C2×#65178C2semidirect
10. C2×#65162C2semidirect
11. C2×#65082C2semidirect
12. C2×#65107C2semidirect
13. C2×#65056C2semidirect
15. C2×#65004C2semidirect
16. C2×#64990C2semidirect
35. #65901C22semidirect
51. C5×#440C22semidirect
57. #65456C22semidirect
62. #65317C22semidirect
63. #65308C22semidirect
69. #65178C22semidirect
70. #65162C22semidirect
71. #65107C22semidirect
72. #65082C22semidirect
73. #65056C22semidirect
75. #65004C22semidirect
76. #64990C22semidirect
200. C2×#440D5semidirect
346. #440C2×D5semidirect
660. C2×C5#3400semidirect
729. C5C2×#3400semidirect
759. C2#10611495direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#659012
C2×#658932
C2×C5×#4402
C2×#654562
C2×#654642
C2×#653172
C2×#653082
#106114952
C2×#651782
C2×#651622
C2×#650822
C2×#651072
C2×#650562
C2×#650512
C2×#650042
C2×#649902
C2×#34005