Finite Group Databasebeta

← C2×#10611394 #12969022

Subgroups — C2×#10611394 #12969022

Order 1280.

2070 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65914C211yesmaximal, characteristic, complemented
2C2×#65891C211yesmaximal, characteristic, complemented
3C2×C4×C5×SD16C211yesmaximal, characteristic, complemented
4C2×#65460C211yesmaximal, characteristic, complemented
5C2×#65457C211yesmaximal, characteristic, complemented
6C2×C4×#689C211yesmaximal, characteristic, complemented
7C2×C4×#686C211yesmaximal, characteristic, complemented
8#10611394C2116yesmaximal, direct product factor
9C2×#65153C211yesmaximal, characteristic, complemented
10C2×#65147C211yesmaximal, characteristic, complemented
11C2×#65102C211yesmaximal, characteristic, complemented
12C2×#65089C211yesmaximal, characteristic, complemented
13C2×#65064C211yesmaximal, characteristic
14C2×#65057C211yesmaximal, characteristic, complemented
15C2×C4×#677C211yesmaximal, characteristic, complemented
16C2×C4×C8×D5C211yesmaximal, characteristic, complemented
17C22×C5×SD16C2211yescharacteristic
18C2×C4×C5×Q8C2211yescharacteristic
19C2×C4×C5×D4C2211yescharacteristic
20C2×#4093C2211yescharacteristic
21C2×#4092C2211yescharacteristic
22C22×#689C2211yescharacteristic
23C2×#4084C2211yescharacteristic
24C2×#4082C2211yescharacteristic
25C22×#686C2211yescharacteristic
26C2×C4×C22⋊D5—21no—
27C2×#4072—21no—
28C22×#677C2211yescharacteristic
29C22×C8×D5C2211yescharacteristic
30C22×C8×D5C2211yescharacteristic
31#65914—24no—
32#65914C2218yescomplemented
33#65891—24no—
34#65891C2218yescomplemented
35C2×#4044—21no—
36C2×#4043C2211yescharacteristic
37C2×#4041C2211yescharacteristic
38C2×#4040—21no—
39C2×#4036C2211yescharacteristic
40C2×#4036C2211yescharacteristic
41C2×#4029—21no—
42C2×#4025—21no—
43C2×C4×D20—21no—
44C2×C4×D20C2211yescharacteristic
45C2×#4018—21no—
46C2×C42×D5C2211yescharacteristic
47C2×C4×Dic10C2211yescharacteristic
48C4×C5×SD16C2218yescomplemented
49C2×C5×#106C2211yescharacteristic
50C2×C5×#103C2211yescharacteristic
51C2×C5×#102C2211yescharacteristic
52C2×C4×C5×C8C2211yescharacteristic
53C2×#3967C2211yescharacteristic
54C2×#3964C2211yescharacteristic
55#65460C2218yescomplemented
56#65457C2218yescomplemented
57C2×#3953C2211yescharacteristic
58C2×#3949C2211yescharacteristic
59C2×#3948C2211yescharacteristic
60C2×C8×Dic5C2211yescharacteristic
61C2×C8×Dic5C2211yescharacteristic
62C4×#689C2218yescomplemented
63C4×#686C2218yescomplemented
64C2×#3942C2211yescharacteristic
65C2×#3941C2211yescharacteristic
66C2×#3939C2211yescharacteristic
67C2×#3939C2211yescharacteristic
68C2×C4×#168C2211yescharacteristic
69#65153C2218yescomplemented
70#65147C2218yescomplemented
71#65102C2218yescomplemented
72#65089C2218yescomplemented
73#65064C2218yes—
74#65057C2218yescomplemented
75C4×#677C2218yescomplemented
76C4×C8×D5C2218yescomplemented
77C2×#3168—51nomaximal, Sylow
78C22×C5×Q8C2311yescharacteristic
79C22×C5×D4C2311yescharacteristic
80C23×C4×C5—21no—
81C22×C22⋊D5—21no—
82C22×D20—21no—
83C22×D20C2311yescharacteristic
84C22×C4×D5—21no—
85C22×C4×D5D411yescharacteristic
86C22×C4×D5D411yescharacteristic
87C22×C4×D5C2311yescharacteristic
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—
105C2×C22⋊Dic5—21no—
106#4093—22no—
107#4093C2314yes—
108#4092—22no—
109#4092C2314yes—
110C2×#689—24no—
111C2×#689C2314yes—
112#4084—22no—
113#4084C2314yes—
114#4082—22no—
115#4082C2314yes—
116C2×#686—24no—
117C2×#686C2314yes—
118C4×C22⋊D5—28no—
119C2×#685—21no—
120C2×#685—21no—
121C2×#685—21no—
122C2×#685—21no—
123C2×#685—21no—
124C2×#685—21no—
125#4072—28no—
126C2×C4⋊Dic5—21no—
127C2×C4⋊Dic5—21no—
128C2×C4⋊Dic5—21no—
129C2×C4⋊Dic5C2311yescharacteristic
130C2×C4⋊Dic5C2311yescharacteristic
131C2×#683—21no—
132C2×#683—21no—
133C2×#683—21no—
134C2×#683—21no—
135C2×C4×Dic5—21no—
136C2×C4×Dic5D411yescharacteristic
137C2×C4×Dic5D411yescharacteristic
138C2×C4×Dic5C2311yescharacteristic
139C22×#168C2311yescharacteristic
140C22×#168C2311yescharacteristic
141C2×#677—24no—
142C2×#677C2314yes—
143C2×C8×D5—24no—
144C2×C8×D5—24no—
145C2×C8×D5C2314yes—
146C2×C8×D5C2314yes—
147#4044—28no—
148#4043—22no—
149#4043C2314yes—
150#4041—22no—
151#4041C2314yes—
152#4040—28no—
153#4036—22no—
154#4036—22no—
155#4036C2314yes—
156#4036C2314yes—
157#4029—28no—
158#4025—28no—
159C4×D20—28no—
160C4×D20—22no—
161C4×D20C2314yes—
162#4018—28no—
163C42×D5D414yes—
164C42×D5C2314yes—
165C4×Dic10—22no—
166C4×Dic10C2314yes—
167C5×#106C2314yes—
168C5×#103C2314yes—
169C5×#102C2314yes—
170C4×C5×C8C2314yes—
171#3967C2314yes—
172#3964C2314yes—
173#3953C2314yes—
174#3949C2314yes—
175#3948C2314yes—
176C8×Dic5C2314yes—
177C8×Dic5C2314yes—
178#3942C2314yes—
179#3941C2314yes—
180#3939C2314yes—
181#3939C2314yes—
182C4×#168C2314yes—
183C2×#529—51no—
184C2×#529—51no—
185#3168—516no—
186C2×#499—51no—
187C2×#495—51no—
188C2×#488—51no—
189C2×#488—51no—
190C2×#467—51no—
191C2×#466—51no—
192C2×#465—51no—
193C2×#465—51no—
194C2×C4×Q16—51no—
195C2×C4×SD16—51no—
196C2×C4×SD16D511yescharacteristic, complemented
197C2×C4×D8—51no—
198C22×C4×C8—51no—
199C24×C5—21no—
200C23×D5—21no—
201C23×D5C2×D411yescharacteristic
202C2×C5×Q8—21no—
203C2×C5×Q8—22no—
204C2×C5×Q8—22no—
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—44no—
215C22×C4×C5C2×D411yescharacteristic
216C22×C4×C5C2×D411yescharacteristic
217C22×C4×C5C2411yescharacteristic
218C2×C22⋊D5—24no—
219C2×C22⋊D5—44no—
220C22×Dic5—21no—
221C22×Dic5—21no—
222C22×Dic5—21no—
223C22×Dic5C2×D411yescharacteristic
224C22×Dic5C2×D411yescharacteristic
225C22×Dic5C2×D411yescharacteristic
226C2×D20—22no—
227C2×D20—22no—
228C2×D20—24no—
229C2×D20—21no—
230C2×D20—44no—
231C2×D20C2412yes—
232C2×C4×D5—24no—
233C2×C4×D5—24no—
234C2×C4×D5—22no—
235C2×C4×D5—22no—
236C2×C4×D5—24no—
237C2×C4×D5—44no—
238C2×C4×D5C2×D414yes—
239C2×C4×D5C2×D414yes—
240C2×C4×D5C2×D412yes—
241C2×C4×D5C2412yes—
242C2×Dic10—22no—
243C2×Dic10—22no—
244C2×Dic10—21no—
245C2×Dic10C2412yes—
246C5×SD16—28no—
247C2×C5×C8—22no—
248C2×C5×C8#4114yes—
249C2×C5×C8C2412yes—
250C2×C5×C8C2412yes—
251C5×C4⋊C4—24no—
252C5×C4⋊C4—21no—
253C5×C4⋊C4—21no—
254C5×C4⋊C4C2412yes—
255C5×C4⋊C4C2412yes—
256C5×C22⋊C4—24no—
257C42×C5—24no—
258C42×C5C2×D412yes—
259C42×C5C2412yes—
260C22⋊Dic5—24no—
261C22⋊Dic5—24no—
262C22⋊Dic5—24no—
263#689—28no—
264#686—28no—
265#685—24no—
266#685—24no—
267#685—24no—
268#685—24no—
269#685—24no—
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—
282C4×Dic5—24no—
283C4×Dic5C2×D412yes—
284C4×Dic5C2×D414yes—
285C4×Dic5C2×D414yes—
286C4×Dic5C2412yes—
287C2×#168—22no—
288C2×#168#4114yes—
289C2×#168C2412yes—
290C2×#168C2412yes—
291#677—28no—
292C8×D5—28no—
293C8×D5—28no—
294C22×Q16—51no—
295C22×SD16—51no—
296C22×SD16C2×D511yescharacteristic
297C22×D8—51no—
298C23×C8—51no—
299C23×C8—51no—
300#529—58no—
301#529—58no—
302#529—104no—
303#529—104no—
304C2×#126—101no—
305C2×#126—101no—
306C2×#125—51no—
307C2×#125—51no—
308C2×#124—51no—
309C2×#124—51no—
310C2×#123—101no—
311C2×#123—101no—
312C2×C22⋊Q8—51no—
313C2×C22⋊Q8—51no—
314C2×#121—51no—
315C2×#121—51no—
316C2×C4×Q8—51no—
317C2×C4×Q8C2×D511yescharacteristic
318C2×C4×D4—51no—
319C2×C4×D4—101no—
320C2×C4×D4—101no—
321C2×C4×D4C2×D511yescharacteristic
322C2×#117—101no—
323C2×#117—101no—
324C22×C42—51no—
325#499—58no—
326#495—58no—
327#488—58no—
328#488—58no—
329#467—58no—
330#466—58no—
331#465—58no—
332#465—58no—
333C4×Q16—58no—
334C4×SD16—58no—
335C4×SD16C2×D518yescomplemented
336C4×D8—58no—
337C2×#107—51no—
338C2×#107—51no—
339C2×#106—51no—
340C2×#106C2×D511yescharacteristic
341C2×#103—51no—
342C2×#103—51no—
343C2×#103—51no—
344C2×#103C2×D511yescharacteristic
345C2×#102—51no—
346C2×#102—51no—
347C2×#102—51no—
348C2×#102C2×D511yescharacteristic
349C2×C4×C8—51no—
350C2×C4×C8—51no—
351C2×C4×C8—51no—
352C2×C4×C8—58no—
353C2×C4×C8C2×D511yescharacteristic
354C23×C5—22no—
355C23×C5—42no—
356C23×C5—42no—
357C23×C5—42no—
358C23×C5C22×D411yescharacteristic
359C22×D5—22no—
360C22×D5—22no—
361C22×D5—22no—
362C22×D5—42no—
363C22×D5—42no—
364C22×D5—42no—
365C22×D5#13514yes—
366C22×D5C22×D412yes—
367C5×Q8—22no—
368C5×Q8—22no—
369C5×Q8—42no—
370C5×D4—22no—
371C5×D4—22no—
372C5×D4—42no—
373C2×C4×C5—22no—
374C2×C4×C5—22no—
375C2×C4×C5—22no—
376C2×C4×C5—22no—
377C2×C4×C5—42no—
378C2×C4×C5—42no—
379C2×C4×C5—42no—
380C2×C4×C5—48no—
381C2×C4×C5#13514yes—
382C2×C4×C5C22×D412yes—
383C2×C4×C5C22×D411yescharacteristic
384C2×C4×C5C22×D412yes—
385C2×C4×C5C2×#4112yes—
386C2×C4×C5C2×#4112yes—
387C2×C4×C5C2511yescharacteristic
388C22⋊D5—48no—
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—
401D20—22no—
402D20—22no—
403D20—48no—
404D20—42no—
405C4×D5—28no—
406C4×D5—24no—
407C4×D5—28no—
408C4×D5—22no—
409C4×D5—22no—
410C4×D5—48no—
411Dic10—22no—
412Dic10—22no—
413Dic10—42no—
414C5×C8—22no—
415C5×C8C2×#4114yes—
416#168—22no—
417#168C2×#4114yes—
418C22×Q8—51no—
419C22×Q8C22×D511yescharacteristic
420C22×D4—51no—
421C22×D4—101no—
422C22×D4—101no—
423C22×D4C22×D511yescharacteristic
424C23×C4—21no—
425C23×C4—51no—
426C23×C4—51no—
427C23×C4—51no—
428C23×C4—101no—
429C2×Q16—54no—
430C2×Q16—104no—
431C2×SD16—24no—
432C2×SD16—54no—
433C2×SD16—104no—
434C2×SD16C22×D514yes—
435C2×D8—54no—
436C2×D8—104no—
437C22×C8—51no—
438C22×C8—51no—
439C22×C8—54no—
440C22×C8—54no—
441C22×C8—104no—
442C22×C8—104no—
443C22×C8C22×D511yescharacteristic
444C22×C8C22×D511yescharacteristic
445#126—108no—
446#126—108no—
447#125—54no—
448#125—54no—
449#125—102no—
450#125—102no—
451#124—54no—
452#124—54no—
453#124—102no—
454#124—102no—
455#123—108no—
456#123—108no—
457C22⋊Q8—54no—
458C22⋊Q8—54no—
459C22⋊Q8—102no—
460C22⋊Q8—102no—
461#121—54no—
462#121—54no—
463#121—102no—
464#121—102no—
465C4×Q8—22no—
466C4×Q8—54no—
467C4×Q8—102no—
468C4×Q8C22×D514yes—
469C4×D4—22no—
470C4×D4—54no—
471C4×D4—108no—
472C4×D4—108no—
473C4×D4—102no—
474C4×D4C22×D514yes—
475#117—108no—
476#117—108no—
477C2×C4⋊C4—21no—
478C2×C4⋊C4—51no—
479C2×C4⋊C4—51no—
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×C22⋊C4—101no—
495C2×C22⋊C4—101no—
496C2×C22⋊C4—101no—
497C2×C22⋊C4—101no—
498C2×C22⋊C4—101no—
499C2×C42—21no—
500C2×C42—51no—
501C2×C42—51no—
502C2×C42—51no—
503C2×C42—54no—
504C2×C42—54no—
505C2×C42—101no—
506C2×C42C22×D511yescharacteristic
507#107—54no—
508#107—54no—
509#106—54no—
510#106C22×D514yes—
511#103—54no—
512#103—54no—
513#103—54no—
514#103C22×D514yes—
515#102—54no—
516#102—54no—
517#102—54no—
518#102C22×D514yes—
519C4×C8—54no—
520C4×C8—54no—
521C4×C8—54no—
522C4×C8C22×D514yes—
523C22×C5—42no—
524C22×C5—42no—
525C22×C5—42no—
526C22×C5—84no—
527C22×C5#53212yes—
528C22×C5C2×#13512yes—
529C22×C5C2×#13512yes—
530C22×C5C23×D411yescharacteristic
531C2×D5—28no—
532C2×D5—22no—
533C2×D5—22no—
534C2×D5—42no—
535C2×D5—42no—
536C2×D5—42no—
537C2×D5—84no—
538C2×D5C2×#13514yes—
539C4×C5—22no—
540C4×C5—42no—
541C4×C5—42no—
542C4×C5—42no—
543C4×C5#53212yes—
544C4×C5C2×#13514yes—
545C4×C5C22×#4111yescharacteristic
546C4×C5C22×#4111yescharacteristic
547Dic5—22no—
548Dic5—22no—
549Dic5—22no—
550Dic5—42no—
551Dic5—42no—
552Dic5—42no—
553C24—21no—
554C24—51no—
555C24—101no—
556C2×Q8—21no—
557C2×Q8—22no—
558C2×Q8—22no—
559C2×Q8—52no—
560C2×Q8—101no—
561C2×Q8—102no—
562C2×Q8—102no—
563C2×Q8C23×D512yes—
564C2×D4—22no—
565C2×D4—21no—
566C2×D4—22no—
567C2×D4—52no—
568C2×D4—104no—
569C2×D4—104no—
570C2×D4—102no—
571C2×D4—101no—
572C2×D4—102no—
573C2×D4—204no—
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—54no—
587C22×C4—52no—
588C22×C4—104no—
589C22×C4—102no—
590C22×C4—102no—
591C22×C4—104no—
592C22×C4—101no—
593C22×C4—101no—
594C22×C4—101no—
595C22×C4—104no—
596C22×C4—204no—
597C22×C4D4×D511yescharacteristic
598C22×C4D4×D511yescharacteristic
599C22×C4C23×D511yescharacteristic
600Q16—108no—
601SD16—28no—
602SD16—108no—
603D8—108no—
604C2×C8—22no—
605C2×C8—54no—
606C2×C8—52no—
607C2×C8—52no—
608C2×C8—108no—
609C2×C8—102no—
610C2×C8—108no—
611C2×C8#70914yes—
612C2×C8C23×D512yes—
613C2×C8C23×D512yes—
614C4⋊C4—24no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—52no—
618C4⋊C4—52no—
619C4⋊C4—104no—
620C4⋊C4—104no—
621C4⋊C4—104no—
622C4⋊C4—104no—
623C4⋊C4—104no—
624C4⋊C4—104no—
625C4⋊C4—101no—
626C4⋊C4—101no—
627C4⋊C4—104no—
628C4⋊C4C23×D512yes—
629C4⋊C4C23×D512yes—
630C22⋊C4—24no—
631C22⋊C4—104no—
632C22⋊C4—104no—
633C22⋊C4—104no—
634C22⋊C4—104no—
635C22⋊C4—104no—
636C22⋊C4—104no—
637C22⋊C4—104no—
638C22⋊C4—104no—
639C22⋊C4—104no—
640C42—24no—
641C42—54no—
642C42—52no—
643C42—54no—
644C42—52no—
645C42—104no—
646C42D4×D512yes—
647C42C23×D512yes—
648C2×C5—82no—
649C2×C5#316814yescomplemented
650C2×C5C2×#53211yescharacteristic
651C2×C5C22×#13511yescharacteristic
652C2×C5C22×#13511yescharacteristic
653D5—24no—
654D5—82no—
655C23—22no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—54no—
660C23—52no—
661C23—102no—
662C23—102no—
663C23—102no—
664C23—202no—
665C23—202no—
666C23—202no—
667C23C2×D4×D511yescharacteristic
668Q8—22no—
669Q8—22no—
670Q8—42no—
671Q8—102no—
672Q8—102no—
673Q8—202no—
674D4—22no—
675D4—22no—
676D4—42no—
677D4—102no—
678D4—102no—
679D4—208no—
680D4—208no—
681D4—202no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—48no—
690C2×C4—52no—
691C2×C4—52no—
692C2×C4—52no—
693C2×C4—108no—
694C2×C4—102no—
695C2×C4—102no—
696C2×C4—102no—
697C2×C4—108no—
698C2×C4—104no—
699C2×C4—102no—
700C2×C4—102no—
701C2×C4—102no—
702C2×C4—102no—
703C2×C4—102no—
704C2×C4—202no—
705C2×C4—202no—
706C2×C4—202no—
707C2×C4—208no—
708C2×C4#406214yes—
709C2×C4C2×#70912yes—
710C2×C4C2×D4×D512yes—
711C2×C4C2×D4×D512yes—
712C2×C4C2×D4×D511yescharacteristic
713C2×C4D5×#4112yes—
714C2×C4C24×D511yescharacteristic
715C8—22no—
716C8—54no—
717C8—102no—
718C8C2×#70914yes—
719C5C2×#316811yescharacteristic, complemented, Sylow
720C22—42no—
721C22—42no—
722C22—42no—
723C22—54no—
724C22—84no—
725C22—102no—
726C22—108no—
727C22—102no—
728C22—202no—
729C22—202no—
730C22—202no—
731C22—404no—
732C22#6588212yes—
733C22C2×#406212yes—
734C22D5×#13512yes—
735C22C22×D4×D511yescharacteristic
736C4—22no—
737C4—42no—
738C4—42no—
739C4—42no—
740C4—102no—
741C4—102no—
742C4—102no—
743C4—202no—
744C4—202no—
745C4—202no—
746C4#6588212yes—
747C4C2×#406214yes—
748C4C22×#70911yescharacteristic
749C4C2×D5×#4111yescharacteristic
750C2—82no—
751C2—104no—
752C2—402no—
753C2#1061139414yesdirect product factor
754C2C2×#6588211yescharacteristic
755C2C22×#406211yescharacteristic
756C2C2×D5×#13511yescharacteristic
subgroupG/H
centerC22×C4D4×D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C4×C5×SD16C2
socleC23×C5C22×D4
prime radicalC2×#65064C2
hypercenterC2×C4×SD16D5
hypocenterC5C2×#3168
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#65914C2semidirect
2. C2×#65891C2semidirect
3. C2×C4×C5×SD16C2semidirect
4. C2×#65460C2semidirect
5. C2×#65457C2semidirect
6. C2×C4×#689C2semidirect
7. C2×C4×#686C2semidirect
8. #10611394C2direct (N × H)
9. C2×#65153C2semidirect
10. C2×#65147C2semidirect
11. C2×#65102C2semidirect
12. C2×#65089C2semidirect
14. C2×#65057C2semidirect
15. C2×C4×#677C2semidirect
16. C2×C4×C8×D5C2semidirect
32. #65914C22semidirect
34. #65891C22semidirect
48. C4×C5×SD16C22semidirect
55. #65460C22semidirect
56. #65457C22semidirect
62. C4×#689C22semidirect
63. C4×#686C22semidirect
69. #65153C22semidirect
70. #65147C22semidirect
71. #65102C22semidirect
72. #65089C22semidirect
74. #65057C22semidirect
75. C4×#677C22semidirect
76. C4×C8×D5C22semidirect
196. C2×C4×SD16D5semidirect
335. C4×SD16C2×D5semidirect
649. C2×C5#3168semidirect
719. C5C2×#3168semidirect
753. C2#10611394direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#659142
C2×#658912
C2×C4×C5×SD162
C2×#654602
C2×#654572
C2×C4×#6892
C2×C4×#6862
#106113942
C2×#651532
C2×#651472
C2×#651022
C2×#650892
C2×#650642
C2×#650572
C2×C4×#6772
C2×C4×C8×D52
C2×#31685