Finite Group Databasebeta

← C2×#10611950 #12967624

Subgroups — C2×#10611950 #12967624

Order 1280.

2134 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×#66161C211yesmaximal, characteristic, complemented
2C2×#65977C211yesmaximal, characteristic, complemented
3C2×C5×#452C211yesmaximal, characteristic, complemented
4C2×#65527C211yesmaximal, characteristic
5C2×#65474C211yesmaximal, characteristic, complemented
6C2×#65473C211yesmaximal, characteristic, complemented
7C2×#65454C211yesmaximal, characteristic, complemented
8C2×SD16×Dic5C211yesmaximal, characteristic, complemented
9C2×#65332C211yesmaximal, characteristic, complemented
10#10611950C2116yesmaximal, direct product factor
11C2×#65080C211yesmaximal, characteristic, complemented
12C2×#65077C211yesmaximal, characteristic, complemented
13C2×#65050C211yesmaximal, characteristic, complemented
14C2×#65074C211yesmaximal, characteristic, complemented
15C2×#65024C211yesmaximal, characteristic, complemented
16C2×#65009C211yesmaximal, characteristic, complemented
17C22×C5×#41C2211yescharacteristic
18C22×C5×Q16C2211yescharacteristic
19C22×C5×SD16C2211yescharacteristic
20C2×C5×C22⋊Q8C2211yescharacteristic
21#66161—24no—
22#66161C2218yescomplemented
23C2×#4093C2211yescharacteristic
24C2×Q8×Dic5C2211yescharacteristic
25C2×Q8×Dic5C2211yescharacteristic
26C2×Q8×Dic5C2211yescharacteristic
27C22×#688C2211yescharacteristic
28C2×D4×Dic5—21no—
29C2×D4×Dic5—21no—
30C2×D4×Dic5C2211yescharacteristic
31C2×D4×Dic5C2211yescharacteristic
32C22×#686C2211yescharacteristic
33C2×#4076C2211yescharacteristic
34C2×#4072—21no—
35C2×#4072C2211yescharacteristic
36C22×C4⋊Dic5—21no—
37C22×C4⋊Dic5C2211yescharacteristic
38#65977—24no—
39#65977C2218yescomplemented
40C2×#4044—21no—
41C2×#4043—21no—
42C2×#4039C2211yescharacteristic
43C2×#4034C2211yescharacteristic
44C2×#4031—21no—
45C2×#4029—21no—
46C5×#452C2218yescomplemented
47C2×C5×#103C2211yescharacteristic
48C2×C5×#102C2211yescharacteristic
49C2×C5×C22⋊C8C2211yescharacteristic
50#65527C2218yes—
51C2×#3967C2211yescharacteristic
52C2×#3967C2211yescharacteristic
53C2×#3967C2211yescharacteristic
54C2×#3964C2211yescharacteristic
55C2×C22⋊#168C2211yescharacteristic
56#65474C2218yescomplemented
57#65473C2218yescomplemented
58#65454C2218yescomplemented
59SD16×Dic5C2218yescomplemented
60C2×#3953C2211yescharacteristic
61C2×#3953C2211yescharacteristic
62C2×#3949C2211yescharacteristic
63C2×#3949C2211yescharacteristic
64C2×#3947C2211yescharacteristic
65C2×#3946C2211yescharacteristic
66C2×#3946C2211yescharacteristic
67C2×C8×Dic5C2211yescharacteristic
68#65332C2218yescomplemented
69C2×#3940C2211yescharacteristic
70C2×#3940C2211yescharacteristic
71#65080C2218yescomplemented
72#65077C2218yescomplemented
73#65074C2218yescomplemented
74#65050C2218yescomplemented
75#65024C2218yescomplemented
76#65009C2218yescomplemented
77C2×#3125—51nomaximal, Sylow
78C2×C5×#41—24no—
79C2×C5×#41—24no—
80C2×C5×#41—22no—
81C2×C5×#41C2314yes—
82C22×C5×Q8C2311yescharacteristic
83C22×C5×Q8C2311yescharacteristic
84C22×C5×D4—21no—
85C22×C5×D4C2311yescharacteristic
86C23×C4×C5—21no—
87C23×C4×C5C2311yescharacteristic
88C22×C22⋊D5—21no—
89C23×Dic5—21no—
90C23×Dic5—21no—
91C23×Dic5—21no—
92C22×D20C2311yescharacteristic
93C22×C4×D5—21no—
94C22×Dic10—21no—
95C2×C5×Q16—24no—
96C2×C5×Q16C2314yes—
97C2×C5×SD16—24no—
98C2×C5×SD16C2314yes—
99C22×C5×C8C2311yescharacteristic
100C22×C5×C8C2311yescharacteristic
101C5×C22⋊Q8—22no—
102C5×C22⋊Q8C2314yes—
103C2×C5×C4⋊C4—21no—
104C2×C5×C4⋊C4C2311yescharacteristic
105C2×C5×C22⋊C4—21no—
106C2×C22⋊Dic5—21no—
107C2×C22⋊Dic5—21no—
108C2×C22⋊Dic5D411yescharacteristic
109C2×C22⋊Dic5D411yescharacteristic
110#4093—22no—
111#4093C2314yes—
112Q8×Dic5—22no—
113Q8×Dic5—22no—
114Q8×Dic5—22no—
115Q8×Dic5C2314yes—
116Q8×Dic5C2314yes—
117Q8×Dic5C2314yes—
118C2×#688—24no—
119C2×#688C2314yes—
120D4×Dic5—28no—
121D4×Dic5—28no—
122D4×Dic5—22no—
123D4×Dic5—22no—
124D4×Dic5C2314yes—
125D4×Dic5C2314yes—
126C2×#686—24no—
127C2×#686C2314yes—
128#4076—22no—
129#4076C2314yes—
130C2×#685—21no—
131C2×#685—21no—
132C2×#685—21no—
133C2×#685—21no—
134#4072—28no—
135#4072D414yes—
136#4072C2314yes—
137C2×C4⋊Dic5—21no—
138C2×C4⋊Dic5—22no—
139C2×C4⋊Dic5—21no—
140C2×C4⋊Dic5—21no—
141C2×C4⋊Dic5—21no—
142C2×C4⋊Dic5—28no—
143C2×C4⋊Dic5D411yescharacteristic
144C2×C4⋊Dic5D411yescharacteristic
145C2×C4⋊Dic5C2314yes—
146C2×C4⋊Dic5C2311yescharacteristic
147C2×C4⋊Dic5C2311yescharacteristic
148C2×C4⋊Dic5C2311yescharacteristic
149C2×#683—21no—
150C2×C4×Dic5—21no—
151C2×C4×Dic5—21no—
152C2×C4×Dic5—21no—
153C2×C4×Dic5C2311yescharacteristic
154C2×C4×Dic5C2311yescharacteristic
155C22×#168C2311yescharacteristic
156C22×#168C2311yescharacteristic
157#4044—28no—
158#4043—28no—
159#4039—22no—
160#4039C2314yes—
161#4034—22no—
162#4034C2314yes—
163#4031—28no—
164#4029—28no—
165C5×#103C2314yes—
166C5×#102C2314yes—
167C5×C22⋊C8C2314yes—
168#3967C2314yes—
169#3967C2314yes—
170#3967C2314yes—
171#3964C2314yes—
172C22⋊#168C2314yes—
173#3953C2314yes—
174#3953C2314yes—
175#3949C2314yes—
176#3949C2314yes—
177#3947C2314yes—
178#3946C2314yes—
179#3946C2314yes—
180C8×Dic5C2314yes—
181#3940C2314yes—
182#3940C2314yes—
183C2×#542—51no—
184C2×#520—51no—
185#3125—516no—
186C2×#481—51no—
187C2×#483—51no—
188C2×#475—51no—
189C2×#476—51no—
190C2×#464—51no—
191C2×#463—51no—
192C2×#452D511yescharacteristic, complemented
193C2×#449—51no—
194C2×#442—51no—
195C2×#441—51no—
196C2×C4×SD16—51no—
197C2×C4×SD16—51no—
198C2×#433—51no—
199C24×C5—21no—
200C24×C5C2×D411yescharacteristic
201C23×D5—21no—
202C5×#41—216no—
203C5×#41—28no—
204C5×#41—28no—
205C2×C5×Q8—21no—
206C2×C5×Q8—21no—
207C2×C5×Q8—22no—
208C2×C5×Q8—22no—
209C2×C5×Q8—22no—
210C2×C5×Q8#4114yes—
211C2×C5×Q8C2412yes—
212C2×C5×Q8C2412yes—
213C2×C5×D4—28no—
214C2×C5×D4—24no—
215C2×C5×D4—21no—
216C2×C5×D4—22no—
217C2×C5×D4#4114yes—
218C2×C5×D4C2412yes—
219C22×C4×C5—28no—
220C22×C4×C5—21no—
221C22×C4×C5—24no—
222C22×C4×C5—22no—
223C22×C4×C5—22no—
224C22×C4×C5—21no—
225C22×C4×C5—21no—
226C22×C4×C5C2×D411yescharacteristic
227C22×C4×C5C2×D412yes—
228C22×C4×C5C2412yes—
229C22×C4×C5C2411yescharacteristic
230C2×C22⋊D5—24no—
231C2×C22⋊D5—82no—
232C22×Dic5—21no—
233C22×Dic5—21no—
234C22×Dic5—21no—
235C22×Dic5—24no—
236C22×Dic5—24no—
237C22×Dic5—24no—
238C22×Dic5—82no—
239C22×Dic5—82no—
240C22×Dic5—82no—
241C22×Dic5C2×D411yescharacteristic
242C22×Dic5C2×D411yescharacteristic
243C22×Dic5C2×D411yescharacteristic
244C22×Dic5C2×D411yescharacteristic
245C2×D20—22no—
246C2×D20—22no—
247C2×D20—21no—
248C2×D20C2412yes—
249C2×C4×D5—24no—
250C2×C4×D5—82no—
251C2×Dic10—24no—
252C2×Dic10—82no—
253C5×Q16—28no—
254C5×SD16—28no—
255C2×C5×C8—22no—
256C2×C5×C8—22no—
257C2×C5×C8C2412yes—
258C2×C5×C8C2412yes—
259C5×C4⋊C4—24no—
260C5×C4⋊C4—21no—
261C5×C4⋊C4C2412yes—
262C5×C22⋊C4—24no—
263C22⋊Dic5—24no—
264C22⋊Dic5—24no—
265C22⋊Dic5C2×D414yes—
266C22⋊Dic5C2×D414yes—
267#688—28no—
268#686—28no—
269#685—24no—
270#685—24no—
271#685—24no—
272#685—24no—
273C4⋊Dic5—21no—
274C4⋊Dic5—24no—
275C4⋊Dic5—21no—
276C4⋊Dic5—21no—
277C4⋊Dic5—24no—
278C4⋊Dic5—24no—
279C4⋊Dic5—24no—
280C4⋊Dic5C2×D414yes—
281C4⋊Dic5C2×D414yes—
282C4⋊Dic5C2412yes—
283C4⋊Dic5C2412yes—
284C4⋊Dic5C2412yes—
285#683—24no—
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—
297C22×#41C2×D511yescharacteristic
298C22×Q16C2×D511yescharacteristic
299C22×SD16—51no—
300C22×SD16C2×D511yescharacteristic
301C22×D8—51no—
302#542—58no—
303#542—104no—
304C2×C4⋊Q8—51no—
305C2×#126—101no—
306C2×#124—51no—
307C2×#124—101no—
308C2×#123—101no—
309C2×C22⋊Q8—101no—
310C2×C22⋊Q8C2×D511yescharacteristic
311C2×#121—51no—
312#520—58no—
313#520—104no—
314C2×C4×Q8—51no—
315C2×C4×Q8—51no—
316C2×C4×Q8—51no—
317C2×C4×D4—51no—
318C2×C4×D4—51no—
319C2×C4×D4—51no—
320C2×C4×D4—101no—
321C2×C4×D4—101no—
322C2×#117—51no—
323C2×#117—101no—
324C22×C4⋊C4—51no—
325C22×C4⋊C4—101no—
326#483—58no—
327#481—58no—
328#476—58no—
329#475—58no—
330#464—58no—
331#463—58no—
332#452C2×D518yescomplemented
333#449—58no—
334#442—58no—
335#441—58no—
336C4×SD16—58no—
337C4×SD16—58no—
338#433—58no—
339C2×#106—51no—
340C2×#106—51no—
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⋊C8C2×D511yescharacteristic
355C2×#97—51no—
356C2×C4×C8—51no—
357C23×C5—22no—
358C23×C5—24no—
359C23×C5—22no—
360C23×C5—22no—
361C23×C5—22no—
362C23×C5—42no—
363C23×C5—42no—
364C23×C5C22×D412yes—
365C23×C5C22×D411yescharacteristic
366C22×D5—22no—
367C22×D5—42no—
368C22×D5—42no—
369C22×D5—42no—
370C5×Q8—24no—
371C5×Q8—22no—
372C5×Q8—22no—
373C5×Q8—22no—
374C5×Q8—42no—
375C5×Q8C2×#4114yes—
376C5×D4—216no—
377C5×D4—24no—
378C5×D4—22no—
379C5×D4C2×#4114yes—
380C2×C4×C5—216no—
381C2×C4×C5—22no—
382C2×C4×C5—24no—
383C2×C4×C5—22no—
384C2×C4×C5—24no—
385C2×C4×C5—22no—
386C2×C4×C5—22no—
387C2×C4×C5—22no—
388C2×C4×C5—22no—
389C2×C4×C5—42no—
390C2×C4×C5—42no—
391C2×C4×C5C22×D412yes—
392C2×C4×C5C22×D411yescharacteristic
393C2×C4×C5C2×#4112yes—
394C2×C4×C5C2×#4112yes—
395C2×C4×C5C2511yescharacteristic
396C22⋊D5—84no—
397C2×Dic5—22no—
398C2×Dic5—22no—
399C2×Dic5—22no—
400C2×Dic5—22no—
401C2×Dic5—22no—
402C2×Dic5—22no—
403C2×Dic5—22no—
404C2×Dic5—42no—
405C2×Dic5—42no—
406C2×Dic5—42no—
407C2×Dic5—84no—
408C2×Dic5—84no—
409C2×Dic5—84no—
410C2×Dic5C22×D412yes—
411C2×Dic5C22×D412yes—
412C2×Dic5C22×D412yes—
413C2×Dic5C22×D412yes—
414D20—22no—
415D20—22no—
416D20—42no—
417C4×D5—84no—
418Dic10—84no—
419C5×C8—22no—
420C5×C8—22no—
421#168—22no—
422#168—22no—
423C2×#41—24no—
424C2×#41—24no—
425C2×#41—22no—
426C2×#41C22×D514yes—
427C22×Q8—101no—
428C22×Q8C22×D511yescharacteristic
429C22×Q8C22×D511yescharacteristic
430C22×D4—21no—
431C22×D4—51no—
432C22×D4—101no—
433C22×D4C22×D511yescharacteristic
434C23×C4—21no—
435C23×C4—101no—
436C23×C4—101no—
437C23×C4—101no—
438C23×C4—101no—
439C23×C4C22×D511yescharacteristic
440C2×Q16—24no—
441C2×Q16C22×D514yes—
442C2×SD16—24no—
443C2×SD16—54no—
444C2×SD16—104no—
445C2×SD16C22×D514yes—
446C2×D8—54no—
447C2×D8—104no—
448C22×C8—51no—
449C22×C8—51no—
450C22×C8C22×D511yescharacteristic
451C22×C8C22×D511yescharacteristic
452C4⋊Q8—54no—
453C4⋊Q8—102no—
454#126—108no—
455#124—54no—
456#124—102no—
457#124—108no—
458#123—108no—
459C22⋊Q8—22no—
460C22⋊Q8—108no—
461C22⋊Q8C22×D514yes—
462#121—54no—
463#121—102no—
464C4×Q8—54no—
465C4×Q8—54no—
466C4×Q8—54no—
467C4×Q8—102no—
468C4×Q8—102no—
469C4×Q8—102no—
470C4×D4—54no—
471C4×D4—54no—
472C4×D4—54no—
473C4×D4—102no—
474C4×D4—102no—
475C4×D4—102no—
476C4×D4—108no—
477C4×D4—108no—
478#117—54no—
479#117—54no—
480#117—108no—
481C2×C4⋊C4—21no—
482C2×C4⋊C4—51no—
483C2×C4⋊C4—51no—
484C2×C4⋊C4—51no—
485C2×C4⋊C4—51no—
486C2×C4⋊C4—54no—
487C2×C4⋊C4—51no—
488C2×C4⋊C4—108no—
489C2×C4⋊C4—101no—
490C2×C4⋊C4—101no—
491C2×C4⋊C4—101no—
492C2×C4⋊C4—101no—
493C2×C4⋊C4—101no—
494C2×C4⋊C4—102no—
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×C22⋊C4—101no—
504C2×C22⋊C4—101no—
505C2×C42—51no—
506C2×C42—51no—
507C2×C42—101no—
508C2×C42—101no—
509C2×C42—101no—
510#106—54no—
511#106—54no—
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⋊C8C22×D514yes—
526#97—54no—
527C4×C8—54no—
528C22×C5—22no—
529C22×C5—24no—
530C22×C5—22no—
531C22×C5—22no—
532C22×C5—44no—
533C22×C5—48no—
534C22×C5—42no—
535C22×C5—42no—
536C22×C5#52512yes—
537C22×C5#57712yes—
538C22×C5#57712yes—
539C22×C5C23×D411yescharacteristic
540C2×D5—42no—
541C2×D5—42no—
542C2×D5—42no—
543C2×D5—84no—
544C4×C5—22no—
545C4×C5—24no—
546C4×C5—42no—
547C4×C5—42no—
548C4×C5#52512yes—
549C4×C5C22×#4111yescharacteristic
550C4×C5C22×#4111yescharacteristic
551Dic5—22no—
552Dic5—22no—
553Dic5—22no—
554Dic5—22no—
555Dic5—42no—
556Dic5—42no—
557Dic5—42no—
558C24—21no—
559C24—101no—
560C24D4×D511yescharacteristic
561#41—216no—
562#41—28no—
563#41—28no—
564C2×Q8—21no—
565C2×Q8—21no—
566C2×Q8—22no—
567C2×Q8—22no—
568C2×Q8—22no—
569C2×Q8—104no—
570C2×Q8—402no—
571C2×Q8#71114yes—
572C2×Q8C23×D512yes—
573C2×Q8C23×D512yes—
574C2×D4—28no—
575C2×D4—24no—
576C2×D4—21no—
577C2×D4—22no—
578C2×D4—52no—
579C2×D4—104no—
580C2×D4—101no—
581C2×D4—102no—
582C2×D4—102no—
583C2×D4—402no—
584C2×D4#71114yes—
585C2×D4C23×D512yes—
586C22×C4—28no—
587C22×C4—21no—
588C22×C4—24no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—51no—
594C22×C4—51no—
595C22×C4—51no—
596C22×C4—51no—
597C22×C4—104no—
598C22×C4—104no—
599C22×C4—104no—
600C22×C4—101no—
601C22×C4—101no—
602C22×C4—101no—
603C22×C4—104no—
604C22×C4—402no—
605C22×C4—402no—
606C22×C4—402no—
607C22×C4—402no—
608C22×C4D4×D512yes—
609C22×C4D4×D511yescharacteristic
610C22×C4C23×D512yes—
611C22×C4C23×D511yescharacteristic
612Q16—28no—
613SD16—28no—
614SD16—108no—
615D8—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—54no—
627C4⋊C4—54no—
628C4⋊C4—52no—
629C4⋊C4—52no—
630C4⋊C4—52no—
631C4⋊C4—104no—
632C4⋊C4—104no—
633C4⋊C4—104no—
634C4⋊C4—104no—
635C4⋊C4—104no—
636C4⋊C4—101no—
637C4⋊C4—101no—
638C4⋊C4—101no—
639C4⋊C4C23×D512yes—
640C22⋊C4—24no—
641C22⋊C4—54no—
642C22⋊C4—54no—
643C22⋊C4—104no—
644C22⋊C4—104no—
645C22⋊C4—104no—
646C22⋊C4—104no—
647C22⋊C4—104no—
648C22⋊C4—104no—
649C42—52no—
650C42—52no—
651C42—52no—
652C42—52no—
653C42—104no—
654C42—104no—
655C42—104no—
656C2×C5—42no—
657C2×C5—44no—
658C2×C5#312514yescomplemented
659C2×C5C2×#52511yescharacteristic
660C2×C5C2×#57711yescharacteristic
661C2×C5C2×#57711yescharacteristic
662D5—82no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—24no—
667C23—22no—
668C23—42no—
669C23—42no—
670C23—102no—
671C23—202no—
672C23—202no—
673C23—202no—
674C23C2×D4×D512yes—
675C23C2×D4×D511yescharacteristic
676Q8—24no—
677Q8—22no—
678Q8—22no—
679Q8—22no—
680Q8—42no—
681Q8—404no—
682Q8C2×#71114yes—
683D4—216no—
684D4—24no—
685D4—22no—
686D4—102no—
687D4—102no—
688D4—202no—
689D4—404no—
690D4C2×#71114yes—
691C2×C4—216no—
692C2×C4—22no—
693C2×C4—24no—
694C2×C4—22no—
695C2×C4—24no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—52no—
703C2×C4—52no—
704C2×C4—52no—
705C2×C4—52no—
706C2×C4—102no—
707C2×C4—102no—
708C2×C4—102no—
709C2×C4—102no—
710C2×C4—102no—
711C2×C4—102no—
712C2×C4—102no—
713C2×C4—202no—
714C2×C4—202no—
715C2×C4—202no—
716C2×C4—404no—
717C2×C4—404no—
718C2×C4—404no—
719C2×C4—404no—
720C2×C4C2×D4×D512yes—
721C2×C4C2×D4×D511yescharacteristic
722C2×C4C2×#71112yes—
723C2×C4C2×#71112yes—
724C2×C4C24×D511yescharacteristic
725C8—22no—
726C8—22no—
727C8—102no—
728C8—102no—
729C5C2×#312511yescharacteristic, complemented, Sylow
730C22—22no—
731C22—22no—
732C22—24no—
733C22—22no—
734C22—42no—
735C22—42no—
736C22—44no—
737C22—48no—
738C22—202no—
739C22—202no—
740C22—202no—
741C22—404no—
742C22#6592012yes—
743C22#6610412yes—
744C22#6611212yes—
745C22C22×D4×D511yescharacteristic
746C4—22no—
747C4—24no—
748C4—42no—
749C4—42no—
750C4—102no—
751C4—102no—
752C4—102no—
753C4—102no—
754C4—202no—
755C4—202no—
756C4—202no—
757C4#6592012yes—
758C4C22×#71111yescharacteristic
759C4C22×#71111yescharacteristic
760C2—42no—
761C2—44no—
762C2—402no—
763C2#1061195014yesdirect product factor
764C2C2×#6592011yescharacteristic
765C2C2×#6610411yescharacteristic
766C2C2×#6611211yescharacteristic
subgroupG/H
centerC23C2×D4×D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×#452C2
socleC23×C5C22×D4
prime radicalC2×#65527C2
hypercenterC2×#452D5
hypocenterC5C2×#3125
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#452

Complements

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

NH ≅ G/Ntype
1. C2×#66161C2semidirect
2. C2×#65977C2semidirect
3. C2×C5×#452C2semidirect
5. C2×#65474C2semidirect
6. C2×#65473C2semidirect
7. C2×#65454C2semidirect
8. C2×SD16×Dic5C2semidirect
9. C2×#65332C2semidirect
10. #10611950C2direct (N × H)
11. C2×#65080C2semidirect
12. C2×#65077C2semidirect
13. C2×#65050C2semidirect
14. C2×#65074C2semidirect
15. C2×#65024C2semidirect
16. C2×#65009C2semidirect
22. #66161C22semidirect
39. #65977C22semidirect
46. C5×#452C22semidirect
56. #65474C22semidirect
57. #65473C22semidirect
58. #65454C22semidirect
59. SD16×Dic5C22semidirect
68. #65332C22semidirect
71. #65080C22semidirect
72. #65077C22semidirect
73. #65074C22semidirect
74. #65050C22semidirect
75. #65024C22semidirect
76. #65009C22semidirect
192. C2×#452D5semidirect
332. #452C2×D5semidirect
658. C2×C5#3125semidirect
729. C5C2×#3125semidirect
763. C2#10611950direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#661612
C2×#659772
C2×C5×#4522
C2×#655272
C2×#654742
C2×#654732
C2×#654542
C2×SD16×Dic52
C2×#653322
#106119502
C2×#650802
C2×#650772
C2×#650502
C2×#650742
C2×#650242
C2×#650092
C2×#31255