Finite Group Databasebeta

← C2×#10611805 #12967608

Subgroups — C2×#10611805 #12967608

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×#65937C211yesmaximal, characteristic, complemented
3C2×C5×#449C211yesmaximal, characteristic
4C2×#65528C211yesmaximal, characteristic, complemented
5C2×#65455C211yesmaximal, characteristic, complemented
6C2×#65453C211yesmaximal, characteristic, complemented
7C2×#65442C211yesmaximal, characteristic, complemented
8C2×D8×Dic5C211yesmaximal, characteristic, complemented
9C2×#65322C211yesmaximal, characteristic, complemented
10#10611805C2116yesmaximal, direct product factor
11C2×#65083C211yesmaximal, characteristic, complemented
12C2×#65079C211yesmaximal, characteristic, complemented
13C2×#65048C211yesmaximal, characteristic, complemented
14C2×#65046C211yesmaximal, characteristic, complemented
15C2×#65011C211yesmaximal, characteristic, complemented
16C2×#65009C211yesmaximal, characteristic, complemented
17C22×C5×#41C2211yescharacteristic
18C22×C5×SD16C2211yescharacteristic
19C22×C5×D8C2211yescharacteristic
20C2×C5×#121C2211yescharacteristic
21#66161—24no—
22#66161C2218yescomplemented
23C2×Q8×Dic5C2211yescharacteristic
24C2×Q8×Dic5C2211yescharacteristic
25C22×#689C2211yescharacteristic
26C2×#4082—21no—
27C2×#4082C2211yescharacteristic
28C2×#4081—21no—
29C2×D4×Dic5—21no—
30C2×D4×Dic5—21no—
31C2×D4×Dic5C2211yescharacteristic
32C2×D4×Dic5C2211yescharacteristic
33C2×D4×Dic5C2211yescharacteristic
34C22×#687C2211yescharacteristic
35C2×#4072—21no—
36C2×#4072C2211yescharacteristic
37C22×C4⋊Dic5—21no—
38C22×C4⋊Dic5C2211yescharacteristic
39C2×#4070C2211yescharacteristic
40#65937—24no—
41#65937C2218yescomplemented
42C2×#4034C2211yescharacteristic
43C2×#4033C2211yescharacteristic
44C2×#4025—21no—
45C2×#4024—21no—
46C5×#449C2218yes—
47C2×C5×#103C2211yescharacteristic
48C2×C5×#102C2211yescharacteristic
49C2×C5×C22⋊C8C2211yescharacteristic
50#65528C2218yescomplemented
51C2×#3967C2211yescharacteristic
52C2×#3964C2211yescharacteristic
53C2×#3964C2211yescharacteristic
54C2×#3964C2211yescharacteristic
55C2×C22⋊#168C2211yescharacteristic
56#65455C2218yescomplemented
57#65453C2218yescomplemented
58#65442C2218yescomplemented
59D8×Dic5C2218yescomplemented
60C2×#3950C2211yescharacteristic
61C2×#3950C2211yescharacteristic
62C2×#3948C2211yescharacteristic
63C2×#3948C2211yescharacteristic
64C2×#3947C2211yescharacteristic
65C2×#3946C2211yescharacteristic
66C2×#3946C2211yescharacteristic
67C2×C8×Dic5C2211yescharacteristic
68#65322C2218yescomplemented
69C2×#3939C2211yescharacteristic
70C2×#3939C2211yescharacteristic
71#65083C2218yescomplemented
72#65079C2218yescomplemented
73#65048C2218yescomplemented
74#65046C2218yescomplemented
75#65011C2218yescomplemented
76#65009C2218yescomplemented
77C2×#3124—51nomaximal, Sylow
78C2×C5×#41—24no—
79C2×C5×#41—24no—
80C2×C5×#41—22no—
81C2×C5×#41C2314yes—
82C22×C5×Q8C2311yescharacteristic
83C22×C5×D4—21no—
84C22×C5×D4—21no—
85C22×C5×D4C2311yescharacteristic
86C22×C5×D4C2311yescharacteristic
87C23×C4×C5—21no—
88C23×C4×C5C2311yescharacteristic
89C23×Dic5—21no—
90C23×Dic5—21no—
91C23×Dic5—21no—
92C23×Dic5—21no—
93C22×Dic10—21no—
94C22×Dic10C2311yescharacteristic
95C2×C5×SD16—24no—
96C2×C5×SD16C2314yes—
97C2×C5×D8—24no—
98C2×C5×D8C2314yes—
99C22×C5×C8C2311yescharacteristic
100C22×C5×C8C2311yescharacteristic
101C5×#121—22no—
102C5×#121C2314yes—
103C2×C5×C4⋊C4C2311yescharacteristic
104C2×C5×C22⋊C4—21no—
105C2×C22⋊Dic5—21no—
106C2×C22⋊Dic5—21no—
107C2×C22⋊Dic5—21no—
108C2×C22⋊Dic5—21no—
109C2×C22⋊Dic5—21no—
110C2×C22⋊Dic5—21no—
111C2×C22⋊Dic5D411yescharacteristic
112C2×C22⋊Dic5D411yescharacteristic
113Q8×Dic5—22no—
114Q8×Dic5—22no—
115Q8×Dic5C2314yes—
116Q8×Dic5C2314yes—
117C2×#689—24no—
118C2×#689C2314yes—
119#4082—28no—
120#4082—22no—
121#4082C2314yes—
122#4081—28no—
123D4×Dic5—28no—
124D4×Dic5—28no—
125D4×Dic5—22no—
126D4×Dic5—22no—
127D4×Dic5—22no—
128D4×Dic5C2314yes—
129D4×Dic5C2314yes—
130D4×Dic5C2314yes—
131C2×#687—24no—
132C2×#687C2314yes—
133#4072—28no—
134#4072D414yes—
135#4072C2314yes—
136C2×C4⋊Dic5—21no—
137C2×C4⋊Dic5—22no—
138C2×C4⋊Dic5—21no—
139C2×C4⋊Dic5—21no—
140C2×C4⋊Dic5—28no—
141C2×C4⋊Dic5D411yescharacteristic
142C2×C4⋊Dic5D411yescharacteristic
143C2×C4⋊Dic5C2311yescharacteristic
144C2×C4⋊Dic5C2314yes—
145C2×C4⋊Dic5C2311yescharacteristic
146C2×C4⋊Dic5C2311yescharacteristic
147#4070—22no—
148#4070C2314yes—
149C2×#683—21no—
150C2×#683—21no—
151C2×#683—21no—
152C2×C4×Dic5—21no—
153C2×C4×Dic5—21no—
154C2×C4×Dic5—21no—
155C2×C4×Dic5C2311yescharacteristic
156C2×C4×Dic5C2311yescharacteristic
157C22×#168C2311yescharacteristic
158C22×#168C2311yescharacteristic
159#4034—22no—
160#4034C2314yes—
161#4033—22no—
162#4033C2314yes—
163#4025—28no—
164#4024—28no—
165C5×#103C2314yes—
166C5×#102C2314yes—
167C5×C22⋊C8C2314yes—
168#3967C2314yes—
169#3964C2314yes—
170#3964C2314yes—
171#3964C2314yes—
172C22⋊#168C2314yes—
173#3950C2314yes—
174#3950C2314yes—
175#3948C2314yes—
176#3948C2314yes—
177#3947C2314yes—
178#3946C2314yes—
179#3946C2314yes—
180C8×Dic5C2314yes—
181#3939C2314yes—
182#3939C2314yes—
183C2×#542—51no—
184C2×#520—51no—
185#3124—516no—
186C2×#484—51no—
187C2×#480—51no—
188C2×#477—51no—
189C2×#474—51no—
190C2×#464—51no—
191C2×#463—51no—
192C2×#452—51no—
193C2×#449D511yescharacteristic
194C2×#440—51no—
195C2×#440—51no—
196C2×C4×Q16—51no—
197C2×C4×D8—51no—
198C2×#433—51no—
199C24×C5—21no—
200C24×C5—21no—
201C24×C5C2×D411yescharacteristic
202C5×#41—216no—
203C5×#41—28no—
204C5×#41—28no—
205C2×C5×Q8—21no—
206C2×C5×Q8—22no—
207C2×C5×Q8#4114yes—
208C2×C5×Q8C2412yes—
209C2×C5×D4—28no—
210C2×C5×D4—24no—
211C2×C5×D4—24no—
212C2×C5×D4—21no—
213C2×C5×D4—21no—
214C2×C5×D4—22no—
215C2×C5×D4—22no—
216C2×C5×D4—22no—
217C2×C5×D4—82no—
218C2×C5×D4#4114yes—
219C2×C5×D4C2412yes—
220C2×C5×D4C2412yes—
221C22×C4×C5—28no—
222C22×C4×C5—21no—
223C22×C4×C5—24no—
224C22×C4×C5—22no—
225C22×C4×C5—22no—
226C22×C4×C5—21no—
227C22×C4×C5C2×D411yescharacteristic
228C22×C4×C5C2×D412yes—
229C22×C4×C5C2412yes—
230C22×C4×C5C2411yescharacteristic
231C22×Dic5—21no—
232C22×Dic5—21no—
233C22×Dic5—21no—
234C22×Dic5—21no—
235C22×Dic5—24no—
236C22×Dic5—24no—
237C22×Dic5—24no—
238C22×Dic5—24no—
239C22×Dic5—82no—
240C22×Dic5—82no—
241C22×Dic5—82no—
242C22×Dic5—82no—
243C22×Dic5C2×D411yescharacteristic
244C22×Dic5C2×D411yescharacteristic
245C22×Dic5C2×D411yescharacteristic
246C22×Dic5C2×D411yescharacteristic
247C2×Dic10—22no—
248C2×Dic10—22no—
249C2×Dic10—21no—
250C2×Dic10—24no—
251C2×Dic10—82no—
252C2×Dic10C2412yes—
253C5×SD16—28no—
254C5×D8—28no—
255C2×C5×C8—22no—
256C2×C5×C8—22no—
257C2×C5×C8C2412yes—
258C2×C5×C8C2412yes—
259C5×C4⋊C4—21no—
260C5×C4⋊C4C2412yes—
261C5×C22⋊C4—24no—
262C22⋊Dic5—24no—
263C22⋊Dic5—24no—
264C22⋊Dic5—24no—
265C22⋊Dic5—24no—
266C22⋊Dic5—24no—
267C22⋊Dic5—24no—
268C22⋊Dic5C2×D414yes—
269C22⋊Dic5C2×D414yes—
270#689—28no—
271#687—28no—
272C4⋊Dic5—21no—
273C4⋊Dic5—24no—
274C4⋊Dic5—21no—
275C4⋊Dic5—21no—
276C4⋊Dic5—24no—
277C4⋊Dic5—24no—
278C4⋊Dic5C2×D414yes—
279C4⋊Dic5C2×D414yes—
280C4⋊Dic5C2412yes—
281C4⋊Dic5C2412yes—
282C4⋊Dic5C2412yes—
283#683—24no—
284#683—24no—
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×Q16—51no—
299C22×SD16—51no—
300C22×SD16C2×D511yescharacteristic
301C22×D8C2×D511yescharacteristic
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—51no—
310C2×C22⋊Q8—101no—
311C2×#121C2×D511yescharacteristic
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#484—58no—
327#480—58no—
328#477—58no—
329#474—58no—
330#464—58no—
331#463—58no—
332#452—58no—
333#449C2×D518yes—
334#440—58no—
335#440—58no—
336C4×Q16—58no—
337C4×D8—58no—
338#433—58no—
339C2×#107—51no—
340C2×#107—51no—
341C2×#107—51no—
342C2×#107—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—22no—
363C23×C5—42no—
364C23×C5—42no—
365C23×C5—42no—
366C23×C5—42no—
367C23×C5—42no—
368C23×C5C22×D412yes—
369C23×C5C22×D411yescharacteristic
370C5×Q8—24no—
371C5×Q8—22no—
372C5×Q8C2×#4114yes—
373C5×D4—216no—
374C5×D4—24no—
375C5×D4—22no—
376C5×D4—22no—
377C5×D4—22no—
378C5×D4—42no—
379C5×D4—84no—
380C5×D4C2×#4114yes—
381C2×C4×C5—216no—
382C2×C4×C5—22no—
383C2×C4×C5—24no—
384C2×C4×C5—22no—
385C2×C4×C5—24no—
386C2×C4×C5—22no—
387C2×C4×C5—22no—
388C2×C4×C5—22no—
389C2×C4×C5—42no—
390C2×C4×C5C22×D412yes—
391C2×C4×C5C22×D411yescharacteristic
392C2×C4×C5C2×#4112yes—
393C2×C4×C5C2×#4112yes—
394C2×C4×C5C2511yescharacteristic
395C2×Dic5—22no—
396C2×Dic5—22no—
397C2×Dic5—22no—
398C2×Dic5—22no—
399C2×Dic5—22no—
400C2×Dic5—22no—
401C2×Dic5—22no—
402C2×Dic5—22no—
403C2×Dic5—42no—
404C2×Dic5—42no—
405C2×Dic5—42no—
406C2×Dic5—42no—
407C2×Dic5—84no—
408C2×Dic5—84no—
409C2×Dic5—84no—
410C2×Dic5—84no—
411C2×Dic5C22×D412yes—
412C2×Dic5C22×D412yes—
413C2×Dic5C22×D412yes—
414C2×Dic5C22×D412yes—
415Dic10—22no—
416Dic10—22no—
417Dic10—42no—
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—51no—
428C22×Q8—101no—
429C22×Q8C22×D511yescharacteristic
430C22×D4—21no—
431C22×D4—21no—
432C22×D4C22×D511yescharacteristic
433C22×D4C22×D511yescharacteristic
434C23×C4—21no—
435C23×C4—101no—
436C23×C4—101no—
437C23×C4—101no—
438C23×C4—101no—
439C23×C4C22×D511yescharacteristic
440C2×Q16—54no—
441C2×Q16—104no—
442C2×SD16—24no—
443C2×SD16—54no—
444C2×SD16—104no—
445C2×SD16C22×D514yes—
446C2×D8—24no—
447C2×D8C22×D514yes—
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—54no—
460C22⋊Q8—108no—
461C22⋊Q8—102no—
462#121—22no—
463#121C22×D514yes—
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—51no—
482C2×C4⋊C4—51no—
483C2×C4⋊C4—51no—
484C2×C4⋊C4—51no—
485C2×C4⋊C4—54no—
486C2×C4⋊C4—51no—
487C2×C4⋊C4—108no—
488C2×C4⋊C4—101no—
489C2×C4⋊C4—101no—
490C2×C4⋊C4—101no—
491C2×C4⋊C4—101no—
492C2×C4⋊C4—101no—
493C2×C4⋊C4—102no—
494C2×C4⋊C4—101no—
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#107—54no—
511#107—54no—
512#107—54no—
513#107—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—42no—
537C22×C5—42no—
538C22×C5—42no—
539C22×C5—84no—
540C22×C5#52512yes—
541C22×C5#57612yes—
542C22×C5#57812yes—
543C22×C5C23×D411yescharacteristic
544C4×C5—22no—
545C4×C5—24no—
546C4×C5—42no—
547C4×C5#52512yes—
548C4×C5C22×#4111yescharacteristic
549C4×C5C22×#4111yescharacteristic
550Dic5—22no—
551Dic5—22no—
552Dic5—22no—
553Dic5—22no—
554Dic5—42no—
555Dic5—42no—
556Dic5—42no—
557Dic5—42no—
558C24—21no—
559C24—21no—
560C24D4×D511yescharacteristic
561#41—216no—
562#41—28no—
563#41—28no—
564C2×Q8—21no—
565C2×Q8—22no—
566C2×Q8—52no—
567C2×Q8—104no—
568C2×Q8—101no—
569C2×Q8—102no—
570C2×Q8—102no—
571C2×Q8—402no—
572C2×Q8#71114yes—
573C2×Q8C23×D512yes—
574C2×D4—28no—
575C2×D4—24no—
576C2×D4—24no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—22no—
580C2×D4—22no—
581C2×D4—22no—
582C2×D4—82no—
583C2×D4#71114yes—
584C2×D4C23×D512yes—
585C2×D4C23×D512yes—
586C22×C4—28no—
587C22×C4—21no—
588C22×C4—24no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—21no—
592C22×C4—51no—
593C22×C4—51no—
594C22×C4—51no—
595C22×C4—51no—
596C22×C4—104no—
597C22×C4—104no—
598C22×C4—104no—
599C22×C4—101no—
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—108no—
613SD16—28no—
614SD16—108no—
615D8—28no—
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—21no—
625C4⋊C4—54no—
626C4⋊C4—54no—
627C4⋊C4—52no—
628C4⋊C4—52no—
629C4⋊C4—52no—
630C4⋊C4—104no—
631C4⋊C4—104no—
632C4⋊C4—104no—
633C4⋊C4—104no—
634C4⋊C4—104no—
635C4⋊C4—101no—
636C4⋊C4—101no—
637C4⋊C4—101no—
638C4⋊C4—104no—
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—82no—
659C2×C5#312414yescomplemented
660C2×C5C2×#52511yescharacteristic
661C2×C5C2×#57611yescharacteristic
662C2×C5C2×#57811yescharacteristic
663C23—22no—
664C23—22no—
665C23—22no—
666C23—24no—
667C23—22no—
668C23—22no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23C2×D4×D512yes—
675C23C2×D4×D511yescharacteristic
676Q8—24no—
677Q8—22no—
678Q8—102no—
679Q8—102no—
680Q8—202no—
681Q8—404no—
682Q8C2×#71114yes—
683D4—216no—
684D4—24no—
685D4—22no—
686D4—22no—
687D4—22no—
688D4—42no—
689D4—84no—
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—42no—
700C2×C4—52no—
701C2×C4—52no—
702C2×C4—52no—
703C2×C4—52no—
704C2×C4—102no—
705C2×C4—102no—
706C2×C4—102no—
707C2×C4—102no—
708C2×C4—102no—
709C2×C4—102no—
710C2×C4—102no—
711C2×C4—102no—
712C2×C4—202no—
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×#312411yescharacteristic, complemented, Sylow
730C22—22no—
731C22—22no—
732C22—24no—
733C22—22no—
734C22—44no—
735C22—48no—
736C22—42no—
737C22—42no—
738C22—42no—
739C22—42no—
740C22—42no—
741C22—84no—
742C22#6592012yes—
743C22#6610512yes—
744C22#6610812yes—
745C22C22×D4×D511yescharacteristic
746C4—22no—
747C4—24no—
748C4—42no—
749C4—102no—
750C4—102no—
751C4—102no—
752C4—102no—
753C4—202no—
754C4—202no—
755C4—202no—
756C4—202no—
757C4#6592012yes—
758C4C22×#71111yescharacteristic
759C4C22×#71111yescharacteristic
760C2—42no—
761C2—44no—
762C2—82no—
763C2#1061180514yesdirect product factor
764C2C2×#6592011yescharacteristic
765C2C2×#6610511yescharacteristic
766C2C2×#6610811yescharacteristic
subgroupG/H
centerC23C2×D4×D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
Fitting, prime radicalC2×C5×#449C2
socleC23×C5C22×D4
hypercenterC2×#449D5
hypocenterC5C2×#3124
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#449

Complements

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

NH ≅ G/Ntype
1. C2×#66161C2semidirect
2. C2×#65937C2semidirect
4. C2×#65528C2semidirect
5. C2×#65455C2semidirect
6. C2×#65453C2semidirect
7. C2×#65442C2semidirect
8. C2×D8×Dic5C2semidirect
9. C2×#65322C2semidirect
10. #10611805C2direct (N × H)
11. C2×#65083C2semidirect
12. C2×#65079C2semidirect
13. C2×#65048C2semidirect
14. C2×#65046C2semidirect
15. C2×#65011C2semidirect
16. C2×#65009C2semidirect
22. #66161C22semidirect
41. #65937C22semidirect
50. #65528C22semidirect
56. #65455C22semidirect
57. #65453C22semidirect
58. #65442C22semidirect
59. D8×Dic5C22semidirect
68. #65322C22semidirect
71. #65083C22semidirect
72. #65079C22semidirect
73. #65048C22semidirect
74. #65046C22semidirect
75. #65011C22semidirect
76. #65009C22semidirect
659. C2×C5#3124semidirect
729. C5C2×#3124semidirect
763. C2#10611805direct (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×#659372
C2×C5×#4492
C2×#655282
C2×#654552
C2×#654532
C2×#654422
C2×D8×Dic52
C2×#653222
#106118052
C2×#650832
C2×#650792
C2×#650482
C2×#650462
C2×#650112
C2×#650092
C2×#31245