Finite Group Databasebeta

← C2×#10612442 #12977869

Subgroups — C2×#10612442 #12977869

Order 1280.

2158 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65952C211yesmaximal, characteristic, complemented
2C2×#65945C211yesmaximal, characteristic, complemented
3C2×C5×#466C211yesmaximal, characteristic, complemented
4C2×#65448C211yesmaximal, characteristic, complemented
5C2×#65441C211yesmaximal, characteristic, complemented
6C2×#65400C211yesmaximal, characteristic, complemented
7C22×#3949C211yesmaximal, characteristic, complemented
8C2×#65323C211yesmaximal, characteristic, complemented
9C2×#65322C211yesmaximal, characteristic, complemented
10#10612442C2116yesmaximal, direct product factor
11C2×#65170C211yesmaximal, characteristic, complemented
12C2×#65165C211yesmaximal, characteristic, complemented
13C2×#65066C211yesmaximal, characteristic, complemented
14C2×#65068C211yesmaximal, characteristic, complemented
15C2×#65052C211yesmaximal, characteristic, complemented
16C2×#65050C211yesmaximal, characteristic, complemented
17C22×#711—21no—
18C22×C5×D8C2211yescharacteristic
19C23×C5×C8C2211yescharacteristic
20C2×C5×#121C2211yescharacteristic
21C2×C5×#121C2211yescharacteristic
22C2×#4085—21no—
23C2×#4084C2211yescharacteristic
24C2×#4084C2211yescharacteristic
25C2×#4081—21no—
26C2×D4×Dic5—21no—
27C2×D4×Dic5C2211yescharacteristic
28C2×D4×Dic5C2211yescharacteristic
29C2×C4×C22⋊D5C2211yescharacteristic
30C22×C4⋊Dic5C2211yescharacteristic
31C22×C4⋊Dic5C2211yescharacteristic
32C22×#676C2211yescharacteristic
33#65952—24no—
34#65952C2218yescomplemented
35#65945—24no—
36#65945C2218yescomplemented
37C2×#4038C2211yescharacteristic
38C2×D5×C4⋊C4C2211yescharacteristic
39C2×#4036C2211yescharacteristic
40C2×#4034C2211yescharacteristic
41C2×#4032—21no—
42C2×#4029—21no—
43C2×#4025—21no—
44C2×#4024—21no—
45C5×#466C2218yescomplemented
46C2×C5×#107C2211yescharacteristic
47C2×C5×#102C2211yescharacteristic
48C2×C5×#102C2211yescharacteristic
49C2×#3964C2211yescharacteristic
50C2×#3964C2211yescharacteristic
51C2×#3964C2211yescharacteristic
52C2×#3964C2211yescharacteristic
53C2×C22⋊#168C2211yescharacteristic
54#65448C2218yescomplemented
55#65441C2218yescomplemented
56#65400C2218yescomplemented
57C2×#3952C2211yescharacteristic
58C2×#3949C2211yescharacteristic
59C2×#3949C2211yescharacteristic
60C2×#3949C2211yescharacteristic
61C2×#3949C2211yescharacteristic
62C2×#3949C2218yescomplemented
63C2×#3947C2211yescharacteristic
64C2×#3946C2211yescharacteristic
65#65323C2218yescomplemented
66#65322C2218yescomplemented
67C2×#3940C2211yescharacteristic
68C2×#3940C2211yescharacteristic
69C2×#3939C2211yescharacteristic
70C2×#3939C2211yescharacteristic
71#65170C2218yescomplemented
72#65165C2218yescomplemented
73#65068C2218yescomplemented
74#65066C2218yescomplemented
75#65052C2218yescomplemented
76#65050C2218yescomplemented
77C2×#3345—51nomaximal, Sylow
78C22×C5×D4—21no—
79C22×C5×D4—21no—
80C22×C5×D4C2311yescharacteristic
81C22×C5×D4C2311yescharacteristic
82C23×C4×C5C2311yescharacteristic
83C22×C22⋊D5—21no—
84C22×C22⋊D5—21no—
85C22×C22⋊D5D411yescharacteristic
86C23×Dic5—21no—
87C23×Dic5—21no—
88C23×Dic5—21no—
89C23×Dic5—21no—
90C2×#711—28no—
91C2×#711—48no—
92C22×C4×D5—21no—
93C22×C4×D5C2311yescharacteristic
94C22×Dic10—21no—
95C2×C5×D8—24no—
96C2×C5×D8C2314yes—
97C22×C5×C8—24no—
98C22×C5×C8C2311yescharacteristic
99C22×C5×C8C2314yes—
100C22×C5×C8C2311yescharacteristic
101C5×#121—22no—
102C5×#121—22no—
103C5×#121C2314yes—
104C5×#121C2314yes—
105C2×C5×C4⋊C4C2311yescharacteristic
106C2×C5×C4⋊C4C2311yescharacteristic
107C2×C5×C22⋊C4—21no—
108C2×C5×C22⋊C4—21no—
109C2×C22⋊Dic5—21no—
110C2×C22⋊Dic5—21no—
111C2×C22⋊Dic5—21no—
112C2×C22⋊Dic5—21no—
113C2×C22⋊Dic5D411yescharacteristic
114#4085—28no—
115#4084—22no—
116#4084—22no—
117#4084C2314yes—
118#4084C2314yes—
119#4081—28no—
120D4×Dic5—28no—
121D4×Dic5—22no—
122D4×Dic5—22no—
123D4×Dic5C2314yes—
124D4×Dic5C2314yes—
125C4×C22⋊D5D414yes—
126C4×C22⋊D5C2314yes—
127C2×#685—21no—
128C2×#685D411yescharacteristic
129C2×C4⋊Dic5—21no—
130C2×C4⋊Dic5—21no—
131C2×C4⋊Dic5—22no—
132C2×C4⋊Dic5—22no—
133C2×C4⋊Dic5—21no—
134C2×C4⋊Dic5C2311yescharacteristic
135C2×C4⋊Dic5C2311yescharacteristic
136C2×C4⋊Dic5C2314yes—
137C2×C4⋊Dic5C2311yescharacteristic
138C2×C4⋊Dic5C2314yes—
139C2×C4⋊Dic5C2311yescharacteristic
140C2×#683—21no—
141C2×#683—21no—
142C2×#683—21no—
143C2×#683D411yescharacteristic
144C2×C4×Dic5—21no—
145C2×C4×Dic5C2311yescharacteristic
146C22×#168C2311yescharacteristic
147C22×#168C2311yescharacteristic
148C2×#676—24no—
149C2×#676C2314yes—
150#4038—22no—
151#4038C2314yes—
152D5×C4⋊C4—22no—
153D5×C4⋊C4C2314yes—
154#4036—22no—
155#4036C2314yes—
156#4034—22no—
157#4034C2314yes—
158#4032—28no—
159#4029—28no—
160#4025—28no—
161#4024—28no—
162C5×#107C2314yes—
163C5×#102C2314yes—
164C5×#102C2314yes—
165#3964C2314yes—
166#3964C2314yes—
167#3964C2314yes—
168#3964C2314yes—
169C22⋊#168C2314yes—
170#3952C2314yes—
171#3949C2314yes—
172#3949C2314yes—
173#3949C2314yes—
174#3949C2314yes—
175#3947C2314yes—
176#3946C2314yes—
177#3940C2314yes—
178#3940C2314yes—
179#3939C2314yes—
180#3939C2314yes—
181C2×#553—51no—
182C2×#547—51no—
183#3345—516no—
184C2×#501—51no—
185C2×#481—51no—
186C2×#481—51no—
187C2×#482—51no—
188C2×#480—51no—
189C2×#478—51no—
190C2×#476—51no—
191C2×#469—51no—
192C2×#466D511yescharacteristic, complemented
193C2×#442—51no—
194C2×#435—51no—
195C2×#428—51no—
196C22×#106—51no—
197C24×C5—21no—
198C24×C5—21no—
199C24×C5C2×D411yescharacteristic
200C23×D5C2×D411yescharacteristic
201C2×C5×D4—24no—
202C2×C5×D4—24no—
203C2×C5×D4—21no—
204C2×C5×D4—21no—
205C2×C5×D4—22no—
206C2×C5×D4—22no—
207C2×C5×D4—22no—
208C2×C5×D4—22no—
209C2×C5×D4—44no—
210C2×C5×D4—44no—
211C2×C5×D4C2412yes—
212C2×C5×D4C2412yes—
213C22×C4×C5—22no—
214C22×C4×C5—22no—
215C22×C4×C5—21no—
216C22×C4×C5—21no—
217C22×C4×C5C2×D411yescharacteristic
218C22×C4×C5C2×D412yes—
219C22×C4×C5C2412yes—
220C22×C4×C5C2411yescharacteristic
221C2×C22⋊D5—24no—
222C2×C22⋊D5—24no—
223C2×C22⋊D5—24no—
224C2×C22⋊D5—44no—
225C2×C22⋊D5—82no—
226C2×C22⋊D5C2×D414yes—
227C22×Dic5—21no—
228C22×Dic5—21no—
229C22×Dic5—21no—
230C22×Dic5—21no—
231C22×Dic5—24no—
232C22×Dic5—24no—
233C22×Dic5—24no—
234C22×Dic5—24no—
235C22×Dic5—44no—
236C22×Dic5—44no—
237C22×Dic5—82no—
238C22×Dic5—82no—
239C22×Dic5C2×D411yescharacteristic
240C22×Dic5C2×D411yescharacteristic
241C22×Dic5C2×D411yescharacteristic
242#711—432no—
243C2×C4×D5—22no—
244C2×C4×D5—22no—
245C2×C4×D5—24no—
246C2×C4×D5—44no—
247C2×C4×D5C2×D412yes—
248C2×C4×D5C2412yes—
249C2×Dic10—24no—
250C2×Dic10—44no—
251C5×D8—28no—
252C2×C5×C8—22no—
253C2×C5×C8—28no—
254C2×C5×C8#4114yescomplemented
255C2×C5×C8C2412yes—
256C2×C5×C8C2412yes—
257C5×C4⋊C4—21no—
258C5×C4⋊C4—21no—
259C5×C4⋊C4C2412yes—
260C5×C4⋊C4C2412yes—
261C5×C22⋊C4—24no—
262C5×C22⋊C4—24no—
263C22⋊Dic5—24no—
264C22⋊Dic5—24no—
265C22⋊Dic5—24no—
266C22⋊Dic5—24no—
267C22⋊Dic5C2×D414yes—
268#685—24no—
269#685C2×D414yes—
270C4⋊Dic5—24no—
271C4⋊Dic5—24no—
272C4⋊Dic5—21no—
273C4⋊Dic5—21no—
274C4⋊Dic5—21no—
275C4⋊Dic5—21no—
276C4⋊Dic5—24no—
277C4⋊Dic5C2412yes—
278C4⋊Dic5C2412yes—
279C4⋊Dic5C2412yes—
280C4⋊Dic5C2412yes—
281#683—24no—
282#683—24no—
283#683—24no—
284#683C2×D414yes—
285C4×Dic5—24no—
286C4×Dic5C2×D412yes—
287C4×Dic5C2412yes—
288C2×#168—22no—
289C2×#168—22no—
290C2×#168C2412yes—
291C2×#168C2412yes—
292#676—28no—
293C22×#41—101no—
294C22×D8C2×D511yescharacteristic
295C22×M16—51no—
296C23×C8C2×D511yescharacteristic
297#553—58no—
298#553—104no—
299#547—58no—
300#547—104no—
301C2×C4⋊Q8—51no—
302C2×#126—101no—
303C2×#125—51no—
304C2×#123—101no—
305C2×#123—101no—
306C2×#123—101no—
307C2×C22⋊Q8—101no—
308C2×#121—51no—
309C2×#121—51no—
310C2×#121—101no—
311C2×#121C2×D511yescharacteristic
312C2×#121C2×D511yescharacteristic
313C2×C4×D4—51no—
314C2×C4×D4—51no—
315C2×C4×D4—51no—
316C2×C4×D4—101no—
317C2×#117—51no—
318C22×C4⋊C4—51no—
319C22×C4⋊C4—51no—
320C22×C4⋊C4—51no—
321#501—58no—
322#482—58no—
323#481—58no—
324#481—58no—
325#480—58no—
326#478—58no—
327#476—58no—
328#469—58no—
329#466C2×D518yescomplemented
330#442—58no—
331#435—58no—
332#428—58no—
333C2×#107—51no—
334C2×#107—51no—
335C2×#107C2×D511yescharacteristic
336C2×#106—51no—
337C2×#106—51no—
338C2×#106—58no—
339C2×#106—51no—
340C2×#106—51no—
341C2×#106—51no—
342C2×#106—51no—
343C2×C4⋊C8—51no—
344C2×#102—51no—
345C2×#102—51no—
346C2×#102—51no—
347C2×#102—51no—
348C2×#102C2×D511yescharacteristic
349C2×#102C2×D511yescharacteristic
350C2×C22⋊C8—51no—
351C2×C22⋊C8—51no—
352C2×#97—51no—
353C23×C5—22no—
354C23×C5—22no—
355C23×C5—22no—
356C23×C5—22no—
357C23×C5—42no—
358C23×C5—42no—
359C23×C5—42no—
360C23×C5—42no—
361C23×C5—42no—
362C23×C5—42no—
363C23×C5AGL(1,ℤ/8)14yes—
364C23×C5C22×D412yes—
365C23×C5C22×D411yescharacteristic
366C22×D5—22no—
367C22×D5—22no—
368C22×D5—22no—
369C22×D5C22×D412yes—
370C5×D4—22no—
371C5×D4—22no—
372C5×D4—22no—
373C5×D4—22no—
374C5×D4—48no—
375C5×D4—48no—
376C5×D4—42no—
377C5×D4—42no—
378C2×C4×C5—22no—
379C2×C4×C5—24no—
380C2×C4×C5—22no—
381C2×C4×C5—22no—
382C2×C4×C5—22no—
383C2×C4×C5—22no—
384C2×C4×C5—42no—
385C2×C4×C5—42no—
386C2×C4×C5C22×D412yes—
387C2×C4×C5C22×D411yescharacteristic
388C2×C4×C5C2×#4112yes—
389C2×C4×C52−1+412yes—
390C2×C4×C5C2511yescharacteristic
391C22⋊D5—28no—
392C22⋊D5—48no—
393C22⋊D5—84no—
394C2×Dic5—22no—
395C2×Dic5—22no—
396C2×Dic5—22no—
397C2×Dic5—22no—
398C2×Dic5—22no—
399C2×Dic5—22no—
400C2×Dic5—22no—
401C2×Dic5—48no—
402C2×Dic5—42no—
403C2×Dic5—42no—
404C2×Dic5—48no—
405C2×Dic5—42no—
406C2×Dic5—42no—
407C2×Dic5—84no—
408C2×Dic5—84no—
409C2×Dic5C22×D412yes—
410C2×Dic5C22×D412yes—
411C2×Dic5C22×D412yes—
412C4×D5—24no—
413C4×D5—22no—
414C4×D5—22no—
415C4×D5—48no—
416Dic10—48no—
417C5×C8—22no—
418C5×C8C2×#4114yescomplemented
419#168—22no—
420#168—22no—
421C2×#41—108no—
422C2×#41—208no—
423C22×Q8—101no—
424C22×D4—21no—
425C22×D4—21no—
426C22×D4—51no—
427C22×D4—101no—
428C22×D4—101no—
429C22×D4C22×D511yescharacteristic
430C22×D4C22×D511yescharacteristic
431C23×C4—51no—
432C23×C4—101no—
433C23×C4—101no—
434C23×C4—101no—
435C23×C4—101no—
436C23×C4—101no—
437C23×C4C22×D511yescharacteristic
438C2×D8—24no—
439C2×D8C22×D514yes—
440C2×M16—54no—
441C2×M16—104no—
442C22×C8—24no—
443C22×C8—51no—
444C22×C8—51no—
445C22×C8C22×D511yescharacteristic
446C22×C8C22×D514yes—
447C22×C8C22×D511yescharacteristic
448C4⋊Q8—54no—
449C4⋊Q8—102no—
450#126—108no—
451#125—54no—
452#125—102no—
453#123—108no—
454#123—108no—
455#123—108no—
456C22⋊Q8—108no—
457#121—22no—
458#121—22no—
459#121—54no—
460#121—54no—
461#121—102no—
462#121—102no—
463#121—108no—
464#121C22×D514yes—
465#121C22×D514yes—
466C4×D4—54no—
467C4×D4—54no—
468C4×D4—54no—
469C4×D4—54no—
470C4×D4—102no—
471C4×D4—102no—
472C4×D4—108no—
473#117—54no—
474#117—102no—
475C2×C4⋊C4—51no—
476C2×C4⋊C4—51no—
477C2×C4⋊C4—51no—
478C2×C4⋊C4—51no—
479C2×C4⋊C4—51no—
480C2×C4⋊C4—54no—
481C2×C4⋊C4—54no—
482C2×C4⋊C4—54no—
483C2×C4⋊C4—102no—
484C2×C4⋊C4—101no—
485C2×C4⋊C4—101no—
486C2×C4⋊C4—101no—
487C2×C4⋊C4—101no—
488C2×C4⋊C4—101no—
489C2×C4⋊C4—101no—
490C2×C4⋊C4—102no—
491C2×C4⋊C4—102no—
492C2×C4⋊C4C22×D511yescharacteristic
493C2×C4⋊C4C22×D511yescharacteristic
494C2×C22⋊C4—21no—
495C2×C22⋊C4—21no—
496C2×C22⋊C4—51no—
497C2×C22⋊C4—51no—
498C2×C22⋊C4—101no—
499C2×C22⋊C4—101no—
500C2×C22⋊C4—101no—
501C2×C22⋊C4—101no—
502C2×C22⋊C4—101no—
503C2×C42—51no—
504C2×C42—101no—
505#107—54no—
506#107—54no—
507#107C22×D514yes—
508#106—54no—
509#106—54no—
510#106—54no—
511#106—54no—
512#106—54no—
513#106—54no—
514C4⋊C8—54no—
515#102—54no—
516#102—54no—
517#102—54no—
518#102—54no—
519#102C22×D514yes—
520#102C22×D514yes—
521C22⋊C8—54no—
522C22⋊C8—54no—
523#97—54no—
524C22×C5—28no—
525C22×C5—22no—
526C22×C5—22no—
527C22×C5—42no—
528C22×C5—42no—
529C22×C5—42no—
530C22×C5—42no—
531C22×C5—42no—
532C22×C5—42no—
533C22×C5—84no—
534C22×C5—84no—
535C22×C5#54712yes—
536C22×C5C2×AGL(1,ℤ/8)14yes—
537C22×C5C2×AGL(1,ℤ/8)12yes—
538C22×C5#57712yes—
539C22×C5C23×D411yescharacteristic
540C2×D5—22no—
541C2×D5—22no—
542C2×D5—22no—
543C2×D5—44no—
544C4×C5—22no—
545C4×C5—42no—
546C4×C5—42no—
547C4×C5#54712yes—
548C4×C5C22×#4111yescharacteristic
549C4×C5C2×2−1+411yescharacteristic
550Dic5—22no—
551Dic5—22no—
552Dic5—22no—
553Dic5—42no—
554Dic5—42no—
555Dic5—42no—
556Dic5—42no—
557C24—21no—
558C24—21no—
559C24—51no—
560C24D4×D511yescharacteristic
561#41—2032no—
562C2×Q8—104no—
563C2×Q8—204no—
564C2×D4—24no—
565C2×D4—24no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—22no—
569C2×D4—22no—
570C2×D4—22no—
571C2×D4—22no—
572C2×D4—44no—
573C2×D4—44no—
574C2×D4—54no—
575C2×D4—104no—
576C2×D4—104no—
577C2×D4—104no—
578C2×D4—204no—
579C2×D4—402no—
580C2×D4C23×D512yes—
581C2×D4C23×D512yes—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—51no—
587C22×C4—51no—
588C22×C4—51no—
589C22×C4—52no—
590C22×C4—52no—
591C22×C4—104no—
592C22×C4—104no—
593C22×C4—104no—
594C22×C4—102no—
595C22×C4—102no—
596C22×C4—104no—
597C22×C4—101no—
598C22×C4—101no—
599C22×C4—101no—
600C22×C4—101no—
601C22×C4—104no—
602C22×C4—204no—
603C22×C4—204no—
604C22×C4—204no—
605C22×C4—402no—
606C22×C4—402no—
607C22×C4D4×D512yes—
608C22×C4D4×D511yescharacteristic
609C22×C4C23×D512yes—
610C22×C4C23×D511yescharacteristic
611D8—28no—
612M16—108no—
613C2×C8—22no—
614C2×C8—28no—
615C2×C8—52no—
616C2×C8—52no—
617C2×C8—102no—
618C2×C8—102no—
619C2×C8#71114yescomplemented
620C2×C8C23×D512yes—
621C2×C8C23×D512yes—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—54no—
625C4⋊C4—52no—
626C4⋊C4—52no—
627C4⋊C4—52no—
628C4⋊C4—52no—
629C4⋊C4—104no—
630C4⋊C4—104no—
631C4⋊C4—104no—
632C4⋊C4—104no—
633C4⋊C4—101no—
634C4⋊C4—101no—
635C4⋊C4—101no—
636C4⋊C4—101no—
637C4⋊C4—104no—
638C4⋊C4—104no—
639C4⋊C4C23×D512yes—
640C4⋊C4C23×D512yes—
641C22⋊C4—24no—
642C22⋊C4—24no—
643C22⋊C4—54no—
644C22⋊C4—54no—
645C22⋊C4—104no—
646C22⋊C4—104no—
647C22⋊C4—104no—
648C22⋊C4—104no—
649C22⋊C4—104no—
650C42—52no—
651C42—52no—
652C42—104no—
653C2×C5—24no—
654C2×C5—82no—
655C2×C5—82no—
656C2×C5#334514yescomplemented
657C2×C5C2×#54711yescharacteristic
658C2×C5C22×AGL(1,ℤ/8)11yescharacteristic
659C2×C5C2×#57711yescharacteristic
660D5—42no—
661C23—22no—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—52no—
672C23—102no—
673C23—102no—
674C23—102no—
675C23#405714yes—
676C23C2×D4×D512yes—
677C23C2×D4×D511yescharacteristic
678Q8—208no—
679D4—22no—
680D4—22no—
681D4—22no—
682D4—22no—
683D4—48no—
684D4—48no—
685D4—42no—
686D4—42no—
687D4—108no—
688D4—208no—
689D4—404no—
690C2×C4—22no—
691C2×C4—24no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—52no—
699C2×C4—52no—
700C2×C4—52no—
701C2×C4—102no—
702C2×C4—102no—
703C2×C4—102no—
704C2×C4—104no—
705C2×C4—102no—
706C2×C4—102no—
707C2×C4—102no—
708C2×C4—102no—
709C2×C4—102no—
710C2×C4—102no—
711C2×C4—208no—
712C2×C4—208no—
713C2×C4—202no—
714C2×C4—202no—
715C2×C4—208no—
716C2×C4—202no—
717C2×C4—202no—
718C2×C4—404no—
719C2×C4—404no—
720C2×C4C2×D4×D512yes—
721C2×C4C2×D4×D511yescharacteristic
722C2×C4C2×#71112yes—
723C2×C4#415012yes—
724C2×C4C24×D511yescharacteristic
725C8—22no—
726C8—102no—
727C8—102no—
728C8C2×#71114yescomplemented
729C5C2×#334511yescharacteristic, complemented, Sylow
730C22—22no—
731C22—28no—
732C22—22no—
733C22—42no—
734C22—42no—
735C22—42no—
736C22—42no—
737C22—42no—
738C22—42no—
739C22—84no—
740C22—84no—
741C22—102no—
742C22—102no—
743C22—102no—
744C22—204no—
745C22#6594512yes—
746C22C2×#405714yes—
747C22C2×#405712yes—
748C22#6610412yes—
749C22C22×D4×D511yescharacteristic
750C4—22no—
751C4—42no—
752C4—42no—
753C4—102no—
754C4—102no—
755C4—102no—
756C4—202no—
757C4—202no—
758C4—202no—
759C4—202no—
760C4#6594512yes—
761C4C22×#71111yescharacteristic
762C4C2×#415011yescharacteristic
763C2—24no—
764C2—82no—
765C2—82no—
766C2—202no—
767C2#1061244214yesdirect product factor
768C2C2×#6594511yescharacteristic
769C2C22×#405711yescharacteristic
770C2C2×#6610411yescharacteristic
subgroupG/H
centerC23C2×D4×D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×#466C2
socleC23×C5C22×D4
hypercenterC2×#466D5
hypocenterC5C2×#3345
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#466

Complements

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

NH ≅ G/Ntype
1. C2×#65952C2semidirect
2. C2×#65945C2semidirect
3. C2×C5×#466C2semidirect
4. C2×#65448C2semidirect
5. C2×#65441C2semidirect
6. C2×#65400C2semidirect
7. C22×#3949C2semidirect
8. C2×#65323C2semidirect
9. C2×#65322C2semidirect
10. #10612442C2direct (N × H)
11. C2×#65170C2semidirect
12. C2×#65165C2semidirect
13. C2×#65066C2semidirect
14. C2×#65068C2semidirect
15. C2×#65052C2semidirect
16. C2×#65050C2semidirect
34. #65952C22semidirect
36. #65945C22semidirect
45. C5×#466C22semidirect
54. #65448C22semidirect
55. #65441C22semidirect
56. #65400C22semidirect
62. C2×#3949C22semidirect
65. #65323C22semidirect
66. #65322C22semidirect
71. #65170C22semidirect
72. #65165C22semidirect
73. #65068C22semidirect
74. #65066C22semidirect
75. #65052C22semidirect
76. #65050C22semidirect
192. C2×#466D5semidirect
254. C2×C5×C8#41semidirect
329. #466C2×D5semidirect
418. C5×C8C2×#41semidirect
619. C2×C8#711semidirect
656. C2×C5#3345semidirect
728. C8C2×#711semidirect
729. C5C2×#3345semidirect
767. C2#10612442direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#659522
C2×#659452
C2×C5×#4662
C2×#654482
C2×#654412
C2×#654002
C22×#39492
C2×#653232
C2×#653222
#106124422
C2×#651702
C2×#651652
C2×#650662
C2×#650682
C2×#650522
C2×#650502
C2×#33455