Finite Group Databasebeta

← C2×#10613025 #12977867

Subgroups — C2×#10613025 #12977867

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×#65841C211yesmaximal, characteristic, complemented
3C2×C5×#480C211yesmaximal, characteristic, complemented
4C2×#65327C211yesmaximal, characteristic, complemented
5C22×#3940C211yesmaximal, characteristic, complemented
6#10613025C2116yesmaximal, direct product factor
7C2×#65180C211yesmaximal, characteristic, complemented
8C2×#65170C211yesmaximal, characteristic, complemented
9C2×#65174C211yesmaximal, characteristic, complemented
10C2×#65165C211yesmaximal, characteristic, complemented
11C2×#65066C211yesmaximal, characteristic, complemented
12C2×#65071C211yesmaximal, characteristic, complemented
13C2×#65050C211yesmaximal, characteristic, complemented
14C2×#65074C211yesmaximal, characteristic, complemented
15C2×#65019C211yesmaximal, characteristic, complemented
16C2×#65024C211yesmaximal, characteristic, complemented
17C22×#709—21no—
18C2×C5×#121C2211yescharacteristic
19C22×C5×C4⋊C4C2211yescharacteristic
20C2×#4085—21no—
21C2×#4084C2211yescharacteristic
22C2×D4×Dic5—21no—
23C2×D4×Dic5C2211yescharacteristic
24C22×#686C2211yescharacteristic
25C2×#4076C2211yescharacteristic
26C2×#4075—21no—
27C2×C4×C22⋊D5C2211yescharacteristic
28C22×C4⋊Dic5C2211yescharacteristic
29C23×#168C2211yescharacteristic
30C22×#676C2211yescharacteristic
31#65952—24no—
32#65952C2218yescomplemented
33C2×#4042—21no—
34#65841—24no—
35#65841C2218yescomplemented
36C2×#4041C2211yescharacteristic
37C2×#4040—21no—
38C2×#4039C2211yescharacteristic
39C2×#4038C2211yescharacteristic
40C2×D5×C4⋊C4C2211yescharacteristic
41C2×#4036C2211yescharacteristic
42C2×#4034C2211yescharacteristic
43C2×#4032—21no—
44C2×#4025—21no—
45C5×#480C2218yescomplemented
46C2×C5×#107C2211yescharacteristic
47C2×C5×#107C2211yescharacteristic
48C2×C5×#102C2211yescharacteristic
49C2×C5×#102C2211yescharacteristic
50C2×C5×C22⋊C8C2211yescharacteristic
51C2×#3964C2211yescharacteristic
52C2×#3953C2211yescharacteristic
53C2×#3953C2211yescharacteristic
54C2×#3952C2211yescharacteristic
55C2×#3949C2211yescharacteristic
56C2×#3949C2211yescharacteristic
57C2×#3947C2211yescharacteristic
58C2×#3946C2211yescharacteristic
59#65327C2218yescomplemented
60C2×#3941C2211yescharacteristic
61C2×#3940C2211yescharacteristic
62C2×#3940C2211yescharacteristic
63C2×#3940C2211yescharacteristic
64C2×#3940C2211yescharacteristic
65C2×#3940C2218yescomplemented
66C2×#3939C2211yescharacteristic
67#65180C2218yescomplemented
68#65174C2218yescomplemented
69#65170C2218yescomplemented
70#65165C2218yescomplemented
71#65074C2218yescomplemented
72#65071C2218yescomplemented
73#65066C2218yescomplemented
74#65050C2218yescomplemented
75#65024C2218yescomplemented
76#65019C2218yescomplemented
77C2×#3345—51nomaximal, Sylow
78C22×C5×D4—21no—
79C22×C5×D4C2311yescharacteristic
80C23×C4×C5—21no—
81C23×C4×C5C2311yescharacteristic
82C22×C22⋊D5—21no—
83C22×C22⋊D5—21no—
84C22×C22⋊D5D411yescharacteristic
85C23×Dic5—21no—
86C23×Dic5—21no—
87C2×#709—28no—
88C2×#709—48no—
89C22×D20—21no—
90C22×D20C2311yescharacteristic
91C22×C4×D5—21no—
92C22×C4×D5—21no—
93C22×C4×D5C2311yescharacteristic
94C22×Dic10—21no—
95C22×C5×C8C2311yescharacteristic
96C22×C5×C8C2311yescharacteristic
97C5×#121—22no—
98C5×#121C2314yes—
99C2×C5×C4⋊C4—21no—
100C2×C5×C4⋊C4—22no—
101C2×C5×C4⋊C4C2311yescharacteristic
102C2×C5×C4⋊C4C2311yescharacteristic
103C2×C5×C4⋊C4C2311yescharacteristic
104C2×C5×C4⋊C4C2314yes—
105C2×C5×C22⋊C4—21no—
106C2×C22⋊Dic5—21no—
107C2×C22⋊Dic5—21no—
108C2×C22⋊Dic5D411yescharacteristic
109#4085—28no—
110#4084—22no—
111#4084C2314yes—
112D4×Dic5—28no—
113D4×Dic5—22no—
114D4×Dic5C2314yes—
115C2×#686—24no—
116C2×#686C2314yes—
117#4076—22no—
118#4076C2314yes—
119#4075—28no—
120C4×C22⋊D5D414yes—
121C4×C22⋊D5C2314yes—
122C2×#685—21no—
123C2×#685—21no—
124C2×#685—21no—
125C2×#685—21no—
126C2×#685D411yescharacteristic
127C2×C4⋊Dic5—21no—
128C2×C4⋊Dic5—22no—
129C2×C4⋊Dic5—21no—
130C2×C4⋊Dic5C2314yes—
131C2×C4⋊Dic5C2311yescharacteristic
132C2×C4⋊Dic5C2311yescharacteristic
133C2×C4⋊Dic5C2311yescharacteristic
134C2×#683—21no—
135C2×#683—21no—
136C2×#683—21no—
137C2×#683D411yescharacteristic
138C2×C4×Dic5—21no—
139C2×C4×Dic5C2311yescharacteristic
140C22×#168—24no—
141C22×#168C2314yes—
142C22×#168C2311yescharacteristic
143C22×#168C2311yescharacteristic
144C2×#676—24no—
145C2×#676C2314yes—
146#4042—28no—
147#4041—22no—
148#4041C2314yes—
149#4040—28no—
150#4039—22no—
151#4039C2314yes—
152#4038—22no—
153#4038C2314yes—
154D5×C4⋊C4—22no—
155D5×C4⋊C4C2314yes—
156#4036—22no—
157#4036C2314yes—
158#4034—22no—
159#4034C2314yes—
160#4032—28no—
161#4025—28no—
162C5×#107C2314yes—
163C5×#107C2314yes—
164C5×#102C2314yes—
165C5×#102C2314yes—
166C5×C22⋊C8C2314yes—
167#3964C2314yes—
168#3953C2314yes—
169#3953C2314yes—
170#3952C2314yes—
171#3949C2314yes—
172#3949C2314yes—
173#3947C2314yes—
174#3946C2314yes—
175#3941C2314yes—
176#3940C2314yes—
177#3940C2314yes—
178#3940C2314yes—
179#3940C2314yes—
180#3939C2314yes—
181C2×#553—51no—
182C2×#547—51no—
183#3345—516no—
184C2×#501—51no—
185C2×#481—51no—
186C2×#481—51no—
187C2×#482—51no—
188C2×#480D511yescharacteristic, complemented
189C2×#478—51no—
190C2×#476—51no—
191C2×#469—51no—
192C2×#466—51no—
193C2×#442—51no—
194C2×#435—51no—
195C2×#428—51no—
196C22×#106—51no—
197C24×C5—21no—
198C24×C5C2×D411yescharacteristic
199C23×D5—21no—
200C23×D5C2×D411yescharacteristic
201C2×C5×D4—24no—
202C2×C5×D4—21no—
203C2×C5×D4—22no—
204C2×C5×D4—22no—
205C2×C5×D4—44no—
206C2×C5×D4C2412yes—
207C22×C4×C5—22no—
208C22×C4×C5—22no—
209C22×C4×C5—21no—
210C22×C4×C5—21no—
211C22×C4×C5—21no—
212C22×C4×C5—24no—
213C22×C4×C5—44no—
214C22×C4×C5C2×D411yescharacteristic
215C22×C4×C5C2×D412yes—
216C22×C4×C5C2412yes—
217C22×C4×C5C2411yescharacteristic
218C2×C22⋊D5—24no—
219C2×C22⋊D5—24no—
220C2×C22⋊D5—24no—
221C2×C22⋊D5—44no—
222C2×C22⋊D5—82no—
223C2×C22⋊D5C2×D414yes—
224C22×Dic5—21no—
225C22×Dic5—21no—
226C22×Dic5—21no—
227C22×Dic5—24no—
228C22×Dic5—24no—
229C22×Dic5—82no—
230C22×Dic5—82no—
231C22×Dic5C2×D411yescharacteristic
232C22×Dic5C2×D411yescharacteristic
233C22×Dic5C2×D411yescharacteristic
234#709—432no—
235C2×D20—22no—
236C2×D20—22no—
237C2×D20—24no—
238C2×D20—21no—
239C2×D20—44no—
240C2×D20C2412yes—
241C2×C4×D5—22no—
242C2×C4×D5—22no—
243C2×C4×D5—24no—
244C2×C4×D5—24no—
245C2×C4×D5—44no—
246C2×C4×D5—44no—
247C2×C4×D5C2×D412yes—
248C2×C4×D5C2412yes—
249C2×Dic10—24no—
250C2×Dic10—44no—
251C2×C5×C8—22no—
252C2×C5×C8—22no—
253C2×C5×C8C2412yes—
254C2×C5×C8C2412yes—
255C5×C4⋊C4—21no—
256C5×C4⋊C4—21no—
257C5×C4⋊C4—24no—
258C5×C4⋊C4—21no—
259C5×C4⋊C4C2412yes—
260C5×C4⋊C4C2412yes—
261C5×C4⋊C4C2412yes—
262C5×C22⋊C4—24no—
263C22⋊Dic5—24no—
264C22⋊Dic5—24no—
265C22⋊Dic5C2×D414yes—
266#686—28no—
267#685—24no—
268#685—24no—
269#685—24no—
270#685—24no—
271#685C2×D414yes—
272C4⋊Dic5—24no—
273C4⋊Dic5—21no—
274C4⋊Dic5—21no—
275C4⋊Dic5—21no—
276C4⋊Dic5—24no—
277C4⋊Dic5C2412yes—
278C4⋊Dic5C2412yes—
279C4⋊Dic5C2412yes—
280#683—24no—
281#683—24no—
282#683—24no—
283#683C2×D414yes—
284C4×Dic5—24no—
285C4×Dic5C2×D412yes—
286C4×Dic5C2412yes—
287C2×#168—22no—
288C2×#168—28no—
289C2×#168#4114yescomplemented
290C2×#168C2412yes—
291C2×#168C2412yes—
292#676—28no—
293C22×#41—101no—
294C22×D8—51no—
295C22×M16—51no—
296C23×C8—51no—
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—51no—
311C2×#121—101no—
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⋊C4C2×D511yescharacteristic
321#501—58no—
322#482—58no—
323#481—58no—
324#481—58no—
325#480C2×D518yescomplemented
326#478—58no—
327#476—58no—
328#469—58no—
329#466—58no—
330#442—58no—
331#435—58no—
332#428—58no—
333C2×#107—51no—
334C2×#107C2×D511yescharacteristic
335C2×#107C2×D511yescharacteristic
336C2×#106—51no—
337C2×#106—51no—
338C2×#106—51no—
339C2×#106—51no—
340C2×#106—58no—
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⋊C8C2×D511yescharacteristic
352C2×#97—51no—
353C23×C5—22no—
354C23×C5—22no—
355C23×C5—22no—
356C23×C5—42no—
357C23×C5—42no—
358C23×C5—42no—
359C23×C5AGL(1,ℤ/8)14yes—
360C23×C5C22×D412yes—
361C23×C5C22×D411yescharacteristic
362C22×D5—22no—
363C22×D5—22no—
364C22×D5—22no—
365C22×D5—22no—
366C22×D5—42no—
367C22×D5—42no—
368C22×D5—42no—
369C22×D5C22×D412yes—
370C5×D4—22no—
371C5×D4—22no—
372C5×D4—48no—
373C5×D4—42no—
374C2×C4×C5—22no—
375C2×C4×C5—24no—
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—48no—
384C2×C4×C5—42no—
385C2×C4×C5C22×D412yes—
386C2×C4×C5C22×D411yescharacteristic
387C2×C4×C5C2×#4112yes—
388C2×C4×C52−1+412yes—
389C2×C4×C5C2511yescharacteristic
390C22⋊D5—28no—
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—84no—
403C2×Dic5—84no—
404C2×Dic5C22×D412yes—
405C2×Dic5C22×D412yes—
406C2×Dic5C22×D412yes—
407D20—22no—
408D20—22no—
409D20—48no—
410D20—42no—
411C4×D5—24no—
412C4×D5—22no—
413C4×D5—22no—
414C4×D5—48no—
415C4×D5—48no—
416Dic10—48no—
417C5×C8—22no—
418C5×C8—22no—
419#168—22no—
420#168C2×#4114yescomplemented
421C2×#41—108no—
422C2×#41—208no—
423C22×Q8—101no—
424C22×D4—21no—
425C22×D4—51no—
426C22×D4—51no—
427C22×D4—101no—
428C22×D4—101no—
429C22×D4—101no—
430C22×D4C22×D511yescharacteristic
431C23×C4—21no—
432C23×C4—51no—
433C23×C4—101no—
434C23×C4—101no—
435C23×C4—101no—
436C23×C4—101no—
437C23×C4C22×D511yescharacteristic
438C2×D8—54no—
439C2×D8—104no—
440C2×M16—54no—
441C2×M16—104no—
442C22×C8—51no—
443C22×C8—51no—
444C22×C8—54no—
445C22×C8—104no—
446C22×C8C22×D511yescharacteristic
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—54no—
459#121—54no—
460#121—54no—
461#121—102no—
462#121—102no—
463#121—108no—
464#121—102no—
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—21no—
476C2×C4⋊C4—22no—
477C2×C4⋊C4—51no—
478C2×C4⋊C4—51no—
479C2×C4⋊C4—51no—
480C2×C4⋊C4—51no—
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—102no—
490C2×C4⋊C4C22×D511yescharacteristic
491C2×C4⋊C4C22×D511yescharacteristic
492C2×C4⋊C4C22×D514yes—
493C2×C4⋊C4C22×D511yescharacteristic
494C2×C22⋊C4—21no—
495C2×C22⋊C4—51no—
496C2×C22⋊C4—51no—
497C2×C22⋊C4—101no—
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#107C22×D514yes—
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⋊C8C22×D514yes—
523#97—54no—
524C22×C5—28no—
525C22×C5—22no—
526C22×C5—22no—
527C22×C5—42no—
528C22×C5—42no—
529C22×C5—42no—
530C22×C5—84no—
531C22×C5#54712yes—
532C22×C5C2×AGL(1,ℤ/8)14yes—
533C22×C5C2×AGL(1,ℤ/8)12yes—
534C22×C5#57712yes—
535C22×C5C23×D411yescharacteristic
536C2×D5—22no—
537C2×D5—22no—
538C2×D5—22no—
539C2×D5—44no—
540C2×D5—42no—
541C2×D5—42no—
542C2×D5—42no—
543C2×D5—84no—
544C4×C5—22no—
545C4×C5—42no—
546C4×C5—42no—
547C4×C5—42no—
548C4×C5#54712yes—
549C4×C5C22×#4111yescharacteristic
550C4×C5C2×2−1+411yescharacteristic
551Dic5—22no—
552Dic5—22no—
553Dic5—22no—
554Dic5—42no—
555Dic5—42no—
556Dic5—42no—
557C24—21no—
558C24—51no—
559C24—101no—
560C24D4×D511yescharacteristic
561#41—2032no—
562C2×Q8—104no—
563C2×Q8—204no—
564C2×D4—24no—
565C2×D4—21no—
566C2×D4—22no—
567C2×D4—22no—
568C2×D4—44no—
569C2×D4—54no—
570C2×D4—52no—
571C2×D4—104no—
572C2×D4—104no—
573C2×D4—104no—
574C2×D4—104no—
575C2×D4—101no—
576C2×D4—102no—
577C2×D4—102no—
578C2×D4—204no—
579C2×D4—204no—
580C2×D4—402no—
581C2×D4C23×D512yes—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—24no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—44no—
589C22×C4—51no—
590C22×C4—51no—
591C22×C4—51no—
592C22×C4—52no—
593C22×C4—52no—
594C22×C4—104no—
595C22×C4—104no—
596C22×C4—104no—
597C22×C4—102no—
598C22×C4—102no—
599C22×C4—101no—
600C22×C4—101no—
601C22×C4—101no—
602C22×C4—104no—
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—108no—
612M16—108no—
613C2×C8—22no—
614C2×C8—22no—
615C2×C8—54no—
616C2×C8—52no—
617C2×C8—52no—
618C2×C8—108no—
619C2×C8—102no—
620C2×C8C23×D512yes—
621C2×C8C23×D512yes—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—24no—
625C4⋊C4—21no—
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—101no—
635C4⋊C4—101no—
636C4⋊C4—101no—
637C4⋊C4—104no—
638C4⋊C4C23×D512yes—
639C4⋊C4C23×D512yes—
640C4⋊C4C23×D512yes—
641C22⋊C4—24no—
642C22⋊C4—54no—
643C22⋊C4—54no—
644C22⋊C4—104no—
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#334514yescomplemented
656C2×C5C2×#54711yescharacteristic
657C2×C5C22×AGL(1,ℤ/8)11yescharacteristic
658C2×C5C2×#57711yescharacteristic
659D5—42no—
660D5—82no—
661C23—22no—
662C23—22no—
663C23—22no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—52no—
668C23—102no—
669C23—102no—
670C23—102no—
671C23—102no—
672C23—202no—
673C23—202no—
674C23—202no—
675C23#405714yes—
676C23C2×D4×D512yes—
677C23C2×D4×D511yescharacteristic
678Q8—208no—
679D4—22no—
680D4—22no—
681D4—48no—
682D4—42no—
683D4—108no—
684D4—102no—
685D4—102no—
686D4—208no—
687D4—208no—
688D4—202no—
689D4—404no—
690C2×C4—22no—
691C2×C4—24no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—48no—
700C2×C4—42no—
701C2×C4—52no—
702C2×C4—52no—
703C2×C4—52no—
704C2×C4—102no—
705C2×C4—102no—
706C2×C4—102no—
707C2×C4—104no—
708C2×C4—102no—
709C2×C4—102no—
710C2×C4—102no—
711C2×C4—102no—
712C2×C4—102no—
713C2×C4—208no—
714C2×C4—208no—
715C2×C4—202no—
716C2×C4—202no—
717C2×C4—202no—
718C2×C4—404no—
719C2×C4—404no—
720C2×C4C2×D4×D512yes—
721C2×C4C2×D4×D511yescharacteristic
722C2×C4D5×#4112yes—
723C2×C4#415012yes—
724C2×C4C24×D511yescharacteristic
725C8—22no—
726C8—22no—
727C8—54no—
728C8—102no—
729C5C2×#334511yescharacteristic, complemented, Sylow
730C22—28no—
731C22—22no—
732C22—22no—
733C22—42no—
734C22—42no—
735C22—42no—
736C22—84no—
737C22—102no—
738C22—102no—
739C22—102no—
740C22—204no—
741C22—202no—
742C22—202no—
743C22—202no—
744C22—404no—
745C22#6598912yes—
746C22C2×#405714yes—
747C22C2×#405712yes—
748C22#6611212yes—
749C22C22×D4×D511yescharacteristic
750C4—22no—
751C4—42no—
752C4—42no—
753C4—42no—
754C4—102no—
755C4—102no—
756C4—102no—
757C4—202no—
758C4—202no—
759C4—202no—
760C4#6598912yes—
761C4C2×D5×#4111yescharacteristic
762C4C2×#415011yescharacteristic
763C2—24no—
764C2—82no—
765C2—202no—
766C2—402no—
767C2#1061302514yesdirect product factor
768C2C2×#6598911yescharacteristic
769C2C22×#405711yescharacteristic
770C2C2×#6611211yescharacteristic
subgroupG/H
centerC23C2×D4×D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×#480C2
socleC23×C5C22×D4
hypercenterC2×#480D5
hypocenterC5C2×#3345
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#480

Complements

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

NH ≅ G/Ntype
1. C2×#65952C2semidirect
2. C2×#65841C2semidirect
3. C2×C5×#480C2semidirect
4. C2×#65327C2semidirect
5. C22×#3940C2semidirect
6. #10613025C2direct (N × H)
7. C2×#65180C2semidirect
8. C2×#65170C2semidirect
9. C2×#65174C2semidirect
10. C2×#65165C2semidirect
11. C2×#65066C2semidirect
12. C2×#65071C2semidirect
13. C2×#65050C2semidirect
14. C2×#65074C2semidirect
15. C2×#65019C2semidirect
16. C2×#65024C2semidirect
32. #65952C22semidirect
35. #65841C22semidirect
45. C5×#480C22semidirect
59. #65327C22semidirect
65. C2×#3940C22semidirect
67. #65180C22semidirect
68. #65174C22semidirect
69. #65170C22semidirect
70. #65165C22semidirect
71. #65074C22semidirect
72. #65071C22semidirect
73. #65066C22semidirect
74. #65050C22semidirect
75. #65024C22semidirect
76. #65019C22semidirect
188. C2×#480D5semidirect
289. C2×#168#41semidirect
325. #480C2×D5semidirect
420. #168C2×#41semidirect
655. C2×C5#3345semidirect
729. C5C2×#3345semidirect
767. C2#10613025direct (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×#658412
C2×C5×#4802
C2×#653272
C22×#39402
#106130252
C2×#651802
C2×#651702
C2×#651742
C2×#651652
C2×#650662
C2×#650712
C2×#650502
C2×#650742
C2×#650192
C2×#650242
C2×#33455