Finite Group Databasebeta

← C2×#10612379 #12977718

Subgroups — C2×#10612379 #12977718

Order 1280.

2158 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65969C211yesmaximal, characteristic, complemented
2C2×#65945C211yesmaximal, characteristic
3C2×C5×#465C211yesmaximal, characteristic, complemented
4C2×#65460C211yesmaximal, characteristic, complemented
5C2×SD16×Dic5C211yesmaximal, characteristic, complemented
6C2×C8×C22⋊D5C211yesmaximal, characteristic, complemented
7C22×#3949C211yesmaximal, characteristic, complemented
8C2×#65332C211yesmaximal, characteristic, complemented
9C2×#65323C211yesmaximal, characteristic, complemented
10#10612379C2116yesmaximal, direct product factor
11C2×D5×#106C211yesmaximal, characteristic, complemented
12C2×#65144C211yesmaximal, characteristic, complemented
13C2×#65094C211yesmaximal, characteristic, complemented
14C2×#65080C211yesmaximal, characteristic, complemented
15C2×#65066C211yesmaximal, characteristic, complemented
16C2×#65050C211yesmaximal, characteristic, complemented
17C22×#711—21no—
18C22×C5×SD16C2211yescharacteristic
19C23×C5×C8C2211yescharacteristic
20C2×C5×C22⋊Q8C2211yescharacteristic
21C2×C5×#121C2211yescharacteristic
22C2×#4092C2211yescharacteristic
23C2×Q8×Dic5C2211yescharacteristic
24C2×#4084C2211yescharacteristic
25C2×#4081—21no—
26C2×D4×Dic5C2211yescharacteristic
27C2×C4×C22⋊D5C2211yescharacteristic
28C22×C4⋊Dic5C2211yescharacteristic
29C22×C4⋊Dic5C2211yescharacteristic
30C22×C8×D5C2211yescharacteristic
31#65969—24no—
32#65969C2218yescomplemented
33#65945—24no—
34#65945C2218yes—
35C2×#4043—21no—
36C2×D5×C4⋊C4C2211yescharacteristic
37C2×D5×C4⋊C4C2211yescharacteristic
38C2×#4035—21no—
39C2×#4034C2211yescharacteristic
40C2×#4034C2211yescharacteristic
41C2×#4029—21no—
42C2×#4027—21no—
43C2×#4024—21no—
44C2×#4024—21no—
45C5×#465C2218yescomplemented
46C2×C5×#106C2211yescharacteristic
47C2×C5×#103C2211yescharacteristic
48C2×C5×#102C2211yescharacteristic
49C2×#3967C2211yescharacteristic
50C2×#3967C2211yescharacteristic
51C2×#3964C2211yescharacteristic
52C2×#3964C2211yescharacteristic
53C2×C22⋊#168C2211yescharacteristic
54#65460C2218yescomplemented
55SD16×Dic5C2218yescomplemented
56C8×C22⋊D5C2218yescomplemented
57C2×#3952C2211yescharacteristic
58C2×#3949C2211yescharacteristic
59C2×#3949C2211yescharacteristic
60C2×#3949C2211yescharacteristic
61C2×#3949C2211yescharacteristic
62C2×#3949C2218yescomplemented
63C2×#3946C2211yescharacteristic
64C2×C8×Dic5C2211yescharacteristic
65#65332C2218yescomplemented
66#65323C2218yescomplemented
67C2×#3940C2211yescharacteristic
68C2×#3940C2211yescharacteristic
69C2×#3940C2211yescharacteristic
70C2×#3940C2211yescharacteristic
71D5×#106C2218yescomplemented
72#65144C2218yescomplemented
73#65094C2218yescomplemented
74#65080C2218yescomplemented
75#65066C2218yescomplemented
76#65050C2218yescomplemented
77C2×#3335—51nomaximal, Sylow
78C22×C5×Q8C2311yescharacteristic
79C22×C5×D4—21no—
80C22×C5×D4C2311yescharacteristic
81C23×C4×C5C2311yescharacteristic
82C22×C22⋊D5—21no—
83C22×C22⋊D5D411yescharacteristic
84C23×Dic5—21no—
85C23×Dic5—21no—
86C23×Dic5—21no—
87C2×#711—28no—
88C2×#711—48no—
89C22×C4×D5—21no—
90C22×C4×D5—21no—
91C22×C4×D5C2311yescharacteristic
92C22×Dic10—21no—
93C22×Dic10—21no—
94C2×C5×SD16—24no—
95C2×C5×SD16C2314yes—
96C22×C5×C8—24no—
97C22×C5×C8C2311yescharacteristic
98C22×C5×C8C2314yes—
99C22×C5×C8C2311yescharacteristic
100C5×C22⋊Q8—22no—
101C5×C22⋊Q8C2314yes—
102C5×#121—22no—
103C5×#121C2314yes—
104C2×C5×C4⋊C4—21no—
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⋊Dic5D411yescharacteristic
112#4092—22no—
113#4092C2314yes—
114Q8×Dic5—22no—
115Q8×Dic5C2314yes—
116#4084—22no—
117#4084C2314yes—
118#4081—28no—
119D4×Dic5—22no—
120D4×Dic5C2314yes—
121C4×C22⋊D5D414yes—
122C4×C22⋊D5C2314yes—
123C2×#685—21no—
124C2×#685D411yescharacteristic
125C2×C4⋊Dic5—21no—
126C2×C4⋊Dic5—21no—
127C2×C4⋊Dic5—22no—
128C2×C4⋊Dic5—22no—
129C2×C4⋊Dic5—21no—
130C2×C4⋊Dic5C2311yescharacteristic
131C2×C4⋊Dic5C2311yescharacteristic
132C2×C4⋊Dic5C2311yescharacteristic
133C2×C4⋊Dic5C2311yescharacteristic
134C2×C4⋊Dic5C2314yes—
135C2×C4⋊Dic5C2314yes—
136C2×#683—21no—
137C2×#683—21no—
138C2×#683—21no—
139C2×#683—21no—
140C2×#683—21no—
141C2×#683D411yescharacteristic
142C2×C4×Dic5—21no—
143C2×C4×Dic5C2311yescharacteristic
144C22×#168C2311yescharacteristic
145C22×#168C2311yescharacteristic
146C2×C8×D5—24no—
147C2×C8×D5C2314yes—
148#4043—28no—
149D5×C4⋊C4—22no—
150D5×C4⋊C4—22no—
151D5×C4⋊C4C2314yes—
152D5×C4⋊C4C2314yes—
153#4035—28no—
154#4034—22no—
155#4034—22no—
156#4034C2314yes—
157#4034C2314yes—
158#4029—28no—
159#4027—28no—
160#4024—28no—
161#4024—28no—
162C5×#106C2314yes—
163C5×#103C2314yes—
164C5×#102C2314yes—
165#3967C2314yes—
166#3967C2314yes—
167#3964C2314yes—
168#3964C2314yes—
169C22⋊#168C2314yes—
170#3952C2314yes—
171#3949C2314yes—
172#3949C2314yes—
173#3949C2314yes—
174#3949C2314yes—
175#3946C2314yes—
176C8×Dic5C2314yes—
177#3940C2314yes—
178#3940C2314yes—
179#3940C2314yes—
180#3940C2314yes—
181C2×#554—51no—
182C2×#547—51no—
183#3335—516no—
184C2×#498—51no—
185C2×#481—51no—
186C2×#481—51no—
187C2×#483—51no—
188C2×#483—51no—
189C2×#475—51no—
190C2×#476—51no—
191C2×#465—51no—
192C2×#465D511yescharacteristic, complemented
193C2×C4×SD16—51no—
194C2×C8×D4—51no—
195C22×#106—51no—
196C22×#106—51no—
197C24×C5—21no—
198C24×C5C2×D411yescharacteristic
199C23×D5C2×D411yescharacteristic
200C2×C5×Q8—21no—
201C2×C5×Q8—22no—
202C2×C5×Q8—22no—
203C2×C5×Q8C2412yes—
204C2×C5×D4—24no—
205C2×C5×D4—21no—
206C2×C5×D4—22no—
207C2×C5×D4—22no—
208C2×C5×D4—44no—
209C2×C5×D4C2412yes—
210C22×C4×C5—22no—
211C22×C4×C5—22no—
212C22×C4×C5—21no—
213C22×C4×C5—21no—
214C22×C4×C5—21no—
215C22×C4×C5C2×D411yescharacteristic
216C22×C4×C5C2×D412yes—
217C22×C4×C5C2412yes—
218C22×C4×C5C2411yescharacteristic
219C2×C22⋊D5—24no—
220C2×C22⋊D5—44no—
221C2×C22⋊D5SD1618yescomplemented
222C2×C22⋊D5C2×D414yes—
223C22×Dic5—21no—
224C22×Dic5—21no—
225C22×Dic5—21no—
226C22×Dic5—21no—
227C22×Dic5—24no—
228C22×Dic5—24no—
229C22×Dic5—24no—
230C22×Dic5—44no—
231C22×Dic5—44no—
232C22×Dic5—82no—
233C22×Dic5C2×D411yescharacteristic
234C22×Dic5C2×D411yescharacteristic
235C22×Dic5C2×D411yescharacteristic
236#711—432no—
237C2×C4×D5—22no—
238C2×C4×D5—22no—
239C2×C4×D5—24no—
240C2×C4×D5—24no—
241C2×C4×D5—44no—
242C2×C4×D5—82no—
243C2×C4×D5C2×D412yes—
244C2×C4×D5C2412yes—
245C2×Dic10—24no—
246C2×Dic10—24no—
247C2×Dic10—44no—
248C2×Dic10—82no—
249C5×SD16—28no—
250C2×C5×C8—22no—
251C2×C5×C8—28no—
252C2×C5×C8#4114yescomplemented
253C2×C5×C8C2412yes—
254C2×C5×C8C2412yes—
255C5×C4⋊C4—24no—
256C5×C4⋊C4—21no—
257C5×C4⋊C4—21no—
258C5×C4⋊C4C2412yes—
259C5×C4⋊C4C2412yes—
260C5×C22⋊C4—24no—
261C5×C22⋊C4—24no—
262C22⋊Dic5—24no—
263C22⋊Dic5—24no—
264C22⋊Dic5C2×D414yes—
265#685—24no—
266#685C2×D414yes—
267C4⋊Dic5—24no—
268C4⋊Dic5—21no—
269C4⋊Dic5—21no—
270C4⋊Dic5—24no—
271C4⋊Dic5—21no—
272C4⋊Dic5—21no—
273C4⋊Dic5—24no—
274C4⋊Dic5C2412yes—
275C4⋊Dic5C2412yes—
276C4⋊Dic5C2412yes—
277C4⋊Dic5C2412yes—
278#683—24no—
279#683—24no—
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—22no—
289C2×#168C2412yes—
290C2×#168C2412yes—
291C8×D5—28no—
292C22×#41—101no—
293C22×SD16C2×D511yescharacteristic
294C23×C8—51no—
295C23×C8C2×D511yescharacteristic
296#554—58no—
297#554—104no—
298#547—58no—
299#547—104no—
300C2×C4⋊Q8—51no—
301C2×C4⋊Q8—51no—
302C2×#125—101no—
303C2×#123—101no—
304C2×#123—101no—
305C2×C22⋊Q8—51no—
306C2×C22⋊Q8—101no—
307C2×C22⋊Q8—101no—
308C2×C22⋊Q8—101no—
309C2×C22⋊Q8C2×D511yescharacteristic
310C2×#121—51no—
311C2×#121C2×D511yescharacteristic
312C2×C4×Q8—51no—
313C2×C4×D4—51no—
314C2×C4×D4—51no—
315C2×C4×D4—101no—
316C22×C4⋊C4—51no—
317C22×C4⋊C4—51no—
318C22×C4⋊C4—51no—
319C22×C4⋊C4—51no—
320#498—58no—
321#483—58no—
322#483—58no—
323#481—58no—
324#481—58no—
325#476—58no—
326#475—58no—
327#465—58no—
328#465C2×D518yescomplemented
329C4×SD16—58no—
330C8×D4—58no—
331C2×#106—51no—
332C2×#106—58no—
333C2×#106—51no—
334C2×#106—51no—
335C2×#106—51no—
336C2×#106—51no—
337C2×#106—51no—
338C2×#106—51no—
339C2×#106—51no—
340C2×#106—58no—
341C2×#106C2×D511yescharacteristic
342C2×C4⋊C8—51no—
343C2×#103—51no—
344C2×#103—51no—
345C2×#103C2×D511yescharacteristic
346C2×#102—51no—
347C2×#102—51no—
348C2×#102C2×D511yescharacteristic
349C2×C22⋊C8—51no—
350C2×C22⋊C8—51no—
351C2×C4×C8—51no—
352C23×C5—22no—
353C23×C5—22no—
354C23×C5—22no—
355C23×C5—42no—
356C23×C5—42no—
357C23×C5—42no—
358C23×C5C2×SD1614yes—
359C23×C5C22×D412yes—
360C23×C5C22×D411yescharacteristic
361C22×D5—22no—
362C22×D5—22no—
363C22×D5C2×SD1614yes—
364C22×D5C22×D412yes—
365C5×Q8—22no—
366C5×Q8—22no—
367C5×Q8—42no—
368C5×D4—22no—
369C5×D4—22no—
370C5×D4—48no—
371C5×D4—42no—
372C2×C4×C5—22no—
373C2×C4×C5—24no—
374C2×C4×C5—22no—
375C2×C4×C5—22no—
376C2×C4×C5—22no—
377C2×C4×C5—22no—
378C2×C4×C5—22no—
379C2×C4×C5—42no—
380C2×C4×C5—42no—
381C2×C4×C5—42no—
382C2×C4×C5C22×D412yes—
383C2×C4×C5C22×D411yescharacteristic
384C2×C4×C5C2×#4112yes—
385C2×C4×C52−1+412yes—
386C2×C4×C5C2511yescharacteristic
387C22⋊D5—48no—
388C22⋊D5C2×SD16116yescomplemented
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—48no—
398C2×Dic5—42no—
399C2×Dic5—42no—
400C2×Dic5—48no—
401C2×Dic5—84no—
402C2×Dic5C2×SD1614yes—
403C2×Dic5C22×D412yes—
404C2×Dic5C22×D412yes—
405C2×Dic5C22×D412yes—
406C4×D5—24no—
407C4×D5—22no—
408C4×D5—22no—
409C4×D5—48no—
410C4×D5—84no—
411Dic10—48no—
412Dic10—84no—
413C5×C8—22no—
414C5×C8C2×#4114yescomplemented
415#168—22no—
416#168—22no—
417C2×#41—108no—
418C2×#41—208no—
419C22×Q8—101no—
420C22×Q8—101no—
421C22×Q8C22×D511yescharacteristic
422C22×D4—21no—
423C22×D4—51no—
424C22×D4—101no—
425C22×D4C22×D511yescharacteristic
426C23×C4—51no—
427C23×C4—101no—
428C23×C4—101no—
429C23×C4—101no—
430C23×C4—101no—
431C23×C4—101no—
432C23×C4C22×D511yescharacteristic
433C2×SD16—24no—
434C2×SD16C22×D514yes—
435C22×C8—24no—
436C22×C8—51no—
437C22×C8—51no—
438C22×C8—54no—
439C22×C8—104no—
440C22×C8C22×D511yescharacteristic
441C22×C8C22×D514yes—
442C22×C8C22×D511yescharacteristic
443C4⋊Q8—54no—
444C4⋊Q8—54no—
445C4⋊Q8—102no—
446C4⋊Q8—102no—
447#125—108no—
448#123—108no—
449#123—108no—
450C22⋊Q8—22no—
451C22⋊Q8—54no—
452C22⋊Q8—108no—
453C22⋊Q8—108no—
454C22⋊Q8—108no—
455C22⋊Q8—102no—
456C22⋊Q8C22×D514yes—
457#121—22no—
458#121—54no—
459#121—102no—
460#121C22×D514yes—
461C4×Q8—54no—
462C4×Q8—102no—
463C4×D4—54no—
464C4×D4—54no—
465C4×D4—54no—
466C4×D4—102no—
467C4×D4—108no—
468C2×C4⋊C4—21no—
469C2×C4⋊C4—51no—
470C2×C4⋊C4—51no—
471C2×C4⋊C4—51no—
472C2×C4⋊C4—51no—
473C2×C4⋊C4—51no—
474C2×C4⋊C4—54no—
475C2×C4⋊C4—54no—
476C2×C4⋊C4—54no—
477C2×C4⋊C4—54no—
478C2×C4⋊C4—102no—
479C2×C4⋊C4—102no—
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⋊C4—101no—
488C2×C4⋊C4—102no—
489C2×C4⋊C4—102no—
490C2×C4⋊C4C22×D511yescharacteristic
491C2×C4⋊C4C22×D511yescharacteristic
492C2×C22⋊C4—21no—
493C2×C22⋊C4—21no—
494C2×C22⋊C4—51no—
495C2×C22⋊C4—51no—
496C2×C22⋊C4—101no—
497C2×C22⋊C4—101no—
498C2×C22⋊C4—101no—
499C2×C42—51no—
500C2×C42—101no—
501#106—54no—
502#106—54no—
503#106—54no—
504#106—54no—
505#106—54no—
506#106—54no—
507#106—54no—
508#106—54no—
509#106C22×D514yes—
510C4⋊C8—54no—
511#103—54no—
512#103—54no—
513#103C22×D514yes—
514#102—54no—
515#102—54no—
516#102C22×D514yes—
517C22⋊C8—54no—
518C22⋊C8—54no—
519C4×C8—54no—
520C22×C5—28no—
521C22×C5—22no—
522C22×C5—22no—
523C22×C5—42no—
524C22×C5—42no—
525C22×C5—42no—
526C22×C5—84no—
527C22×C5#54712yes—
528C22×C5C22×SD1614yes—
529C22×C5C22×SD1612yes—
530C22×C5#57712yes—
531C22×C5C23×D411yescharacteristic
532C2×D5—28no—
533C2×D5—22no—
534C2×D5—22no—
535C2×D5C22×SD1614yes—
536C4×C5—22no—
537C4×C5—42no—
538C4×C5—42no—
539C4×C5—42no—
540C4×C5#54712yes—
541C4×C5C22×#4111yescharacteristic
542C4×C5C2×2−1+411yescharacteristic
543Dic5—22no—
544Dic5—22no—
545Dic5—42no—
546Dic5—42no—
547Dic5—42no—
548Dic5—42no—
549Dic5C22×SD1614yes—
550C24—21no—
551C24—51no—
552C24D4×D511yescharacteristic
553#41—2032no—
554C2×Q8—21no—
555C2×Q8—22no—
556C2×Q8—22no—
557C2×Q8—104no—
558C2×Q8—104no—
559C2×Q8—204no—
560C2×Q8—402no—
561C2×Q8C23×D512yes—
562C2×D4—24no—
563C2×D4—21no—
564C2×D4—22no—
565C2×D4—22no—
566C2×D4—44no—
567C2×D4—54no—
568C2×D4—58no—
569C2×D4—104no—
570C2×D4—204no—
571C2×D4C23×D512yes—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—51no—
578C22×C4—51no—
579C22×C4—51no—
580C22×C4—52no—
581C22×C4—52no—
582C22×C4—104no—
583C22×C4—104no—
584C22×C4—104no—
585C22×C4—102no—
586C22×C4—102no—
587C22×C4—104no—
588C22×C4—101no—
589C22×C4—101no—
590C22×C4—101no—
591C22×C4—101no—
592C22×C4—104no—
593C22×C4—204no—
594C22×C4—204no—
595C22×C4—204no—
596C22×C4—402no—
597C22×C4—402no—
598C22×C4D4×D512yes—
599C22×C4D4×D511yescharacteristic
600C22×C4C23×D512yes—
601C22×C4C23×D511yescharacteristic
602SD16—28no—
603C2×C8—22no—
604C2×C8—28no—
605C2×C8—52no—
606C2×C8—52no—
607C2×C8—102no—
608C2×C8—102no—
609C2×C8—108no—
610C2×C8#71114yescomplemented
611C2×C8C23×D512yes—
612C2×C8C23×D512yes—
613C4⋊C4—24no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—54no—
617C4⋊C4—52no—
618C4⋊C4—52no—
619C4⋊C4—52no—
620C4⋊C4—52no—
621C4⋊C4—104no—
622C4⋊C4—104no—
623C4⋊C4—104no—
624C4⋊C4—104no—
625C4⋊C4—104no—
626C4⋊C4—104no—
627C4⋊C4—101no—
628C4⋊C4—101no—
629C4⋊C4—101no—
630C4⋊C4—104no—
631C4⋊C4—104no—
632C4⋊C4—101no—
633C4⋊C4C23×D512yes—
634C4⋊C4C23×D512yes—
635C22⋊C4—24no—
636C22⋊C4—24no—
637C22⋊C4—54no—
638C22⋊C4—54no—
639C22⋊C4—104no—
640C22⋊C4—104no—
641C22⋊C4—104no—
642C42—52no—
643C42—52no—
644C42—104no—
645C2×C5—24no—
646C2×C5—82no—
647C2×C5#333514yescomplemented
648C2×C5C2×#54711yescharacteristic
649C2×C5C23×SD1611yescharacteristic
650C2×C5C2×#57711yescharacteristic
651D5—24no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—54no—
659C23—52no—
660C23—102no—
661C23—102no—
662C23D5×SD1614yes—
663C23C2×D4×D512yes—
664C23C2×D4×D511yescharacteristic
665Q8—22no—
666Q8—22no—
667Q8—42no—
668Q8—208no—
669Q8—404no—
670D4—22no—
671D4—22no—
672D4—48no—
673D4—42no—
674D4—516no—
675D4—208no—
676C2×C4—22no—
677C2×C4—24no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—54no—
687C2×C4—52no—
688C2×C4—52no—
689C2×C4—52no—
690C2×C4—102no—
691C2×C4—102no—
692C2×C4—104no—
693C2×C4—102no—
694C2×C4—102no—
695C2×C4—102no—
696C2×C4—102no—
697C2×C4—102no—
698C2×C4—102no—
699C2×C4—208no—
700C2×C4—208no—
701C2×C4—202no—
702C2×C4—202no—
703C2×C4—208no—
704C2×C4—202no—
705C2×C4—202no—
706C2×C4—404no—
707C2×C4—404no—
708C2×C4C2×D4×D512yes—
709C2×C4C2×D4×D511yescharacteristic
710C2×C4C2×#71112yes—
711C2×C4#415012yes—
712C2×C4C24×D511yescharacteristic
713C8—22no—
714C8—102no—
715C8—102no—
716C8C2×#71114yescomplemented
717C5C2×#333511yescharacteristic, complemented, Sylow
718C22—28no—
719C22—22no—
720C22—22no—
721C22—42no—
722C22—42no—
723C22—42no—
724C22—54no—
725C22—84no—
726C22—108no—
727C22—102no—
728C22—102no—
729C22#6594512yes—
730C22C2×D5×SD1614yes—
731C22C2×D5×SD1612yes—
732C22#6610412yes—
733C22C22×D4×D511yescharacteristic
734C4—22no—
735C4—42no—
736C4—42no—
737C4—42no—
738C4—54no—
739C4—102no—
740C4—102no—
741C4—202no—
742C4—202no—
743C4—202no—
744C4—202no—
745C4#6594512yes—
746C4C22×#71111yescharacteristic
747C4C2×#415011yescharacteristic
748C2—24no—
749C2—82no—
750C2—104no—
751C2#1061237914yesdirect product factor
752C2C2×#6594511yescharacteristic
753C2C22×D5×SD1611yescharacteristic
754C2C2×#6610411yescharacteristic
subgroupG/H
centerC23C2×D4×D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×#465C2
socleC23×C5C22×D4
prime radicalC2×#65945C2
hypercenterC2×#465D5
hypocenterC5C2×#3335
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#465

Complements

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

NH ≅ G/Ntype
1. C2×#65969C2semidirect
3. C2×C5×#465C2semidirect
4. C2×#65460C2semidirect
5. C2×SD16×Dic5C2semidirect
6. C2×C8×C22⋊D5C2semidirect
7. C22×#3949C2semidirect
8. C2×#65332C2semidirect
9. C2×#65323C2semidirect
10. #10612379C2direct (N × H)
11. C2×D5×#106C2semidirect
12. C2×#65144C2semidirect
13. C2×#65094C2semidirect
14. C2×#65080C2semidirect
15. C2×#65066C2semidirect
16. C2×#65050C2semidirect
32. #65969C22semidirect
45. C5×#465C22semidirect
54. #65460C22semidirect
55. SD16×Dic5C22semidirect
56. C8×C22⋊D5C22semidirect
62. C2×#3949C22semidirect
65. #65332C22semidirect
66. #65323C22semidirect
71. D5×#106C22semidirect
72. #65144C22semidirect
73. #65094C22semidirect
74. #65080C22semidirect
75. #65066C22semidirect
76. #65050C22semidirect
192. C2×#465D5semidirect
221. C2×C22⋊D5SD16semidirect
252. C2×C5×C8#41semidirect
328. #465C2×D5semidirect
388. C22⋊D5C2×SD16semidirect
414. C5×C8C2×#41semidirect
610. C2×C8#711semidirect
647. C2×C5#3335semidirect
716. C8C2×#711semidirect
717. C5C2×#3335semidirect
751. C2#10612379direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#659692
C2×#659452
C2×C5×#4652
C2×#654602
C2×SD16×Dic52
C2×C8×C22⋊D52
C22×#39492
C2×#653322
C2×#653232
#106123792
C2×D5×#1062
C2×#651442
C2×#650942
C2×#650802
C2×#650662
C2×#650502
C2×#33355