Finite Group Databasebeta

← C2×#10615187 #12969092

Subgroups — C2×#10615187 #12969092

Order 1280.

1970 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#542C211yesmaximal, characteristic, complemented
2C2×#65868C211yesmaximal, characteristic, complemented
3#10615187C2116yesmaximal, direct product factor
4C2×#65368C211yesmaximal, characteristic, complemented
5C2×#65378C211yesmaximal, characteristic, complemented
6C2×#65348C211yesmaximal, characteristic, complemented
7C2×#65344C211yesmaximal, characteristic, complemented
8C2×#65341C211yesmaximal, characteristic, complemented
9C2×#65337C211yesmaximal, characteristic, complemented
10C2×#65328C211yesmaximal, characteristic
11C2×#65330C211yesmaximal, characteristic, complemented
12C2×#65319C211yesmaximal, characteristic, complemented
13C2×C4×#688C211yesmaximal, characteristic, complemented
14C2×C4×#687C211yesmaximal, characteristic, complemented
15C2×#65303C211yesmaximal, characteristic, complemented
16C2×#65286C211yesmaximal, characteristic, complemented
17C5×#542—24no—
18C5×#542C2218yescomplemented
19C2×C5×C4⋊Q8C2211yescharacteristic
20C2×C5×#126—21no—
21C2×C5×#124—21no—
22C2×C5×#124C2211yescharacteristic
23C2×C5×#123—21no—
24C2×C5×C22⋊Q8—21no—
25C2×C5×C22⋊Q8C2211yescharacteristic
26C2×C5×#121C2211yescharacteristic
27C2×C4×C5×Q8C2211yescharacteristic
28C2×C4×C5×D4C2211yescharacteristic
29C2×C5×#117C2211yescharacteristic
30C22×#689C2211yescharacteristic
31C22×#688C2211yescharacteristic
32C22×#687C2211yescharacteristic
33C22×#686C2211yescharacteristic
34C2×#4076C2211yescharacteristic
35C2×#4070C2211yescharacteristic
36C22×#681C2211yescharacteristic
37C23×#168C2211yescharacteristic
38#65868—24no—
39#65868C2218yescomplemented
40C2×#4044—21no—
41C2×#4042—21no—
42C2×#4031—21no—
43C2×#4029—21no—
44C2×#4021C2211yescharacteristic
45C2×C4×D20C2211yescharacteristic
46C2×#4015C2211yescharacteristic
47C2×C4×Dic10C2211yescharacteristic
48C2×#3967C2211yescharacteristic
49C2×#3967C2211yescharacteristic
50C2×#3964C2211yescharacteristic
51C2×#3964C2211yescharacteristic
52#65378C2218yescomplemented
53#65368C2218yescomplemented
54#65348C2218yescomplemented
55#65344C2218yescomplemented
56#65341C2218yescomplemented
57#65337C2218yescomplemented
58#65330C2218yescomplemented
59#65328C2218yes—
60#65319C2218yescomplemented
61C4×#688C2218yescomplemented
62C4×#687C2218yescomplemented
63#65303C2218yescomplemented
64#65286C2218yescomplemented
65C2×#3942C2211yescharacteristic
66C2×#3942C2211yescharacteristic
67C2×#3941C2211yescharacteristic
68C2×#3941C2211yescharacteristic
69C2×#3940C2211yescharacteristic
70C2×#3940C2211yescharacteristic
71C2×#3940C2211yescharacteristic
72C2×#3940C2211yescharacteristic
73C2×#3935C2211yescharacteristic
74C2×#3935C2211yescharacteristic
75C2×C4×#168C2211yescharacteristic
76C2×C4×#168C2211yescharacteristic
77C2×#3173—51nomaximal, Sylow
78C22×C5×Q8—21no—
79C22×C5×Q8C2311yescharacteristic
80C22×C5×D4—21no—
81C22×C5×D4C2311yescharacteristic
82C23×C4×C5—21no—
83C23×C4×C5C2311yescharacteristic
84C22×C22⋊D5—21no—
85C22×D20C2311yescharacteristic
86C22×C4×D5—21no—
87C22×Dic10—21no—
88C22×Dic10C2311yescharacteristic
89C5×C4⋊Q8—22no—
90C5×C4⋊Q8C2314yes—
91C5×#126—28no—
92C5×#124—28no—
93C5×#124—22no—
94C5×#124C2314yes—
95C5×#123—28no—
96C5×C22⋊Q8—22no—
97C5×C22⋊Q8—28no—
98C5×C22⋊Q8C2314yes—
99C5×#121—22no—
100C5×#121C2314yes—
101C4×C5×Q8—22no—
102C4×C5×Q8C2314yes—
103C4×C5×D4—22no—
104C4×C5×D4C2314yes—
105C5×#117D414yes—
106C5×#117C2314yes—
107C2×C5×C4⋊C4—21no—
108C2×C5×C4⋊C4—21no—
109C2×C5×C4⋊C4—21no—
110C2×C5×C4⋊C4D411yescharacteristic
111C2×C5×C4⋊C4D411yescharacteristic
112C2×C5×C4⋊C4C2311yescharacteristic
113C2×C5×C4⋊C4C2311yescharacteristic
114C2×C5×C22⋊C4—21no—
115C2×C5×C22⋊C4—21no—
116C2×C5×C22⋊C4—21no—
117C2×C5×C22⋊C4—21no—
118C2×C5×C22⋊C4—21no—
119C2×C5×C22⋊C4D411yescharacteristic
120C2×C5×C22⋊C4D411yescharacteristic
121C2×C42×C5—21no—
122C2×C42×C5C2311yescharacteristic
123C2×C42×C5C2311yescharacteristic
124C2×C22⋊Dic5—21no—
125C2×#689—24no—
126C2×#689C2314yes—
127C2×#688—24no—
128C2×#688C2314yes—
129C2×#687—24no—
130C2×#687C2314yes—
131C2×#686—24no—
132C2×#686C2314yes—
133#4076—22no—
134#4076C2314yes—
135C2×#685—21no—
136C2×#685—21no—
137C2×#685—21no—
138C2×#685—21no—
139C2×C4⋊Dic5—21no—
140C2×C4⋊Dic5C2311yescharacteristic
141C2×C4⋊Dic5C2311yescharacteristic
142#4070—22no—
143#4070C2314yes—
144C2×#683—21no—
145C2×#683—21no—
146C2×C4×Dic5—21no—
147C2×#681—24no—
148C2×#681C2314yes—
149C22×#168—24no—
150C22×#168C2314yes—
151C22×#168C2311yescharacteristic
152C22×#168C2311yescharacteristic
153C22×#168C2311yescharacteristic
154C22×#168C2311yescharacteristic
155#4044—28no—
156#4042—28no—
157#4031—28no—
158#4029—28no—
159#4021—22no—
160#4021C2314yes—
161C4×D20—22no—
162C4×D20C2314yes—
163#4015—22no—
164#4015C2314yes—
165C4×Dic10—22no—
166C4×Dic10C2314yes—
167#3967C2314yes—
168#3967C2314yes—
169#3964C2314yes—
170#3964C2314yes—
171#3942C2314yes—
172#3942C2314yes—
173#3941C2314yes—
174#3941C2314yes—
175#3940C2314yes—
176#3940C2314yes—
177#3940C2314yes—
178#3940C2314yes—
179#3935C2314yes—
180#3935C2314yes—
181C4×#168C2314yes—
182C4×#168C2314yes—
183C2×#542—51no—
184C2×#542D511yescharacteristic, complemented
185#3173—516no—
186C2×#498—51no—
187C2×#495—51no—
188C2×#489—51no—
189C2×#489—51no—
190C2×#470—51no—
191C2×#469—51no—
192C2×#465—51no—
193C2×#465—51no—
194C2×#442—51no—
195C2×#441—51no—
196C2×C4×SD16—51no—
197C2×C4×SD16—51no—
198C2×#405—51no—
199C24×C5—21no—
200C24×C5C2×D411yescharacteristic
201C23×D5—21no—
202C2×C5×Q8—21no—
203C2×C5×Q8—24no—
204C2×C5×Q8—22no—
205C2×C5×Q8—22no—
206C2×C5×Q8—82no—
207C2×C5×Q8C2412yes—
208C2×C5×D4—24no—
209C2×C5×D4—21no—
210C2×C5×D4—22no—
211C2×C5×D4—22no—
212C2×C5×D4—82no—
213C2×C5×D4C2412yes—
214C22×C4×C5—22no—
215C22×C4×C5—22no—
216C22×C4×C5—21no—
217C22×C4×C5—21no—
218C22×C4×C5—21no—
219C22×C4×C5—24no—
220C22×C4×C5—82no—
221C22×C4×C5C2×D411yescharacteristic
222C22×C4×C5C2×D411yescharacteristic
223C22×C4×C5C2×D411yescharacteristic
224C22×C4×C5C2×D411yescharacteristic
225C22×C4×C5C2×D411yescharacteristic
226C22×C4×C5C2×D412yes—
227C22×C4×C5C2412yes—
228C22×C4×C5C2411yescharacteristic
229C2×C22⋊D5—24no—
230C2×C22⋊D5—82no—
231C22×Dic5—21no—
232C22×Dic5—21no—
233C22×Dic5—21no—
234C2×D20—22no—
235C2×D20—22no—
236C2×D20—21no—
237C2×D20C2412yes—
238C2×C4×D5—24no—
239C2×C4×D5—82no—
240C2×Dic10—22no—
241C2×Dic10—22no—
242C2×Dic10—21no—
243C2×Dic10—24no—
244C2×Dic10—82no—
245C2×Dic10C2412yes—
246C5×C4⋊C4—24no—
247C5×C4⋊C4—24no—
248C5×C4⋊C4—24no—
249C5×C4⋊C4—21no—
250C5×C4⋊C4—21no—
251C5×C4⋊C4C2×D414yes—
252C5×C4⋊C4C2×D414yes—
253C5×C4⋊C4C2412yes—
254C5×C4⋊C4C2412yes—
255C5×C22⋊C4—24no—
256C5×C22⋊C4—24no—
257C5×C22⋊C4—24no—
258C5×C22⋊C4—24no—
259C5×C22⋊C4—24no—
260C5×C22⋊C4C2×D414yes—
261C5×C22⋊C4C2×D414yes—
262C42×C5—24no—
263C42×C5C2×D412yes—
264C42×C5C2×D412yes—
265C42×C5C2412yes—
266C42×C5C2412yes—
267C22⋊Dic5—24no—
268#689—28no—
269#688—28no—
270#687—28no—
271#686—28no—
272#685—24no—
273#685—24no—
274#685—24no—
275#685—24no—
276C4⋊Dic5—21no—
277C4⋊Dic5—21no—
278C4⋊Dic5—24no—
279C4⋊Dic5C2412yes—
280C4⋊Dic5C2412yes—
281#683—24no—
282#683—24no—
283C4×Dic5—24no—
284#681—28no—
285C2×#168—22no—
286C2×#168—22no—
287C2×#168—28no—
288C2×#168#4114yes—
289C2×#168#4114yes—
290C2×#168C2412yes—
291C2×#168C2412yes—
292C2×#168C2412yes—
293C2×#168C2412yes—
294C22×Q16—51no—
295C22×SD16—51no—
296C22×SD16—51no—
297C22×D8—51no—
298C22×M16—51no—
299C23×C8—51no—
300#542—24no—
301#542—58no—
302#542—104no—
303#542C2×D518yescomplemented
304C2×C4⋊Q8—51no—
305C2×C4⋊Q8C2×D511yescharacteristic
306C2×#126—21no—
307C2×#126—101no—
308C2×#124—21no—
309C2×#124—51no—
310C2×#124—101no—
311C2×#124C2×D511yescharacteristic
312C2×#123—21no—
313C2×#123—101no—
314C2×C22⋊Q8—21no—
315C2×C22⋊Q8—51no—
316C2×C22⋊Q8—101no—
317C2×C22⋊Q8C2×D511yescharacteristic
318C2×#121—51no—
319C2×#121C2×D511yescharacteristic
320C2×C4×Q8—51no—
321C2×C4×Q8C2×D511yescharacteristic
322C2×C4×D4—51no—
323C2×C4×D4C2×D511yescharacteristic
324C2×#117C2×D511yescharacteristic
325#498—58no—
326#495—58no—
327#489—58no—
328#489—58no—
329#470—58no—
330#469—58no—
331#465—58no—
332#465—58no—
333#442—58no—
334#441—58no—
335C4×SD16—58no—
336C4×SD16—58no—
337C2×#106—51no—
338C2×#106—51no—
339C2×#106—51no—
340C2×#106—51no—
341C2×#103—51no—
342C2×#103—51no—
343C2×#103—51no—
344C2×#103—51no—
345C2×#102—51no—
346C2×#102—51no—
347C2×#102—51no—
348C2×#102—51no—
349#405—58no—
350C2×#97—51no—
351C2×#97—51no—
352C2×C4×C8—51no—
353C2×C4×C8—51no—
354C23×C5—22no—
355C23×C5—22no—
356C23×C5—22no—
357C23×C5—22no—
358C23×C5—42no—
359C23×C5—42no—
360C23×C5—42no—
361C23×C5C22×D412yes—
362C23×C5C22×D411yescharacteristic
363C22×D5—22no—
364C22×D5—42no—
365C22×D5—42no—
366C22×D5—42no—
367C5×Q8—22no—
368C5×Q8—22no—
369C5×Q8—42no—
370C5×Q8—84no—
371C5×D4—22no—
372C5×D4—22no—
373C5×D4—42no—
374C5×D4—84no—
375C2×C4×C5—22no—
376C2×C4×C5—22no—
377C2×C4×C5—22no—
378C2×C4×C5—22no—
379C2×C4×C5—22no—
380C2×C4×C5—24no—
381C2×C4×C5—22no—
382C2×C4×C5—22no—
383C2×C4×C5—22no—
384C2×C4×C5—22no—
385C2×C4×C5—22no—
386C2×C4×C5—42no—
387C2×C4×C5—42no—
388C2×C4×C5—42no—
389C2×C4×C5—84no—
390C2×C4×C5C22×D412yes—
391C2×C4×C5C22×D412yes—
392C2×C4×C5C22×D412yes—
393C2×C4×C5C22×D412yes—
394C2×C4×C5C22×D412yes—
395C2×C4×C5C22×D411yescharacteristic
396C2×C4×C5C2×#4112yes—
397C2×C4×C5C2×#4112yes—
398C2×C4×C5C2511yescharacteristic
399C22⋊D5—84no—
400C2×Dic5—22no—
401C2×Dic5—22no—
402C2×Dic5—22no—
403C2×Dic5—42no—
404C2×Dic5—42no—
405C2×Dic5—42no—
406D20—22no—
407D20—22no—
408D20—42no—
409C4×D5—84no—
410Dic10—22no—
411Dic10—22no—
412Dic10—42no—
413Dic10—84no—
414#168—22no—
415#168—22no—
416#168C2×#4114yes—
417#168C2×#4114yes—
418C22×Q8—21no—
419C22×Q8—51no—
420C22×Q8—101no—
421C22×Q8C22×D511yescharacteristic
422C22×D4—21no—
423C22×D4—51no—
424C22×D4—101no—
425C22×D4C22×D511yescharacteristic
426C23×C4—21no—
427C23×C4—101no—
428C23×C4C22×D511yescharacteristic
429C2×Q16—54no—
430C2×Q16—104no—
431C2×SD16—54no—
432C2×SD16—54no—
433C2×SD16—104no—
434C2×SD16—104no—
435C2×D8—54no—
436C2×D8—104no—
437C2×M16—54no—
438C2×M16—104no—
439C22×C8—51no—
440C22×C8—51no—
441C22×C8—51no—
442C22×C8—54no—
443C22×C8—51no—
444C22×C8—104no—
445C4⋊Q8—22no—
446C4⋊Q8—54no—
447C4⋊Q8—102no—
448C4⋊Q8C22×D514yes—
449#126—28no—
450#126—108no—
451#124—28no—
452#124—22no—
453#124—54no—
454#124—108no—
455#124—102no—
456#124C22×D514yes—
457#123—28no—
458#123—108no—
459C22⋊Q8—22no—
460C22⋊Q8—28no—
461C22⋊Q8—54no—
462C22⋊Q8—102no—
463C22⋊Q8—108no—
464C22⋊Q8C22×D514yes—
465#121—22no—
466#121—54no—
467#121—102no—
468#121C22×D514yes—
469C4×Q8—22no—
470C4×Q8—54no—
471C4×Q8—102no—
472C4×Q8C22×D514yes—
473C4×D4—22no—
474C4×D4—54no—
475C4×D4—102no—
476C4×D4C22×D514yes—
477#117C22⋊D514yes—
478#117C22×D514yes—
479C2×C4⋊C4—21no—
480C2×C4⋊C4—21no—
481C2×C4⋊C4—21no—
482C2×C4⋊C4—51no—
483C2×C4⋊C4—51no—
484C2×C4⋊C4—101no—
485C2×C4⋊C4—101no—
486C2×C4⋊C4—101no—
487C2×C4⋊C4C22⋊D511yescharacteristic
488C2×C4⋊C4C22⋊D511yescharacteristic
489C2×C4⋊C4C22×D511yescharacteristic
490C2×C4⋊C4C22×D511yescharacteristic
491C2×C22⋊C4—21no—
492C2×C22⋊C4—21no—
493C2×C22⋊C4—21no—
494C2×C22⋊C4—21no—
495C2×C22⋊C4—21no—
496C2×C22⋊C4—101no—
497C2×C22⋊C4—101no—
498C2×C22⋊C4—101no—
499C2×C22⋊C4—101no—
500C2×C22⋊C4—101no—
501C2×C22⋊C4C22⋊D511yescharacteristic
502C2×C22⋊C4C22⋊D511yescharacteristic
503C2×C42—21no—
504C2×C42—101no—
505C2×C42C22×D511yescharacteristic
506C2×C42C22×D511yescharacteristic
507#106—54no—
508#106—54no—
509#106—54no—
510#106—54no—
511#103—54no—
512#103—54no—
513#103—54no—
514#103—54no—
515#102—54no—
516#102—54no—
517#102—54no—
518#102—54no—
519#97—54no—
520#97—54no—
521C4×C8—54no—
522C4×C8—54no—
523C22×C5—22no—
524C22×C5—22no—
525C22×C5—22no—
526C22×C5—44no—
527C22×C5—42no—
528C22×C5—42no—
529C22×C5—42no—
530C22×C5—84no—
531C22×C5#53212yes—
532C22×C5#57712yes—
533C22×C5#57712yes—
534C22×C5C23×D411yescharacteristic
535C2×D5—42no—
536C2×D5—42no—
537C2×D5—42no—
538C2×D5—84no—
539C4×C5—22no—
540C4×C5—22no—
541C4×C5—22no—
542C4×C5—22no—
543C4×C5—22no—
544C4×C5—42no—
545C4×C5—42no—
546C4×C5—42no—
547C4×C5#53212yes—
548C4×C5C22×#4111yescharacteristic
549C4×C5C22×#4111yescharacteristic
550Dic5—42no—
551Dic5—42no—
552Dic5—42no—
553C24—21no—
554C24—101no—
555C24C2×C22⋊D511yescharacteristic
556C2×Q8—21no—
557C2×Q8—24no—
558C2×Q8—22no—
559C2×Q8—22no—
560C2×Q8—52no—
561C2×Q8—82no—
562C2×Q8—101no—
563C2×Q8—104no—
564C2×Q8—102no—
565C2×Q8—102no—
566C2×Q8—402no—
567C2×Q8C23×D512yes—
568C2×D4—24no—
569C2×D4—22no—
570C2×D4—22no—
571C2×D4—21no—
572C2×D4—52no—
573C2×D4—82no—
574C2×D4—104no—
575C2×D4—102no—
576C2×D4—102no—
577C2×D4—101no—
578C2×D4—402no—
579C2×D4C23×D512yes—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—24no—
586C22×C4—82no—
587C22×C4—101no—
588C22×C4—101no—
589C22×C4—101no—
590C22×C4—104no—
591C22×C4—402no—
592C22×C4C2×C22⋊D512yes—
593C22×C4C2×C22⋊D511yescharacteristic
594C22×C4C2×C22⋊D511yescharacteristic
595C22×C4C2×C22⋊D511yescharacteristic
596C22×C4C2×C22⋊D511yescharacteristic
597C22×C4C2×C22⋊D511yescharacteristic
598C22×C4C23×D512yes—
599C22×C4C23×D511yescharacteristic
600Q16—108no—
601SD16—108no—
602SD16—108no—
603D8—108no—
604M16—108no—
605C2×C8—54no—
606C2×C8—54no—
607C2×C8—52no—
608C2×C8—52no—
609C2×C8—52no—
610C2×C8—52no—
611C2×C8—108no—
612C2×C8—102no—
613C2×C8—102no—
614C4⋊C4—24no—
615C4⋊C4—24no—
616C4⋊C4—24no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—52no—
620C4⋊C4—52no—
621C4⋊C4—101no—
622C4⋊C4—101no—
623C4⋊C4—104no—
624C4⋊C4—104no—
625C4⋊C4—104no—
626C4⋊C4C2×C22⋊D514yes—
627C4⋊C4C2×C22⋊D514yes—
628C4⋊C4C23×D512yes—
629C4⋊C4C23×D512yes—
630C22⋊C4—24no—
631C22⋊C4—24no—
632C22⋊C4—24no—
633C22⋊C4—24no—
634C22⋊C4—24no—
635C22⋊C4—104no—
636C22⋊C4—104no—
637C22⋊C4—104no—
638C22⋊C4—104no—
639C22⋊C4—104no—
640C22⋊C4C2×C22⋊D514yes—
641C22⋊C4C2×C22⋊D514yes—
642C42—24no—
643C42—104no—
644C42C2×C22⋊D512yes—
645C42C2×C22⋊D512yes—
646C42C23×D512yes—
647C42C23×D512yes—
648C2×C5—42no—
649C2×C5—82no—
650C2×C5#317314yescomplemented
651C2×C5C2×#53211yescharacteristic
652C2×C5C2×#57711yescharacteristic
653C2×C5C2×#57711yescharacteristic
654D5—82no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—102no—
663C23—202no—
664C23—202no—
665C23—202no—
666C23C22×C22⋊D512yes—
667C23C22×C22⋊D511yescharacteristic
668Q8—22no—
669Q8—22no—
670Q8—42no—
671Q8—84no—
672Q8—102no—
673Q8—102no—
674Q8—202no—
675Q8—404no—
676D4—22no—
677D4—22no—
678D4—42no—
679D4—84no—
680D4—102no—
681D4—102no—
682D4—202no—
683D4—404no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—24no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—84no—
699C2×C4—102no—
700C2×C4—102no—
701C2×C4—102no—
702C2×C4—202no—
703C2×C4—202no—
704C2×C4—202no—
705C2×C4—404no—
706C2×C4D5×#4112yes—
707C2×C4D5×#4112yes—
708C2×C4C22×C22⋊D512yes—
709C2×C4C22×C22⋊D512yes—
710C2×C4C22×C22⋊D512yes—
711C2×C4C22×C22⋊D512yes—
712C2×C4C22×C22⋊D512yes—
713C2×C4C22×C22⋊D511yescharacteristic
714C2×C4C24×D511yescharacteristic
715C8—54no—
716C8—54no—
717C8—102no—
718C8—102no—
719C5C2×#317311yescharacteristic, complemented, Sylow
720C22—22no—
721C22—22no—
722C22—22no—
723C22—44no—
724C22—42no—
725C22—42no—
726C22—42no—
727C22—84no—
728C22—202no—
729C22—202no—
730C22—202no—
731C22—404no—
732C22#6616612yes—
733C22#6617012yes—
734C22#6617112yes—
735C22C23×C22⋊D511yescharacteristic
736C4—22no—
737C4—22no—
738C4—22no—
739C4—22no—
740C4—22no—
741C4—42no—
742C4—42no—
743C4—42no—
744C4—202no—
745C4—202no—
746C4—202no—
747C4#6616612yes—
748C4C2×D5×#4111yescharacteristic
749C4C2×D5×#4111yescharacteristic
750C2—42no—
751C2—82no—
752C2—402no—
753C2#1061518714yesdirect product factor
754C2C2×#6616611yescharacteristic
755C2C2×#6617011yescharacteristic
756C2C2×#6617111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×#542C2
socleC23×C5C22×D4
prime radicalC2×#65328C2
hypercenterC2×#542D5
hypocenterC5C2×#3173
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#542

Complements

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

NH ≅ G/Ntype
1. C2×C5×#542C2semidirect
2. C2×#65868C2semidirect
3. #10615187C2direct (N × H)
4. C2×#65368C2semidirect
5. C2×#65378C2semidirect
6. C2×#65348C2semidirect
7. C2×#65344C2semidirect
8. C2×#65341C2semidirect
9. C2×#65337C2semidirect
11. C2×#65330C2semidirect
12. C2×#65319C2semidirect
13. C2×C4×#688C2semidirect
14. C2×C4×#687C2semidirect
15. C2×#65303C2semidirect
16. C2×#65286C2semidirect
18. C5×#542C22semidirect
39. #65868C22semidirect
52. #65378C22semidirect
53. #65368C22semidirect
54. #65348C22semidirect
55. #65344C22semidirect
56. #65341C22semidirect
57. #65337C22semidirect
58. #65330C22semidirect
60. #65319C22semidirect
61. C4×#688C22semidirect
62. C4×#687C22semidirect
63. #65303C22semidirect
64. #65286C22semidirect
184. C2×#542D5semidirect
303. #542C2×D5semidirect
650. C2×C5#3173semidirect
719. C5C2×#3173semidirect
753. C2#10615187direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#5422
C2×#658682
#106151872
C2×#653682
C2×#653782
C2×#653482
C2×#653442
C2×#653412
C2×#653372
C2×#653282
C2×#653302
C2×#653192
C2×C4×#6882
C2×C4×#6872
C2×#653032
C2×#652862
C2×#31735