Finite Group Databasebeta

← C2×#10607101 #12269507

Subgroups — C2×#10607101 #12269507

Order 1280.

3374 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D5×C4⋊C4C211yesmaximal, characteristic, complemented
2C22×C4×D20C211yesmaximal, characteristic
3C2×C5×#387C211yesmaximal, characteristic, complemented
4C2×#65283C211yesmaximal, characteristic, complemented
5C2×#65278C211yesmaximal, characteristic, complemented
6C2×#65278C211yesmaximal, characteristic, complemented
7C2×#65222C211yesmaximal, characteristic, complemented
8#10607101C2116yesmaximal, direct product factor
9C2×#64965C211yesmaximal, characteristic, complemented
10C2×#64954C211yesmaximal, characteristic
11C2×#64954C211yesmaximal, characteristic
12C2×#64957C211yesmaximal, characteristic, complemented
13C2×#64957C211yesmaximal, characteristic, complemented
14C2×#64956C211yesmaximal, characteristic, complemented
15C2×#64950C211yesmaximal, characteristic, complemented
16C2×#64946C211yesmaximal, characteristic, complemented
17C23×D20C2211yescharacteristic
18C23×C4×D5C2211yescharacteristic
19C23×C4×D5C2211yescharacteristic
20C23×C4×D5C2211yescharacteristic
21C23×C4×D5C2211yescharacteristic
22C22×C5×C4⋊C4C2211yescharacteristic
23C22×C5×C4⋊C4C2211yescharacteristic
24C22×C42×C5C2211yescharacteristic
25C22×#685C2211yescharacteristic
26C22×#685C2211yescharacteristic
27C22×#685C2211yescharacteristic
28C22×#685C2211yescharacteristic
29C22×#685C2211yescharacteristic
30C22×#685C2211yescharacteristic
31C22×#685C2211yescharacteristic
32C22×#685C2211yescharacteristic
33C22×C4⋊Dic5C2211yescharacteristic
34C22×C4⋊Dic5C2211yescharacteristic
35C22×C4⋊Dic5C2211yescharacteristic
36C22×#683C2211yescharacteristic
37C22×#683C2211yescharacteristic
38C22×#683C2211yescharacteristic
39C22×#683C2211yescharacteristic
40C22×#683C2211yescharacteristic
41C22×#683C2211yescharacteristic
42C2×D5×C4⋊C4—28no—
43C2×D5×C4⋊C4C2218yescomplemented
44C2×C4×D20—28no—
45C2×C4×D20C2218yes—
46C5×#387C2218yescomplemented
47C2×C5×#95C2211yescharacteristic
48C2×C5×#95C2211yescharacteristic
49C2×C5×#95C2211yescharacteristic
50C2×C5×#95C2211yescharacteristic
51C2×#3963C2211yescharacteristic
52C2×#3963C2211yescharacteristic
53C2×#3963C2211yescharacteristic
54C2×#3963C2211yescharacteristic
55C2×#3963C2211yescharacteristic
56C2×#3963C2211yescharacteristic
57#65283C2218yescomplemented
58#65278C2218yescomplemented
59#65278C2218yescomplemented
60#65222C2218yescomplemented
61#64965C2218yescomplemented
62#64957C2218yescomplemented
63#64957C2218yescomplemented
64#64956C2218yescomplemented
65#64954C2218yes—
66#64954C2218yes—
67#64950C2218yescomplemented
68#64946C2218yescomplemented
69C2×#2579—51nomaximal, Sylow
70C24×D5C2311yescharacteristic
71C24×D5C2311yescharacteristic
72C23×C4×C5C2311yescharacteristic
73C23×C4×C5C2311yescharacteristic
74C23×C4×C5C2311yescharacteristic
75C23×C4×C5C2311yescharacteristic
76C23×C4×C5C2311yescharacteristic
77C23×C4×C5C2311yescharacteristic
78C23×C4×C5C2311yescharacteristic
79C23×Dic5C2311yescharacteristic
80C23×Dic5C2311yescharacteristic
81C23×Dic5C2311yescharacteristic
82C23×Dic5C2311yescharacteristic
83C23×Dic5C2311yescharacteristic
84C23×Dic5C2311yescharacteristic
85C22×D20—24no—
86C22×D20—24no—
87C22×D20Q818yes—
88C22×D20C2314yes—
89C22×C4×D5—24no—
90C22×C4×D5—24no—
91C22×C4×D5—24no—
92C22×C4×D5—24no—
93C22×C4×D5—24no—
94C22×C4×D5—42no—
95C22×C4×D5—42no—
96C22×C4×D5—42no—
97C22×C4×D5—42no—
98C22×C4×D5—42no—
99C22×C4×D5—42no—
100C22×C4×D5D418yes—
101C22×C4×D5C2314yes—
102C22×C4×D5C2314yes—
103C22×C4×D5C2314yes—
104C22×C4×D5C2314yes—
105C2×C5×C4⋊C4—24no—
106C2×C5×C4⋊C4—24no—
107C2×C5×C4⋊C4C2314yes—
108C2×C5×C4⋊C4C2314yes—
109C2×C42×C5—24no—
110C2×C42×C5C2314yes—
111C2×#685—24no—
112C2×#685—24no—
113C2×#685—24no—
114C2×#685—24no—
115C2×#685—24no—
116C2×#685—24no—
117C2×#685—42no—
118C2×#685—42no—
119C2×#685C2314yes—
120C2×#685C2314yes—
121C2×#685C2314yes—
122C2×#685C2314yes—
123C2×#685C2314yes—
124C2×#685C2314yes—
125C2×#685C2314yes—
126C2×#685C2314yes—
127C2×C4⋊Dic5—24no—
128C2×C4⋊Dic5—24no—
129C2×C4⋊Dic5—42no—
130C2×C4⋊Dic5C2314yes—
131C2×C4⋊Dic5C2314yes—
132C2×C4⋊Dic5C2314yes—
133C2×#683—24no—
134C2×#683—24no—
135C2×#683—24no—
136C2×#683—42no—
137C2×#683—42no—
138C2×#683—42no—
139C2×#683C2314yes—
140C2×#683C2314yes—
141C2×#683C2314yes—
142C2×#683C2314yes—
143C2×#683C2314yes—
144C2×#683C2314yes—
145D5×C4⋊C4—232no—
146C4×D20—232no—
147C5×#95C2314yes—
148C5×#95C2314yes—
149C5×#95C2314yes—
150C5×#95C2314yes—
151#3963C2314yes—
152#3963C2314yes—
153#3963C2314yes—
154#3963C2314yes—
155#3963C2314yes—
156#3963C2314yes—
157C22×C4×D4—51no—
158C23×C4⋊C4—51no—
159#2579—516no—
160C2×#398—51no—
161C2×#398—51no—
162C2×#396—51no—
163C2×#396—51no—
164C2×#387—51no—
165C2×#387D511yescharacteristic, complemented
166C2×#386—51no—
167C2×#386—51no—
168C2×#385—51no—
169C2×#385—51no—
170C2×#385—51no—
171C2×#385—51no—
172C2×#380—51no—
173C24×C5C2411yescharacteristic
174C23×D5—22no—
175C23×D5—22no—
176C23×D5—22no—
177C23×D5—22no—
178C23×D5—22no—
179C23×D5—22no—
180C23×D5—22no—
181C23×D5—22no—
182C23×D5—22no—
183C23×D5—22no—
184C23×D5C2×D414yes—
185C23×D5C2×Q814yes—
186C23×D5C2×Q814yes—
187C23×D5#4114yes—
188C23×D5C2412yes—
189C23×D5C2412yes—
190C22×C4×C5—22no—
191C22×C4×C5—22no—
192C22×C4×C5—22no—
193C22×C4×C5—22no—
194C22×C4×C5—22no—
195C22×C4×C5—22no—
196C22×C4×C5—22no—
197C22×C4×C5—22no—
198C22×C4×C5—22no—
199C22×C4×C5—22no—
200C22×C4×C5—22no—
201C22×C4×C5—22no—
202C22×C4×C5—22no—
203C22×C4×C5—22no—
204C22×C4×C5—22no—
205C22×C4×C5—22no—
206C22×C4×C5—22no—
207C22×C4×C5—22no—
208C22×C4×C5C2×D414yes—
209C22×C4×C5C2×Q814yes—
210C22×C4×C5#4114yes—
211C22×C4×C5C2412yes—
212C22×C4×C5C2412yes—
213C22×C4×C5C2412yes—
214C22×C4×C5C2412yes—
215C22×C4×C5C2412yes—
216C22×C4×C5C2412yes—
217C22×C4×C5C2412yes—
218C22×Dic5—22no—
219C22×Dic5—22no—
220C22×Dic5—22no—
221C22×Dic5—22no—
222C22×Dic5—22no—
223C22×Dic5—22no—
224C22×Dic5—22no—
225C22×Dic5—22no—
226C22×Dic5—22no—
227C22×Dic5—22no—
228C22×Dic5—22no—
229C22×Dic5—22no—
230C22×Dic5—22no—
231C22×Dic5—22no—
232C22×Dic5—22no—
233C22×Dic5—22no—
234C22×Dic5C2×D414yes—
235C22×Dic5#4114yes—
236C22×Dic5C2412yes—
237C22×Dic5C2412yes—
238C22×Dic5C2412yes—
239C22×Dic5C2412yes—
240C22×Dic5C2412yes—
241C22×Dic5C2412yes—
242C2×D20—232no—
243C2×D20—28no—
244C2×D20—28no—
245C2×D20C2×Q8116yes—
246C2×C4×D5—232no—
247C2×C4×D5—28no—
248C2×C4×D5—28no—
249C2×C4×D5—28no—
250C2×C4×D5—28no—
251C2×C4×D5—28no—
252C2×C4×D5—416no—
253C2×C4×D5—44no—
254C2×C4×D5—44no—
255C2×C4×D5—44no—
256C2×C4×D5—44no—
257C2×C4×D5—44no—
258C2×C4×D5—44no—
259C2×C4×D5—416no—
260C2×C4×D5—416no—
261C2×C4×D5C2×D4116yes—
262C5×C4⋊C4—28no—
263C5×C4⋊C4—28no—
264C42×C5—28no—
265#685—28no—
266#685—28no—
267#685—28no—
268#685—28no—
269#685—28no—
270#685—28no—
271#685—44no—
272#685—44no—
273C4⋊Dic5—28no—
274C4⋊Dic5—28no—
275C4⋊Dic5—44no—
276#683—28no—
277#683—28no—
278#683—28no—
279#683—44no—
280#683—44no—
281#683—44no—
282C23×D4—51no—
283C24×C4—51no—
284C24×C4—51no—
285C24×C4—51no—
286C24×C4—51no—
287C2×C4×D4—58no—
288C2×C4×D4—108no—
289C22×C4⋊C4—51no—
290C22×C4⋊C4—51no—
291C22×C4⋊C4—51no—
292C22×C4⋊C4—51no—
293C22×C4⋊C4—51no—
294C22×C4⋊C4—51no—
295C22×C4⋊C4—51no—
296C22×C4⋊C4—51no—
297C22×C4⋊C4—51no—
298C22×C4⋊C4—58no—
299C22×C4⋊C4—108no—
300C22×C4⋊C4C2×D511yescharacteristic
301C22×C4⋊C4C2×D511yescharacteristic
302C22×C22⋊C4—51no—
303C22×C22⋊C4—51no—
304C22×C22⋊C4—51no—
305C22×C22⋊C4—51no—
306C22×C22⋊C4—51no—
307C22×C22⋊C4—51no—
308C22×C22⋊C4—51no—
309C22×C22⋊C4—51no—
310C22×C42C2×D511yescharacteristic
311#398—58no—
312#398—58no—
313#396—58no—
314#396—58no—
315#387—58no—
316#387C2×D518yescomplemented
317#386—58no—
318#386—58no—
319#385—58no—
320#385—58no—
321#385—58no—
322#385—58no—
323#380—58no—
324C2×#95—51no—
325C2×#95—51no—
326C2×#95—51no—
327C2×#95—51no—
328C2×#95—51no—
329C2×#95—51no—
330C2×#95C2×D511yescharacteristic
331C2×#95C2×D511yescharacteristic
332C2×#95C2×D511yescharacteristic
333C2×#95C2×D511yescharacteristic
334C23×C5C22×D412yes—
335C23×C5C22×Q812yes—
336C23×C5C2×#4112yes—
337C23×C5C2×#4112yes—
338C23×C5C2×#4112yes—
339C23×C5H(5,𝔽2)12yes—
340C23×C5H(5,𝔽2)12yes—
341C23×C5C2511yescharacteristic
342C22×D5—28no—
343C22×D5—28no—
344C22×D5—28no—
345C22×D5—28no—
346C22×D5—28no—
347C22×D5—28no—
348C22×D5—22no—
349C22×D5—22no—
350C22×D5—22no—
351C22×D5—22no—
352C22×D5—28no—
353C22×D5—28no—
354C22×D5—28no—
355C22×D5—22no—
356C22×D5—22no—
357C22×D5—22no—
358C22×D5—22no—
359C22×D5—22no—
360C22×D5—22no—
361C22×D5—44no—
362C22×D5—44no—
363C22×D5—44no—
364C22×D5—44no—
365C22×D5C22⋊Q8116yes—
366C22×D5C22×D414yes—
367C22×D5C22×Q814yes—
368C22×D5C22×Q814yes—
369C22×D5C2×#4114yes—
370C2×C4×C5—28no—
371C2×C4×C5—28no—
372C2×C4×C5—28no—
373C2×C4×C5—22no—
374C2×C4×C5—22no—
375C2×C4×C5—22no—
376C2×C4×C5—22no—
377C2×C4×C5—22no—
378C2×C4×C5—22no—
379C2×C4×C5—22no—
380C2×C4×C5—22no—
381C2×C4×C5—22no—
382C2×C4×C5—22no—
383C2×C4×C5—22no—
384C2×C4×C5—22no—
385C2×C4×C5—22no—
386C2×C4×C5—22no—
387C2×C4×C5—22no—
388C2×C4×C5—22no—
389C2×C4×C5—22no—
390C2×C4×C5—22no—
391C2×C4×C5—44no—
392C2×C4×C5—44no—
393C2×C4×C5—44no—
394C2×C4×C5—44no—
395C2×C4×C5C22×D414yes—
396C2×C4×C5C22×Q814yes—
397C2×C4×C5C2×#4114yes—
398C2×Dic5—28no—
399C2×Dic5—28no—
400C2×Dic5—22no—
401C2×Dic5—22no—
402C2×Dic5—22no—
403C2×Dic5—22no—
404C2×Dic5—22no—
405C2×Dic5—22no—
406C2×Dic5—22no—
407C2×Dic5—22no—
408C2×Dic5—22no—
409C2×Dic5—22no—
410C2×Dic5—22no—
411C2×Dic5—22no—
412C2×Dic5—22no—
413C2×Dic5—22no—
414C2×Dic5—22no—
415C2×Dic5—22no—
416C2×Dic5—44no—
417C2×Dic5—44no—
418C2×Dic5—44no—
419C2×Dic5—44no—
420C2×Dic5C22×D414yes—
421C2×Dic5C2×#4114yes—
422D20—232no—
423C4×D5—232no—
424C4×D5—416no—
425C4×D5—416no—
426C4×D5—416no—
427C25—51no—
428C25—51no—
429C22×D4—58no—
430C22×D4—54no—
431C22×D4—104no—
432C22×D4—104no—
433C23×C4—51no—
434C23×C4—51no—
435C23×C4—58no—
436C23×C4—54no—
437C23×C4—51no—
438C23×C4—51no—
439C23×C4—51no—
440C23×C4—51no—
441C23×C4—54no—
442C23×C4—54no—
443C23×C4—54no—
444C23×C4—104no—
445C23×C4—104no—
446C23×C4—104no—
447C23×C4—104no—
448C23×C4—104no—
449C23×C4—202no—
450C23×C4—202no—
451C23×C4—202no—
452C23×C4—202no—
453C23×C4—202no—
454C23×C4—202no—
455C23×C4C22×D511yescharacteristic
456C23×C4C22×D511yescharacteristic
457C23×C4C22×D511yescharacteristic
458C23×C4C22×D511yescharacteristic
459C23×C4C22×D511yescharacteristic
460C23×C4C22×D511yescharacteristic
461C23×C4C22×D511yescharacteristic
462C4×D4—1032no—
463C2×C4⋊C4—24no—
464C2×C4⋊C4—24no—
465C2×C4⋊C4—54no—
466C2×C4⋊C4—54no—
467C2×C4⋊C4—54no—
468C2×C4⋊C4—54no—
469C2×C4⋊C4—54no—
470C2×C4⋊C4—54no—
471C2×C4⋊C4—54no—
472C2×C4⋊C4—54no—
473C2×C4⋊C4—54no—
474C2×C4⋊C4—1032no—
475C2×C4⋊C4—104no—
476C2×C4⋊C4—104no—
477C2×C4⋊C4—104no—
478C2×C4⋊C4—104no—
479C2×C4⋊C4—104no—
480C2×C4⋊C4—202no—
481C2×C4⋊C4—202no—
482C2×C4⋊C4—202no—
483C2×C4⋊C4—202no—
484C2×C4⋊C4C22×D514yes—
485C2×C4⋊C4C22×D514yes—
486C2×C22⋊C4—54no—
487C2×C22⋊C4—54no—
488C2×C22⋊C4—54no—
489C2×C22⋊C4—54no—
490C2×C22⋊C4—54no—
491C2×C22⋊C4—54no—
492C2×C22⋊C4—54no—
493C2×C22⋊C4—54no—
494C2×C22⋊C4—104no—
495C2×C22⋊C4—104no—
496C2×C22⋊C4—104no—
497C2×C22⋊C4—104no—
498C2×C22⋊C4—104no—
499C2×C22⋊C4—104no—
500C2×C22⋊C4—202no—
501C2×C22⋊C4—202no—
502C2×C42—24no—
503C2×C42C22×D514yes—
504#95—54no—
505#95—54no—
506#95—54no—
507#95—54no—
508#95—54no—
509#95—54no—
510#95C22×D514yes—
511#95C22×D514yes—
512#95C22×D514yes—
513#95C22×D514yes—
514C22×C5C2×C22⋊Q814yes—
515C22×C5#52514yes—
516C22×C5#53414yes—
517C22×C5#55314yes—
518C22×C5#55314yes—
519C22×C5#55414yes—
520C22×C5#55414yes—
521C22×C5C23×D411yescharacteristic
522C22×C5C23×Q811yescharacteristic
523C22×C5C22×#4111yescharacteristic
524C22×C5C22×#4111yescharacteristic
525C22×C5C22×#4111yescharacteristic
526C22×C5C2×H(5,𝔽2)11yescharacteristic
527C22×C5C2×H(5,𝔽2)11yescharacteristic
528C2×D5—232no—
529C2×D5—24no—
530C2×D5—24no—
531C2×D5—24no—
532C2×D5—24no—
533C2×D5—24no—
534C2×D5—24no—
535C2×D5—24no—
536C2×D5—24no—
537C2×D5—24no—
538C2×D5—416no—
539C2×D5—42no—
540C2×D5—42no—
541C2×D5—42no—
542C2×D5—42no—
543C2×D5C2×C22⋊Q818yes—
544C4×C5—24no—
545C4×C5—24no—
546C4×C5—24no—
547C4×C5—42no—
548C4×C5—42no—
549C4×C5—42no—
550C4×C5—42no—
551Dic5—24no—
552Dic5—24no—
553Dic5—42no—
554Dic5—42no—
555Dic5—42no—
556Dic5—42no—
557C24—54no—
558C24—54no—
559C24—54no—
560C24—52no—
561C24—54no—
562C24—52no—
563C24—102no—
564C24—102no—
565C24—102no—
566C24—102no—
567C24—102no—
568C24—102no—
569C24—102no—
570C24—102no—
571C24—102no—
572C24—102no—
573C24C23×D511yescharacteristic
574C2×D4—516no—
575C2×D4—108no—
576C2×D4—1032no—
577C2×D4—108no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—54no—
597C22×C4—54no—
598C22×C4—52no—
599C22×C4—52no—
600C22×C4—516no—
601C22×C4—52no—
602C22×C4—52no—
603C22×C4—52no—
604C22×C4—52no—
605C22×C4—108no—
606C22×C4—108no—
607C22×C4—1032no—
608C22×C4—108no—
609C22×C4—102no—
610C22×C4—102no—
611C22×C4—102no—
612C22×C4—102no—
613C22×C4—108no—
614C22×C4—102no—
615C22×C4—102no—
616C22×C4—102no—
617C22×C4—102no—
618C22×C4—102no—
619C22×C4—102no—
620C22×C4—102no—
621C22×C4—102no—
622C22×C4—102no—
623C22×C4—102no—
624C22×C4—102no—
625C22×C4—102no—
626C22×C4—108no—
627C22×C4—2016no—
628C22×C4—204no—
629C22×C4—204no—
630C22×C4—204no—
631C22×C4—204no—
632C22×C4—204no—
633C22×C4—204no—
634C22×C4—2016no—
635C22×C4—2016no—
636C22×C4#70914yes—
637C22×C4D4×D514yes—
638C22×C4Q8×D514yes—
639C22×C4C23×D512yes—
640C22×C4C23×D512yes—
641C22×C4C23×D512yes—
642C22×C4C23×D512yes—
643C22×C4C23×D512yes—
644C22×C4C23×D512yes—
645C22×C4C23×D512yes—
646C4⋊C4—28no—
647C4⋊C4—28no—
648C4⋊C4—108no—
649C4⋊C4—108no—
650C4⋊C4—108no—
651C4⋊C4—108no—
652C4⋊C4—108no—
653C4⋊C4—204no—
654C4⋊C4—204no—
655C4⋊C4—204no—
656C4⋊C4—204no—
657C22⋊C4—108no—
658C22⋊C4—108no—
659C22⋊C4—108no—
660C22⋊C4—108no—
661C22⋊C4—108no—
662C22⋊C4—108no—
663C22⋊C4—204no—
664C22⋊C4—204no—
665C42—28no—
666C2×C5#257918yescomplemented
667C2×C5C22×C22⋊Q811yescharacteristic
668C2×C5C2×#52511yescharacteristic
669C2×C5C2×#53411yescharacteristic
670C2×C5C2×#55311yescharacteristic
671C2×C5C2×#55311yescharacteristic
672C2×C5C2×#55411yescharacteristic
673C2×C5C2×#55411yescharacteristic
674D5—28no—
675D5—44no—
676C23—516no—
677C23—54no—
678C23—54no—
679C23—54no—
680C23—54no—
681C23—108no—
682C23—108no—
683C23—108no—
684C23—108no—
685C23—102no—
686C23—108no—
687C23—102no—
688C23—102no—
689C23—102no—
690C23—108no—
691C23—108no—
692C23—108no—
693C23—102no—
694C23—102no—
695C23—108no—
696C23—102no—
697C23—102no—
698C23—102no—
699C23—102no—
700C23—204no—
701C23—204no—
702C23—204no—
703C23—204no—
704C23C2×#70912yes—
705C23C2×D4×D512yes—
706C23C2×Q8×D512yes—
707C23D5×#4112yes—
708C23D5×#4112yes—
709C23#414912yes—
710C23#414912yes—
711C23C24×D511yescharacteristic
712D4—1032no—
713C2×C4—28no—
714C2×C4—28no—
715C2×C4—28no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—44no—
735C2×C4—44no—
736C2×C4—44no—
737C2×C4—44no—
738C2×C4—54no—
739C2×C4—54no—
740C2×C4—1032no—
741C2×C4—108no—
742C2×C4—108no—
743C2×C4—102no—
744C2×C4—102no—
745C2×C4—102no—
746C2×C4—102no—
747C2×C4—102no—
748C2×C4—102no—
749C2×C4—102no—
750C2×C4—102no—
751C2×C4—102no—
752C2×C4—102no—
753C2×C4—102no—
754C2×C4—102no—
755C2×C4—102no—
756C2×C4—102no—
757C2×C4—102no—
758C2×C4—102no—
759C2×C4—2016no—
760C2×C4—2016no—
761C2×C4—2016no—
762C2×C4—204no—
763C2×C4—204no—
764C2×C4—204no—
765C2×C4—204no—
766C2×C4C2×#70914yes—
767C2×C4C2×D4×D514yes—
768C2×C4C2×Q8×D514yes—
769C5C2×#257911yescharacteristic, complemented, Sylow
770C22—58no—
771C22—104no—
772C22—104no—
773C22—104no—
774C22—104no—
775C22—104no—
776C22—104no—
777C22—1032no—
778C22—104no—
779C22—104no—
780C22—104no—
781C22—202no—
782C22—202no—
783C22—202no—
784C22—202no—
785C22—2016no—
786C22#6586414yes—
787C22#6588114yes—
788C22#6591314yes—
789C22D5×C22⋊Q814yes—
790C22#6598714yes—
791C22#6602414yes—
792C22#6604314yes—
793C22C22×#70911yescharacteristic
794C22C22×D4×D511yescharacteristic
795C22C22×Q8×D511yescharacteristic
796C22C2×D5×#4111yescharacteristic
797C22C2×D5×#4111yescharacteristic
798C22C2×#414911yescharacteristic
799C22C2×#414911yescharacteristic
800C4—24no—
801C4—24no—
802C4—24no—
803C4—42no—
804C4—42no—
805C4—42no—
806C4—42no—
807C4—104no—
808C4—104no—
809C4—202no—
810C4—202no—
811C4—202no—
812C4—202no—
813C2—108no—
814C2—204no—
815C2#1060710118yesdirect product factor
816C2C2×#6586411yescharacteristic
817C2C2×#6588111yescharacteristic
818C2C2×#6591311yescharacteristic
819C2C2×D5×C22⋊Q811yescharacteristic
820C2C2×#6598711yescharacteristic
821C2C2×#6602411yescharacteristic
822C2C2×#6604311yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC2×C5×#387C2
socleC24×C5C24
prime radicalC23×D20C22
hypercenterC2×#387D5
hypocenterC5C2×#2579
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
1. C22×D5×C4⋊C4C2semidirect
3. C2×C5×#387C2semidirect
4. C2×#65283C2semidirect
5. C2×#65278C2semidirect
6. C2×#65278C2semidirect
7. C2×#65222C2semidirect
8. #10607101C2direct (N × H)
9. C2×#64965C2semidirect
12. C2×#64957C2semidirect
13. C2×#64957C2semidirect
14. C2×#64956C2semidirect
15. C2×#64950C2semidirect
16. C2×#64946C2semidirect
43. C2×D5×C4⋊C4C22semidirect
46. C5×#387C22semidirect
57. #65283C22semidirect
58. #65278C22semidirect
59. #65278C22semidirect
60. #65222C22semidirect
61. #64965C22semidirect
62. #64957C22semidirect
63. #64957C22semidirect
64. #64956C22semidirect
67. #64950C22semidirect
68. #64946C22semidirect
165. C2×#387D5semidirect
316. #387C2×D5semidirect
666. C2×C5#2579semidirect
769. C5C2×#2579semidirect
815. C2#10607101direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D5×C4⋊C42
C22×C4×D202
C2×C5×#3872
C2×#652832
C2×#652782
C2×#652222
#106071012
C2×#649652
C2×#649542
C2×#649572
C2×#649562
C2×#649502
C2×#649462
C2×#25795