Finite Group Databasebeta

← C2×#10609035 #12266923

Subgroups — C2×#10609035 #12266923

Order 1280.

3114 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D5×C4⋊C4C211yesmaximal, characteristic, complemented
2C22×#4025C211yesmaximal, characteristic, complemented
3C2×C5×#396C211yesmaximal, characteristic, complemented
4C2×#65278C211yesmaximal, characteristic, complemented
5C2×#65276C211yesmaximal, characteristic, complemented
6C2×#65275C211yesmaximal, characteristic, complemented
7C2×#65267C211yesmaximal, characteristic, complemented
8C2×#65270C211yesmaximal, characteristic, complemented
9C2×#65245C211yesmaximal, characteristic
10C2×#65245C211yesmaximal, characteristic
11C2×#65245C211yesmaximal, characteristic
12C2×#65241C211yesmaximal, characteristic, complemented
13C2×#65240C211yesmaximal, characteristic, complemented
14#10609035C2116yesmaximal, direct product factor
15C2×#64947C211yesmaximal, characteristic, complemented
16C2×#64955C211yesmaximal, characteristic, complemented
17C23×C22⋊D5C2211yescharacteristic
18C23×C4×D5C2211yescharacteristic
19C23×C4×D5C2211yescharacteristic
20C23×C4×D5C2211yescharacteristic
21C22×C5×C4⋊C4C2211yescharacteristic
22C22×C5×C4⋊C4C2211yescharacteristic
23C22×C5×C4⋊C4C2211yescharacteristic
24C22×C5×C22⋊C4C2211yescharacteristic
25C22×C5×C22⋊C4C2211yescharacteristic
26C22×C5×C22⋊C4C2211yescharacteristic
27C22×C22⋊Dic5C2211yescharacteristic
28C22×C22⋊Dic5C2211yescharacteristic
29C22×C22⋊Dic5C2211yescharacteristic
30C22×#685C2211yescharacteristic
31C22×#685C2211yescharacteristic
32C22×#685C2211yescharacteristic
33C22×C4⋊Dic5C2211yescharacteristic
34C22×C4⋊Dic5C2211yescharacteristic
35C22×#683C2211yescharacteristic
36C22×#683C2211yescharacteristic
37C22×#683C2211yescharacteristic
38C22×C4×Dic5C2211yescharacteristic
39C22×C4×Dic5C2211yescharacteristic
40C2×D5×C4⋊C4—28no—
41C2×D5×C4⋊C4C2218yescomplemented
42C2×#4025—28no—
43C2×#4025C2218yescomplemented
44C5×#396C2218yescomplemented
45C2×C5×#95C2211yescharacteristic
46C2×#3963C2211yescharacteristic
47C2×#3963C2211yescharacteristic
48C2×#3963C2211yescharacteristic
49C2×#3963C2211yescharacteristic
50C2×#3963C2211yescharacteristic
51C2×#3963C2211yescharacteristic
52C2×#3963C2211yescharacteristic
53C2×#3963C2211yescharacteristic
54C2×#3963C2211yescharacteristic
55C2×#3963C2211yescharacteristic
56C2×#3963C2211yescharacteristic
57#65278C2218yescomplemented
58#65276C2218yescomplemented
59#65275C2218yescomplemented
60#65270C2218yescomplemented
61#65267C2218yescomplemented
62#65245C2218yes—
63#65245C2218yes—
64#65245C2218yes—
65#65241C2218yescomplemented
66#65240C2218yescomplemented
67#64955C2218yescomplemented
68#64947C2218yescomplemented
69C2×#2481—51nomaximal, Sylow
70C25×C5C2311yescharacteristic
71C24×D5C2311yescharacteristic
72C23×C4×C5C2311yescharacteristic
73C23×C4×C5C2311yescharacteristic
74C23×C4×C5C2311yescharacteristic
75C23×C4×C5C2311yescharacteristic
76C23×C4×C5C2311yescharacteristic
77C23×C4×C5C2311yescharacteristic
78C22×C22⋊D5—24no—
79C22×C22⋊D5—24no—
80C22×C22⋊D5—24no—
81C22×C22⋊D5C2314yes—
82C23×Dic5C2311yescharacteristic
83C23×Dic5C2311yescharacteristic
84C23×Dic5C2311yescharacteristic
85C23×Dic5C2311yescharacteristic
86C23×Dic5C2311yescharacteristic
87C23×Dic5C2311yescharacteristic
88C23×Dic5C2311yescharacteristic
89C22×C4×D5—24no—
90C22×C4×D5—24no—
91C22×C4×D5—24no—
92C22×C4×D5—24no—
93C22×C4×D5—24no—
94C22×C4×D5—24no—
95C22×C4×D5—24no—
96C22×C4×D5—42no—
97C22×C4×D5—42no—
98C22×C4×D5C2314yes—
99C22×C4×D5C2314yes—
100C22×C4×D5C2314yes—
101C2×C5×C4⋊C4—24no—
102C2×C5×C4⋊C4—24no—
103C2×C5×C4⋊C4—42no—
104C2×C5×C4⋊C4C2314yes—
105C2×C5×C4⋊C4C2314yes—
106C2×C5×C4⋊C4C2314yes—
107C2×C5×C22⋊C4—24no—
108C2×C5×C22⋊C4—24no—
109C2×C5×C22⋊C4—42no—
110C2×C5×C22⋊C4C2314yes—
111C2×C5×C22⋊C4C2314yes—
112C2×C5×C22⋊C4C2314yes—
113C2×C22⋊Dic5—24no—
114C2×C22⋊Dic5—24no—
115C2×C22⋊Dic5—42no—
116C2×C22⋊Dic5C2314yes—
117C2×C22⋊Dic5C2314yes—
118C2×C22⋊Dic5C2314yes—
119C2×#685—24no—
120C2×#685—24no—
121C2×#685—24no—
122C2×#685C2314yes—
123C2×#685C2314yes—
124C2×#685C2314yes—
125C2×C4⋊Dic5—24no—
126C2×C4⋊Dic5—24no—
127C2×C4⋊Dic5C2314yes—
128C2×C4⋊Dic5C2314yes—
129C2×#683—24no—
130C2×#683—24no—
131C2×#683D418yescomplemented
132C2×#683C2314yes—
133C2×#683C2314yes—
134C2×#683C2314yes—
135C2×C4×Dic5—24no—
136C2×C4×Dic5—42no—
137C2×C4×Dic5C2314yes—
138C2×C4×Dic5C2314yes—
139D5×C4⋊C4—232no—
140#4025—232no—
141C5×#95C2314yes—
142#3963C2314yes—
143#3963C2314yes—
144#3963C2314yes—
145#3963C2314yes—
146#3963C2314yes—
147#3963C2314yes—
148#3963C2314yes—
149#3963C2314yes—
150#3963C2314yes—
151#3963C2314yes—
152#3963C2314yes—
153C22×#126—51no—
154C23×C4⋊C4—51no—
155#2481—516no—
156C2×#400—51no—
157C2×#400—51no—
158C2×#397—51no—
159C2×#396D511yescharacteristic, complemented
160C2×#388—51no—
161C2×#387—51no—
162C2×#387—51no—
163C2×#386—51no—
164C2×#386—51no—
165C2×#386—51no—
166C2×#385—51no—
167C2×#380—51no—
168C2×C4×C22⋊C4—51no—
169C24×C5—22no—
170C24×C5—22no—
171C24×C5—22no—
172C24×C5—22no—
173C24×C5—22no—
174C24×C5—22no—
175C24×C5—22no—
176C24×C5C2412yes—
177C24×C5C2411yescharacteristic
178C23×D5—22no—
179C23×D5—22no—
180C23×D5—22no—
181C23×D5—22no—
182C23×D5#4114yes—
183C23×D5#4114yes—
184C23×D5#4114yes—
185C23×D5C2412yes—
186C22×C4×C5—22no—
187C22×C4×C5—22no—
188C22×C4×C5—22no—
189C22×C4×C5—22no—
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×C5C2×D414yes—
203C22×C4×C5#4114yes—
204C22×C4×C5C2412yes—
205C22×C4×C5C2412yes—
206C22×C4×C5C2412yes—
207C22×C4×C5C2412yes—
208C22×C4×C5C2412yes—
209C22×C4×C5C2412yes—
210C2×C22⋊D5—28no—
211C2×C22⋊D5—28no—
212C2×C22⋊D5—28no—
213C2×C22⋊D5—416no—
214C22×Dic5—22no—
215C22×Dic5—22no—
216C22×Dic5—22no—
217C22×Dic5—22no—
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×Dic5C2×D414yes—
234C22×Dic5C2×D414yes—
235C22×Dic5C2412yes—
236C22×Dic5C2412yes—
237C22×Dic5C2412yes—
238C22×Dic5C2412yes—
239C22×Dic5C2412yes—
240C22×Dic5C2412yes—
241C22×Dic5C2412yes—
242C2×C4×D5—232no—
243C2×C4×D5—28no—
244C2×C4×D5—28no—
245C2×C4×D5—28no—
246C2×C4×D5—28no—
247C2×C4×D5—28no—
248C2×C4×D5—28no—
249C2×C4×D5—28no—
250C2×C4×D5—44no—
251C2×C4×D5—44no—
252C2×C4×D5—416no—
253C2×C4×D5—416no—
254C5×C4⋊C4—28no—
255C5×C4⋊C4—28no—
256C5×C4⋊C4—44no—
257C5×C22⋊C4—28no—
258C5×C22⋊C4—28no—
259C5×C22⋊C4—44no—
260C22⋊Dic5—28no—
261C22⋊Dic5—28no—
262C22⋊Dic5—44no—
263#685—28no—
264#685—28no—
265#685—28no—
266C4⋊Dic5—28no—
267C4⋊Dic5—28no—
268#683—28no—
269#683—28no—
270#683C2×D4116yescomplemented
271C4×Dic5—28no—
272C4×Dic5—44no—
273C23×D4—51no—
274C24×C4—51no—
275C24×C4—51no—
276C24×C4—51no—
277C2×#126—58no—
278C2×#126—108no—
279C22×C4⋊C4—51no—
280C22×C4⋊C4—51no—
281C22×C4⋊C4—51no—
282C22×C4⋊C4—51no—
283C22×C4⋊C4—51no—
284C22×C4⋊C4—58no—
285C22×C4⋊C4—108no—
286C22×C4⋊C4C2×D511yescharacteristic
287C22×C4⋊C4C2×D511yescharacteristic
288C22×C4⋊C4C2×D511yescharacteristic
289C22×C22⋊C4—51no—
290C22×C22⋊C4—51no—
291C22×C22⋊C4—51no—
292C22×C22⋊C4—51no—
293C22×C22⋊C4—51no—
294C22×C22⋊C4—51no—
295C22×C22⋊C4C2×D511yescharacteristic
296C22×C22⋊C4C2×D511yescharacteristic
297C22×C22⋊C4C2×D511yescharacteristic
298C22×C42—51no—
299C22×C42—51no—
300#400—58no—
301#400—58no—
302#397—58no—
303#396C2×D518yescomplemented
304#388—58no—
305#387—58no—
306#387—58no—
307#386—58no—
308#386—58no—
309#386—58no—
310#385—58no—
311#380—58no—
312C4×C22⋊C4—58no—
313C2×#95—51no—
314C2×#95—51no—
315C2×#95—51no—
316C2×#95—51no—
317C2×#95—51no—
318C2×#95—51no—
319C2×#95—51no—
320C2×#95—51no—
321C2×#95—51no—
322C2×#95—51no—
323C2×#95—51no—
324C2×#95C2×D511yescharacteristic
325C23×C5—22no—
326C23×C5—22no—
327C23×C5—22no—
328C23×C5—22no—
329C23×C5—22no—
330C23×C5—22no—
331C23×C5—22no—
332C23×C5—44no—
333C23×C5—44no—
334C23×C5—44no—
335C23×C5—44no—
336C23×C5—44no—
337C23×C5—44no—
338C23×C5—44no—
339C23×C5C22×D412yes—
340C23×C5C2×#4112yes—
341C23×C5C2×#4112yes—
342C23×C5C2×#4112yes—
343C23×C5C2×#4112yes—
344C23×C5H(5,𝔽2)12yes—
345C23×C52−1+412yes—
346C23×C5C2511yescharacteristic
347C22×D5—28no—
348C22×D5—28no—
349C22×D5—28no—
350C22×D5—28no—
351C22×D5—28no—
352C22×D5—28no—
353C22×D5—22no—
354C22×D5—22no—
355C22×D5—22no—
356C22×D5—22no—
357C22×D5#126116yescomplemented
358C22×D5C2×#4114yes—
359C22×D5C2×#4114yes—
360C22×D5C2×#4114yes—
361C2×C4×C5—28no—
362C2×C4×C5—28no—
363C2×C4×C5—22no—
364C2×C4×C5—22no—
365C2×C4×C5—22no—
366C2×C4×C5—22no—
367C2×C4×C5—22no—
368C2×C4×C5—22no—
369C2×C4×C5—22no—
370C2×C4×C5—22no—
371C2×C4×C5—22no—
372C2×C4×C5—22no—
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—44no—
380C2×C4×C5—44no—
381C2×C4×C5—44no—
382C2×C4×C5—44no—
383C2×C4×C5C22×D414yes—
384C2×C4×C5C2×#4114yes—
385C22⋊D5—416no—
386C2×Dic5—28no—
387C2×Dic5—28no—
388C2×Dic5—22no—
389C2×Dic5—22no—
390C2×Dic5—22no—
391C2×Dic5—22no—
392C2×Dic5—22no—
393C2×Dic5—22no—
394C2×Dic5—22no—
395C2×Dic5—22no—
396C2×Dic5—22no—
397C2×Dic5—22no—
398C2×Dic5—22no—
399C2×Dic5—22no—
400C2×Dic5—22no—
401C2×Dic5—22no—
402C2×Dic5—22no—
403C2×Dic5—22no—
404C2×Dic5—22no—
405C2×Dic5—22no—
406C2×Dic5—22no—
407C2×Dic5—44no—
408C2×Dic5—44no—
409C2×Dic5—44no—
410C2×Dic5—44no—
411C2×Dic5—44no—
412C2×Dic5C22×D414yes—
413C2×Dic5C22×D414yes—
414C4×D5—232no—
415C4×D5—416no—
416C4×D5—416no—
417C25—51no—
418C25C22×D511yescharacteristic
419C22×D4—54no—
420C22×D4—104no—
421C22×D4—104no—
422C22×D4—104no—
423C23×C4—51no—
424C23×C4—51no—
425C23×C4—51no—
426C23×C4—51no—
427C23×C4—51no—
428C23×C4—51no—
429C23×C4—51no—
430C23×C4—54no—
431C23×C4—54no—
432C23×C4—54no—
433C23×C4—104no—
434C23×C4—104no—
435C23×C4—104no—
436C23×C4—104no—
437C23×C4—104no—
438C23×C4—104no—
439C23×C4—104no—
440C23×C4—202no—
441C23×C4—202no—
442C23×C4C22×D511yescharacteristic
443C23×C4C22×D511yescharacteristic
444C23×C4C22×D511yescharacteristic
445C23×C4C22×D511yescharacteristic
446C23×C4C22×D511yescharacteristic
447C23×C4C22×D511yescharacteristic
448#126—1032no—
449C2×C4⋊C4—24no—
450C2×C4⋊C4—24no—
451C2×C4⋊C4—42no—
452C2×C4⋊C4—58no—
453C2×C4⋊C4—54no—
454C2×C4⋊C4—54no—
455C2×C4⋊C4—54no—
456C2×C4⋊C4—54no—
457C2×C4⋊C4—54no—
458C2×C4⋊C4—1032no—
459C2×C4⋊C4—104no—
460C2×C4⋊C4—104no—
461C2×C4⋊C4—104no—
462C2×C4⋊C4—104no—
463C2×C4⋊C4C22×D514yes—
464C2×C4⋊C4C22×D514yes—
465C2×C4⋊C4C22×D514yes—
466C2×C22⋊C4—24no—
467C2×C22⋊C4—24no—
468C2×C22⋊C4—42no—
469C2×C22⋊C4—54no—
470C2×C22⋊C4—54no—
471C2×C22⋊C4—54no—
472C2×C22⋊C4—54no—
473C2×C22⋊C4—54no—
474C2×C22⋊C4—54no—
475C2×C22⋊C4—104no—
476C2×C22⋊C4—104no—
477C2×C22⋊C4—104no—
478C2×C22⋊C4—104no—
479C2×C22⋊C4—104no—
480C2×C22⋊C4—202no—
481C2×C22⋊C4C22×D514yes—
482C2×C22⋊C4C22×D514yes—
483C2×C22⋊C4C22×D514yes—
484C2×C42—54no—
485C2×C42—54no—
486C2×C42—104no—
487C2×C42—202no—
488#95—54no—
489#95—54no—
490#95—54no—
491#95—54no—
492#95—54no—
493#95—54no—
494#95—54no—
495#95—54no—
496#95—54no—
497#95—54no—
498#95—54no—
499#95C22×D514yes—
500C22×C5—42no—
501C22×C5—42no—
502C22×C5—42no—
503C22×C5—42no—
504C22×C5—42no—
505C22×C5—42no—
506C22×C5—42no—
507C22×C5—88no—
508C22×C5#52514yes—
509C22×C5C2×#12614yes—
510C22×C5#53914yes—
511C22×C5#54614yes—
512C22×C5#54814yes—
513C22×C5#55214yes—
514C22×C5#55314yes—
515C22×C5C23×D411yescharacteristic
516C22×C5C22×#4111yescharacteristic
517C22×C5C22×#4111yescharacteristic
518C22×C5C22×#4111yescharacteristic
519C22×C5C22×#4111yescharacteristic
520C22×C5C2×H(5,𝔽2)11yescharacteristic
521C22×C5C2×2−1+411yescharacteristic
522C2×D5—24no—
523C2×D5—24no—
524C2×D5—24no—
525C2×D5—24no—
526C2×D5—24no—
527C2×D5—24no—
528C2×D5—232no—
529C2×D5C2×#12618yescomplemented
530C4×C5—24no—
531C4×C5—24no—
532C4×C5—42no—
533C4×C5—42no—
534C4×C5—42no—
535C4×C5—42no—
536Dic5—24no—
537Dic5—24no—
538Dic5—42no—
539Dic5—42no—
540Dic5—42no—
541Dic5—42no—
542Dic5—42no—
543C24—22no—
544C24—22no—
545C24—22no—
546C24—22no—
547C24—22no—
548C24—22no—
549C24—22no—
550C24—54no—
551C24—54no—
552C24—54no—
553C24—52no—
554C24—102no—
555C24—102no—
556C24—102no—
557C24—102no—
558C24C23×D512yes—
559C24C23×D511yescharacteristic
560C2×D4—108no—
561C2×D4—108no—
562C2×D4—108no—
563C2×D4—2016no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—54no—
581C22×C4—54no—
582C22×C4—52no—
583C22×C4—52no—
584C22×C4—52no—
585C22×C4—52no—
586C22×C4—52no—
587C22×C4—52no—
588C22×C4—52no—
589C22×C4—108no—
590C22×C4—108no—
591C22×C4—108no—
592C22×C4—1032no—
593C22×C4—108no—
594C22×C4—108no—
595C22×C4—102no—
596C22×C4—102no—
597C22×C4—102no—
598C22×C4—102no—
599C22×C4—108no—
600C22×C4—102no—
601C22×C4—102no—
602C22×C4—102no—
603C22×C4—102no—
604C22×C4—102no—
605C22×C4—102no—
606C22×C4—102no—
607C22×C4—102no—
608C22×C4—102no—
609C22×C4—102no—
610C22×C4—102no—
611C22×C4—102no—
612C22×C4—102no—
613C22×C4—102no—
614C22×C4—102no—
615C22×C4—108no—
616C22×C4—204no—
617C22×C4—204no—
618C22×C4—2016no—
619C22×C4—2016no—
620C22×C4D4×D514yes—
621C22×C4#71114yes—
622C22×C4C23×D512yes—
623C22×C4C23×D512yes—
624C22×C4C23×D512yes—
625C22×C4C23×D512yes—
626C22×C4C23×D512yes—
627C22×C4C23×D512yes—
628C4⋊C4—28no—
629C4⋊C4—28no—
630C4⋊C4—44no—
631C4⋊C4—516no—
632C4⋊C4—108no—
633C4⋊C4—108no—
634C4⋊C4—108no—
635C4⋊C4—108no—
636C22⋊C4—28no—
637C22⋊C4—28no—
638C22⋊C4—44no—
639C22⋊C4—108no—
640C22⋊C4—108no—
641C22⋊C4—108no—
642C22⋊C4—108no—
643C22⋊C4—108no—
644C22⋊C4—204no—
645C42—108no—
646C42—204no—
647C2×C5—82no—
648C2×C5#248118yescomplemented
649C2×C5C2×#52511yescharacteristic
650C2×C5C22×#12611yescharacteristic
651C2×C5C2×#53911yescharacteristic
652C2×C5C2×#54611yescharacteristic
653C2×C5C2×#54811yescharacteristic
654C2×C5C2×#55211yescharacteristic
655C2×C5C2×#55311yescharacteristic
656D5—28no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—22no—
664C23—44no—
665C23—44no—
666C23—44no—
667C23—44no—
668C23—44no—
669C23—44no—
670C23—44no—
671C23—54no—
672C23—54no—
673C23—54no—
674C23—516no—
675C23—108no—
676C23—108no—
677C23—108no—
678C23—108no—
679C23—108no—
680C23—108no—
681C23—102no—
682C23—102no—
683C23—102no—
684C23—102no—
685C23C2×D4×D512yes—
686C23C2×#71112yes—
687C23#414412yes—
688C23#414712yes—
689C23D5×#4112yes—
690C23D5×#4112yes—
691C23D5×#4112yes—
692C23C24×D511yescharacteristic
693D4—2016no—
694C2×C4—28no—
695C2×C4—28no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—44no—
713C2×C4—44no—
714C2×C4—44no—
715C2×C4—44no—
716C2×C4—54no—
717C2×C4—54no—
718C2×C4—1032no—
719C2×C4—108no—
720C2×C4—108no—
721C2×C4—102no—
722C2×C4—102no—
723C2×C4—102no—
724C2×C4—102no—
725C2×C4—102no—
726C2×C4—102no—
727C2×C4—102no—
728C2×C4—102no—
729C2×C4—102no—
730C2×C4—102no—
731C2×C4—102no—
732C2×C4—102no—
733C2×C4—102no—
734C2×C4—102no—
735C2×C4—102no—
736C2×C4—102no—
737C2×C4—102no—
738C2×C4—102no—
739C2×C4—102no—
740C2×C4—2016no—
741C2×C4—2016no—
742C2×C4—204no—
743C2×C4—204no—
744C2×C4—204no—
745C2×C4—204no—
746C2×C4—204no—
747C2×C4C2×D4×D514yes—
748C2×C4C2×#71114yes—
749C5C2×#248111yescharacteristic, complemented, Sylow
750C22—42no—
751C22—42no—
752C22—42no—
753C22—42no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—58no—
758C22—88no—
759C22—104no—
760C22—104no—
761C22—104no—
762C22—1032no—
763C22—104no—
764C22—104no—
765C22—104no—
766C22#6594014yes—
767C22#6594414yes—
768C22#6594814yes—
769C22#6596714yes—
770C22#6597214yes—
771C22#6597314yes—
772C22D5×#12614yes—
773C22C22×D4×D511yescharacteristic
774C22C22×#71111yescharacteristic
775C22C2×#414411yescharacteristic
776C22C2×#414711yescharacteristic
777C22C2×D5×#4111yescharacteristic
778C22C2×D5×#4111yescharacteristic
779C22C2×D5×#4111yescharacteristic
780C4—24no—
781C4—24no—
782C4—42no—
783C4—42no—
784C4—42no—
785C4—42no—
786C4—104no—
787C4—104no—
788C4—202no—
789C4—202no—
790C4—202no—
791C4—202no—
792C4—202no—
793C2—82no—
794C2—108no—
795C2#1060903518yesdirect product factor
796C2C2×#6594011yescharacteristic
797C2C2×#6594411yescharacteristic
798C2C2×#6594811yescharacteristic
799C2C2×#6597211yescharacteristic
800C2C2×#6596711yescharacteristic
801C2C2×#6597311yescharacteristic
802C2C2×D5×#12611yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC2×C5×#396C2
socleC24×C5C24
prime radicalC23×C22⋊D5C22
hypercenterC2×#396D5
hypocenterC5C2×#2481
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#396

Complements

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

NH ≅ G/Ntype
1. C22×D5×C4⋊C4C2semidirect
2. C22×#4025C2semidirect
3. C2×C5×#396C2semidirect
4. C2×#65278C2semidirect
5. C2×#65276C2semidirect
6. C2×#65275C2semidirect
7. C2×#65267C2semidirect
8. C2×#65270C2semidirect
12. C2×#65241C2semidirect
13. C2×#65240C2semidirect
14. #10609035C2direct (N × H)
15. C2×#64947C2semidirect
16. C2×#64955C2semidirect
41. C2×D5×C4⋊C4C22semidirect
43. C2×#4025C22semidirect
44. C5×#396C22semidirect
57. #65278C22semidirect
58. #65276C22semidirect
59. #65275C22semidirect
60. #65270C22semidirect
61. #65267C22semidirect
65. #65241C22semidirect
66. #65240C22semidirect
67. #64955C22semidirect
68. #64947C22semidirect
131. C2×#683D4semidirect
159. C2×#396D5semidirect
270. #683C2×D4semidirect
303. #396C2×D5semidirect
357. C22×D5#126semidirect
529. C2×D5C2×#126semidirect
648. C2×C5#2481semidirect
749. C5C2×#2481semidirect
795. C2#10609035direct (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×#40252
C2×C5×#3962
C2×#652782
C2×#652762
C2×#652752
C2×#652672
C2×#652702
C2×#652452
C2×#652412
C2×#652402
#106090352
C2×#649472
C2×#649552
C2×#24815