Finite Group Databasebeta

← C2×#10606168 #12267405

Subgroups — C2×#10606168 #12267405

Order 1280.

3006 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D5C211yesmaximal, characteristic
2C22×#4044C211yesmaximal, characteristic, complemented
3C2×C5×#385C211yesmaximal, characteristic, complemented
4C2×#65501C211yesmaximal, characteristic, complemented
5C2×#65278C211yesmaximal, characteristic, complemented
6C2×#65273C211yesmaximal, characteristic, complemented
7C2×C4⋊C4×Dic5C211yesmaximal, characteristic, complemented
8C2×#65250C211yesmaximal, characteristic
9C2×#65250C211yesmaximal, characteristic
10C2×#65234C211yesmaximal, characteristic, complemented
11C2×#65233C211yesmaximal, characteristic, complemented
12#10606168C2116yesmaximal, direct product factor
13C2×#64953C211yesmaximal, characteristic, complemented
14C2×#64950C211yesmaximal, characteristic, complemented
15C2×#64959C211yesmaximal, characteristic, complemented
16C2×#64943C211yesmaximal, characteristic, complemented
17C24×C4×C5C2211yescharacteristic
18C23×C22⋊D5C2211yescharacteristic
19C23×C4×D5C2211yescharacteristic
20C22×C5×C4⋊C4C2211yescharacteristic
21C22×C5×C4⋊C4C2211yescharacteristic
22C22×C5×C22⋊C4C2211yescharacteristic
23C22×C5×C22⋊C4C2211yescharacteristic
24C22×C22⋊Dic5C2211yescharacteristic
25C22×C22⋊Dic5C2211yescharacteristic
26C22×C22⋊Dic5C2211yescharacteristic
27C2×C4×C22⋊D5—28no—
28C2×C4×C22⋊D5C2218yes—
29C22×#685C2211yescharacteristic
30C22×#685C2211yescharacteristic
31C22×#685C2211yescharacteristic
32C22×#685C2211yescharacteristic
33C22×#685C2211yescharacteristic
34C22×C4⋊Dic5C2211yescharacteristic
35C22×C4⋊Dic5C2211yescharacteristic
36C22×C4⋊Dic5C2211yescharacteristic
37C22×C4⋊Dic5C2211yescharacteristic
38C22×#683C2211yescharacteristic
39C22×#683C2211yescharacteristic
40C22×#683C2211yescharacteristic
41C22×C4×Dic5C2211yescharacteristic
42C22×C4×Dic5C2211yescharacteristic
43C22×C4×Dic5C2211yescharacteristic
44C2×#4044—28no—
45C2×#4044C2218yescomplemented
46C5×#385C2218yescomplemented
47C2×C5×#95C2211yescharacteristic
48C2×C5×#95C2211yescharacteristic
49#65501C2218yescomplemented
50C2×#3963C2211yescharacteristic
51C2×#3963C2211yescharacteristic
52C2×#3963C2211yescharacteristic
53C2×#3963C2211yescharacteristic
54C2×#3963C2211yescharacteristic
55C2×#3963C2211yescharacteristic
56C2×#3963C2211yescharacteristic
57C2×#3963C2211yescharacteristic
58#65278C2218yescomplemented
59#65273C2218yescomplemented
60C4⋊C4×Dic5C2218yescomplemented
61#65250C2218yes—
62#65250C2218yes—
63#65234C2218yescomplemented
64#65233C2218yescomplemented
65#64959C2218yescomplemented
66#64953C2218yescomplemented
67#64950C2218yescomplemented
68#64943C2218yescomplemented
69C2×#2468—51nomaximal, Sylow
70C25×C5C2311yescharacteristic
71C24×D5C2311yescharacteristic
72C23×C4×C5—24no—
73C23×C4×C5—24no—
74C23×C4×C5—42no—
75C23×C4×C5C2311yescharacteristic
76C23×C4×C5C2311yescharacteristic
77C23×C4×C5C2311yescharacteristic
78C23×C4×C5C2314yes—
79C23×C4×C5C2311yescharacteristic
80C23×C4×C5C2311yescharacteristic
81C23×C4×C5C2311yescharacteristic
82C22×C22⋊D5—24no—
83C22×C22⋊D5—24no—
84C22×C22⋊D5—24no—
85C22×C22⋊D5C2314yes—
86C23×Dic5C2311yescharacteristic
87C23×Dic5C2311yescharacteristic
88C23×Dic5C2311yescharacteristic
89C23×Dic5C2311yescharacteristic
90C23×Dic5C2311yescharacteristic
91C23×Dic5C2311yescharacteristic
92C23×Dic5C2311yescharacteristic
93C22×C4×D5—24no—
94C22×C4×D5—24no—
95C22×C4×D5—42no—
96C22×C4×D5C2314yes—
97C2×C5×C4⋊C4—24no—
98C2×C5×C4⋊C4—24no—
99C2×C5×C4⋊C4C2314yes—
100C2×C5×C4⋊C4C2314yes—
101C2×C5×C22⋊C4—24no—
102C2×C5×C22⋊C4—42no—
103C2×C5×C22⋊C4C2314yes—
104C2×C5×C22⋊C4C2314yes—
105C2×C22⋊Dic5—24no—
106C2×C22⋊Dic5—24no—
107C2×C22⋊Dic5—24no—
108C2×C22⋊Dic5C2314yes—
109C2×C22⋊Dic5C2314yes—
110C2×C22⋊Dic5C2314yes—
111C4×C22⋊D5—232no—
112C2×#685—24no—
113C2×#685—24no—
114C2×#685—24no—
115C2×#685—42no—
116C2×#685D418yes—
117C2×#685C2314yes—
118C2×#685C2314yes—
119C2×#685C2314yes—
120C2×#685C2314yes—
121C2×#685C2314yes—
122C2×C4⋊Dic5—24no—
123C2×C4⋊Dic5—24no—
124C2×C4⋊Dic5—24no—
125C2×C4⋊Dic5—42no—
126C2×C4⋊Dic5C2314yes—
127C2×C4⋊Dic5C2314yes—
128C2×C4⋊Dic5C2314yes—
129C2×C4⋊Dic5C2314yes—
130C2×#683—24no—
131C2×#683—24no—
132C2×#683—42no—
133C2×#683C2314yes—
134C2×#683C2314yes—
135C2×#683C2314yes—
136C2×C4×Dic5—24no—
137C2×C4×Dic5—24no—
138C2×C4×Dic5—24no—
139C2×C4×Dic5C2314yes—
140C2×C4×Dic5C2314yes—
141C2×C4×Dic5C2314yes—
142#4044—232no—
143C5×#95C2314yes—
144C5×#95C2314yes—
145#3963C2314yes—
146#3963C2314yes—
147#3963C2314yes—
148#3963C2314yes—
149#3963C2314yes—
150#3963C2314yes—
151#3963C2314yes—
152#3963C2314yes—
153C22×#126—51no—
154C22×C4×D4—51no—
155#2468—516no—
156C2×#398—51no—
157C2×#398—51no—
158C2×#394—51no—
159C2×#394—51no—
160C2×#388—51no—
161C2×#388—51no—
162C2×#388—51no—
163C2×#387—51no—
164C2×#385—51no—
165C2×#385D511yescharacteristic, complemented
166C2×#381—51no—
167C2×#380—51no—
168C2×C4×C4⋊C4—51no—
169C24×C5—22no—
170C24×C5—22no—
171C24×C5—22no—
172C24×C5—22no—
173C24×C5—22no—
174C24×C5—22no—
175C24×C5#4114yes—
176C24×C5C2412yes—
177C24×C5C2411yescharacteristic
178C23×D5—22no—
179C23×D5—22no—
180C23×D5—22no—
181C23×D5—22no—
182C23×D5—22no—
183C23×D5—22no—
184C23×D5C2×D414yes—
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—28no—
202C22×C4×C5—28no—
203C22×C4×C5—44no—
204C22×C4×C5—416no—
205C22×C4×C5C2×D414yes—
206C22×C4×C5#4114yes—
207C22×C4×C5#4114yes—
208C22×C4×C5C2412yes—
209C22×C4×C5C2412yes—
210C22×C4×C5C2412yes—
211C22×C4×C5C2412yes—
212C22×C4×C5C2412yes—
213C22×C4×C5C2412yes—
214C2×C22⋊D5—232no—
215C2×C22⋊D5—28no—
216C2×C22⋊D5—28no—
217C2×C22⋊D5—28no—
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×Dic5—22no—
235C22×Dic5—22no—
236C22×Dic5—22no—
237C22×Dic5C2×D414yes—
238C22×Dic5#4114yes—
239C22×Dic5C2412yes—
240C22×Dic5C2412yes—
241C22×Dic5C2412yes—
242C22×Dic5C2412yes—
243C22×Dic5C2412yes—
244C22×Dic5C2412yes—
245C22×Dic5C2412yes—
246C2×C4×D5—28no—
247C2×C4×D5—28no—
248C2×C4×D5—44no—
249C2×C4×D5—416no—
250C5×C4⋊C4—28no—
251C5×C4⋊C4—28no—
252C5×C22⋊C4—28no—
253C5×C22⋊C4—44no—
254C22⋊Dic5—28no—
255C22⋊Dic5—28no—
256C22⋊Dic5—28no—
257#685—28no—
258#685—28no—
259#685—28no—
260#685—44no—
261#685C2×D4116yes—
262C4⋊Dic5—28no—
263C4⋊Dic5—28no—
264C4⋊Dic5—28no—
265C4⋊Dic5—44no—
266#683—28no—
267#683—28no—
268#683—44no—
269C4×Dic5—28no—
270C4×Dic5—28no—
271C4×Dic5—28no—
272C23×D4—51no—
273C24×C4—51no—
274C24×C4C2×D511yescharacteristic
275C2×#126—58no—
276C2×#126—108no—
277C2×C4×D4—58no—
278C2×C4×D4—108no—
279C22×C4⋊C4—51no—
280C22×C4⋊C4—51no—
281C22×C4⋊C4—51no—
282C22×C4⋊C4—51no—
283C22×C4⋊C4—51no—
284C22×C4⋊C4—51no—
285C22×C4⋊C4—51no—
286C22×C4⋊C4C2×D511yescharacteristic
287C22×C4⋊C4C2×D511yescharacteristic
288C22×C22⋊C4—51no—
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⋊C4—51no—
296C22×C22⋊C4C2×D511yescharacteristic
297C22×C22⋊C4C2×D511yescharacteristic
298C22×C42—51no—
299C22×C42—51no—
300C22×C42—51no—
301#398—58no—
302#398—58no—
303#394—58no—
304#394—58no—
305#388—58no—
306#388—58no—
307#388—58no—
308#387—58no—
309#385—58no—
310#385C2×D518yescomplemented
311#381—58no—
312#380—58no—
313C4×C4⋊C4—58no—
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×#95C2×D511yescharacteristic
323C2×#95C2×D511yescharacteristic
324C23×C5—28no—
325C23×C5—28no—
326C23×C5—28no—
327C23×C5—22no—
328C23×C5—22no—
329C23×C5—22no—
330C23×C5—22no—
331C23×C5—22no—
332C23×C5—22no—
333C23×C5—44no—
334C23×C5—44no—
335C23×C5—44no—
336C23×C5—44no—
337C23×C5C22×D412yes—
338C23×C5C2×#4112yes—
339C23×C5C2×#4112yes—
340C23×C5C2×#4114yes—
341C23×C5C2×#4112yes—
342C23×C5C2×#4112yes—
343C23×C5H(5,𝔽2)12yes—
344C23×C52−1+412yes—
345C23×C5C2511yescharacteristic
346C22×D5—28no—
347C22×D5—28no—
348C22×D5—28no—
349C22×D5—22no—
350C22×D5—22no—
351C22×D5—22no—
352C22×D5—22no—
353C22×D5—22no—
354C22×D5—22no—
355C22×D5—44no—
356C22×D5—44no—
357C22×D5—44no—
358C22×D5—44no—
359C22×D5C22×D414yes—
360C2×C4×C5—28no—
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—416no—
379C2×C4×C5—44no—
380C2×C4×C5—44no—
381C2×C4×C5—44no—
382C2×C4×C5C22×D414yes—
383C2×C4×C5C2×#4114yes—
384C2×C4×C5C2×#4114yes—
385C22⋊D5—232no—
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×Dic5C2×#4114yes—
414C4×D5—416no—
415C25—51no—
416C25C22×D511yescharacteristic
417C22×D4—54no—
418C22×D4—104no—
419C22×D4—104no—
420C22×D4—104no—
421C23×C4—24no—
422C23×C4—24no—
423C23×C4—42no—
424C23×C4—51no—
425C23×C4—51no—
426C23×C4—51no—
427C23×C4—51no—
428C23×C4—51no—
429C23×C4—51no—
430C23×C4—51no—
431C23×C4—54no—
432C23×C4—104no—
433C23×C4—104no—
434C23×C4—202no—
435C23×C4C22×D511yescharacteristic
436C23×C4C22×D511yescharacteristic
437C23×C4C22×D511yescharacteristic
438C23×C4C22×D514yes—
439C23×C4C22×D511yescharacteristic
440C23×C4C22×D511yescharacteristic
441C23×C4C22×D511yescharacteristic
442#126—1032no—
443C4×D4—1032no—
444C2×C4⋊C4—24no—
445C2×C4⋊C4—24no—
446C2×C4⋊C4—54no—
447C2×C4⋊C4—54no—
448C2×C4⋊C4—54no—
449C2×C4⋊C4—54no—
450C2×C4⋊C4—54no—
451C2×C4⋊C4—54no—
452C2×C4⋊C4—54no—
453C2×C4⋊C4—104no—
454C2×C4⋊C4—104no—
455C2×C4⋊C4—104no—
456C2×C4⋊C4—104no—
457C2×C4⋊C4—104no—
458C2×C4⋊C4—202no—
459C2×C4⋊C4—202no—
460C2×C4⋊C4C22×D514yes—
461C2×C4⋊C4C22×D514yes—
462C2×C22⋊C4—24no—
463C2×C22⋊C4—42no—
464C2×C22⋊C4—58no—
465C2×C22⋊C4—54no—
466C2×C22⋊C4—54no—
467C2×C22⋊C4—54no—
468C2×C22⋊C4—54no—
469C2×C22⋊C4—54no—
470C2×C22⋊C4—54no—
471C2×C22⋊C4—54no—
472C2×C22⋊C4—54no—
473C2×C22⋊C4—104no—
474C2×C22⋊C4—104no—
475C2×C22⋊C4—104no—
476C2×C22⋊C4—104no—
477C2×C22⋊C4—104no—
478C2×C22⋊C4—104no—
479C2×C22⋊C4—202no—
480C2×C22⋊C4C22×D514yes—
481C2×C22⋊C4C22×D514yes—
482C2×C42—54no—
483C2×C42—54no—
484C2×C42—54no—
485C2×C42—104no—
486C2×C42—104no—
487C2×C42—104no—
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#95C22×D514yes—
497#95C22×D514yes—
498C22×C5—24no—
499C22×C5—24no—
500C22×C5—24no—
501C22×C5—42no—
502C22×C5—42no—
503C22×C5—42no—
504C22×C5—42no—
505C22×C5—416no—
506C22×C5#52514yes—
507C22×C5#52914yes—
508C22×C5#54214yes—
509C22×C5#54614yes—
510C22×C5#54714yes—
511C22×C5#55214yes—
512C22×C5#55314yes—
513C22×C5C23×D411yescharacteristic
514C22×C5C22×#4111yescharacteristic
515C22×C5C22×#4111yescharacteristic
516C22×C5C22×#4111yescharacteristic
517C22×C5C22×#4111yescharacteristic
518C22×C5C2×H(5,𝔽2)11yescharacteristic
519C22×C5C2×2−1+411yescharacteristic
520C2×D5—24no—
521C2×D5—24no—
522C2×D5—24no—
523C2×D5—42no—
524C2×D5—42no—
525C2×D5—42no—
526C2×D5—42no—
527C2×D5—416no—
528C4×C5—24no—
529C4×C5—24no—
530C4×C5—24no—
531C4×C5—42no—
532C4×C5—42no—
533C4×C5—42no—
534Dic5—24no—
535Dic5—24no—
536Dic5—42no—
537Dic5—42no—
538Dic5—42no—
539Dic5—42no—
540Dic5—42no—
541C24—22no—
542C24—22no—
543C24—22no—
544C24—22no—
545C24—22no—
546C24—22no—
547C24—54no—
548C24—52no—
549C24—102no—
550C24—102no—
551C24—102no—
552C24—102no—
553C24—102no—
554C24—102no—
555C24#71314yes—
556C24C23×D512yes—
557C24C23×D511yescharacteristic
558C2×D4—108no—
559C2×D4—108no—
560C2×D4—1032no—
561C2×D4—108no—
562C22×C4—22no—
563C22×C4—22no—
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—28no—
578C22×C4—28no—
579C22×C4—44no—
580C22×C4—416no—
581C22×C4—54no—
582C22×C4—54no—
583C22×C4—52no—
584C22×C4—52no—
585C22×C4—52no—
586C22×C4—52no—
587C22×C4—52no—
588C22×C4—52no—
589C22×C4—52no—
590C22×C4—108no—
591C22×C4—102no—
592C22×C4—102no—
593C22×C4—102no—
594C22×C4—102no—
595C22×C4—102no—
596C22×C4—102no—
597C22×C4—102no—
598C22×C4—102no—
599C22×C4—102no—
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—108no—
611C22×C4—204no—
612C22×C4—2016no—
613C22×C4#70914yes—
614C22×C4D4×D514yes—
615C22×C4#71114yes—
616C22×C4C23×D512yes—
617C22×C4C23×D512yes—
618C22×C4C23×D512yes—
619C22×C4C23×D512yes—
620C22×C4C23×D512yes—
621C22×C4C23×D512yes—
622C4⋊C4—28no—
623C4⋊C4—28no—
624C4⋊C4—108no—
625C4⋊C4—108no—
626C4⋊C4—108no—
627C4⋊C4—108no—
628C4⋊C4—108no—
629C4⋊C4—204no—
630C4⋊C4—204no—
631C22⋊C4—28no—
632C22⋊C4—44no—
633C22⋊C4—516no—
634C22⋊C4—108no—
635C22⋊C4—108no—
636C22⋊C4—108no—
637C22⋊C4—108no—
638C22⋊C4—108no—
639C22⋊C4—108no—
640C22⋊C4—204no—
641C42—108no—
642C42—108no—
643C42—108no—
644C2×C5—44no—
645C2×C5#246818yescomplemented
646C2×C5C2×#52511yescharacteristic
647C2×C5C2×#52911yescharacteristic
648C2×C5C2×#54211yescharacteristic
649C2×C5C2×#54611yescharacteristic
650C2×C5C2×#54711yescharacteristic
651C2×C5C2×#55211yescharacteristic
652C2×C5C2×#55311yescharacteristic
653D5—44no—
654C23—28no—
655C23—28no—
656C23—28no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—44no—
664C23—44no—
665C23—44no—
666C23—44no—
667C23—54no—
668C23—108no—
669C23—108no—
670C23—108no—
671C23—102no—
672C23—102no—
673C23—102no—
674C23—102no—
675C23—102no—
676C23—102no—
677C23—204no—
678C23—204no—
679C23—204no—
680C23—204no—
681C23C2×#70912yes—
682C23C2×D4×D512yes—
683C23C2×#71112yes—
684C23#414412yes—
685C23C2×#71314yes—
686C23C2×#71312yes—
687C23D5×#4112yes—
688C23#415012yes—
689C23C24×D511yescharacteristic
690D4—1032no—
691C2×C4—28no—
692C2×C4—28no—
693C2×C4—28no—
694C2×C4—22no—
695C2×C4—22no—
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—416no—
710C2×C4—44no—
711C2×C4—44no—
712C2×C4—44no—
713C2×C4—54no—
714C2×C4—54no—
715C2×C4—108no—
716C2×C4—108no—
717C2×C4—102no—
718C2×C4—102no—
719C2×C4—102no—
720C2×C4—102no—
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—2016no—
737C2×C4—204no—
738C2×C4—204no—
739C2×C4—204no—
740C2×C4—204no—
741C2×C4—204no—
742C2×C4C2×#70914yes—
743C2×C4C2×D4×D514yes—
744C2×C4C2×#71114yes—
745C5C2×#246811yescharacteristic, complemented, Sylow
746C22—24no—
747C22—24no—
748C22—24no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—416no—
753C22—42no—
754C22—104no—
755C22—104no—
756C22—104no—
757C22—202no—
758C22—202no—
759C22—202no—
760C22—202no—
761C22—2016no—
762C22#6584814yes—
763C22#6587214yes—
764C22#6588514yes—
765C22#6592514yes—
766C22#6596114yes—
767C22#6597614yes—
768C22#6599614yes—
769C22C22×#70911yescharacteristic
770C22C22×D4×D511yescharacteristic
771C22C22×#71111yescharacteristic
772C22C2×#414411yescharacteristic
773C22C22×#71311yescharacteristic
774C22C2×D5×#4111yescharacteristic
775C22C2×#415011yescharacteristic
776C4—24no—
777C4—24no—
778C4—24no—
779C4—42no—
780C4—42no—
781C4—42no—
782C4—104no—
783C4—104no—
784C4—202no—
785C4—202no—
786C4—202no—
787C4—202no—
788C4—202no—
789C2—44no—
790C2—204no—
791C2#1060616818yesdirect product factor
792C2C2×#6584811yescharacteristic
793C2C2×#6587211yescharacteristic
794C2C2×#6588511yescharacteristic
795C2C2×#6592511yescharacteristic
796C2C2×#6596111yescharacteristic
797C2C2×#6597611yescharacteristic
798C2C2×#6599611yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC2×C5×#385C2
socleC24×C5C24
prime radicalC23×C22⋊D5C22
hypercenterC2×#385D5
hypocenterC5C2×#2468
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
2. C22×#4044C2semidirect
3. C2×C5×#385C2semidirect
4. C2×#65501C2semidirect
5. C2×#65278C2semidirect
6. C2×#65273C2semidirect
7. C2×C4⋊C4×Dic5C2semidirect
10. C2×#65234C2semidirect
11. C2×#65233C2semidirect
12. #10606168C2direct (N × H)
13. C2×#64953C2semidirect
14. C2×#64950C2semidirect
15. C2×#64959C2semidirect
16. C2×#64943C2semidirect
45. C2×#4044C22semidirect
46. C5×#385C22semidirect
49. #65501C22semidirect
58. #65278C22semidirect
59. #65273C22semidirect
60. C4⋊C4×Dic5C22semidirect
63. #65234C22semidirect
64. #65233C22semidirect
65. #64959C22semidirect
66. #64953C22semidirect
67. #64950C22semidirect
68. #64943C22semidirect
165. C2×#385D5semidirect
310. #385C2×D5semidirect
645. C2×C5#2468semidirect
745. C5C2×#2468semidirect
791. C2#10606168direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D52
C22×#40442
C2×C5×#3852
C2×#655012
C2×#652782
C2×#652732
C2×C4⋊C4×Dic52
C2×#652502
C2×#652342
C2×#652332
#106061682
C2×#649532
C2×#649502
C2×#649592
C2×#649432
C2×#24685