Finite Group Databasebeta

← C2×#10609049 #12269442

Subgroups — C2×#10609049 #12269442

Order 1280.

2834 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#4036C211yesmaximal, characteristic, complemented
2C22×#4032C211yesmaximal, characteristic
3C2×C5×#396C211yesmaximal, characteristic, complemented
4C2×#65283C211yesmaximal, characteristic, complemented
5C2×#65274C211yesmaximal, characteristic, complemented
6C2×#65279C211yesmaximal, characteristic, complemented
7C2×#65279C211yesmaximal, characteristic, complemented
8C2×C4⋊C4×Dic5C211yesmaximal, characteristic, complemented
9C2×#65250C211yesmaximal, characteristic
10C2×#65246C211yesmaximal, characteristic
11C2×#65234C211yesmaximal, characteristic, complemented
12C2×#65239C211yesmaximal, characteristic, complemented
13C2×C22⋊C4×Dic5C211yesmaximal, characteristic, complemented
14#10609049C2116yesmaximal, direct product factor
15C2×#64949C211yesmaximal, characteristic, complemented
16C2×#64959C211yesmaximal, characteristic, complemented
17C23×C22⋊D5C2211yescharacteristic
18C24×Dic5C2211yescharacteristic
19C22×C5×C4⋊C4C2211yescharacteristic
20C22×C5×C4⋊C4C2211yescharacteristic
21C22×C5×C4⋊C4C2211yescharacteristic
22C22×C5×C22⋊C4C2211yescharacteristic
23C22×C5×C22⋊C4C2211yescharacteristic
24C22×C5×C22⋊C4C2211yescharacteristic
25C22×C22⋊Dic5C2211yescharacteristic
26C22×C22⋊Dic5C2211yescharacteristic
27C22×#685C2211yescharacteristic
28C22×#685C2211yescharacteristic
29C22×#685C2211yescharacteristic
30C22×#685C2211yescharacteristic
31C22×#685C2211yescharacteristic
32C22×#685C2211yescharacteristic
33C22×C4⋊Dic5C2211yescharacteristic
34C22×C4⋊Dic5C2211yescharacteristic
35C22×C4⋊Dic5C2211yescharacteristic
36C22×C4⋊Dic5C2211yescharacteristic
37C22×C4⋊Dic5C2211yescharacteristic
38C22×#683C2211yescharacteristic
39C22×#683C2211yescharacteristic
40C22×C4×Dic5C2211yescharacteristic
41C22×C4×Dic5C2211yescharacteristic
42C22×C4×Dic5C2211yescharacteristic
43C22×C4×Dic5C2211yescharacteristic
44C2×#4036—28no—
45C2×#4036C2218yescomplemented
46C2×#4032—28no—
47C2×#4032C2218yes—
48C5×#396C2218yescomplemented
49C2×C5×#95C2211yescharacteristic
50C2×#3963C2211yescharacteristic
51C2×#3963C2211yescharacteristic
52C2×#3963C2211yescharacteristic
53C2×#3963C2211yescharacteristic
54C2×#3963C2211yescharacteristic
55C2×#3963C2211yescharacteristic
56C2×#3963C2211yescharacteristic
57#65283C2218yescomplemented
58#65279C2218yescomplemented
59#65279C2218yescomplemented
60#65274C2218yescomplemented
61C4⋊C4×Dic5C2218yescomplemented
62#65250C2218yes—
63#65246C2218yes—
64#65239C2218yescomplemented
65#65234C2218yescomplemented
66C22⋊C4×Dic5C2218yescomplemented
67#64959C2218yescomplemented
68#64949C2218yescomplemented
69C2×#2558—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—42no—
81C22×C22⋊D5C2314yes—
82C23×Dic5—24no—
83C23×Dic5—24no—
84C23×Dic5—42no—
85C23×Dic5C2311yescharacteristic
86C23×Dic5C2311yescharacteristic
87C23×Dic5C2311yescharacteristic
88C23×Dic5C2311yescharacteristic
89C23×Dic5C2314yes—
90C23×Dic5C2311yescharacteristic
91C23×Dic5C2311yescharacteristic
92C23×Dic5C2311yescharacteristic
93C2×C5×C4⋊C4—24no—
94C2×C5×C4⋊C4—24no—
95C2×C5×C4⋊C4—24no—
96C2×C5×C4⋊C4C2314yes—
97C2×C5×C4⋊C4C2314yes—
98C2×C5×C4⋊C4C2314yes—
99C2×C5×C22⋊C4—24no—
100C2×C5×C22⋊C4—24no—
101C2×C5×C22⋊C4—24no—
102C2×C5×C22⋊C4C2314yes—
103C2×C5×C22⋊C4C2314yes—
104C2×C5×C22⋊C4C2314yes—
105C2×C22⋊Dic5—24no—
106C2×C22⋊Dic5—24no—
107C2×C22⋊Dic5C2314yes—
108C2×C22⋊Dic5C2314yes—
109C2×#685—24no—
110C2×#685—24no—
111C2×#685—24no—
112C2×#685—24no—
113C2×#685—24no—
114C2×#685—42no—
115C2×#685C2314yes—
116C2×#685C2314yes—
117C2×#685C2314yes—
118C2×#685C2314yes—
119C2×#685C2314yes—
120C2×#685C2314yes—
121C2×C4⋊Dic5—24no—
122C2×C4⋊Dic5—24no—
123C2×C4⋊Dic5—24no—
124C2×C4⋊Dic5—42no—
125C2×C4⋊Dic5D418yes—
126C2×C4⋊Dic5C2314yes—
127C2×C4⋊Dic5C2314yes—
128C2×C4⋊Dic5C2314yes—
129C2×C4⋊Dic5C2314yes—
130C2×C4⋊Dic5C2314yes—
131C2×#683—24no—
132C2×#683—24no—
133C2×#683C2314yes—
134C2×#683C2314yes—
135C2×C4×Dic5—24no—
136C2×C4×Dic5—24no—
137C2×C4×Dic5—42no—
138C2×C4×Dic5—42no—
139C2×C4×Dic5C2314yes—
140C2×C4×Dic5C2314yes—
141C2×C4×Dic5C2314yes—
142C2×C4×Dic5C2314yes—
143#4036—232no—
144#4032—232no—
145C5×#95C2314yes—
146#3963C2314yes—
147#3963C2314yes—
148#3963C2314yes—
149#3963C2314yes—
150#3963C2314yes—
151#3963C2314yes—
152#3963C2314yes—
153C22×#125—51no—
154C22×#123—51no—
155#2558—516no—
156C2×#400—51no—
157C2×#396—51no—
158C2×#396D511yescharacteristic, complemented
159C2×#394—51no—
160C2×#390—51no—
161C2×#389—51no—
162C2×#388—51no—
163C2×#388—51no—
164C2×#388—51no—
165C2×#388—51no—
166C2×#385—51no—
167C2×C4×C4⋊C4—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#4114yes—
176C24×C5C2412yes—
177C24×C5C2411yescharacteristic
178C23×D5—22no—
179C23×D5—22no—
180C23×D5—22no—
181C23×D5—22no—
182C23×D5—22no—
183C23×D5—22no—
184C23×D5—22no—
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×C5C2×D414yes—
202C22×C4×C5#4114yes—
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—44no—
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—28no—
227C22×Dic5—22no—
228C22×Dic5—22no—
229C22×Dic5—22no—
230C22×Dic5—22no—
231C22×Dic5—22no—
232C22×Dic5—22no—
233C22×Dic5—28no—
234C22×Dic5—44no—
235C22×Dic5—416no—
236C22×Dic5C2×D414yes—
237C22×Dic5C2×D414yes—
238C22×Dic5#4114yes—
239C22×Dic5C2412yes—
240C22×Dic5C2412yes—
241C22×Dic5C2412yes—
242C22×Dic5C2412yes—
243C22×Dic5C2412yes—
244C22×Dic5C2412yes—
245C22×Dic5C2412yes—
246C5×C4⋊C4—28no—
247C5×C4⋊C4—28no—
248C5×C4⋊C4—28no—
249C5×C22⋊C4—28no—
250C5×C22⋊C4—28no—
251C5×C22⋊C4—28no—
252C22⋊Dic5—28no—
253C22⋊Dic5—28no—
254#685—28no—
255#685—28no—
256#685—28no—
257#685—28no—
258#685—28no—
259#685—44no—
260C4⋊Dic5—28no—
261C4⋊Dic5—28no—
262C4⋊Dic5—28no—
263C4⋊Dic5—44no—
264C4⋊Dic5C2×D4116yes—
265#683—28no—
266#683—28no—
267C4×Dic5—28no—
268C4×Dic5—28no—
269C4×Dic5—44no—
270C4×Dic5—44no—
271C23×D4—51no—
272C24×C4—51no—
273C2×#125—58no—
274C2×#125—108no—
275C2×#123—58no—
276C2×#123—108no—
277C22×C4⋊C4—51no—
278C22×C4⋊C4—51no—
279C22×C4⋊C4—51no—
280C22×C4⋊C4—51no—
281C22×C4⋊C4—51no—
282C22×C4⋊C4—51no—
283C22×C4⋊C4—51no—
284C22×C4⋊C4C2×D511yescharacteristic
285C22×C4⋊C4C2×D511yescharacteristic
286C22×C4⋊C4C2×D511yescharacteristic
287C22×C22⋊C4—51no—
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⋊C4C2×D511yescharacteristic
296C22×C22⋊C4C2×D511yescharacteristic
297C22×C22⋊C4C2×D511yescharacteristic
298C22×C42—51no—
299C22×C42—51no—
300C22×C42—51no—
301C22×C42—51no—
302#400—58no—
303#396—58no—
304#396C2×D518yescomplemented
305#394—58no—
306#390—58no—
307#389—58no—
308#388—58no—
309#388—58no—
310#388—58no—
311#388—58no—
312#385—58no—
313C4×C4⋊C4—58no—
314C4×C22⋊C4—58no—
315C2×#95—51no—
316C2×#95—51no—
317C2×#95—51no—
318C2×#95—51no—
319C2×#95—51no—
320C2×#95—51no—
321C2×#95—51no—
322C2×#95C2×D511yescharacteristic
323C23×C5—28no—
324C23×C5—28no—
325C23×C5—28no—
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×C5C22×D412yes—
337C23×C5C2×#4112yes—
338C23×C5C2×#4112yes—
339C23×C5C2×#4114yes—
340C23×C5C2×#4112yes—
341C23×C5C2×#4112yes—
342C23×C5H(5,𝔽2)12yes—
343C23×C52−1+412yes—
344C23×C5C2511yescharacteristic
345C22×D5—22no—
346C22×D5—22no—
347C22×D5—22no—
348C22×D5—22no—
349C22×D5—22no—
350C22×D5—22no—
351C22×D5—22no—
352C22×D5—44no—
353C22×D5—44no—
354C22×D5—44no—
355C22×D5—44no—
356C22×D5—44no—
357C22×D5—44no—
358C22×D5—44no—
359C2×C4×C5—28no—
360C2×C4×C5—28no—
361C2×C4×C5—28no—
362C2×C4×C5—22no—
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—44no—
378C2×C4×C5—44no—
379C2×C4×C5—44no—
380C2×C4×C5C22×D414yes—
381C2×C4×C5C2×#4114yes—
382C2×C4×C5C2×#4114yes—
383C22⋊D5—416no—
384C2×Dic5—28no—
385C2×Dic5—28no—
386C2×Dic5—28no—
387C2×Dic5—22no—
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—416no—
406C2×Dic5—44no—
407C2×Dic5—44no—
408C2×Dic5—44no—
409C2×Dic5—44no—
410C2×Dic5C22×D414yes—
411C2×Dic5C22×D414yes—
412C2×Dic5C2×#4114yes—
413C25—51no—
414C25C22×D511yescharacteristic
415C22×D4—54no—
416C22×D4—104no—
417C22×D4—104no—
418C22×D4—202no—
419C23×C4—51no—
420C23×C4—51no—
421C23×C4—51no—
422C23×C4—51no—
423C23×C4—51no—
424C23×C4—51no—
425C23×C4—51no—
426C23×C4—54no—
427C23×C4—104no—
428C23×C4—104no—
429C23×C4—202no—
430C23×C4C22×D511yescharacteristic
431C23×C4C22×D511yescharacteristic
432C23×C4C22×D511yescharacteristic
433C23×C4C22×D511yescharacteristic
434C23×C4C22×D511yescharacteristic
435C23×C4C22×D511yescharacteristic
436#125—1032no—
437#123—1032no—
438C2×C4⋊C4—24no—
439C2×C4⋊C4—24no—
440C2×C4⋊C4—24no—
441C2×C4⋊C4—58no—
442C2×C4⋊C4—54no—
443C2×C4⋊C4—54no—
444C2×C4⋊C4—54no—
445C2×C4⋊C4—54no—
446C2×C4⋊C4—54no—
447C2×C4⋊C4—54no—
448C2×C4⋊C4—54no—
449C2×C4⋊C4—104no—
450C2×C4⋊C4—104no—
451C2×C4⋊C4—104no—
452C2×C4⋊C4—104no—
453C2×C4⋊C4—104no—
454C2×C4⋊C4—202no—
455C2×C4⋊C4C22×D514yes—
456C2×C4⋊C4C22×D514yes—
457C2×C4⋊C4C22×D514yes—
458C2×C22⋊C4—24no—
459C2×C22⋊C4—24no—
460C2×C22⋊C4—24no—
461C2×C22⋊C4—54no—
462C2×C22⋊C4—54no—
463C2×C22⋊C4—54no—
464C2×C22⋊C4—54no—
465C2×C22⋊C4—54no—
466C2×C22⋊C4—54no—
467C2×C22⋊C4—54no—
468C2×C22⋊C4—54no—
469C2×C22⋊C4—104no—
470C2×C22⋊C4—104no—
471C2×C22⋊C4—104no—
472C2×C22⋊C4—104no—
473C2×C22⋊C4—104no—
474C2×C22⋊C4—104no—
475C2×C22⋊C4—104no—
476C2×C22⋊C4—202no—
477C2×C22⋊C4C22×D514yes—
478C2×C22⋊C4C22×D514yes—
479C2×C22⋊C4C22×D514yes—
480C2×C42—54no—
481C2×C42—54no—
482C2×C42—54no—
483C2×C42—54no—
484C2×C42—104no—
485C2×C42—104no—
486C2×C42—202no—
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#95C22×D514yes—
496C22×C5—24no—
497C22×C5—24no—
498C22×C5—24no—
499C22×C5—42no—
500C22×C5—42no—
501C22×C5—42no—
502C22×C5—42no—
503C22×C5—416no—
504C22×C5#52914yes—
505C22×C5#53214yes—
506C22×C5#53914yes—
507C22×C5#54614yes—
508C22×C5#54814yes—
509C22×C5#55214yes—
510C22×C5#55314yes—
511C22×C5C23×D411yescharacteristic
512C22×C5C22×#4111yescharacteristic
513C22×C5C22×#4111yescharacteristic
514C22×C5C22×#4111yescharacteristic
515C22×C5C22×#4111yescharacteristic
516C22×C5C2×H(5,𝔽2)11yescharacteristic
517C22×C5C2×2−1+411yescharacteristic
518C2×D5—42no—
519C2×D5—42no—
520C2×D5—42no—
521C2×D5—42no—
522C2×D5—42no—
523C2×D5—42no—
524C2×D5—42no—
525C2×D5—88no—
526C4×C5—24no—
527C4×C5—24no—
528C4×C5—24no—
529C4×C5—42no—
530C4×C5—42no—
531C4×C5—42no—
532Dic5—24no—
533Dic5—24no—
534Dic5—24no—
535Dic5—42no—
536Dic5—42no—
537Dic5—42no—
538Dic5—42no—
539C24—22no—
540C24—22no—
541C24—22no—
542C24—22no—
543C24—22no—
544C24—22no—
545C24—52no—
546C24—102no—
547C24—102no—
548C24—102no—
549C24—102no—
550C24—102no—
551C24—102no—
552C24—102no—
553C24#71314yes—
554C24C23×D512yes—
555C24C23×D511yescharacteristic
556C2×D4—108no—
557C2×D4—108no—
558C2×D4—204no—
559C2×D4—2016no—
560C22×C4—22no—
561C22×C4—22no—
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—54no—
576C22×C4—54no—
577C22×C4—54no—
578C22×C4—52no—
579C22×C4—52no—
580C22×C4—52no—
581C22×C4—52no—
582C22×C4—52no—
583C22×C4—52no—
584C22×C4—52no—
585C22×C4—108no—
586C22×C4—102no—
587C22×C4—102no—
588C22×C4—102no—
589C22×C4—102no—
590C22×C4—102no—
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—108no—
600C22×C4—102no—
601C22×C4—102no—
602C22×C4—102no—
603C22×C4—102no—
604C22×C4—102no—
605C22×C4—204no—
606C22×C4—2016no—
607C22×C4D4×D514yes—
608C22×C4#71114yes—
609C22×C4#71114yes—
610C22×C4C23×D512yes—
611C22×C4C23×D512yes—
612C22×C4C23×D512yes—
613C22×C4C23×D512yes—
614C22×C4C23×D512yes—
615C22×C4C23×D512yes—
616C4⋊C4—28no—
617C4⋊C4—28no—
618C4⋊C4—28no—
619C4⋊C4—516no—
620C4⋊C4—108no—
621C4⋊C4—108no—
622C4⋊C4—108no—
623C4⋊C4—108no—
624C4⋊C4—108no—
625C4⋊C4—204no—
626C22⋊C4—28no—
627C22⋊C4—28no—
628C22⋊C4—28no—
629C22⋊C4—108no—
630C22⋊C4—108no—
631C22⋊C4—108no—
632C22⋊C4—108no—
633C22⋊C4—108no—
634C22⋊C4—108no—
635C22⋊C4—108no—
636C22⋊C4—204no—
637C42—108no—
638C42—108no—
639C42—204no—
640C42—204no—
641C2×C5—44no—
642C2×C5#255818yescomplemented
643C2×C5C2×#52911yescharacteristic
644C2×C5C2×#53211yescharacteristic
645C2×C5C2×#53911yescharacteristic
646C2×C5C2×#54611yescharacteristic
647C2×C5C2×#54811yescharacteristic
648C2×C5C2×#55211yescharacteristic
649C2×C5C2×#55311yescharacteristic
650D5—82no—
651C23—28no—
652C23—28no—
653C23—28no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—44no—
661C23—44no—
662C23—44no—
663C23—44no—
664C23—102no—
665C23—102no—
666C23—102no—
667C23—102no—
668C23—102no—
669C23—102no—
670C23—102no—
671C23—204no—
672C23—204no—
673C23—204no—
674C23—204no—
675C23—204no—
676C23—204no—
677C23—204no—
678C23C2×D4×D512yes—
679C23C2×#71112yes—
680C23C2×#71112yes—
681C23C2×#71314yes—
682C23C2×#71312yes—
683C23D5×#4112yes—
684C23#414912yes—
685C23#415012yes—
686C23C24×D511yescharacteristic
687D4—2016no—
688C2×C4—28no—
689C2×C4—28no—
690C2×C4—28no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
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—44no—
707C2×C4—44no—
708C2×C4—44no—
709C2×C4—54no—
710C2×C4—54no—
711C2×C4—54no—
712C2×C4—108no—
713C2×C4—108no—
714C2×C4—102no—
715C2×C4—102no—
716C2×C4—102no—
717C2×C4—102no—
718C2×C4—102no—
719C2×C4—102no—
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—2016no—
734C2×C4—204no—
735C2×C4—204no—
736C2×C4—204no—
737C2×C4—204no—
738C2×C4C2×D4×D514yes—
739C2×C4C2×#71114yes—
740C2×C4C2×#71114yes—
741C5C2×#255811yescharacteristic, complemented, Sylow
742C22—24no—
743C22—24no—
744C22—24no—
745C22—416no—
746C22—42no—
747C22—42no—
748C22—42no—
749C22—42no—
750C22—202no—
751C22—202no—
752C22—202no—
753C22—202no—
754C22—202no—
755C22—202no—
756C22—202no—
757C22—408no—
758C22#6593014yes—
759C22#6593214yes—
760C22#6595214yes—
761C22#6595814yes—
762C22#6596414yes—
763C22#6597614yes—
764C22#6604114yes—
765C22C22×D4×D511yescharacteristic
766C22C22×#71111yescharacteristic
767C22C22×#71111yescharacteristic
768C22C22×#71311yescharacteristic
769C22C2×D5×#4111yescharacteristic
770C22C2×#414911yescharacteristic
771C22C2×#415011yescharacteristic
772C4—24no—
773C4—24no—
774C4—24no—
775C4—42no—
776C4—42no—
777C4—42no—
778C4—104no—
779C4—104no—
780C4—104no—
781C4—202no—
782C4—202no—
783C4—202no—
784C4—202no—
785C2—44no—
786C2—402no—
787C2#1060904918yesdirect product factor
788C2C2×#6593011yescharacteristic
789C2C2×#6593211yescharacteristic
790C2C2×#6595211yescharacteristic
791C2C2×#6595811yescharacteristic
792C2C2×#6597611yescharacteristic
793C2C2×#6596411yescharacteristic
794C2C2×#6604111yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC2×C5×#396C2
socleC24×C5C24
prime radicalC23×C22⋊D5C22
hypercenterC2×#396D5
hypocenterC5C2×#2558
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#396

Complements

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

NH ≅ G/Ntype
1. C22×#4036C2semidirect
3. C2×C5×#396C2semidirect
4. C2×#65283C2semidirect
5. C2×#65274C2semidirect
6. C2×#65279C2semidirect
7. C2×#65279C2semidirect
8. C2×C4⋊C4×Dic5C2semidirect
11. C2×#65234C2semidirect
12. C2×#65239C2semidirect
13. C2×C22⋊C4×Dic5C2semidirect
14. #10609049C2direct (N × H)
15. C2×#64949C2semidirect
16. C2×#64959C2semidirect
45. C2×#4036C22semidirect
48. C5×#396C22semidirect
57. #65283C22semidirect
58. #65279C22semidirect
59. #65279C22semidirect
60. #65274C22semidirect
61. C4⋊C4×Dic5C22semidirect
64. #65239C22semidirect
65. #65234C22semidirect
66. C22⋊C4×Dic5C22semidirect
67. #64959C22semidirect
68. #64949C22semidirect
158. C2×#396D5semidirect
304. #396C2×D5semidirect
642. C2×C5#2558semidirect
741. C5C2×#2558semidirect
787. C2#10609049direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#40362
C22×#40322
C2×C5×#3962
C2×#652832
C2×#652742
C2×#652792
C2×C4⋊C4×Dic52
C2×#652502
C2×#652462
C2×#652342
C2×#652392
C2×C22⋊C4×Dic52
#106090492
C2×#649492
C2×#649592
C2×#25585