Finite Group Databasebeta

← C2×#10606749 #12267857

Subgroups — C2×#10606749 #12267857

Order 1280.

2898 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×#4044C211yesmaximal, characteristic, complemented
2C22×#4038C211yesmaximal, characteristic, complemented
3C2×C5×#387C211yesmaximal, characteristic, complemented
4C2×#65280C211yesmaximal, characteristic
5C2×#65274C211yesmaximal, characteristic, complemented
6C2×#65228C211yesmaximal, characteristic
7C2×C4×C4⋊Dic5C211yesmaximal, characteristic, complemented
8#10606749C2116yesmaximal, direct product factor
9C2×#64966C211yesmaximal, characteristic, complemented
10C2×#64966C211yesmaximal, characteristic, complemented
11C2×#64954C211yesmaximal, characteristic
12C2×#64957C211yesmaximal, characteristic, complemented
13C2×#64950C211yesmaximal, characteristic, complemented
14C2×#64959C211yesmaximal, characteristic, complemented
15C2×#64959C211yesmaximal, characteristic, complemented
16C2×#64959C211yesmaximal, characteristic, complemented
17C23×D20C2211yescharacteristic
18C23×C4×D5C2211yescharacteristic
19C22×C5×C4⋊C4C2211yescharacteristic
20C22×C5×C4⋊C4C2211yescharacteristic
21C22×C42×C5C2211yescharacteristic
22C22×#685C2211yescharacteristic
23C22×#685C2211yescharacteristic
24C22×#685C2211yescharacteristic
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×C4⋊Dic5C2211yescharacteristic
37C22×C4⋊Dic5C2211yescharacteristic
38C22×C4⋊Dic5C2211yescharacteristic
39C22×C4⋊Dic5C2211yescharacteristic
40C22×#683C2211yescharacteristic
41C22×C4×Dic5C2211yescharacteristic
42C22×C4×Dic5C2211yescharacteristic
43C22×C4×Dic5C2211yescharacteristic
44C2×#4044—28no—
45C2×#4044C2218yescomplemented
46C2×#4038—28no—
47C2×#4038C2218yescomplemented
48C5×#387C2218yescomplemented
49C2×C5×#95C2211yescharacteristic
50C2×C5×#95C2211yescharacteristic
51C2×C5×#95C2211yescharacteristic
52C2×C5×#95C2211yescharacteristic
53C2×#3963C2211yescharacteristic
54C2×#3963C2211yescharacteristic
55C2×#3963C2211yescharacteristic
56C2×#3963C2211yescharacteristic
57#65280C2218yes—
58#65274C2218yescomplemented
59#65228C2218yes—
60C4×C4⋊Dic5C2218yescomplemented
61#64966C2218yescomplemented
62#64966C2218yescomplemented
63#64959C2218yescomplemented
64#64959C2218yescomplemented
65#64959C2218yescomplemented
66#64957C2218yescomplemented
67#64954C2218yes—
68#64950C2218yescomplemented
69C2×#2479—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×D20—42no—
88C22×D20C2314yes—
89C22×C4×D5—24no—
90C22×C4×D5—24no—
91C22×C4×D5—24no—
92C22×C4×D5C2314yes—
93C2×C5×C4⋊C4—24no—
94C2×C5×C4⋊C4D418yescomplemented
95C2×C5×C4⋊C4C2314yes—
96C2×C5×C4⋊C4C2314yes—
97C2×C42×C5—24no—
98C2×C42×C5C2314yes—
99C2×#685—24no—
100C2×#685—24no—
101C2×#685—24no—
102C2×#685—24no—
103C2×#685—24no—
104C2×#685—24no—
105C2×#685—24no—
106C2×#685—24no—
107C2×#685—24no—
108C2×#685—42no—
109C2×#685—42no—
110C2×#685C2314yes—
111C2×#685C2314yes—
112C2×#685C2314yes—
113C2×#685C2314yes—
114C2×#685C2314yes—
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—24no—
125C2×C4⋊Dic5—42no—
126C2×C4⋊Dic5—42no—
127C2×C4⋊Dic5—42no—
128C2×C4⋊Dic5C2314yes—
129C2×C4⋊Dic5C2314yes—
130C2×C4⋊Dic5C2314yes—
131C2×C4⋊Dic5C2314yes—
132C2×C4⋊Dic5C2314yes—
133C2×C4⋊Dic5C2314yes—
134C2×C4⋊Dic5C2314yes—
135C2×#683—24no—
136C2×#683C2314yes—
137C2×C4×Dic5—24no—
138C2×C4×Dic5—24no—
139C2×C4×Dic5—24no—
140C2×C4×Dic5C2314yes—
141C2×C4×Dic5C2314yes—
142C2×C4×Dic5C2314yes—
143#4044—232no—
144#4038—232no—
145C5×#95C2314yes—
146C5×#95C2314yes—
147C5×#95C2314yes—
148C5×#95C2314yes—
149#3963C2314yes—
150#3963C2314yes—
151#3963C2314yes—
152#3963C2314yes—
153C22×#126—51no—
154C22×#117—51no—
155#2479—516no—
156C2×#399—51no—
157C2×#399—51no—
158C2×#398—51no—
159C2×#394—51no—
160C2×#390—51no—
161C2×#389—51no—
162C2×#388—51no—
163C2×#388—51no—
164C2×#388—51no—
165C2×#387D511yescharacteristic, complemented
166C2×#386—51no—
167C2×#385—51no—
168C2×C4×C4⋊C4—51no—
169C24×C5C2411yescharacteristic
170C23×D5—22no—
171C23×D5—22no—
172C23×D5—22no—
173C23×D5—22no—
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#4114yes—
184C23×D5C2412yes—
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×C5C2×D414yes—
204C22×C4×C5C2×D414yes—
205C22×C4×C5#4114yes—
206C22×C4×C5#4114yes—
207C22×C4×C5C2412yes—
208C22×C4×C5C2412yes—
209C22×C4×C5C2412yes—
210C22×C4×C5C2412yes—
211C22×C4×C5C2412yes—
212C22×C4×C5C2412yes—
213C22×C4×C5C2412yes—
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#4114yes—
232C22×Dic5C2412yes—
233C22×Dic5C2412yes—
234C22×Dic5C2412yes—
235C22×Dic5C2412yes—
236C22×Dic5C2412yes—
237C22×Dic5C2412yes—
238C2×D20—28no—
239C2×D20—28no—
240C2×D20—44no—
241C2×D20—416no—
242C2×C4×D5—232no—
243C2×C4×D5—28no—
244C2×C4×D5—28no—
245C2×C4×D5—28no—
246C5×C4⋊C4—28no—
247C5×C4⋊C4C2×D4116yescomplemented
248C42×C5—28no—
249#685—28no—
250#685—28no—
251#685—28no—
252#685—28no—
253#685—28no—
254#685—28no—
255#685—28no—
256#685—28no—
257#685—28no—
258#685—44no—
259#685—44no—
260C4⋊Dic5—28no—
261C4⋊Dic5—28no—
262C4⋊Dic5—28no—
263C4⋊Dic5—28no—
264C4⋊Dic5—44no—
265C4⋊Dic5—44no—
266C4⋊Dic5—44no—
267#683—28no—
268C4×Dic5—28no—
269C4×Dic5—28no—
270C4×Dic5—28no—
271C23×D4—51no—
272C24×C4—51no—
273C2×#126—58no—
274C2×#126—108no—
275C2×#117—58no—
276C2×#117—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⋊C4—51no—
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⋊C4—51no—
296C22×C22⋊C4—51no—
297C22×C22⋊C4—51no—
298C22×C42—51no—
299C22×C42—51no—
300C22×C42—51no—
301C22×C42C2×D511yescharacteristic
302#399—58no—
303#399—58no—
304#398—58no—
305#394—58no—
306#390—58no—
307#389—58no—
308#388—58no—
309#388—58no—
310#388—58no—
311#387C2×D518yescomplemented
312#386—58no—
313#385—58no—
314C4×C4⋊C4—58no—
315C2×#95—51no—
316C2×#95—51no—
317C2×#95—51no—
318C2×#95—51no—
319C2×#95C2×D511yescharacteristic
320C2×#95C2×D511yescharacteristic
321C2×#95C2×D511yescharacteristic
322C2×#95C2×D511yescharacteristic
323C23×C5C22×D412yes—
324C23×C5C2×#4112yes—
325C23×C5C2×#4112yes—
326C23×C5C2×#4112yes—
327C23×C5C2×#4112yes—
328C23×C5H(5,𝔽2)12yes—
329C23×C52−1+412yes—
330C23×C5C2511yescharacteristic
331C22×D5—28no—
332C22×D5—28no—
333C22×D5—28no—
334C22×D5—22no—
335C22×D5—22no—
336C22×D5—22no—
337C22×D5—22no—
338C22×D5—22no—
339C22×D5—22no—
340C22×D5—22no—
341C22×D5—22no—
342C22×D5—22no—
343C22×D5—22no—
344C22×D5—22no—
345C22×D5—22no—
346C22×D5—22no—
347C22×D5—44no—
348C22×D5—44no—
349C22×D5—44no—
350C22×D5—44no—
351C22×D5—44no—
352C22×D5—44no—
353C22×D5—44no—
354C22×D5—44no—
355C22×D5—44no—
356C22×D5—44no—
357C22×D5—44no—
358C22×D5C2×#4114yes—
359C2×C4×C5—28no—
360C2×C4×C5—28no—
361C2×C4×C5—28no—
362C2×C4×C5—28no—
363C2×C4×C5—28no—
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—22no—
380C2×C4×C5—44no—
381C2×C4×C5—44no—
382C2×C4×C5C22×D414yes—
383C2×C4×C5C22×D414yes—
384C2×C4×C5C22×D414yes—
385C2×C4×C5C2×#4114yes—
386C2×C4×C5C2×#4114yes—
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—44no—
406C2×Dic5—44no—
407C2×Dic5—44no—
408C2×Dic5—44no—
409C2×Dic5—44no—
410C2×Dic5C2×#4114yes—
411D20—416no—
412C4×D5—232no—
413C25—51no—
414C25—51no—
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—54no—
426C23×C4—104no—
427C23×C4—104no—
428C23×C4—104no—
429C23×C4C22×D511yescharacteristic
430C23×C4C22×D511yescharacteristic
431C23×C4C22×D511yescharacteristic
432C23×C4C22×D511yescharacteristic
433C23×C4C22×D511yescharacteristic
434C23×C4C22×D511yescharacteristic
435C23×C4C22×D511yescharacteristic
436#126—1032no—
437#117—1032no—
438C2×C4⋊C4—24no—
439C2×C4⋊C4—54no—
440C2×C4⋊C4—54no—
441C2×C4⋊C4—54no—
442C2×C4⋊C4—54no—
443C2×C4⋊C4—54no—
444C2×C4⋊C4—54no—
445C2×C4⋊C4—54no—
446C2×C4⋊C4—54no—
447C2×C4⋊C4—104no—
448C2×C4⋊C4—104no—
449C2×C4⋊C4—104no—
450C2×C4⋊C4—104no—
451C2×C4⋊C4—104no—
452C2×C4⋊C4—202no—
453C2×C4⋊C4—202no—
454C2×C4⋊C4—202no—
455C2×C4⋊C4D2018yescomplemented
456C2×C4⋊C4C22×D514yes—
457C2×C4⋊C4C22×D514yes—
458C2×C22⋊C4—54no—
459C2×C22⋊C4—54no—
460C2×C22⋊C4—54no—
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—104no—
477C2×C22⋊C4—104no—
478C2×C22⋊C4—202no—
479C2×C22⋊C4—202no—
480C2×C42—24no—
481C2×C42—54no—
482C2×C42—54no—
483C2×C42—54no—
484C2×C42—104no—
485C2×C42—104no—
486C2×C42—104no—
487C2×C42C22×D514yes—
488#95—54no—
489#95—54no—
490#95—54no—
491#95—54no—
492#95C22×D514yes—
493#95C22×D514yes—
494#95C22×D514yes—
495#95C22×D514yes—
496C22×C5#52514yes—
497C22×C5#52914yes—
498C22×C5#54214yes—
499C22×C5#54714yes—
500C22×C5#55014yes—
501C22×C5#55114yes—
502C22×C5#55214yes—
503C22×C5C23×D411yescharacteristic
504C22×C5C22×#4111yescharacteristic
505C22×C5C22×#4111yescharacteristic
506C22×C5C22×#4111yescharacteristic
507C22×C5C22×#4111yescharacteristic
508C22×C5C2×H(5,𝔽2)11yescharacteristic
509C22×C5C2×2−1+411yescharacteristic
510C2×D5—24no—
511C2×D5—24no—
512C2×D5—24no—
513C2×D5—42no—
514C2×D5—42no—
515C2×D5—42no—
516C2×D5—42no—
517C2×D5—416no—
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—24no—
530C4×C5—24no—
531C4×C5—42no—
532C4×C5—42no—
533Dic5—24no—
534Dic5—42no—
535Dic5—42no—
536Dic5—42no—
537Dic5—42no—
538Dic5—42no—
539C24—54no—
540C24—52no—
541C24—52no—
542C24—102no—
543C24—102no—
544C24—102no—
545C24—102no—
546C24—102no—
547C24—102no—
548C24—102no—
549C24—102no—
550C24—102no—
551C24—102no—
552C24—102no—
553C24—102no—
554C24—102no—
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—22no—
576C22×C4—54no—
577C22×C4—52no—
578C22×C4—52no—
579C22×C4—52no—
580C22×C4—52no—
581C22×C4—52no—
582C22×C4—52no—
583C22×C4—108no—
584C22×C4—108no—
585C22×C4—1032no—
586C22×C4—102no—
587C22×C4—102no—
588C22×C4—108no—
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—102no—
600C22×C4—102no—
601C22×C4—102no—
602C22×C4—102no—
603C22×C4—102no—
604C22×C4C2×D2014yes—
605C22×C4C2×D2014yes—
606C22×C4C2×D2014yes—
607C22×C4#71114yes—
608C22×C4#71314yes—
609C22×C4C23×D512yes—
610C22×C4C23×D512yes—
611C22×C4C23×D512yes—
612C22×C4C23×D512yes—
613C22×C4C23×D512yes—
614C22×C4C23×D512yes—
615C22×C4C23×D512yes—
616C4⋊C4—28no—
617C4⋊C4—108no—
618C4⋊C4—108no—
619C4⋊C4—108no—
620C4⋊C4—108no—
621C4⋊C4—108no—
622C4⋊C4—204no—
623C4⋊C4—204no—
624C4⋊C4—204no—
625C4⋊C4C2×D20116yescomplemented
626C22⋊C4—108no—
627C22⋊C4—108no—
628C22⋊C4—108no—
629C22⋊C4—108no—
630C22⋊C4—108no—
631C22⋊C4—108no—
632C22⋊C4—108no—
633C22⋊C4—108no—
634C22⋊C4—108no—
635C22⋊C4—204no—
636C22⋊C4—204no—
637C42—28no—
638C42—108no—
639C42—108no—
640C42—108no—
641C2×C5#247918yescomplemented
642C2×C5C2×#52511yescharacteristic
643C2×C5C2×#52911yescharacteristic
644C2×C5C2×#54211yescharacteristic
645C2×C5C2×#54711yescharacteristic
646C2×C5C2×#55011yescharacteristic
647C2×C5C2×#55111yescharacteristic
648C2×C5C2×#55211yescharacteristic
649D5—44no—
650D5—82no—
651C23—54no—
652C23—108no—
653C23—108no—
654C23—102no—
655C23—102no—
656C23—102no—
657C23—102no—
658C23—102no—
659C23—102no—
660C23—108no—
661C23—102no—
662C23—102no—
663C23—102no—
664C23—102no—
665C23—102no—
666C23—102no—
667C23—102no—
668C23—204no—
669C23—204no—
670C23—204no—
671C23—204no—
672C23—204no—
673C23—204no—
674C23—204no—
675C23—204no—
676C23—204no—
677C23—204no—
678C23—204no—
679C23C22×D2012yes—
680C23C2×#71112yes—
681C23C2×#71312yes—
682C23D5×#4112yes—
683C23D5×#4112yes—
684C23#414912yes—
685C23#415012yes—
686C23C24×D511yescharacteristic
687D4—2016no—
688C2×C4—28no—
689C2×C4—28no—
690C2×C4—28no—
691C2×C4—28no—
692C2×C4—28no—
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—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—44no—
710C2×C4—44no—
711C2×C4—54no—
712C2×C4—1032no—
713C2×C4—108no—
714C2×C4—102no—
715C2×C4—102no—
716C2×C4—102no—
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—204no—
732C2×C4—204no—
733C2×C4—204no—
734C2×C4—204no—
735C2×C4—204no—
736C2×C4C22×D2014yes—
737C2×C4C22×D2014yes—
738C2×C4C22×D2014yes—
739C2×C4C2×#71114yes—
740C2×C4C2×#71314yes—
741C5C2×#247911yescharacteristic, complemented, Sylow
742C22—104no—
743C22—104no—
744C22—104no—
745C22—202no—
746C22—202no—
747C22—202no—
748C22—202no—
749C22—2016no—
750C22—202no—
751C22—202no—
752C22—202no—
753C22—202no—
754C22—202no—
755C22—202no—
756C22—202no—
757C22—408no—
758C22#6585814yes—
759C22#6588914yes—
760C22#6591114yes—
761C22#6595814yes—
762C22#6599214yes—
763C22#6602814yes—
764C22#6604414yes—
765C22C23×D2011yescharacteristic
766C22C22×#71111yescharacteristic
767C22C22×#71311yescharacteristic
768C22C2×D5×#4111yescharacteristic
769C22C2×D5×#4111yescharacteristic
770C22C2×#414911yescharacteristic
771C22C2×#415011yescharacteristic
772C4—24no—
773C4—24no—
774C4—24no—
775C4—24no—
776C4—24no—
777C4—42no—
778C4—42no—
779C4—104no—
780C4—202no—
781C4—202no—
782C4—202no—
783C4—202no—
784C4—202no—
785C2—204no—
786C2—402no—
787C2#1060674918yesdirect product factor
788C2C2×#6585811yescharacteristic
789C2C2×#6588911yescharacteristic
790C2C2×#6591111yescharacteristic
791C2C2×#6595811yescharacteristic
792C2C2×#6599211yescharacteristic
793C2C2×#6602811yescharacteristic
794C2C2×#6604411yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC2×C5×#387C2
socleC24×C5C24
prime radicalC23×D20C22
hypercenterC2×#387D5
hypocenterC5C2×#2479
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
1. C22×#4044C2semidirect
2. C22×#4038C2semidirect
3. C2×C5×#387C2semidirect
5. C2×#65274C2semidirect
7. C2×C4×C4⋊Dic5C2semidirect
8. #10606749C2direct (N × H)
9. C2×#64966C2semidirect
10. C2×#64966C2semidirect
12. C2×#64957C2semidirect
13. C2×#64950C2semidirect
14. C2×#64959C2semidirect
15. C2×#64959C2semidirect
16. C2×#64959C2semidirect
45. C2×#4044C22semidirect
47. C2×#4038C22semidirect
48. C5×#387C22semidirect
58. #65274C22semidirect
60. C4×C4⋊Dic5C22semidirect
61. #64966C22semidirect
62. #64966C22semidirect
63. #64959C22semidirect
64. #64959C22semidirect
65. #64959C22semidirect
66. #64957C22semidirect
68. #64950C22semidirect
94. C2×C5×C4⋊C4D4semidirect
165. C2×#387D5semidirect
247. C5×C4⋊C4C2×D4semidirect
311. #387C2×D5semidirect
455. C2×C4⋊C4D20semidirect
625. C4⋊C4C2×D20semidirect
641. C2×C5#2479semidirect
741. C5C2×#2479semidirect
787. C2#10606749direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#40442
C22×#40382
C2×C5×#3872
C2×#652802
C2×#652742
C2×#652282
C2×C4×C4⋊Dic52
#106067492
C2×#649662
C2×#649542
C2×#649572
C2×#649502
C2×#649592
C2×#24795