Finite Group Databasebeta

← C2×#10608915 #12268376

Subgroups — C2×#10608915 #12268376

Order 1280.

2898 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×#4093C211yesmaximal, characteristic
2C22×#4044C211yesmaximal, characteristic, complemented
3C2×C5×#395C211yesmaximal, characteristic, complemented
4C2×#65519C211yesmaximal, characteristic, complemented
5C2×#65280C211yesmaximal, characteristic
6C2×#65276C211yesmaximal, characteristic, complemented
7C2×#65279C211yesmaximal, characteristic, complemented
8C2×#65279C211yesmaximal, characteristic, complemented
9C2×C4⋊C4×Dic5C211yesmaximal, characteristic, complemented
10#10608915C2116yesmaximal, direct product factor
11C2×#64966C211yesmaximal, characteristic, complemented
12C2×#64954C211yesmaximal, characteristic
13C2×#64963C211yesmaximal, characteristic, complemented
14C2×#64958C211yesmaximal, characteristic, complemented
15C2×#64943C211yesmaximal, characteristic, complemented
16C2×#64955C211yesmaximal, characteristic, complemented
17C23×C5×Q8C2211yescharacteristic
18C23×D20C2211yescharacteristic
19C23×C4×D5C2211yescharacteristic
20C22×C5×C4⋊C4C2211yescharacteristic
21C22×C5×C4⋊C4C2211yescharacteristic
22C22×C5×C4⋊C4C2211yescharacteristic
23C2×#4093—28no—
24C2×#4093C2218yes—
25C22×#685C2211yescharacteristic
26C22×#685C2211yescharacteristic
27C22×#685C2211yescharacteristic
28C22×#685C2211yescharacteristic
29C22×#685C2211yescharacteristic
30C22×#685C2211yescharacteristic
31C22×#685C2211yescharacteristic
32C22×#685C2211yescharacteristic
33C22×#685C2211yescharacteristic
34C22×#685C2211yescharacteristic
35C22×#685C2211yescharacteristic
36C22×C4⋊Dic5C2211yescharacteristic
37C22×C4⋊Dic5C2211yescharacteristic
38C22×C4⋊Dic5C2211yescharacteristic
39C22×#683C2211yescharacteristic
40C22×C4×Dic5C2211yescharacteristic
41C22×C4×Dic5C2211yescharacteristic
42C22×C4×Dic5C2211yescharacteristic
43C22×C4×Dic5C2211yescharacteristic
44C2×#4044—28no—
45C2×#4044C2218yescomplemented
46C5×#395C2218yescomplemented
47C2×C5×#95C2211yescharacteristic
48C2×C5×#95C2211yescharacteristic
49C2×C5×#95C2211yescharacteristic
50#65519C2218yescomplemented
51C2×#3963C2211yescharacteristic
52C2×#3963C2211yescharacteristic
53C2×#3963C2211yescharacteristic
54C2×#3963C2211yescharacteristic
55C2×#3963C2211yescharacteristic
56C2×#3963C2211yescharacteristic
57C2×#3963C2211yescharacteristic
58#65280C2218yes—
59#65279C2218yescomplemented
60#65279C2218yescomplemented
61#65276C2218yescomplemented
62C4⋊C4×Dic5C2218yescomplemented
63#64966C2218yescomplemented
64#64963C2218yescomplemented
65#64958C2218yescomplemented
66#64955C2218yescomplemented
67#64954C2218yes—
68#64943C2218yescomplemented
69C2×#2521—51nomaximal, Sylow
70C24×D5C2311yescharacteristic
71C24×D5C2311yescharacteristic
72C22×C5×Q8—24no—
73C22×C5×Q8—24no—
74C22×C5×Q8—42no—
75C22×C5×Q8C2314yes—
76C23×C4×C5C2311yescharacteristic
77C23×C4×C5C2311yescharacteristic
78C23×C4×C5C2311yescharacteristic
79C23×C4×C5C2311yescharacteristic
80C23×C4×C5C2311yescharacteristic
81C23×C4×C5C2311yescharacteristic
82C23×C4×C5C2311yescharacteristic
83C23×Dic5C2311yescharacteristic
84C23×Dic5C2311yescharacteristic
85C23×Dic5C2311yescharacteristic
86C23×Dic5C2311yescharacteristic
87C23×Dic5C2311yescharacteristic
88C23×Dic5C2311yescharacteristic
89C22×D20—24no—
90C22×D20—24no—
91C22×D20—42no—
92C22×D20C2314yes—
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⋊C4—42no—
100C2×C5×C4⋊C4C2314yes—
101C2×C5×C4⋊C4C2314yes—
102C2×C5×C4⋊C4C2314yes—
103#4093—232no—
104C2×#685—24no—
105C2×#685—24no—
106C2×#685—24no—
107C2×#685—24no—
108C2×#685—24no—
109C2×#685—24no—
110C2×#685—24no—
111C2×#685—24no—
112C2×#685—24no—
113C2×#685—42no—
114C2×#685D418yes—
115C2×#685C2314yes—
116C2×#685C2314yes—
117C2×#685C2314yes—
118C2×#685C2314yes—
119C2×#685C2314yes—
120C2×#685C2314yes—
121C2×#685C2314yes—
122C2×#685C2314yes—
123C2×#685C2314yes—
124C2×#685C2314yes—
125C2×#685C2314yes—
126C2×C4⋊Dic5—24no—
127C2×C4⋊Dic5—24no—
128C2×C4⋊Dic5—24no—
129C2×C4⋊Dic5C2314yes—
130C2×C4⋊Dic5C2314yes—
131C2×C4⋊Dic5C2314yes—
132C2×#683—24no—
133C2×#683C2314yes—
134C2×C4×Dic5—24no—
135C2×C4×Dic5—24no—
136C2×C4×Dic5—24no—
137C2×C4×Dic5—42no—
138C2×C4×Dic5C2314yes—
139C2×C4×Dic5C2314yes—
140C2×C4×Dic5C2314yes—
141C2×C4×Dic5C2314yes—
142#4044—232no—
143C5×#95C2314yes—
144C5×#95C2314yes—
145C5×#95C2314yes—
146#3963C2314yes—
147#3963C2314yes—
148#3963C2314yes—
149#3963C2314yes—
150#3963C2314yes—
151#3963C2314yes—
152#3963C2314yes—
153C22×#126—51no—
154C22×#124—51no—
155#2521—516no—
156C2×#399—51no—
157C2×#397—51no—
158C2×#395D511yescharacteristic, complemented
159C2×#394—51no—
160C2×#391—51no—
161C2×#388—51no—
162C2×#388—51no—
163C2×#388—51no—
164C2×#387—51no—
165C2×#386—51no—
166C2×#380—51no—
167C2×C4×C4⋊C4—51no—
168C2×C4×C22⋊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×D5C2×D414yes—
184C23×D5C2412yes—
185C23×D5C2412yes—
186C2×C5×Q8—28no—
187C2×C5×Q8—28no—
188C2×C5×Q8—44no—
189C2×C5×Q8—416no—
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×C5C2×D414yes—
208C22×C4×C5#4114yes—
209C22×C4×C5#4114yes—
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—28no—
243C2×D20—28no—
244C2×D20—44no—
245C2×D20—416no—
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×C4⋊C4—44no—
253#685—28no—
254#685—28no—
255#685—28no—
256#685—28no—
257#685—28no—
258#685—28no—
259#685—28no—
260#685—28no—
261#685—28no—
262#685—44no—
263#685C2×D4116yes—
264C4⋊Dic5—28no—
265C4⋊Dic5—28no—
266C4⋊Dic5—28no—
267#683—28no—
268C4×Dic5—28no—
269C4×Dic5—28no—
270C4×Dic5—28no—
271C4×Dic5—44no—
272C23×Q8C2×D511yescharacteristic
273C23×D4—51no—
274C24×C4—51no—
275C2×#126—58no—
276C2×#126—108no—
277C2×#124—58no—
278C2×#124—108no—
279C22×C4⋊C4—51no—
280C22×C4⋊C4—51no—
281C22×C4⋊C4—51no—
282C22×C4⋊C4—51no—
283C22×C4⋊C4C2×D511yescharacteristic
284C22×C4⋊C4C2×D511yescharacteristic
285C22×C4⋊C4C2×D511yescharacteristic
286C22×C22⋊C4—51no—
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×C42—51no—
298C22×C42—51no—
299C22×C42—51no—
300C22×C42—51no—
301#399—58no—
302#397—58no—
303#395C2×D518yescomplemented
304#394—58no—
305#391—58no—
306#388—58no—
307#388—58no—
308#388—58no—
309#387—58no—
310#386—58no—
311#380—58no—
312C4×C4⋊C4—58no—
313C4×C22⋊C4—58no—
314C2×#95—51no—
315C2×#95—51no—
316C2×#95—51no—
317C2×#95—51no—
318C2×#95—51no—
319C2×#95—51no—
320C2×#95—51no—
321C2×#95C2×D511yescharacteristic
322C2×#95C2×D511yescharacteristic
323C2×#95C2×D511yescharacteristic
324C23×C5C22×D412yes—
325C23×C5C2×#4112yes—
326C23×C5C2×#4112yes—
327C23×C5C2×#4112yes—
328C23×C5C2×#4112yes—
329C23×C5H(5,𝔽2)12yes—
330C23×C52−1+412yes—
331C23×C5C2511yescharacteristic
332C22×D5—28no—
333C22×D5—28no—
334C22×D5—28no—
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—22no—
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×D5—44no—
359C22×D5C22×D414yes—
360C5×Q8—416no—
361C2×C4×C5—28no—
362C2×C4×C5—28no—
363C2×C4×C5—28no—
364C2×C4×C5—28no—
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—22no—
381C2×C4×C5—22no—
382C2×C4×C5—44no—
383C2×C4×C5—44no—
384C2×C4×C5—44no—
385C2×C4×C5C22×D414yes—
386C2×C4×C5C2×#4114yes—
387C2×C4×C5C2×#4114yes—
388C2×C4×C5C2×#4114yes—
389C2×Dic5—28no—
390C2×Dic5—28no—
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×Dic5C22×D414yes—
412C2×Dic5C2×#4114yes—
413D20—416no—
414C4×D5—416no—
415C25—51no—
416C25—51no—
417C22×Q8—24no—
418C22×Q8—24no—
419C22×Q8—42no—
420C22×Q8C22×D514yes—
421C22×D4—54no—
422C22×D4—104no—
423C22×D4—104no—
424C22×D4—202no—
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×D511yescharacteristic
439C23×C4C22×D511yescharacteristic
440C23×C4C22×D511yescharacteristic
441C23×C4C22×D511yescharacteristic
442#126—1032no—
443#124—1032no—
444C2×C4⋊C4—24no—
445C2×C4⋊C4—24no—
446C2×C4⋊C4—42no—
447C2×C4⋊C4—54no—
448C2×C4⋊C4—54no—
449C2×C4⋊C4—54no—
450C2×C4⋊C4—54no—
451C2×C4⋊C4—104no—
452C2×C4⋊C4—104no—
453C2×C4⋊C4—104no—
454C2×C4⋊C4—104no—
455C2×C4⋊C4C22×D514yes—
456C2×C4⋊C4C22×D514yes—
457C2×C4⋊C4C22×D514yes—
458C2×C22⋊C4—58no—
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—54no—
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—104no—
479C2×C22⋊C4—202no—
480C2×C42—54no—
481C2×C42—54no—
482C2×C42—54no—
483C2×C42—54no—
484C2×C42—104no—
485C2×C42—104no—
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#95C22×D514yes—
496#95C22×D514yes—
497#95C22×D514yes—
498C22×C5#52914yes—
499C22×C5#53214yes—
500C22×C5#54214yes—
501C22×C5#54614yes—
502C22×C5#54714yes—
503C22×C5#55114yes—
504C22×C5#55614yes—
505C22×C5C23×D411yescharacteristic
506C22×C5C22×#4111yescharacteristic
507C22×C5C22×#4111yescharacteristic
508C22×C5C22×#4111yescharacteristic
509C22×C5C22×#4111yescharacteristic
510C22×C5C2×H(5,𝔽2)11yescharacteristic
511C22×C5C2×2−1+411yescharacteristic
512C2×D5—24no—
513C2×D5—24no—
514C2×D5—24no—
515C2×D5—42no—
516C2×D5—42no—
517C2×D5—42no—
518C2×D5—42no—
519C2×D5—416no—
520C2×D5—42no—
521C2×D5—42no—
522C2×D5—42no—
523C2×D5—42no—
524C2×D5—42no—
525C2×D5—42no—
526C2×D5—42no—
527C2×D5—88no—
528C4×C5—24no—
529C4×C5—24no—
530C4×C5—24no—
531C4×C5—24no—
532C4×C5—42no—
533C4×C5—42no—
534C4×C5—42no—
535Dic5—24no—
536Dic5—24no—
537Dic5—42no—
538Dic5—42no—
539Dic5—42no—
540Dic5—42no—
541C24—54no—
542C24—52no—
543C24—52no—
544C24—102no—
545C24—102no—
546C24—102no—
547C24—102no—
548C24—102no—
549C24—102no—
550C24—102no—
551C24—102no—
552C24—102no—
553C24—102no—
554C24—102no—
555C24—102no—
556C24—102no—
557C24C23×D511yescharacteristic
558C2×Q8—28no—
559C2×Q8—28no—
560C2×Q8—44no—
561C2×Q8—416no—
562C2×D4—108no—
563C2×D4—108no—
564C2×D4—204no—
565C2×D4—2016no—
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—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—54no—
584C22×C4—54no—
585C22×C4—52no—
586C22×C4—52no—
587C22×C4—52no—
588C22×C4—52no—
589C22×C4—52no—
590C22×C4—52no—
591C22×C4—108no—
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—108no—
609C22×C4—204no—
610C22×C4—2016no—
611C22×C4D4×D514yes—
612C22×C4#71114yes—
613C22×C4#71314yes—
614C22×C4#71314yes—
615C22×C4C23×D512yes—
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—44no—
625C4⋊C4—108no—
626C4⋊C4—108no—
627C4⋊C4—108no—
628C4⋊C4—108no—
629C22⋊C4—516no—
630C22⋊C4—108no—
631C22⋊C4—108no—
632C22⋊C4—108no—
633C22⋊C4—108no—
634C22⋊C4—108no—
635C22⋊C4—108no—
636C22⋊C4—108no—
637C22⋊C4—108no—
638C22⋊C4—108no—
639C22⋊C4—204no—
640C42—108no—
641C42—108no—
642C42—108no—
643C42—204no—
644C2×C5#252118yescomplemented
645C2×C5C2×#52911yescharacteristic
646C2×C5C2×#53211yescharacteristic
647C2×C5C2×#54211yescharacteristic
648C2×C5C2×#54611yescharacteristic
649C2×C5C2×#54711yescharacteristic
650C2×C5C2×#55111yescharacteristic
651C2×C5C2×#55611yescharacteristic
652D5—44no—
653D5—82no—
654C23—54no—
655C23—108no—
656C23—108no—
657C23—108no—
658C23—102no—
659C23—102no—
660C23—102no—
661C23—102no—
662C23—102no—
663C23—102no—
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—
678C23—204no—
679C23—204no—
680C23—204no—
681C23—204no—
682C23C2×D4×D512yes—
683C23C2×#71112yes—
684C23#414412yes—
685C23C2×#71312yes—
686C23C2×#71312yes—
687C23#414712yes—
688C23D5×#4112yes—
689C23C24×D511yescharacteristic
690Q8—416no—
691D4—2016no—
692C2×C4—28no—
693C2×C4—28no—
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—22no—
713C2×C4—44no—
714C2×C4—44no—
715C2×C4—44no—
716C2×C4—54no—
717C2×C4—54no—
718C2×C4—108no—
719C2×C4—108no—
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×C4C2×D4×D514yes—
742C2×C4C2×#71114yes—
743C2×C4C2×#71314yes—
744C2×C4C2×#71314yes—
745C5C2×#252111yescharacteristic, complemented, Sylow
746C22—104no—
747C22—104no—
748C22—104no—
749C22—202no—
750C22—2016no—
751C22—202no—
752C22—202no—
753C22—202no—
754C22—202no—
755C22—202no—
756C22—202no—
757C22—202no—
758C22—202no—
759C22—202no—
760C22—202no—
761C22—408no—
762C22#6592514yes—
763C22#6595814yes—
764C22#6596514yes—
765C22#6597114yes—
766C22#6605914yes—
767C22#6606614yes—
768C22#6606714yes—
769C22C22×D4×D511yescharacteristic
770C22C22×#71111yescharacteristic
771C22C2×#414411yescharacteristic
772C22C22×#71311yescharacteristic
773C22C22×#71311yescharacteristic
774C22C2×#414711yescharacteristic
775C22C2×D5×#4111yescharacteristic
776C4—24no—
777C4—24no—
778C4—24no—
779C4—24no—
780C4—42no—
781C4—42no—
782C4—42no—
783C4—104no—
784C4—104no—
785C4—202no—
786C4—202no—
787C4—202no—
788C4—202no—
789C2—204no—
790C2—402no—
791C2#1060891518yesdirect product factor
792C2C2×#6592511yescharacteristic
793C2C2×#6595811yescharacteristic
794C2C2×#6596511yescharacteristic
795C2C2×#6597111yescharacteristic
796C2C2×#6605911yescharacteristic
797C2C2×#6606611yescharacteristic
798C2C2×#6606711yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC2×C5×#395C2
socleC24×C5C24
prime radicalC23×D20C22
hypercenterC2×#395D5
hypocenterC5C2×#2521
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#395

Complements

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

NH ≅ G/Ntype
2. C22×#4044C2semidirect
3. C2×C5×#395C2semidirect
4. C2×#65519C2semidirect
6. C2×#65276C2semidirect
7. C2×#65279C2semidirect
8. C2×#65279C2semidirect
9. C2×C4⋊C4×Dic5C2semidirect
10. #10608915C2direct (N × H)
11. C2×#64966C2semidirect
13. C2×#64963C2semidirect
14. C2×#64958C2semidirect
15. C2×#64943C2semidirect
16. C2×#64955C2semidirect
45. C2×#4044C22semidirect
46. C5×#395C22semidirect
50. #65519C22semidirect
59. #65279C22semidirect
60. #65279C22semidirect
61. #65276C22semidirect
62. C4⋊C4×Dic5C22semidirect
63. #64966C22semidirect
64. #64963C22semidirect
65. #64958C22semidirect
66. #64955C22semidirect
68. #64943C22semidirect
158. C2×#395D5semidirect
303. #395C2×D5semidirect
644. C2×C5#2521semidirect
745. C5C2×#2521semidirect
791. C2#10608915direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#40932
C22×#40442
C2×C5×#3952
C2×#655192
C2×#652802
C2×#652762
C2×#652792
C2×C4⋊C4×Dic52
#106089152
C2×#649662
C2×#649542
C2×#649632
C2×#649582
C2×#649432
C2×#649552
C2×#25215