Finite Group Databasebeta

← C2×#10605106 #12267006

Subgroups — C2×#10605106 #12267006

Order 1280.

3222 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#4075C211yesmaximal, characteristic
2C22×C4×C22⋊D5C211yesmaximal, characteristic
3C22×C5×#95C211yesmaximal, characteristic, complemented
4C2×#65502C211yesmaximal, characteristic
5C2×#65499C211yesmaximal, characteristic, complemented
6C2×#65500C211yesmaximal, characteristic, complemented
7C2×#65501C211yesmaximal, characteristic, complemented
8#10605106C2116yesmaximal, direct product factor
9C2×#64964C211yesmaximal, characteristic, complemented
10C2×#64957C211yesmaximal, characteristic, complemented
11C2×#64953C211yesmaximal, characteristic, complemented
12C2×#64947C211yesmaximal, characteristic, complemented
13C2×#64946C211yesmaximal, characteristic, complemented
14C2×#64963C211yesmaximal, characteristic, complemented
15C2×#64943C211yesmaximal, characteristic, complemented
16C2×#64941C211yesmaximal, characteristic, complemented
17C24×C4×C5C2211yescharacteristic
18C24×C4×C5C2211yescharacteristic
19C24×C4×C5C2211yescharacteristic
20C23×C22⋊D5C2211yescharacteristic
21C23×C4×D5C2211yescharacteristic
22C22×C22⋊Dic5C2211yescharacteristic
23C22×C22⋊Dic5C2211yescharacteristic
24C22×C22⋊Dic5C2211yescharacteristic
25C2×#4075—28no—
26C2×#4075C2218yes—
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×#683C2211yescharacteristic
37C22×#683C2211yescharacteristic
38C22×#683C2211yescharacteristic
39C22×#683C2211yescharacteristic
40C22×#683C2211yescharacteristic
41C22×C4×Dic5C2211yescharacteristic
42C2×C5×#95C2211yescharacteristic
43C2×C5×#95C2211yescharacteristic
44C2×C5×#95C2211yescharacteristic
45C2×C5×#95C2211yescharacteristic
46C2×C5×#95C2218yescomplemented
47#65502C2218yes—
48#65501C2218yescomplemented
49#65500C2218yescomplemented
50#65499C2218yescomplemented
51C2×#3963C2211yescharacteristic
52C2×#3963C2211yescharacteristic
53C2×#3963C2211yescharacteristic
54C2×#3963C2211yescharacteristic
55C2×#3963C2211yescharacteristic
56C2×#3963C2211yescharacteristic
57C2×#3963C2211yescharacteristic
58C2×#3963C2211yescharacteristic
59C2×#3963C2211yescharacteristic
60C2×#3963C2211yescharacteristic
61#64964C2218yescomplemented
62#64963C2218yescomplemented
63#64957C2218yescomplemented
64#64953C2218yescomplemented
65#64947C2218yescomplemented
66#64946C2218yescomplemented
67#64943C2218yescomplemented
68#64941C2218yescomplemented
69C2×#2419—51nomaximal, Sylow
70C25×C5C2311yescharacteristic
71C24×D5C2311yescharacteristic
72C23×C4×C5—24no—
73C23×C4×C5—24no—
74C23×C4×C5—24no—
75C23×C4×C5—24no—
76C23×C4×C5—24no—
77C23×C4×C5—24no—
78C23×C4×C5—24no—
79C23×C4×C5—42no—
80C23×C4×C5—42no—
81C23×C4×C5C2311yescharacteristic
82C23×C4×C5C2311yescharacteristic
83C23×C4×C5C2311yescharacteristic
84C23×C4×C5C2311yescharacteristic
85C23×C4×C5C2314yes—
86C23×C4×C5C2314yes—
87C23×C4×C5C2314yes—
88C23×C4×C5C2311yescharacteristic
89C23×C4×C5C2311yescharacteristic
90C22×C22⋊D5—24no—
91C22×C22⋊D5—24no—
92C22×C22⋊D5D418yes—
93C22×C22⋊D5C2314yes—
94C23×Dic5C2311yescharacteristic
95C23×Dic5C2311yescharacteristic
96C23×Dic5C2311yescharacteristic
97C23×Dic5C2311yescharacteristic
98C23×Dic5C2311yescharacteristic
99C23×Dic5C2311yescharacteristic
100C23×Dic5C2311yescharacteristic
101C22×C4×D5—24no—
102C22×C4×D5—24no—
103C22×C4×D5—42no—
104C22×C4×D5C2314yes—
105C2×C22⋊Dic5—24no—
106C2×C22⋊Dic5—24no—
107C2×C22⋊Dic5—24no—
108C2×C22⋊Dic5C2314yes—
109C2×C22⋊Dic5C2314yes—
110C2×C22⋊Dic5C2314yes—
111#4075—232no—
112C4×C22⋊D5—232no—
113C2×#685—24no—
114C2×#685—24no—
115C2×#685—24no—
116C2×#685—24no—
117C2×#685—42no—
118C2×#685C2314yes—
119C2×#685C2314yes—
120C2×#685C2314yes—
121C2×#685C2314yes—
122C2×#685C2314yes—
123C2×C4⋊Dic5—24no—
124C2×C4⋊Dic5—42no—
125C2×C4⋊Dic5C2314yes—
126C2×C4⋊Dic5C2314yes—
127C2×#683—24no—
128C2×#683—24no—
129C2×#683—24no—
130C2×#683—24no—
131C2×#683—42no—
132C2×#683C2314yes—
133C2×#683C2314yes—
134C2×#683C2314yes—
135C2×#683C2314yes—
136C2×#683C2314yes—
137C2×C4×Dic5—24no—
138C2×C4×Dic5C2314yes—
139C5×#95C2314yes—
140C5×#95C2314yes—
141C5×#95C2314yes—
142C5×#95C2314yes—
143#3963C2314yes—
144#3963C2314yes—
145#3963C2314yes—
146#3963C2314yes—
147#3963C2314yes—
148#3963C2314yes—
149#3963C2314yes—
150#3963C2314yes—
151#3963C2314yes—
152#3963C2314yes—
153C22×#123—51no—
154C22×C4×D4—51no—
155#2419—516no—
156C2×#400—51no—
157C2×#398—51no—
158C2×#397—51no—
159C2×#397—51no—
160C2×#387—51no—
161C2×#387—51no—
162C2×#386—51no—
163C2×#385—51no—
164C2×#385—51no—
165C2×#381—51no—
166C2×#381—51no—
167C2×#380—51no—
168C22×#95D511yescharacteristic, complemented
169C24×C5—22no—
170C24×C5—22no—
171C24×C5—22no—
172C24×C5—22no—
173C24×C5C2×D414yes—
174C24×C5#4114yes—
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—28no—
194C22×C4×C5—28no—
195C22×C4×C5—28no—
196C22×C4×C5—22no—
197C22×C4×C5—22no—
198C22×C4×C5—22no—
199C22×C4×C5—22no—
200C22×C4×C5—28no—
201C22×C4×C5—28no—
202C22×C4×C5—22no—
203C22×C4×C5—22no—
204C22×C4×C5—22no—
205C22×C4×C5—22no—
206C22×C4×C5—22no—
207C22×C4×C5—28no—
208C22×C4×C5—28no—
209C22×C4×C5—44no—
210C22×C4×C5—44no—
211C22×C4×C5—416no—
212C22×C4×C5—416no—
213C22×C4×C5—416no—
214C22×C4×C5#4114yes—
215C22×C4×C5#4114yes—
216C22×C4×C5C2412yes—
217C22×C4×C5C2412yes—
218C22×C4×C5C2412yes—
219C22×C4×C5C2412yes—
220C22×C4×C5C2412yes—
221C22×C4×C5C2412yes—
222C2×C22⋊D5—232no—
223C2×C22⋊D5—28no—
224C2×C22⋊D5—28no—
225C2×C22⋊D5C2×D4116yes—
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×Dic5—22no—
238C22×Dic5—22no—
239C22×Dic5—22no—
240C22×Dic5—22no—
241C22×Dic5—22no—
242C22×Dic5—22no—
243C22×Dic5—22no—
244C22×Dic5—22no—
245C22×Dic5—22no—
246C22×Dic5C2×D414yes—
247C22×Dic5C2412yes—
248C22×Dic5C2412yes—
249C22×Dic5C2412yes—
250C22×Dic5C2412yes—
251C22×Dic5C2412yes—
252C22×Dic5C2412yes—
253C22×Dic5C2412yes—
254C2×C4×D5—28no—
255C2×C4×D5—28no—
256C2×C4×D5—44no—
257C2×C4×D5—416no—
258C22⋊Dic5—28no—
259C22⋊Dic5—28no—
260C22⋊Dic5—28no—
261#685—28no—
262#685—28no—
263#685—28no—
264#685—28no—
265#685—44no—
266C4⋊Dic5—28no—
267C4⋊Dic5—44no—
268#683—28no—
269#683—28no—
270#683—28no—
271#683—28no—
272#683—44no—
273C4×Dic5—28no—
274C23×D4—51no—
275C24×C4—51no—
276C24×C4C2×D511yescharacteristic
277C24×C4C2×D511yescharacteristic
278C24×C4C2×D511yescharacteristic
279C2×#123—58no—
280C2×#123—108no—
281C2×C4×D4—58no—
282C2×C4×D4—108no—
283C22×C4⋊C4—51no—
284C22×C4⋊C4—51no—
285C22×C4⋊C4—51no—
286C22×C4⋊C4—51no—
287C22×C4⋊C4—51no—
288C22×C4⋊C4—51no—
289C22×C4⋊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—
299#400—58no—
300#398—58no—
301#397—58no—
302#397—58no—
303#387—58no—
304#387—58no—
305#386—58no—
306#385—58no—
307#385—58no—
308#381—58no—
309#381—58no—
310#380—58no—
311C2×#95—51no—
312C2×#95—51no—
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×#95C2×D511yescharacteristic
322C2×#95C2×D511yescharacteristic
323C2×#95C2×D511yescharacteristic
324C2×#95C2×D511yescharacteristic
325C2×#95C2×D518yescomplemented
326C23×C5—28no—
327C23×C5—28no—
328C23×C5—28no—
329C23×C5—28no—
330C23×C5—28no—
331C23×C5—28no—
332C23×C5—22no—
333C23×C5—22no—
334C23×C5—22no—
335C23×C5—22no—
336C23×C5#123116yes—
337C23×C5C22×D414yes—
338C23×C5C22×D412yes—
339C23×C5C2×#4114yes—
340C23×C5C2×#4112yes—
341C23×C5C2×#4112yes—
342C23×C5C2×#4112yes—
343C23×C5C2×#4114yes—
344C23×C5C2×#4112yes—
345C23×C5H(5,𝔽2)12yes—
346C23×C52−1+412yes—
347C23×C5C2511yescharacteristic
348C22×D5—28no—
349C22×D5—28no—
350C22×D5—28no—
351C22×D5—22no—
352C22×D5—22no—
353C22×D5—22no—
354C22×D5—22no—
355C22×D5—22no—
356C22×D5—22no—
357C22×D5—44no—
358C22×D5—44no—
359C22×D5—44no—
360C22×D5—44no—
361C22×D5C22×D414yes—
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—416no—
381C2×C4×C5—416no—
382C2×C4×C5—416no—
383C2×C4×C5—44no—
384C2×C4×C5—44no—
385C2×C4×C5—44no—
386C2×C4×C5—44no—
387C2×C4×C5C2×#4114yes—
388C2×C4×C5C2×#4114yes—
389C22⋊D5—232no—
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—22no—
408C2×Dic5—22no—
409C2×Dic5—22no—
410C2×Dic5—22no—
411C2×Dic5—44no—
412C2×Dic5—44no—
413C2×Dic5—44no—
414C2×Dic5—44no—
415C2×Dic5—44no—
416C2×Dic5—44no—
417C2×Dic5C22×D414yes—
418C4×D5—416no—
419C25—51no—
420C25C22×D511yescharacteristic
421C22×D4—58no—
422C22×D4—54no—
423C22×D4—104no—
424C22×D4—104no—
425C23×C4—24no—
426C23×C4—24no—
427C23×C4—24no—
428C23×C4—24no—
429C23×C4—24no—
430C23×C4—24no—
431C23×C4—24no—
432C23×C4—42no—
433C23×C4—42no—
434C23×C4—51no—
435C23×C4—51no—
436C23×C4—51no—
437C23×C4—51no—
438C23×C4—51no—
439C23×C4—51no—
440C23×C4—51no—
441C23×C4—54no—
442C23×C4—104no—
443C23×C4—104no—
444C23×C4—202no—
445C23×C4C22×D514yes—
446C23×C4C22×D511yescharacteristic
447C23×C4C22×D511yescharacteristic
448C23×C4C22×D511yescharacteristic
449C23×C4C22×D511yescharacteristic
450C23×C4C22×D514yes—
451C23×C4C22×D514yes—
452C23×C4C22×D511yescharacteristic
453C23×C4C22×D511yescharacteristic
454#123—1032no—
455C4×D4—1032no—
456C2×C4⋊C4—54no—
457C2×C4⋊C4—54no—
458C2×C4⋊C4—54no—
459C2×C4⋊C4—54no—
460C2×C4⋊C4—54no—
461C2×C4⋊C4—54no—
462C2×C4⋊C4—54no—
463C2×C4⋊C4—104no—
464C2×C4⋊C4—104no—
465C2×C4⋊C4—104no—
466C2×C4⋊C4—104no—
467C2×C4⋊C4—104no—
468C2×C4⋊C4—202no—
469C2×C4⋊C4—202no—
470C2×C22⋊C4—54no—
471C2×C22⋊C4—54no—
472C2×C22⋊C4—54no—
473C2×C22⋊C4—54no—
474C2×C22⋊C4—54no—
475C2×C22⋊C4—54no—
476C2×C22⋊C4—54no—
477C2×C22⋊C4—54no—
478C2×C22⋊C4—104no—
479C2×C22⋊C4—104no—
480C2×C22⋊C4—104no—
481C2×C22⋊C4—104no—
482C2×C22⋊C4—104no—
483C2×C22⋊C4—104no—
484C2×C22⋊C4—104no—
485C2×C22⋊C4—202no—
486C2×C42—54no—
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#95—54no—
497#95—54no—
498#95C22×D514yes—
499#95C22×D514yes—
500#95C22×D514yes—
501#95C22×D514yes—
502C22×C5—24no—
503C22×C5—232no—
504C22×C5—24no—
505C22×C5—24no—
506C22×C5—24no—
507C22×C5—24no—
508C22×C5—24no—
509C22×C5C2×#12318yes—
510C22×C5C2×#12314yes—
511C22×C5#52914yes—
512C22×C5#53914yes—
513C22×C5#54614yes—
514C22×C5#54714yes—
515C22×C5#55114yes—
516C22×C5#55214yes—
517C22×C5C23×D411yescharacteristic
518C22×C5C22×#4111yescharacteristic
519C22×C5C22×#4111yescharacteristic
520C22×C5C22×#4111yescharacteristic
521C22×C5C22×#4111yescharacteristic
522C22×C5C2×H(5,𝔽2)11yescharacteristic
523C22×C5C2×2−1+411yescharacteristic
524C2×D5—24no—
525C2×D5—24no—
526C2×D5—24no—
527C2×D5—42no—
528C2×D5—416no—
529C2×D5—42no—
530C2×D5—42no—
531C2×D5—42no—
532C4×C5—24no—
533C4×C5—24no—
534C4×C5—42no—
535C4×C5—42no—
536C4×C5—42no—
537C4×C5—42no—
538Dic5—24no—
539Dic5—42no—
540Dic5—42no—
541Dic5—42no—
542Dic5—42no—
543Dic5—42no—
544Dic5—42no—
545C24—22no—
546C24—22no—
547C24—22no—
548C24—22no—
549C24—54no—
550C24—52no—
551C24—102no—
552C24—102no—
553C24—102no—
554C24—102no—
555C24—102no—
556C24—102no—
557C24#70914yes—
558C24D4×D514yes—
559C24#71114yes—
560C24C23×D512yes—
561C24C23×D511yescharacteristic
562C2×D4—516no—
563C2×D4—108no—
564C2×D4—108no—
565C2×D4—1032no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—28no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—28no—
579C22×C4—28no—
580C22×C4—28no—
581C22×C4—28no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—28no—
588C22×C4—28no—
589C22×C4—44no—
590C22×C4—44no—
591C22×C4—416no—
592C22×C4—416no—
593C22×C4—416no—
594C22×C4—54no—
595C22×C4—52no—
596C22×C4—52no—
597C22×C4—52no—
598C22×C4—52no—
599C22×C4—52no—
600C22×C4—52no—
601C22×C4—52no—
602C22×C4—108no—
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—102no—
616C22×C4—102no—
617C22×C4—102no—
618C22×C4—102no—
619C22×C4—102no—
620C22×C4—102no—
621C22×C4—102no—
622C22×C4—102no—
623C22×C4—108no—
624C22×C4—204no—
625C22×C4—2016no—
626C22×C4#70914yes—
627C22×C4#70914yes—
628C22×C4C23×D512yes—
629C22×C4C23×D512yes—
630C22×C4C23×D512yes—
631C22×C4C23×D512yes—
632C22×C4C23×D512yes—
633C22×C4C23×D512yes—
634C4⋊C4—108no—
635C4⋊C4—108no—
636C4⋊C4—108no—
637C4⋊C4—108no—
638C4⋊C4—108no—
639C4⋊C4—204no—
640C4⋊C4—204no—
641C22⋊C4—108no—
642C22⋊C4—108no—
643C22⋊C4—108no—
644C22⋊C4—108no—
645C22⋊C4—108no—
646C22⋊C4—108no—
647C22⋊C4—108no—
648C22⋊C4—204no—
649C42—108no—
650C2×C5—28no—
651C2×C5#241918yescomplemented
652C2×C5C22×#12311yescharacteristic
653C2×C5C2×#52911yescharacteristic
654C2×C5C2×#53911yescharacteristic
655C2×C5C2×#54611yescharacteristic
656C2×C5C2×#54711yescharacteristic
657C2×C5C2×#55111yescharacteristic
658C2×C5C2×#55211yescharacteristic
659D5—44no—
660C23—28no—
661C23—28no—
662C23—28no—
663C23—28no—
664C23—28no—
665C23—28no—
666C23—22no—
667C23—22no—
668C23—22no—
669C23—22no—
670C23—54no—
671C23—108no—
672C23—108no—
673C23—108no—
674C23—102no—
675C23—102no—
676C23—102no—
677C23—102no—
678C23—102no—
679C23—102no—
680C23—204no—
681C23—204no—
682C23—204no—
683C23—204no—
684C23#4029116yes—
685C23C2×#70914yes—
686C23C2×#70912yes—
687C23C2×#70912yes—
688C23C2×#70912yes—
689C23C2×D4×D514yes—
690C23C2×D4×D512yes—
691C23C2×#71114yes—
692C23C2×#71112yes—
693C23#414412yes—
694C23#414712yes—
695C23C24×D511yescharacteristic
696D4—1032no—
697C2×C4—28no—
698C2×C4—28no—
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—22no—
714C2×C4—22no—
715C2×C4—416no—
716C2×C4—416no—
717C2×C4—416no—
718C2×C4—44no—
719C2×C4—44no—
720C2×C4—44no—
721C2×C4—44no—
722C2×C4—54no—
723C2×C4—108no—
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—102no—
741C2×C4—102no—
742C2×C4—102no—
743C2×C4—102no—
744C2×C4—2016no—
745C2×C4—204no—
746C2×C4—204no—
747C2×C4—204no—
748C2×C4—204no—
749C2×C4—204no—
750C2×C4—204no—
751C2×C4C2×#70914yes—
752C2×C4C2×#70914yes—
753C5C2×#241911yescharacteristic, complemented, Sylow
754C22—24no—
755C22—24no—
756C22—24no—
757C22—232no—
758C22—24no—
759C22—24no—
760C22—24no—
761C22—104no—
762C22—104no—
763C22—104no—
764C22—202no—
765C22—202no—
766C22—2016no—
767C22—202no—
768C22—202no—
769C22#6581314yes—
770C22C2×#402918yes—
771C22C2×#402914yes—
772C22#6582414yes—
773C22#6582914yes—
774C22#6584114yes—
775C22#6584714yes—
776C22#6584914yes—
777C22C22×#70911yescharacteristic
778C22C22×#70911yescharacteristic
779C22C22×#70911yescharacteristic
780C22C22×D4×D511yescharacteristic
781C22C22×#71111yescharacteristic
782C22C2×#414411yescharacteristic
783C22C2×#414711yescharacteristic
784C4—24no—
785C4—24no—
786C4—42no—
787C4—42no—
788C4—42no—
789C4—42no—
790C4—104no—
791C4—202no—
792C4—202no—
793C4—202no—
794C4—202no—
795C4—202no—
796C4—202no—
797C2—28no—
798C2—204no—
799C2#1060510618yesdirect product factor
800C2C2×#6581311yescharacteristic
801C2C2×#6582911yescharacteristic
802C2C22×#402911yescharacteristic
803C2C2×#6582411yescharacteristic
804C2C2×#6584711yescharacteristic
805C2C2×#6584911yescharacteristic
806C2C2×#6584111yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC22×C5×#95C2
socleC24×C5C24
prime radicalC23×C22⋊D5C22
hypercenterC22×#95D5
hypocenterC5C2×#2419
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C22×#95

Complements

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

NH ≅ G/Ntype
3. C22×C5×#95C2semidirect
5. C2×#65499C2semidirect
6. C2×#65500C2semidirect
7. C2×#65501C2semidirect
8. #10605106C2direct (N × H)
9. C2×#64964C2semidirect
10. C2×#64957C2semidirect
11. C2×#64953C2semidirect
12. C2×#64947C2semidirect
13. C2×#64946C2semidirect
14. C2×#64963C2semidirect
15. C2×#64943C2semidirect
16. C2×#64941C2semidirect
46. C2×C5×#95C22semidirect
48. #65501C22semidirect
49. #65500C22semidirect
50. #65499C22semidirect
61. #64964C22semidirect
62. #64963C22semidirect
63. #64957C22semidirect
64. #64953C22semidirect
65. #64947C22semidirect
66. #64946C22semidirect
67. #64943C22semidirect
68. #64941C22semidirect
168. C22×#95D5semidirect
325. C2×#95C2×D5semidirect
651. C2×C5#2419semidirect
753. C5C2×#2419semidirect
799. C2#10605106direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#40752
C22×C4×C22⋊D52
C22×C5×#952
C2×#655022
C2×#654992
C2×#655002
C2×#655012
#106051062
C2×#649642
C2×#649572
C2×#649532
C2×#649472
C2×#649462
C2×#649632
C2×#649432
C2×#649412
C2×#24195