Finite Group Databasebeta

← C2×#10609678 #12267007

Subgroups — C2×#10609678 #12267007

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×#4040C211yesmaximal, characteristic
2C22×#4039C211yesmaximal, characteristic
3C2×C5×#398C211yesmaximal, characteristic, complemented
4C2×#65282C211yesmaximal, characteristic, complemented
5C2×#65278C211yesmaximal, characteristic, complemented
6C2×#65278C211yesmaximal, characteristic, complemented
7C2×#65276C211yesmaximal, characteristic, complemented
8C2×#65271C211yesmaximal, characteristic, complemented
9C2×#65267C211yesmaximal, characteristic, complemented
10#10609678C2116yesmaximal, direct product factor
11C2×#64954C211yesmaximal, characteristic
12C2×#64953C211yesmaximal, characteristic, complemented
13C2×#64953C211yesmaximal, characteristic, complemented
14C2×D5×#95C211yesmaximal, characteristic, complemented
15C2×#64963C211yesmaximal, characteristic, complemented
16C2×#64942C211yesmaximal, characteristic, complemented
17C23×D20C2211yescharacteristic
18C23×C4×D5C2211yescharacteristic
19C23×C4×D5C2211yescharacteristic
20C23×C4×D5C2211yescharacteristic
21C23×C4×D5C2211yescharacteristic
22C22×C5×C4⋊C4C2211yescharacteristic
23C22×C5×C4⋊C4C2211yescharacteristic
24C22×C5×C4⋊C4C2211yescharacteristic
25C22×C5×C4⋊C4C2211yescharacteristic
26C22×#685C2211yescharacteristic
27C22×#685C2211yescharacteristic
28C22×#685C2211yescharacteristic
29C22×#685C2211yescharacteristic
30C22×#685C2211yescharacteristic
31C22×#685C2211yescharacteristic
32C22×#685C2211yescharacteristic
33C22×#685C2211yescharacteristic
34C22×C4⋊Dic5C2211yescharacteristic
35C22×#683C2211yescharacteristic
36C22×#683C2211yescharacteristic
37C22×C4×Dic5C2211yescharacteristic
38C2×#4040—28no—
39C2×#4040C2218yes—
40C2×#4039—28no—
41C2×#4039C2218yes—
42C5×#398C2218yescomplemented
43C2×C5×#95C2211yescharacteristic
44C2×C5×#95C2211yescharacteristic
45C2×C5×#95C2211yescharacteristic
46C2×#3963C2211yescharacteristic
47C2×#3963C2211yescharacteristic
48C2×#3963C2211yescharacteristic
49C2×#3963C2211yescharacteristic
50C2×#3963C2211yescharacteristic
51C2×#3963C2211yescharacteristic
52C2×#3963C2211yescharacteristic
53C2×#3963C2211yescharacteristic
54C2×#3963C2211yescharacteristic
55C2×#3963C2211yescharacteristic
56C2×#3963C2211yescharacteristic
57#65282C2218yescomplemented
58#65278C2218yescomplemented
59#65278C2218yescomplemented
60#65276C2218yescomplemented
61#65271C2218yescomplemented
62#65267C2218yescomplemented
63#64963C2218yescomplemented
64#64954C2218yes—
65#64953C2218yescomplemented
66#64953C2218yescomplemented
67D5×#95C2218yescomplemented
68#64942C2218yescomplemented
69C2×#2419—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×D20D418yes—
88C22×D20C2314yes—
89C22×C4×D5—24no—
90C22×C4×D5—24no—
91C22×C4×D5—24no—
92C22×C4×D5—24no—
93C22×C4×D5—24no—
94C22×C4×D5—24no—
95C22×C4×D5—24no—
96C22×C4×D5—24no—
97C22×C4×D5—24no—
98C22×C4×D5—42no—
99C22×C4×D5—42no—
100C22×C4×D5—42no—
101C22×C4×D5C2314yes—
102C22×C4×D5C2314yes—
103C22×C4×D5C2314yes—
104C22×C4×D5C2314yes—
105C2×C5×C4⋊C4—24no—
106C2×C5×C4⋊C4—24no—
107C2×C5×C4⋊C4—42no—
108C2×C5×C4⋊C4—42no—
109C2×C5×C4⋊C4C2314yes—
110C2×C5×C4⋊C4C2314yes—
111C2×C5×C4⋊C4C2314yes—
112C2×C5×C4⋊C4C2314yes—
113C2×#685—24no—
114C2×#685—24no—
115C2×#685—24no—
116C2×#685—24no—
117C2×#685—24no—
118C2×#685—24no—
119C2×#685—24no—
120C2×#685—42no—
121C2×#685C2314yes—
122C2×#685C2314yes—
123C2×#685C2314yes—
124C2×#685C2314yes—
125C2×#685C2314yes—
126C2×#685C2314yes—
127C2×#685C2314yes—
128C2×#685C2314yes—
129C2×C4⋊Dic5—24no—
130C2×C4⋊Dic5C2314yes—
131C2×#683—24no—
132C2×#683—24no—
133C2×#683C2314yes—
134C2×#683C2314yes—
135C2×C4×Dic5—24no—
136C2×C4×Dic5C2314yes—
137#4040—232no—
138#4039—232no—
139C5×#95C2314yes—
140C5×#95C2314yes—
141C5×#95C2314yes—
142#3963C2314yes—
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×#398D511yescharacteristic, complemented
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×#95—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×D5C2×D414yes—
181C23×D5C2×D414yes—
182C23×D5#4114yes—
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×C5—22no—
203C22×C4×C5—22no—
204C22×C4×C5—22no—
205C22×C4×C5C2×D414yes—
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—232no—
239C2×D20—28no—
240C2×D20—28no—
241C2×D20C2×D4116yes—
242C2×C4×D5—28no—
243C2×C4×D5—28no—
244C2×C4×D5—28no—
245C2×C4×D5—28no—
246C2×C4×D5—28no—
247C2×C4×D5—28no—
248C2×C4×D5—28no—
249C2×C4×D5—28no—
250C2×C4×D5—28no—
251C2×C4×D5—44no—
252C2×C4×D5—44no—
253C2×C4×D5—44no—
254C2×C4×D5—416no—
255C2×C4×D5—416no—
256C2×C4×D5—416no—
257C2×C4×D5—416no—
258C5×C4⋊C4—28no—
259C5×C4⋊C4—28no—
260C5×C4⋊C4—44no—
261C5×C4⋊C4—44no—
262#685—28no—
263#685—28no—
264#685—28no—
265#685—28no—
266#685—28no—
267#685—28no—
268#685—28no—
269#685—44no—
270C4⋊Dic5—28no—
271#683—28no—
272#683—28no—
273C4×Dic5—28no—
274C23×D4—51no—
275C24×C4—51no—
276C24×C4—51no—
277C24×C4—51no—
278C24×C4—51no—
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⋊C4C2×D511yescharacteristic
287C22×C4⋊C4C2×D511yescharacteristic
288C22×C4⋊C4C2×D511yescharacteristic
289C22×C4⋊C4C2×D511yescharacteristic
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#398C2×D518yescomplemented
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×#95—51no—
322C2×#95—58no—
323C2×#95C2×D511yescharacteristic
324C2×#95C2×D511yescharacteristic
325C2×#95C2×D511yescharacteristic
326C23×C5C22×D412yes—
327C23×C5C2×#4112yes—
328C23×C5C2×#4112yes—
329C23×C5C2×#4112yes—
330C23×C5C2×#4112yes—
331C23×C5H(5,𝔽2)12yes—
332C23×C52−1+412yes—
333C23×C5C2511yescharacteristic
334C22×D5—28no—
335C22×D5—28no—
336C22×D5—28no—
337C22×D5—28no—
338C22×D5—28no—
339C22×D5—28no—
340C22×D5—22no—
341C22×D5—22no—
342C22×D5—22no—
343C22×D5—22no—
344C22×D5—28no—
345C22×D5—28no—
346C22×D5—28no—
347C22×D5—22no—
348C22×D5—22no—
349C22×D5—22no—
350C22×D5—22no—
351C22×D5—22no—
352C22×D5—22no—
353C22×D5—44no—
354C22×D5—44no—
355C22×D5—44no—
356C22×D5—44no—
357C22×D5#123116yes—
358C22×D5C22×D414yes—
359C22×D5C22×D414yes—
360C22×D5C2×#4114yes—
361C22×D5C2×#4114yes—
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—22no—
381C2×C4×C5—22no—
382C2×C4×C5—22no—
383C2×C4×C5—44no—
384C2×C4×C5—44no—
385C2×C4×C5—44no—
386C2×C4×C5—44no—
387C2×C4×C5—44no—
388C2×C4×C5C22×D414yes—
389C2×C4×C5C2×#4114yes—
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—44no—
409C2×Dic5—44no—
410C2×Dic5—44no—
411C2×Dic5—44no—
412C2×Dic5—44no—
413C2×Dic5C2×#4114yes—
414D20—232no—
415C4×D5—416no—
416C4×D5—416no—
417C4×D5—416no—
418C4×D5—416no—
419C25—51no—
420C25—51no—
421C22×D4—58no—
422C22×D4—54no—
423C22×D4—104no—
424C22×D4—104no—
425C23×C4—51no—
426C23×C4—51no—
427C23×C4—51no—
428C23×C4—51no—
429C23×C4—51no—
430C23×C4—51no—
431C23×C4—54no—
432C23×C4—54no—
433C23×C4—54no—
434C23×C4—54no—
435C23×C4—104no—
436C23×C4—104no—
437C23×C4—104no—
438C23×C4—104no—
439C23×C4—104no—
440C23×C4—104no—
441C23×C4—104no—
442C23×C4—104no—
443C23×C4—104no—
444C23×C4—202no—
445C23×C4—202no—
446C23×C4—202no—
447C23×C4C22×D511yescharacteristic
448C23×C4C22×D511yescharacteristic
449C23×C4C22×D511yescharacteristic
450C23×C4C22×D511yescharacteristic
451C23×C4C22×D511yescharacteristic
452C23×C4C22×D511yescharacteristic
453C23×C4C22×D511yescharacteristic
454#123—1032no—
455C4×D4—1032no—
456C2×C4⋊C4—24no—
457C2×C4⋊C4—24no—
458C2×C4⋊C4—42no—
459C2×C4⋊C4—42no—
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⋊C4C22×D514yes—
467C2×C4⋊C4C22×D514yes—
468C2×C4⋊C4C22×D514yes—
469C2×C4⋊C4C22×D514yes—
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#95—54no—
499#95C22×D514yes—
500#95C22×D514yes—
501#95C22×D514yes—
502C22×C5C2×#12314yes—
503C22×C5#52914yes—
504C22×C5#53914yes—
505C22×C5#54614yes—
506C22×C5#54714yes—
507C22×C5#55114yes—
508C22×C5#55214yes—
509C22×C5C23×D411yescharacteristic
510C22×C5C22×#4111yescharacteristic
511C22×C5C22×#4111yescharacteristic
512C22×C5C22×#4111yescharacteristic
513C22×C5C22×#4111yescharacteristic
514C22×C5C2×H(5,𝔽2)11yescharacteristic
515C22×C5C2×2−1+411yescharacteristic
516C2×D5—24no—
517C2×D5—232no—
518C2×D5—24no—
519C2×D5—24no—
520C2×D5—24no—
521C2×D5—24no—
522C2×D5—24no—
523C2×D5—24no—
524C2×D5—24no—
525C2×D5—24no—
526C2×D5—42no—
527C2×D5—416no—
528C2×D5—42no—
529C2×D5—42no—
530C2×D5—42no—
531C2×D5C2×#12318yes—
532C4×C5—24no—
533C4×C5—24no—
534C4×C5—42no—
535C4×C5—42no—
536C4×C5—42no—
537C4×C5—42no—
538C4×C5—42no—
539Dic5—24no—
540Dic5—42no—
541Dic5—42no—
542Dic5—42no—
543Dic5—42no—
544Dic5—42no—
545C24—54no—
546C24—54no—
547C24—54no—
548C24—52no—
549C24—54no—
550C24—52no—
551C24—102no—
552C24—102no—
553C24—102no—
554C24—102no—
555C24—102no—
556C24—102no—
557C24—102no—
558C24—102no—
559C24—102no—
560C24—102no—
561C24C23×D511yescharacteristic
562C2×D4—516no—
563C2×D4—1032no—
564C2×D4—108no—
565C2×D4—108no—
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—22no—
584C22×C4—22no—
585C22×C4—54no—
586C22×C4—52no—
587C22×C4—52no—
588C22×C4—52no—
589C22×C4—52no—
590C22×C4—52no—
591C22×C4—52no—
592C22×C4—108no—
593C22×C4—108no—
594C22×C4—108no—
595C22×C4—108no—
596C22×C4—108no—
597C22×C4—108no—
598C22×C4—108no—
599C22×C4—108no—
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—102no—
611C22×C4—102no—
612C22×C4—102no—
613C22×C4—102no—
614C22×C4—102no—
615C22×C4—102no—
616C22×C4—102no—
617C22×C4—108no—
618C22×C4—204no—
619C22×C4—204no—
620C22×C4—204no—
621C22×C4—2016no—
622C22×C4—2016no—
623C22×C4—2016no—
624C22×C4—2016no—
625C22×C4D4×D514yes—
626C22×C4#71314yes—
627C22×C4C23×D512yes—
628C22×C4C23×D512yes—
629C22×C4C23×D512yes—
630C22×C4C23×D512yes—
631C22×C4C23×D512yes—
632C22×C4C23×D512yes—
633C22×C4C23×D512yes—
634C4⋊C4—28no—
635C4⋊C4—28no—
636C4⋊C4—44no—
637C4⋊C4—44no—
638C4⋊C4—108no—
639C4⋊C4—108no—
640C4⋊C4—108no—
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#241918yescomplemented
651C2×C5C22×#12311yescharacteristic
652C2×C5C2×#52911yescharacteristic
653C2×C5C2×#53911yescharacteristic
654C2×C5C2×#54611yescharacteristic
655C2×C5C2×#54711yescharacteristic
656C2×C5C2×#55111yescharacteristic
657C2×C5C2×#55211yescharacteristic
658D5—28no—
659D5—44no—
660C23—516no—
661C23—54no—
662C23—54no—
663C23—54no—
664C23—54no—
665C23—108no—
666C23—108no—
667C23—108no—
668C23—108no—
669C23—102no—
670C23—102no—
671C23—102no—
672C23—102no—
673C23—108no—
674C23—108no—
675C23—108no—
676C23—108no—
677C23—108no—
678C23—102no—
679C23—102no—
680C23—102no—
681C23—102no—
682C23—102no—
683C23—102no—
684C23—204no—
685C23—204no—
686C23—204no—
687C23—204no—
688C23C2×D4×D512yes—
689C23#414412yes—
690C23C2×#71312yes—
691C23#414712yes—
692C23D5×#4112yes—
693C23D5×#4112yes—
694C23D5×#4112yes—
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—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—44no—
719C2×C4—44no—
720C2×C4—44no—
721C2×C4—44no—
722C2×C4—44no—
723C2×C4—54no—
724C2×C4—108no—
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—2016no—
743C2×C4—2016no—
744C2×C4—2016no—
745C2×C4—2016no—
746C2×C4—204no—
747C2×C4—204no—
748C2×C4—204no—
749C2×C4—204no—
750C2×C4—204no—
751C2×C4C2×D4×D514yes—
752C2×C4C2×#71314yes—
753C5C2×#241911yescharacteristic, complemented, Sylow
754C22—58no—
755C22—104no—
756C22—1032no—
757C22—104no—
758C22—104no—
759C22—104no—
760C22—104no—
761C22—104no—
762C22—104no—
763C22—104no—
764C22—104no—
765C22—2016no—
766C22—202no—
767C22—202no—
768C22—202no—
769C22—202no—
770C22#6594614yes—
771C22#6597114yes—
772C22#6597214yes—
773C22D5×#12314yes—
774C22#6602514yes—
775C22#6602714yes—
776C22#6606014yes—
777C22C22×D4×D511yescharacteristic
778C22C2×#414411yescharacteristic
779C22C22×#71311yescharacteristic
780C22C2×#414711yescharacteristic
781C22C2×D5×#4111yescharacteristic
782C22C2×D5×#4111yescharacteristic
783C22C2×D5×#4111yescharacteristic
784C4—24no—
785C4—24no—
786C4—42no—
787C4—42no—
788C4—42no—
789C4—42no—
790C4—42no—
791C4—104no—
792C4—202no—
793C4—202no—
794C4—202no—
795C4—202no—
796C4—202no—
797C2—108no—
798C2—204no—
799C2#1060967818yesdirect product factor
800C2C2×#6594611yescharacteristic
801C2C2×#6597211yescharacteristic
802C2C2×#6597111yescharacteristic
803C2C2×D5×#12311yescharacteristic
804C2C2×#6602511yescharacteristic
805C2C2×#6602711yescharacteristic
806C2C2×#6606011yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC2×C5×#398C2
socleC24×C5C24
prime radicalC23×D20C22
hypercenterC2×#398D5
hypocenterC5C2×#2419
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#398

Complements

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

NH ≅ G/Ntype
3. C2×C5×#398C2semidirect
4. C2×#65282C2semidirect
5. C2×#65278C2semidirect
6. C2×#65278C2semidirect
7. C2×#65276C2semidirect
8. C2×#65271C2semidirect
9. C2×#65267C2semidirect
10. #10609678C2direct (N × H)
12. C2×#64953C2semidirect
13. C2×#64953C2semidirect
14. C2×D5×#95C2semidirect
15. C2×#64963C2semidirect
16. C2×#64942C2semidirect
42. C5×#398C22semidirect
57. #65282C22semidirect
58. #65278C22semidirect
59. #65278C22semidirect
60. #65276C22semidirect
61. #65271C22semidirect
62. #65267C22semidirect
63. #64963C22semidirect
65. #64953C22semidirect
66. #64953C22semidirect
67. D5×#95C22semidirect
68. #64942C22semidirect
157. C2×#398D5semidirect
300. #398C2×D5semidirect
650. C2×C5#2419semidirect
753. C5C2×#2419semidirect
799. C2#10609678direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#40402
C22×#40392
C2×C5×#3982
C2×#652822
C2×#652782
C2×#652762
C2×#652712
C2×#652672
#106096782
C2×#649542
C2×#649532
C2×D5×#952
C2×#649632
C2×#649422
C2×#24195