Finite Group Databasebeta

← C2×#10607616 #12269449

Subgroups — C2×#10607616 #12269449

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×#4035C211yesmaximal, characteristic, complemented
2C22×#4029C211yesmaximal, characteristic
3C2×C5×#388C211yesmaximal, characteristic, complemented
4C2×#65278C211yesmaximal, characteristic, complemented
5C2×#65248C211yesmaximal, characteristic
6C2×#65237C211yesmaximal, characteristic, complemented
7C2×#65246C211yesmaximal, characteristic
8C2×#65233C211yesmaximal, characteristic, complemented
9C2×#65233C211yesmaximal, characteristic, complemented
10C2×C4×#683C211yesmaximal, characteristic, complemented
11C2×C4×#685C211yesmaximal, characteristic, complemented
12#10607616C2116yesmaximal, direct product factor
13C2×#64965C211yesmaximal, characteristic, complemented
14C2×#64949C211yesmaximal, characteristic, complemented
15C2×#64936C211yesmaximal, characteristic, complemented
16C2×#64959C211yesmaximal, characteristic, complemented
17C23×C22⋊D5C2211yescharacteristic
18C23×C4×D5C2211yescharacteristic
19C22×C5×C4⋊C4C2211yescharacteristic
20C22×C5×C22⋊C4C2211yescharacteristic
21C22×C5×C22⋊C4C2211yescharacteristic
22C22×C5×C22⋊C4C2211yescharacteristic
23C22×C42×C5C2211yescharacteristic
24C22×C22⋊Dic5C2211yescharacteristic
25C22×C22⋊Dic5C2211yescharacteristic
26C22×C22⋊Dic5C2211yescharacteristic
27C22×#685C2211yescharacteristic
28C22×#685C2211yescharacteristic
29C22×#685C2211yescharacteristic
30C22×#685C2211yescharacteristic
31C22×#685C2211yescharacteristic
32C22×C4⋊Dic5C2211yescharacteristic
33C22×C4⋊Dic5C2211yescharacteristic
34C22×#683C2211yescharacteristic
35C22×#683C2211yescharacteristic
36C22×#683C2211yescharacteristic
37C22×#683C2211yescharacteristic
38C22×#683C2211yescharacteristic
39C22×#683C2211yescharacteristic
40C22×#683C2211yescharacteristic
41C22×C4×Dic5C2211yescharacteristic
42C22×C4×Dic5C2211yescharacteristic
43C22×C4×Dic5C2211yescharacteristic
44C2×#4035—28no—
45C2×#4035C2218yescomplemented
46C2×#4029—28no—
47C2×#4029C2218yes—
48C5×#388C2218yescomplemented
49C2×C5×#95C2211yescharacteristic
50C2×C5×#95C2211yescharacteristic
51C2×#3963C2211yescharacteristic
52C2×#3963C2211yescharacteristic
53C2×#3963C2211yescharacteristic
54C2×#3963C2211yescharacteristic
55C2×#3963C2211yescharacteristic
56C2×#3963C2211yescharacteristic
57#65278C2218yescomplemented
58#65248C2218yes—
59#65246C2218yes—
60#65237C2218yescomplemented
61#65233C2218yescomplemented
62#65233C2218yescomplemented
63C4×#685C2218yescomplemented
64C4×#683C2218yescomplemented
65#64965C2218yescomplemented
66#64959C2218yescomplemented
67#64949C2218yescomplemented
68#64936C2218yescomplemented
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×Dic5C2311yescharacteristic
83C23×Dic5C2311yescharacteristic
84C23×Dic5C2311yescharacteristic
85C23×Dic5C2311yescharacteristic
86C23×Dic5C2311yescharacteristic
87C23×Dic5C2311yescharacteristic
88C23×Dic5C2311yescharacteristic
89C22×C4×D5—24no—
90C22×C4×D5—24no—
91C22×C4×D5—42no—
92C22×C4×D5C2314yes—
93C2×C5×C4⋊C4—24no—
94C2×C5×C4⋊C4C2314yes—
95C2×C5×C22⋊C4—24no—
96C2×C5×C22⋊C4—24no—
97C2×C5×C22⋊C4—42no—
98C2×C5×C22⋊C4C2314yes—
99C2×C5×C22⋊C4C2314yes—
100C2×C5×C22⋊C4C2314yes—
101C2×C42×C5—42no—
102C2×C42×C5C2314yes—
103C2×C22⋊Dic5—24no—
104C2×C22⋊Dic5—24no—
105C2×C22⋊Dic5—24no—
106C2×C22⋊Dic5C2314yes—
107C2×C22⋊Dic5C2314yes—
108C2×C22⋊Dic5C2314yes—
109C2×#685—24no—
110C2×#685—24no—
111C2×#685—24no—
112C2×#685—24no—
113C2×#685—24no—
114C2×#685C2314yes—
115C2×#685C2314yes—
116C2×#685C2314yes—
117C2×#685C2314yes—
118C2×#685C2314yes—
119C2×C4⋊Dic5—24no—
120C2×C4⋊Dic5—24no—
121C2×C4⋊Dic5C2314yes—
122C2×C4⋊Dic5C2314yes—
123C2×#683—24no—
124C2×#683—24no—
125C2×#683—24no—
126C2×#683—24no—
127C2×#683—24no—
128C2×#683—42no—
129C2×#683D418yes—
130C2×#683C2314yes—
131C2×#683C2314yes—
132C2×#683C2314yes—
133C2×#683C2314yes—
134C2×#683C2314yes—
135C2×#683C2314yes—
136C2×#683C2314yes—
137C2×C4×Dic5—24no—
138C2×C4×Dic5—24no—
139C2×C4×Dic5—42no—
140C2×C4×Dic5C2314yes—
141C2×C4×Dic5C2314yes—
142C2×C4×Dic5C2314yes—
143#4035—232no—
144#4029—232no—
145C5×#95C2314yes—
146C5×#95C2314yes—
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×#396—51no—
159C2×#394—51no—
160C2×#390—51no—
161C2×#389—51no—
162C2×#388—51no—
163C2×#388—51no—
164C2×#388—51no—
165C2×#388D511yescharacteristic, complemented
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—22no—
176C24×C5C2412yes—
177C24×C5C2411yescharacteristic
178C23×D5—22no—
179C23×D5—22no—
180C23×D5—22no—
181C23×D5—22no—
182C23×D5—22no—
183C23×D5—22no—
184C23×D5#4114yes—
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×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—22no—
227C22×Dic5—22no—
228C22×Dic5—22no—
229C22×Dic5—22no—
230C22×Dic5—22no—
231C22×Dic5C2×D414yes—
232C22×Dic5C2×D414yes—
233C22×Dic5#4114yes—
234C22×Dic5#4114yes—
235C22×Dic5C2412yes—
236C22×Dic5C2412yes—
237C22×Dic5C2412yes—
238C22×Dic5C2412yes—
239C22×Dic5C2412yes—
240C22×Dic5C2412yes—
241C22×Dic5C2412yes—
242C2×C4×D5—28no—
243C2×C4×D5—28no—
244C2×C4×D5—44no—
245C2×C4×D5—416no—
246C5×C4⋊C4—28no—
247C5×C22⋊C4—28no—
248C5×C22⋊C4—28no—
249C5×C22⋊C4—44no—
250C42×C5—44no—
251C22⋊Dic5—28no—
252C22⋊Dic5—28no—
253C22⋊Dic5—28no—
254#685—28no—
255#685—28no—
256#685—28no—
257#685—28no—
258#685—28no—
259C4⋊Dic5—28no—
260C4⋊Dic5—28no—
261#683—28no—
262#683—28no—
263#683—28no—
264#683—28no—
265#683—28no—
266#683—44no—
267#683C2×D4116yes—
268C4×Dic5—28no—
269C4×Dic5—28no—
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⋊C4—51no—
285C22×C4⋊C4—51no—
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×C42C2×D511yescharacteristic
302#400—58no—
303#396—58no—
304#396—58no—
305#394—58no—
306#390—58no—
307#389—58no—
308#388—58no—
309#388—58no—
310#388—58no—
311#388C2×D518yescomplemented
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×#95C2×D511yescharacteristic
322C2×#95C2×D511yescharacteristic
323C23×C5—22no—
324C23×C5—22no—
325C23×C5—22no—
326C23×C5—22no—
327C23×C5—22no—
328C23×C5—22no—
329C23×C5—22no—
330C23×C5—44no—
331C23×C5—44no—
332C23×C5—44no—
333C23×C5—44no—
334C23×C5—44no—
335C23×C5—44no—
336C23×C5—44no—
337C23×C5C22×D412yes—
338C23×C5C2×#4112yes—
339C23×C5C2×#4112yes—
340C23×C5C2×#4112yes—
341C23×C5C2×#4112yes—
342C23×C5H(5,𝔽2)12yes—
343C23×C52−1+412yes—
344C23×C5C2511yescharacteristic
345C22×D5—28no—
346C22×D5—28no—
347C22×D5—28no—
348C22×D5—22no—
349C22×D5—22no—
350C22×D5—22no—
351C22×D5—22no—
352C22×D5—22no—
353C22×D5—22no—
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—22no—
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×C5—44no—
381C2×C4×C5C22×D414yes—
382C2×C4×C5C2×#4114yes—
383C22⋊D5—416no—
384C2×Dic5—28no—
385C2×Dic5—28no—
386C2×Dic5—28no—
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×Dic5C22×D414yes—
409C2×Dic5C22×D414yes—
410C2×Dic5C2×#4114yes—
411C2×Dic5C2×#4114yes—
412C4×D5—416no—
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—58no—
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—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—104no—
455C2×C4⋊C4—104no—
456C2×C4⋊C4—202no—
457C2×C4⋊C4C22×D514yes—
458C2×C22⋊C4—24no—
459C2×C22⋊C4—24no—
460C2×C22⋊C4—42no—
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⋊C4C22×D514yes—
478C2×C22⋊C4C22×D514yes—
479C2×C22⋊C4C22×D514yes—
480C2×C42—42no—
481C2×C42—54no—
482C2×C42—54no—
483C2×C42—54no—
484C2×C42—104no—
485C2×C42—104no—
486C2×C42—202no—
487C2×C42C22×D514yes—
488#95—54no—
489#95—54no—
490#95—54no—
491#95—54no—
492#95—54no—
493#95—54no—
494#95C22×D514yes—
495#95C22×D514yes—
496C22×C5—42no—
497C22×C5—42no—
498C22×C5—42no—
499C22×C5—42no—
500C22×C5—42no—
501C22×C5—42no—
502C22×C5—42no—
503C22×C5—88no—
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—24no—
519C2×D5—24no—
520C2×D5—24no—
521C2×D5—42no—
522C2×D5—42no—
523C2×D5—42no—
524C2×D5—42no—
525C2×D5—416no—
526C4×C5—24no—
527C4×C5—24no—
528C4×C5—42no—
529C4×C5—42no—
530C4×C5—42no—
531C4×C5—42no—
532Dic5—24no—
533Dic5—24no—
534Dic5—24no—
535Dic5—24no—
536Dic5—42no—
537Dic5—42no—
538Dic5—42no—
539C24—22no—
540C24—22no—
541C24—22no—
542C24—22no—
543C24—22no—
544C24—22no—
545C24—22no—
546C24—54no—
547C24—52no—
548C24—102no—
549C24—102no—
550C24—102no—
551C24—102no—
552C24—102no—
553C24—102no—
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—22no—
576C22×C4—54no—
577C22×C4—54no—
578C22×C4—54no—
579C22×C4—54no—
580C22×C4—52no—
581C22×C4—52no—
582C22×C4—52no—
583C22×C4—52no—
584C22×C4—52no—
585C22×C4—52no—
586C22×C4—52no—
587C22×C4—108no—
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—102no—
600C22×C4—102no—
601C22×C4—102no—
602C22×C4—102no—
603C22×C4—102no—
604C22×C4—102no—
605C22×C4—108no—
606C22×C4—204no—
607C22×C4—2016no—
608C22×C4#70914yes—
609C22×C4D4×D514yes—
610C22×C4C23×D512yes—
611C22×C4C23×D512yes—
612C22×C4C23×D512yes—
613C22×C4C23×D512yes—
614C22×C4C23×D512yes—
615C22×C4C23×D512yes—
616C4⋊C4—28no—
617C4⋊C4—516no—
618C4⋊C4—108no—
619C4⋊C4—108no—
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—44no—
629C22⋊C4—108no—
630C22⋊C4—108no—
631C22⋊C4—108no—
632C22⋊C4—108no—
633C22⋊C4—108no—
634C22⋊C4—108no—
635C22⋊C4—108no—
636C22⋊C4—108no—
637C42—44no—
638C42—108no—
639C42—108no—
640C42—204no—
641C2×C5—82no—
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—44no—
651C23—22no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—44no—
659C23—44no—
660C23—44no—
661C23—44no—
662C23—44no—
663C23—44no—
664C23—44no—
665C23—54no—
666C23—108no—
667C23—108no—
668C23—102no—
669C23—102no—
670C23—102no—
671C23—102no—
672C23—102no—
673C23—102no—
674C23—108no—
675C23—204no—
676C23—204no—
677C23—204no—
678C23—204no—
679C23C2×#70912yes—
680C23C2×D4×D512yes—
681C23#414412yes—
682C23D5×#4112yes—
683C23D5×#4112yes—
684C23D5×#4112yes—
685C23#415012yes—
686C23C24×D511yescharacteristic
687D4—2016no—
688C2×C4—28no—
689C2×C4—28no—
690C2×C4—22no—
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—44no—
710C2×C4—54no—
711C2×C4—54no—
712C2×C4—54no—
713C2×C4—54no—
714C2×C4—108no—
715C2×C4—108no—
716C2×C4—108no—
717C2×C4—108no—
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—102no—
732C2×C4—102no—
733C2×C4—102no—
734C2×C4—102no—
735C2×C4—2016no—
736C2×C4—204no—
737C2×C4—204no—
738C2×C4—204no—
739C2×C4C2×#70914yes—
740C2×C4C2×D4×D514yes—
741C5C2×#255811yescharacteristic, complemented, Sylow
742C22—42no—
743C22—42no—
744C22—42no—
745C22—42no—
746C22—42no—
747C22—42no—
748C22—42no—
749C22—88no—
750C22—104no—
751C22—104no—
752C22—104no—
753C22—2016no—
754C22—202no—
755C22—202no—
756C22—202no—
757C22—202no—
758C22#6586214yes—
759C22#6588214yes—
760C22#6589814yes—
761C22#6594414yes—
762C22#6599514yes—
763C22#6601114yes—
764C22#6604214yes—
765C22C22×#70911yescharacteristic
766C22C22×D4×D511yescharacteristic
767C22C2×#414411yescharacteristic
768C22C2×D5×#4111yescharacteristic
769C22C2×D5×#4111yescharacteristic
770C22C2×D5×#4111yescharacteristic
771C22C2×#415011yescharacteristic
772C4—24no—
773C4—24no—
774C4—42no—
775C4—42no—
776C4—42no—
777C4—42no—
778C4—104no—
779C4—104no—
780C4—104no—
781C4—104no—
782C4—202no—
783C4—202no—
784C4—202no—
785C2—82no—
786C2—204no—
787C2#1060761618yesdirect product factor
788C2C2×#6586211yescharacteristic
789C2C2×#6589811yescharacteristic
790C2C2×#6588211yescharacteristic
791C2C2×#6594411yescharacteristic
792C2C2×#6599511yescharacteristic
793C2C2×#6601111yescharacteristic
794C2C2×#6604211yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC2×C5×#388C2
socleC24×C5C24
prime radicalC23×C22⋊D5C22
hypercenterC2×#388D5
hypocenterC5C2×#2558
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
1. C22×#4035C2semidirect
3. C2×C5×#388C2semidirect
4. C2×#65278C2semidirect
6. C2×#65237C2semidirect
8. C2×#65233C2semidirect
9. C2×#65233C2semidirect
10. C2×C4×#683C2semidirect
11. C2×C4×#685C2semidirect
12. #10607616C2direct (N × H)
13. C2×#64965C2semidirect
14. C2×#64949C2semidirect
15. C2×#64936C2semidirect
16. C2×#64959C2semidirect
45. C2×#4035C22semidirect
48. C5×#388C22semidirect
57. #65278C22semidirect
60. #65237C22semidirect
61. #65233C22semidirect
62. #65233C22semidirect
63. C4×#685C22semidirect
64. C4×#683C22semidirect
65. #64965C22semidirect
66. #64959C22semidirect
67. #64949C22semidirect
68. #64936C22semidirect
165. C2×#388D5semidirect
311. #388C2×D5semidirect
642. C2×C5#2558semidirect
741. C5C2×#2558semidirect
787. C2#10607616direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#40352
C22×#40292
C2×C5×#3882
C2×#652782
C2×#652482
C2×#652372
C2×#652462
C2×#652332
C2×C4×#6832
C2×C4×#6852
#106076162
C2×#649652
C2×#649492
C2×#649362
C2×#649592
C2×#25585