Finite Group Databasebeta

← C2×#10607600 #12269076

Subgroups — C2×#10607600 #12269076

Order 1280.

3114 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#4029C211yesmaximal, characteristic
2C22×#4018C211yesmaximal, characteristic, complemented
3C2×C5×#388C211yesmaximal, characteristic, complemented
4C2×#65276C211yesmaximal, characteristic, complemented
5C2×#65273C211yesmaximal, characteristic, complemented
6C2×#65245C211yesmaximal, characteristic
7C2×#65245C211yesmaximal, characteristic
8C2×#65238C211yesmaximal, characteristic, complemented
9C2×#65241C211yesmaximal, characteristic, complemented
10C2×#65233C211yesmaximal, characteristic, complemented
11C2×#65222C211yesmaximal, characteristic, complemented
12#10607600C2116yesmaximal, direct product factor
13C2×#64956C211yesmaximal, characteristic, complemented
14C2×D5×#95C211yesmaximal, characteristic, complemented
15C2×#64949C211yesmaximal, characteristic, complemented
16C2×#64942C211yesmaximal, characteristic, complemented
17C23×C22⋊D5C2211yescharacteristic
18C23×C4×D5C2211yescharacteristic
19C23×C4×D5C2211yescharacteristic
20C23×C4×D5C2211yescharacteristic
21C22×C5×C4⋊C4C2211yescharacteristic
22C22×C5×C22⋊C4C2211yescharacteristic
23C22×C5×C22⋊C4C2211yescharacteristic
24C22×C5×C22⋊C4C2211yescharacteristic
25C22×C42×C5C2211yescharacteristic
26C22×C22⋊Dic5C2211yescharacteristic
27C22×C22⋊Dic5C2211yescharacteristic
28C22×C22⋊Dic5C2211yescharacteristic
29C22×#685C2211yescharacteristic
30C22×#685C2211yescharacteristic
31C22×#685C2211yescharacteristic
32C22×C4⋊Dic5C2211yescharacteristic
33C22×C4⋊Dic5C2211yescharacteristic
34C22×#683C2211yescharacteristic
35C22×#683C2211yescharacteristic
36C22×#683C2211yescharacteristic
37C22×#683C2211yescharacteristic
38C22×#683C2211yescharacteristic
39C22×C4×Dic5C2211yescharacteristic
40C2×#4029—28no—
41C2×#4029C2218yes—
42C2×#4018—28no—
43C2×#4018C2218yescomplemented
44C5×#388C2218yescomplemented
45C2×C5×#95C2211yescharacteristic
46C2×C5×#95C2211yescharacteristic
47C2×#3963C2211yescharacteristic
48C2×#3963C2211yescharacteristic
49C2×#3963C2211yescharacteristic
50C2×#3963C2211yescharacteristic
51C2×#3963C2211yescharacteristic
52C2×#3963C2211yescharacteristic
53C2×#3963C2211yescharacteristic
54C2×#3963C2211yescharacteristic
55C2×#3963C2211yescharacteristic
56C2×#3963C2211yescharacteristic
57#65276C2218yescomplemented
58#65273C2218yescomplemented
59#65245C2218yes—
60#65245C2218yes—
61#65241C2218yescomplemented
62#65238C2218yescomplemented
63#65233C2218yescomplemented
64#65222C2218yescomplemented
65#64956C2218yescomplemented
66D5×#95C2218yescomplemented
67#64949C2218yescomplemented
68#64942C2218yescomplemented
69C2×#2498—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—24no—
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—24no—
92C22×C4×D5—24no—
93C22×C4×D5—24no—
94C22×C4×D5—24no—
95C22×C4×D5—42no—
96C22×C4×D5—42no—
97C22×C4×D5D418yes—
98C22×C4×D5C2314yes—
99C22×C4×D5C2314yes—
100C22×C4×D5C2314yes—
101C2×C5×C4⋊C4—42no—
102C2×C5×C4⋊C4C2314yes—
103C2×C5×C22⋊C4—24no—
104C2×C5×C22⋊C4—24no—
105C2×C5×C22⋊C4—42no—
106C2×C5×C22⋊C4C2314yes—
107C2×C5×C22⋊C4C2314yes—
108C2×C5×C22⋊C4C2314yes—
109C2×C42×C5—24no—
110C2×C42×C5C2314yes—
111C2×C22⋊Dic5—24no—
112C2×C22⋊Dic5—24no—
113C2×C22⋊Dic5—42no—
114C2×C22⋊Dic5C2314yes—
115C2×C22⋊Dic5C2314yes—
116C2×C22⋊Dic5C2314yes—
117C2×#685—24no—
118C2×#685—24no—
119C2×#685—24no—
120C2×#685C2314yes—
121C2×#685C2314yes—
122C2×#685C2314yes—
123C2×C4⋊Dic5—24no—
124C2×C4⋊Dic5—24no—
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—
139#4029—232no—
140#4018—232no—
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×#117—51no—
155#2498—516no—
156C2×#400—51no—
157C2×#399—51no—
158C2×#398—51no—
159C2×#397—51no—
160C2×#388—51no—
161C2×#388D511yescharacteristic, complemented
162C2×#387—51no—
163C2×#387—51no—
164C2×#386—51no—
165C2×#386—51no—
166C2×#380—51no—
167C2×#380—51no—
168C22×#95—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×D5C2×D414yes—
183C23×D5#4114yes—
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—28no—
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×Dic5—22no—
232C22×Dic5—22no—
233C22×Dic5C2×D414yes—
234C22×Dic5#4114yes—
235C22×Dic5C2412yes—
236C22×Dic5C2412yes—
237C22×Dic5C2412yes—
238C22×Dic5C2412yes—
239C22×Dic5C2412yes—
240C22×Dic5C2412yes—
241C22×Dic5C2412yes—
242C2×C4×D5—232no—
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—44no—
250C2×C4×D5—44no—
251C2×C4×D5—416no—
252C2×C4×D5—416no—
253C2×C4×D5C2×D4116yes—
254C5×C4⋊C4—44no—
255C5×C22⋊C4—28no—
256C5×C22⋊C4—28no—
257C5×C22⋊C4—44no—
258C42×C5—28no—
259C22⋊Dic5—28no—
260C22⋊Dic5—28no—
261C22⋊Dic5—44no—
262#685—28no—
263#685—28no—
264#685—28no—
265C4⋊Dic5—28no—
266C4⋊Dic5—28no—
267#683—28no—
268#683—28no—
269#683—28no—
270#683—28no—
271#683—44no—
272C4×Dic5—28no—
273C23×D4—51no—
274C24×C4—51no—
275C24×C4—51no—
276C24×C4—51no—
277C2×#123—58no—
278C2×#123—108no—
279C2×#117—58no—
280C2×#117—108no—
281C22×C4⋊C4—51no—
282C22×C4⋊C4—51no—
283C22×C4⋊C4—51no—
284C22×C4⋊C4—51no—
285C22×C4⋊C4—51no—
286C22×C4⋊C4—51no—
287C22×C4⋊C4—51no—
288C22×C4⋊C4C2×D511yescharacteristic
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×C42C2×D511yescharacteristic
300#400—58no—
301#399—58no—
302#398—58no—
303#397—58no—
304#388—58no—
305#388C2×D518yescomplemented
306#387—58no—
307#387—58no—
308#386—58no—
309#386—58no—
310#380—58no—
311#380—58no—
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
325C23×C5—22no—
326C23×C5—22no—
327C23×C5—22no—
328C23×C5—22no—
329C23×C5—22no—
330C23×C5—22no—
331C23×C5—22no—
332C23×C5—44no—
333C23×C5—44no—
334C23×C5—44no—
335C23×C5—44no—
336C23×C5—44no—
337C23×C5—44no—
338C23×C5—44no—
339C23×C5C22×D412yes—
340C23×C5C2×#4112yes—
341C23×C5C2×#4112yes—
342C23×C5C2×#4112yes—
343C23×C5C2×#4112yes—
344C23×C5H(5,𝔽2)12yes—
345C23×C52−1+412yes—
346C23×C5C2511yescharacteristic
347C22×D5—28no—
348C22×D5—28no—
349C22×D5—28no—
350C22×D5—28no—
351C22×D5—28no—
352C22×D5—28no—
353C22×D5—22no—
354C22×D5—22no—
355C22×D5—22no—
356C22×D5—22no—
357C22×D5#123116yes—
358C22×D5C22×D414yes—
359C22×D5C2×#4114yes—
360C22×D5C2×#4114yes—
361C2×C4×C5—28no—
362C2×C4×C5—28no—
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—22no—
378C2×C4×C5—22no—
379C2×C4×C5—44no—
380C2×C4×C5—44no—
381C2×C4×C5—44no—
382C2×C4×C5—44no—
383C2×C4×C5C22×D414yes—
384C2×C4×C5C2×#4114yes—
385C22⋊D5—416no—
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—22no—
406C2×Dic5—22no—
407C2×Dic5—44no—
408C2×Dic5—44no—
409C2×Dic5—44no—
410C2×Dic5—44no—
411C2×Dic5—44no—
412C2×Dic5C22×D414yes—
413C2×Dic5C2×#4114yes—
414C4×D5—232no—
415C4×D5—416no—
416C4×D5—416no—
417C25—51no—
418C25C22×D511yescharacteristic
419C22×D4—54no—
420C22×D4—104no—
421C22×D4—104no—
422C22×D4—104no—
423C23×C4—51no—
424C23×C4—51no—
425C23×C4—58no—
426C23×C4—54no—
427C23×C4—51no—
428C23×C4—51no—
429C23×C4—51no—
430C23×C4—51no—
431C23×C4—51no—
432C23×C4—54no—
433C23×C4—54no—
434C23×C4—104no—
435C23×C4—104no—
436C23×C4—104no—
437C23×C4—104no—
438C23×C4—104no—
439C23×C4—104no—
440C23×C4—202no—
441C23×C4—202no—
442C23×C4C22×D511yescharacteristic
443C23×C4C22×D511yescharacteristic
444C23×C4C22×D511yescharacteristic
445C23×C4C22×D511yescharacteristic
446C23×C4C22×D511yescharacteristic
447C23×C4C22×D511yescharacteristic
448#123—1032no—
449#117—1032no—
450C2×C4⋊C4—42no—
451C2×C4⋊C4—54no—
452C2×C4⋊C4—54no—
453C2×C4⋊C4—54no—
454C2×C4⋊C4—54no—
455C2×C4⋊C4—54no—
456C2×C4⋊C4—54no—
457C2×C4⋊C4—54no—
458C2×C4⋊C4—104no—
459C2×C4⋊C4—104no—
460C2×C4⋊C4—104no—
461C2×C4⋊C4—104no—
462C2×C4⋊C4—104no—
463C2×C4⋊C4—104no—
464C2×C4⋊C4—202no—
465C2×C4⋊C4C22×D514yes—
466C2×C22⋊C4—24no—
467C2×C22⋊C4—24no—
468C2×C22⋊C4—42no—
469C2×C22⋊C4—54no—
470C2×C22⋊C4—54no—
471C2×C22⋊C4—54no—
472C2×C22⋊C4—54no—
473C2×C22⋊C4—54no—
474C2×C22⋊C4—54no—
475C2×C22⋊C4—104no—
476C2×C22⋊C4—104no—
477C2×C22⋊C4—104no—
478C2×C22⋊C4—104no—
479C2×C22⋊C4—104no—
480C2×C22⋊C4—202no—
481C2×C22⋊C4C22×D514yes—
482C2×C22⋊C4C22×D514yes—
483C2×C22⋊C4C22×D514yes—
484C2×C42—24no—
485C2×C42—54no—
486C2×C42—104no—
487C2×C42C22×D514yes—
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—
500C22×C5—42no—
501C22×C5—42no—
502C22×C5—42no—
503C22×C5—42no—
504C22×C5—42no—
505C22×C5—42no—
506C22×C5—42no—
507C22×C5—88no—
508C22×C5C2×#12314yes—
509C22×C5#53214yes—
510C22×C5#53714yes—
511C22×C5#55114yes—
512C22×C5#55114yes—
513C22×C5#55214yes—
514C22×C5#55214yes—
515C22×C5C23×D411yescharacteristic
516C22×C5C22×#4111yescharacteristic
517C22×C5C22×#4111yescharacteristic
518C22×C5C22×#4111yescharacteristic
519C22×C5C22×#4111yescharacteristic
520C22×C5C2×H(5,𝔽2)11yescharacteristic
521C22×C5C2×2−1+411yescharacteristic
522C2×D5—24no—
523C2×D5—24no—
524C2×D5—24no—
525C2×D5—24no—
526C2×D5—24no—
527C2×D5—24no—
528C2×D5—232no—
529C2×D5C2×#12318yes—
530C4×C5—24no—
531C4×C5—24no—
532C4×C5—42no—
533C4×C5—42no—
534C4×C5—42no—
535C4×C5—42no—
536Dic5—24no—
537Dic5—24no—
538Dic5—42no—
539Dic5—42no—
540Dic5—42no—
541Dic5—42no—
542Dic5—42no—
543C24—22no—
544C24—22no—
545C24—22no—
546C24—22no—
547C24—22no—
548C24—22no—
549C24—22no—
550C24—54no—
551C24—54no—
552C24—54no—
553C24—52no—
554C24—102no—
555C24—102no—
556C24—102no—
557C24—102no—
558C24C23×D512yes—
559C24C23×D511yescharacteristic
560C2×D4—108no—
561C2×D4—108no—
562C2×D4—108no—
563C2×D4—2016no—
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—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—54no—
581C22×C4—54no—
582C22×C4—52no—
583C22×C4—52no—
584C22×C4—516no—
585C22×C4—52no—
586C22×C4—52no—
587C22×C4—52no—
588C22×C4—52no—
589C22×C4—52no—
590C22×C4—108no—
591C22×C4—1032no—
592C22×C4—108no—
593C22×C4—108no—
594C22×C4—108no—
595C22×C4—108no—
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—102no—
609C22×C4—102no—
610C22×C4—102no—
611C22×C4—102no—
612C22×C4—102no—
613C22×C4—102no—
614C22×C4—102no—
615C22×C4—108no—
616C22×C4—204no—
617C22×C4—204no—
618C22×C4—2016no—
619C22×C4—2016no—
620C22×C4#70914yes—
621C22×C4D4×D514yes—
622C22×C4C23×D512yes—
623C22×C4C23×D512yes—
624C22×C4C23×D512yes—
625C22×C4C23×D512yes—
626C22×C4C23×D512yes—
627C22×C4C23×D512yes—
628C4⋊C4—44no—
629C4⋊C4—108no—
630C4⋊C4—108no—
631C4⋊C4—108no—
632C4⋊C4—108no—
633C4⋊C4—108no—
634C4⋊C4—108no—
635C4⋊C4—204no—
636C22⋊C4—28no—
637C22⋊C4—28no—
638C22⋊C4—44no—
639C22⋊C4—108no—
640C22⋊C4—108no—
641C22⋊C4—108no—
642C22⋊C4—108no—
643C22⋊C4—108no—
644C22⋊C4—204no—
645C42—28no—
646C42—108no—
647C2×C5—82no—
648C2×C5#249818yescomplemented
649C2×C5C22×#12311yescharacteristic
650C2×C5C2×#53211yescharacteristic
651C2×C5C2×#53711yescharacteristic
652C2×C5C2×#55111yescharacteristic
653C2×C5C2×#55111yescharacteristic
654C2×C5C2×#55211yescharacteristic
655C2×C5C2×#55211yescharacteristic
656D5—28no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—22no—
664C23—44no—
665C23—44no—
666C23—44no—
667C23—44no—
668C23—44no—
669C23—44no—
670C23—44no—
671C23—516no—
672C23—54no—
673C23—54no—
674C23—54no—
675C23—108no—
676C23—108no—
677C23—108no—
678C23—108no—
679C23—108no—
680C23—102no—
681C23—102no—
682C23—102no—
683C23—102no—
684C23—108no—
685C23C2×#70912yes—
686C23C2×D4×D512yes—
687C23#414412yes—
688C23D5×#4112yes—
689C23D5×#4112yes—
690C23D5×#4112yes—
691C23#415012yes—
692C23C24×D511yescharacteristic
693D4—2016no—
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—44no—
713C2×C4—44no—
714C2×C4—44no—
715C2×C4—44no—
716C2×C4—54no—
717C2×C4—54no—
718C2×C4—1032no—
719C2×C4—108no—
720C2×C4—108no—
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—102no—
737C2×C4—102no—
738C2×C4—102no—
739C2×C4—102no—
740C2×C4—2016no—
741C2×C4—2016no—
742C2×C4—204no—
743C2×C4—204no—
744C2×C4—204no—
745C2×C4—204no—
746C2×C4—204no—
747C2×C4C2×#70914yes—
748C2×C4C2×D4×D514yes—
749C5C2×#249811yescharacteristic, complemented, Sylow
750C22—42no—
751C22—42no—
752C22—42no—
753C22—42no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—58no—
758C22—88no—
759C22—104no—
760C22—104no—
761C22—104no—
762C22—104no—
763C22—104no—
764C22—1032no—
765C22—104no—
766C22#6586314yes—
767C22#6588214yes—
768C22#6589014yes—
769C22#6594214yes—
770C22D5×#12314yes—
771C22#6601314yes—
772C22#6604214yes—
773C22C22×#70911yescharacteristic
774C22C22×D4×D511yescharacteristic
775C22C2×#414411yescharacteristic
776C22C2×D5×#4111yescharacteristic
777C22C2×D5×#4111yescharacteristic
778C22C2×D5×#4111yescharacteristic
779C22C2×#415011yescharacteristic
780C4—24no—
781C4—24no—
782C4—42no—
783C4—42no—
784C4—42no—
785C4—42no—
786C4—104no—
787C4—104no—
788C4—202no—
789C4—202no—
790C4—202no—
791C4—202no—
792C4—202no—
793C2—82no—
794C2—108no—
795C2#1060760018yesdirect product factor
796C2C2×#6586311yescharacteristic
797C2C2×#6588211yescharacteristic
798C2C2×#6589011yescharacteristic
799C2C2×#6594211yescharacteristic
800C2C2×D5×#12311yescharacteristic
801C2C2×#6601311yescharacteristic
802C2C2×#6604211yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC2×C5×#388C2
socleC24×C5C24
prime radicalC23×C22⋊D5C22
hypercenterC2×#388D5
hypocenterC5C2×#2498
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. C22×#4018C2semidirect
3. C2×C5×#388C2semidirect
4. C2×#65276C2semidirect
5. C2×#65273C2semidirect
8. C2×#65238C2semidirect
9. C2×#65241C2semidirect
10. C2×#65233C2semidirect
11. C2×#65222C2semidirect
12. #10607600C2direct (N × H)
13. C2×#64956C2semidirect
14. C2×D5×#95C2semidirect
15. C2×#64949C2semidirect
16. C2×#64942C2semidirect
43. C2×#4018C22semidirect
44. C5×#388C22semidirect
57. #65276C22semidirect
58. #65273C22semidirect
61. #65241C22semidirect
62. #65238C22semidirect
63. #65233C22semidirect
64. #65222C22semidirect
65. #64956C22semidirect
66. D5×#95C22semidirect
67. #64949C22semidirect
68. #64942C22semidirect
161. C2×#388D5semidirect
305. #388C2×D5semidirect
648. C2×C5#2498semidirect
749. C5C2×#2498semidirect
795. C2#10607600direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#40292
C22×#40182
C2×C5×#3882
C2×#652762
C2×#652732
C2×#652452
C2×#652382
C2×#652412
C2×#652332
C2×#652222
#106076002
C2×#649562
C2×D5×#952
C2×#649492
C2×#649422
C2×#24985