Finite Group Databasebeta

← C2×#10607091 #12269519

Subgroups — C2×#10607091 #12269519

Order 1280.

3374 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#4042C211yesmaximal, characteristic, complemented
2C22×C4×D20C211yesmaximal, characteristic
3C2×C5×#387C211yesmaximal, characteristic, complemented
4C2×#65281C211yesmaximal, characteristic, complemented
5C2×#65278C211yesmaximal, characteristic, complemented
6C2×#65276C211yesmaximal, characteristic, complemented
7C2×#65222C211yesmaximal, characteristic, complemented
8#10607091C2116yesmaximal, direct product factor
9C2×#64962C211yesmaximal, characteristic, complemented
10C2×#64954C211yesmaximal, characteristic
11C2×#64954C211yesmaximal, characteristic
12C2×#64957C211yesmaximal, characteristic, complemented
13C2×#64956C211yesmaximal, characteristic, complemented
14C2×D5×#95C211yesmaximal, characteristic, complemented
15C2×#64949C211yesmaximal, characteristic, complemented
16C2×#64945C211yesmaximal, characteristic, complemented
17C23×D20C2211yescharacteristic
18C23×C4×D5C2211yescharacteristic
19C23×C4×D5C2211yescharacteristic
20C23×C4×D5C2211yescharacteristic
21C23×C4×D5C2211yescharacteristic
22C23×Dic10C2211yescharacteristic
23C22×C5×C4⋊C4C2211yescharacteristic
24C22×C5×C4⋊C4C2211yescharacteristic
25C22×C42×C5C2211yescharacteristic
26C22×#685C2211yescharacteristic
27C22×#685C2211yescharacteristic
28C22×#685C2211yescharacteristic
29C22×#685C2211yescharacteristic
30C22×#685C2211yescharacteristic
31C22×#685C2211yescharacteristic
32C22×#685C2211yescharacteristic
33C22×#685C2211yescharacteristic
34C22×C4⋊Dic5C2211yescharacteristic
35C22×C4⋊Dic5C2211yescharacteristic
36C22×#683C2211yescharacteristic
37C22×#683C2211yescharacteristic
38C22×#683C2211yescharacteristic
39C22×#683C2211yescharacteristic
40C2×#4042—28no—
41C2×#4042C2218yescomplemented
42C2×C4×D20—28no—
43C2×C4×D20C2218yes—
44C5×#387C2218yescomplemented
45C2×C5×#95C2211yescharacteristic
46C2×C5×#95C2211yescharacteristic
47C2×C5×#95C2211yescharacteristic
48C2×C5×#95C2211yescharacteristic
49C2×#3963C2211yescharacteristic
50C2×#3963C2211yescharacteristic
51C2×#3963C2211yescharacteristic
52C2×#3963C2211yescharacteristic
53C2×#3963C2211yescharacteristic
54C2×#3963C2211yescharacteristic
55C2×#3963C2211yescharacteristic
56C2×#3963C2211yescharacteristic
57#65281C2218yescomplemented
58#65278C2218yescomplemented
59#65276C2218yescomplemented
60#65222C2218yescomplemented
61#64962C2218yescomplemented
62#64957C2218yescomplemented
63#64956C2218yescomplemented
64#64954C2218yes—
65#64954C2218yes—
66D5×#95C2218yescomplemented
67#64949C2218yescomplemented
68#64945C2218yescomplemented
69C2×#2564—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×D20Q818yescomplemented
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—42no—
95C22×C4×D5—42no—
96C22×C4×D5—42no—
97C22×C4×D5—42no—
98C22×C4×D5—42no—
99C22×C4×D5—42no—
100C22×C4×D5D418yes—
101C22×C4×D5C2314yes—
102C22×C4×D5C2314yes—
103C22×C4×D5C2314yes—
104C22×C4×D5C2314yes—
105C22×Dic10—24no—
106C22×Dic10—42no—
107C22×Dic10—42no—
108C22×Dic10C2314yes—
109C2×C5×C4⋊C4—24no—
110C2×C5×C4⋊C4—24no—
111C2×C5×C4⋊C4C2314yes—
112C2×C5×C4⋊C4C2314yes—
113C2×C42×C5—24no—
114C2×C42×C5C2314yes—
115C2×#685—24no—
116C2×#685—24no—
117C2×#685—24no—
118C2×#685—24no—
119C2×#685—24no—
120C2×#685—24no—
121C2×#685—42no—
122C2×#685—42no—
123C2×#685C2314yes—
124C2×#685C2314yes—
125C2×#685C2314yes—
126C2×#685C2314yes—
127C2×#685C2314yes—
128C2×#685C2314yes—
129C2×#685C2314yes—
130C2×#685C2314yes—
131C2×C4⋊Dic5—24no—
132C2×C4⋊Dic5—42no—
133C2×C4⋊Dic5C2314yes—
134C2×C4⋊Dic5C2314yes—
135C2×#683—24no—
136C2×#683—24no—
137C2×#683—24no—
138C2×#683—42no—
139C2×#683C2314yes—
140C2×#683C2314yes—
141C2×#683C2314yes—
142C2×#683C2314yes—
143#4042—232no—
144C4×D20—232no—
145C5×#95C2314yes—
146C5×#95C2314yes—
147C5×#95C2314yes—
148C5×#95C2314yes—
149#3963C2314yes—
150#3963C2314yes—
151#3963C2314yes—
152#3963C2314yes—
153#3963C2314yes—
154#3963C2314yes—
155#3963C2314yes—
156#3963C2314yes—
157C22×C22⋊Q8—51no—
158C22×C4×D4—51no—
159#2564—516no—
160C2×#400—51no—
161C2×#399—51no—
162C2×#395—51no—
163C2×#393—51no—
164C2×#387—51no—
165C2×#387D511yescharacteristic, complemented
166C2×#386—51no—
167C2×#386—51no—
168C2×#385—51no—
169C2×#385—51no—
170C2×#380—51no—
171C2×#380—51no—
172C22×#95—51no—
173C24×C5C2411yescharacteristic
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×D5—22no—
184C23×D5C2×D414yes—
185C23×D5C2×Q814yes—
186C23×D5C2×Q814yes—
187C23×D5#4114yes—
188C23×D5C2412yes—
189C23×D5C2412yes—
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×C5—22no—
208C22×C4×C5C2×D414yes—
209C22×C4×C5C2×Q814yes—
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—232no—
243C2×D20—28no—
244C2×D20—28no—
245C2×D20C2×Q8116yescomplemented
246C2×C4×D5—28no—
247C2×C4×D5—28no—
248C2×C4×D5—28no—
249C2×C4×D5—28no—
250C2×C4×D5—28no—
251C2×C4×D5—416no—
252C2×C4×D5—44no—
253C2×C4×D5—44no—
254C2×C4×D5—44no—
255C2×C4×D5—44no—
256C2×C4×D5—44no—
257C2×C4×D5—44no—
258C2×C4×D5—416no—
259C2×C4×D5—416no—
260C2×C4×D5—416no—
261C2×C4×D5C2×D4116yes—
262C2×Dic10—28no—
263C2×Dic10—44no—
264C2×Dic10—44no—
265C2×Dic10—416no—
266C5×C4⋊C4—28no—
267C5×C4⋊C4—28no—
268C42×C5—28no—
269#685—28no—
270#685—28no—
271#685—28no—
272#685—28no—
273#685—28no—
274#685—28no—
275#685—44no—
276#685—44no—
277C4⋊Dic5—28no—
278C4⋊Dic5—44no—
279#683—28no—
280#683—28no—
281#683—28no—
282#683—44no—
283C23×Q8—51no—
284C23×D4—51no—
285C24×C4—51no—
286C24×C4—51no—
287C24×C4—51no—
288C24×C4—51no—
289C2×C22⋊Q8—58no—
290C2×C22⋊Q8—108no—
291C2×C4×D4—58no—
292C2×C4×D4—108no—
293C22×C4⋊C4—51no—
294C22×C4⋊C4—51no—
295C22×C4⋊C4—51no—
296C22×C4⋊C4—51no—
297C22×C4⋊C4—51no—
298C22×C4⋊C4—51no—
299C22×C4⋊C4C2×D511yescharacteristic
300C22×C4⋊C4C2×D511yescharacteristic
301C22×C22⋊C4—51no—
302C22×C22⋊C4—51no—
303C22×C22⋊C4—51no—
304C22×C22⋊C4—51no—
305C22×C22⋊C4—51no—
306C22×C22⋊C4—51no—
307C22×C22⋊C4—51no—
308C22×C22⋊C4—51no—
309C22×C42C2×D511yescharacteristic
310#400—58no—
311#399—58no—
312#395—58no—
313#393—58no—
314#387—58no—
315#387C2×D518yescomplemented
316#386—58no—
317#386—58no—
318#385—58no—
319#385—58no—
320#380—58no—
321#380—58no—
322C2×#95—51no—
323C2×#95—51no—
324C2×#95—51no—
325C2×#95—51no—
326C2×#95—51no—
327C2×#95—51no—
328C2×#95—51no—
329C2×#95—51no—
330C2×#95—58no—
331C2×#95C2×D511yescharacteristic
332C2×#95C2×D511yescharacteristic
333C2×#95C2×D511yescharacteristic
334C2×#95C2×D511yescharacteristic
335C23×C5C22×D412yes—
336C23×C5C22×Q812yes—
337C23×C5C2×#4112yes—
338C23×C5C2×#4112yes—
339C23×C5C2×#4112yes—
340C23×C5H(5,𝔽2)12yes—
341C23×C5H(5,𝔽2)12yes—
342C23×C5C2511yescharacteristic
343C22×D5—28no—
344C22×D5—28no—
345C22×D5—28no—
346C22×D5—28no—
347C22×D5—28no—
348C22×D5—28no—
349C22×D5—22no—
350C22×D5—22no—
351C22×D5—22no—
352C22×D5—22no—
353C22×D5—28no—
354C22×D5—28no—
355C22×D5—28no—
356C22×D5—22no—
357C22×D5—22no—
358C22×D5—22no—
359C22×D5—22no—
360C22×D5—22no—
361C22×D5—22no—
362C22×D5—44no—
363C22×D5—44no—
364C22×D5—44no—
365C22×D5—44no—
366C22×D5C22⋊Q8116yes—
367C22×D5C22×D414yes—
368C22×D5C22×Q814yes—
369C22×D5C22×Q814yes—
370C22×D5C2×#4114yes—
371C2×C4×C5—28no—
372C2×C4×C5—28no—
373C2×C4×C5—28no—
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—22no—
384C2×C4×C5—22no—
385C2×C4×C5—22no—
386C2×C4×C5—22no—
387C2×C4×C5—22no—
388C2×C4×C5—22no—
389C2×C4×C5—22no—
390C2×C4×C5—22no—
391C2×C4×C5—22no—
392C2×C4×C5—44no—
393C2×C4×C5—44no—
394C2×C4×C5—44no—
395C2×C4×C5—44no—
396C2×C4×C5C22×D414yes—
397C2×C4×C5C22×Q814yes—
398C2×C4×C5C2×#4114yes—
399C2×Dic5—28no—
400C2×Dic5—28no—
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—22no—
412C2×Dic5—22no—
413C2×Dic5—22no—
414C2×Dic5—22no—
415C2×Dic5—22no—
416C2×Dic5—22no—
417C2×Dic5—44no—
418C2×Dic5—44no—
419C2×Dic5—44no—
420C2×Dic5—44no—
421C2×Dic5C22×D414yes—
422C2×Dic5C2×#4114yes—
423D20—232no—
424C4×D5—416no—
425C4×D5—416no—
426C4×D5—416no—
427C4×D5—416no—
428Dic10—416no—
429C25—51no—
430C25—51no—
431C22×Q8—54no—
432C22×Q8—104no—
433C22×Q8—202no—
434C22×Q8—202no—
435C22×D4—58no—
436C22×D4—54no—
437C22×D4—104no—
438C22×D4—104no—
439C23×C4—51no—
440C23×C4—51no—
441C23×C4—58no—
442C23×C4—54no—
443C23×C4—51no—
444C23×C4—51no—
445C23×C4—51no—
446C23×C4—51no—
447C23×C4—54no—
448C23×C4—54no—
449C23×C4—54no—
450C23×C4—104no—
451C23×C4—104no—
452C23×C4—104no—
453C23×C4—104no—
454C23×C4—104no—
455C23×C4—202no—
456C23×C4—202no—
457C23×C4—202no—
458C23×C4—202no—
459C23×C4—202no—
460C23×C4—202no—
461C23×C4C22×D511yescharacteristic
462C23×C4C22×D511yescharacteristic
463C23×C4C22×D511yescharacteristic
464C23×C4C22×D511yescharacteristic
465C23×C4C22×D511yescharacteristic
466C23×C4C22×D511yescharacteristic
467C23×C4C22×D511yescharacteristic
468C22⋊Q8—1032no—
469C4×D4—1032no—
470C2×C4⋊C4—24no—
471C2×C4⋊C4—24no—
472C2×C4⋊C4—54no—
473C2×C4⋊C4—54no—
474C2×C4⋊C4—54no—
475C2×C4⋊C4—54no—
476C2×C4⋊C4—54no—
477C2×C4⋊C4—54no—
478C2×C4⋊C4—104no—
479C2×C4⋊C4—104no—
480C2×C4⋊C4—104no—
481C2×C4⋊C4—104no—
482C2×C4⋊C4—202no—
483C2×C4⋊C4—202no—
484C2×C4⋊C4C22×D514yes—
485C2×C4⋊C4C22×D514yes—
486C2×C22⋊C4—54no—
487C2×C22⋊C4—54no—
488C2×C22⋊C4—54no—
489C2×C22⋊C4—54no—
490C2×C22⋊C4—54no—
491C2×C22⋊C4—54no—
492C2×C22⋊C4—54no—
493C2×C22⋊C4—54no—
494C2×C22⋊C4—104no—
495C2×C22⋊C4—104no—
496C2×C22⋊C4—104no—
497C2×C22⋊C4—104no—
498C2×C22⋊C4—104no—
499C2×C22⋊C4—104no—
500C2×C22⋊C4—202no—
501C2×C22⋊C4—202no—
502C2×C42—24no—
503C2×C42C22×D514yes—
504#95—54no—
505#95—54no—
506#95—54no—
507#95—54no—
508#95—54no—
509#95—54no—
510#95—54no—
511#95—54no—
512#95C22×D514yes—
513#95C22×D514yes—
514#95C22×D514yes—
515#95C22×D514yes—
516C22×C5C2×C22⋊Q814yes—
517C22×C5#53214yes—
518C22×C5#53414yes—
519C22×C5#55114yes—
520C22×C5#55114yes—
521C22×C5#55414yes—
522C22×C5#55414yes—
523C22×C5C23×D411yescharacteristic
524C22×C5C23×Q811yescharacteristic
525C22×C5C22×#4111yescharacteristic
526C22×C5C22×#4111yescharacteristic
527C22×C5C22×#4111yescharacteristic
528C22×C5C2×H(5,𝔽2)11yescharacteristic
529C22×C5C2×H(5,𝔽2)11yescharacteristic
530C2×D5—232no—
531C2×D5—24no—
532C2×D5—24no—
533C2×D5—24no—
534C2×D5—24no—
535C2×D5—24no—
536C2×D5—24no—
537C2×D5—24no—
538C2×D5—24no—
539C2×D5—24no—
540C2×D5—416no—
541C2×D5—42no—
542C2×D5—42no—
543C2×D5—42no—
544C2×D5—42no—
545C2×D5C2×C22⋊Q818yes—
546C4×C5—24no—
547C4×C5—24no—
548C4×C5—24no—
549C4×C5—42no—
550C4×C5—42no—
551C4×C5—42no—
552C4×C5—42no—
553Dic5—24no—
554Dic5—24no—
555Dic5—42no—
556Dic5—42no—
557Dic5—42no—
558Dic5—42no—
559C24—54no—
560C24—54no—
561C24—54no—
562C24—52no—
563C24—54no—
564C24—52no—
565C24—102no—
566C24—102no—
567C24—102no—
568C24—102no—
569C24—102no—
570C24—102no—
571C24—102no—
572C24—102no—
573C24—102no—
574C24—102no—
575C24C23×D511yescharacteristic
576C2×Q8—108no—
577C2×Q8—204no—
578C2×Q8—204no—
579C2×Q8—2016no—
580C2×D4—516no—
581C2×D4—108no—
582C2×D4—1032no—
583C2×D4—108no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—54no—
603C22×C4—54no—
604C22×C4—52no—
605C22×C4—52no—
606C22×C4—516no—
607C22×C4—52no—
608C22×C4—52no—
609C22×C4—52no—
610C22×C4—52no—
611C22×C4—108no—
612C22×C4—108no—
613C22×C4—108no—
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—102no—
624C22×C4—102no—
625C22×C4—102no—
626C22×C4—102no—
627C22×C4—102no—
628C22×C4—102no—
629C22×C4—102no—
630C22×C4—108no—
631C22×C4—108no—
632C22×C4—2016no—
633C22×C4—204no—
634C22×C4—204no—
635C22×C4—204no—
636C22×C4—204no—
637C22×C4—204no—
638C22×C4—204no—
639C22×C4—2016no—
640C22×C4—2016no—
641C22×C4—2016no—
642C22×C4#70914yes—
643C22×C4D4×D514yes—
644C22×C4Q8×D514yes—
645C22×C4C23×D512yes—
646C22×C4C23×D512yes—
647C22×C4C23×D512yes—
648C22×C4C23×D512yes—
649C22×C4C23×D512yes—
650C22×C4C23×D512yes—
651C22×C4C23×D512yes—
652C4⋊C4—28no—
653C4⋊C4—28no—
654C4⋊C4—108no—
655C4⋊C4—108no—
656C4⋊C4—108no—
657C4⋊C4—108no—
658C4⋊C4—204no—
659C4⋊C4—204no—
660C22⋊C4—108no—
661C22⋊C4—108no—
662C22⋊C4—108no—
663C22⋊C4—108no—
664C22⋊C4—108no—
665C22⋊C4—108no—
666C22⋊C4—204no—
667C22⋊C4—204no—
668C42—28no—
669C2×C5#256418yescomplemented
670C2×C5C22×C22⋊Q811yescharacteristic
671C2×C5C2×#53211yescharacteristic
672C2×C5C2×#53411yescharacteristic
673C2×C5C2×#55111yescharacteristic
674C2×C5C2×#55111yescharacteristic
675C2×C5C2×#55411yescharacteristic
676C2×C5C2×#55411yescharacteristic
677D5—28no—
678D5—44no—
679C23—516no—
680C23—54no—
681C23—54no—
682C23—54no—
683C23—54no—
684C23—108no—
685C23—108no—
686C23—108no—
687C23—108no—
688C23—102no—
689C23—108no—
690C23—102no—
691C23—102no—
692C23—102no—
693C23—108no—
694C23—108no—
695C23—108no—
696C23—102no—
697C23—102no—
698C23—108no—
699C23—102no—
700C23—102no—
701C23—102no—
702C23—102no—
703C23—204no—
704C23—204no—
705C23—204no—
706C23—204no—
707C23C2×#70912yes—
708C23C2×D4×D512yes—
709C23C2×Q8×D512yes—
710C23D5×#4112yes—
711C23D5×#4112yes—
712C23#414912yes—
713C23#414912yes—
714C23C24×D511yescharacteristic
715Q8—2016no—
716D4—1032no—
717C2×C4—28no—
718C2×C4—28no—
719C2×C4—28no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—44no—
739C2×C4—44no—
740C2×C4—44no—
741C2×C4—44no—
742C2×C4—54no—
743C2×C4—54no—
744C2×C4—108no—
745C2×C4—102no—
746C2×C4—102no—
747C2×C4—102no—
748C2×C4—102no—
749C2×C4—108no—
750C2×C4—102no—
751C2×C4—102no—
752C2×C4—102no—
753C2×C4—102no—
754C2×C4—102no—
755C2×C4—102no—
756C2×C4—102no—
757C2×C4—102no—
758C2×C4—102no—
759C2×C4—102no—
760C2×C4—102no—
761C2×C4—102no—
762C2×C4—2016no—
763C2×C4—2016no—
764C2×C4—2016no—
765C2×C4—2016no—
766C2×C4—204no—
767C2×C4—204no—
768C2×C4—204no—
769C2×C4—204no—
770C2×C4C2×#70914yes—
771C2×C4C2×D4×D514yes—
772C2×C4C2×Q8×D514yes—
773C5C2×#256411yescharacteristic, complemented, Sylow
774C22—58no—
775C22—104no—
776C22—104no—
777C22—104no—
778C22—104no—
779C22—104no—
780C22—104no—
781C22—1032no—
782C22—104no—
783C22—104no—
784C22—104no—
785C22—202no—
786C22—202no—
787C22—202no—
788C22—202no—
789C22—2016no—
790C22#6586114yes—
791C22#6588214yes—
792C22#6591314yes—
793C22D5×C22⋊Q814yes—
794C22#6598714yes—
795C22#6602414yes—
796C22#6603914yes—
797C22C22×#70911yescharacteristic
798C22C22×D4×D511yescharacteristic
799C22C22×Q8×D511yescharacteristic
800C22C2×D5×#4111yescharacteristic
801C22C2×D5×#4111yescharacteristic
802C22C2×#414911yescharacteristic
803C22C2×#414911yescharacteristic
804C4—24no—
805C4—24no—
806C4—24no—
807C4—42no—
808C4—42no—
809C4—42no—
810C4—42no—
811C4—104no—
812C4—104no—
813C4—202no—
814C4—202no—
815C4—202no—
816C4—202no—
817C2—108no—
818C2—204no—
819C2#1060709118yesdirect product factor
820C2C2×#6586111yescharacteristic
821C2C2×#6588211yescharacteristic
822C2C2×#6591311yescharacteristic
823C2C2×D5×C22⋊Q811yescharacteristic
824C2C2×#6598711yescharacteristic
825C2C2×#6602411yescharacteristic
826C2C2×#6603911yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC2×C5×#387C2
socleC24×C5C24
prime radicalC23×D20C22
hypercenterC2×#387D5
hypocenterC5C2×#2564
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
1. C22×#4042C2semidirect
3. C2×C5×#387C2semidirect
4. C2×#65281C2semidirect
5. C2×#65278C2semidirect
6. C2×#65276C2semidirect
7. C2×#65222C2semidirect
8. #10607091C2direct (N × H)
9. C2×#64962C2semidirect
12. C2×#64957C2semidirect
13. C2×#64956C2semidirect
14. C2×D5×#95C2semidirect
15. C2×#64949C2semidirect
16. C2×#64945C2semidirect
41. C2×#4042C22semidirect
44. C5×#387C22semidirect
57. #65281C22semidirect
58. #65278C22semidirect
59. #65276C22semidirect
60. #65222C22semidirect
61. #64962C22semidirect
62. #64957C22semidirect
63. #64956C22semidirect
66. D5×#95C22semidirect
67. #64949C22semidirect
68. #64945C22semidirect
87. C22×D20Q8semidirect
165. C2×#387D5semidirect
245. C2×D20C2×Q8semidirect
315. #387C2×D5semidirect
669. C2×C5#2564semidirect
773. C5C2×#2564semidirect
819. C2#10607091direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#40422
C22×C4×D202
C2×C5×#3872
C2×#652812
C2×#652782
C2×#652762
C2×#652222
#106070912
C2×#649622
C2×#649542
C2×#649572
C2×#649562
C2×D5×#952
C2×#649492
C2×#649452
C2×#25645