Finite Group Databasebeta

← C2×#10607621 #12269673

Subgroups — C2×#10607621 #12269673

Order 1280.

4166 conjugacy classes of subgroups.

The subgroup lattice has 900 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#4042C211yesmaximal, characteristic, complemented
2C22×D5×C22⋊C4C211yesmaximal, characteristic
3C2×C5×#388C211yesmaximal, characteristic, complemented
4C2×#65279C211yesmaximal, characteristic, complemented
5C2×#65244C211yesmaximal, characteristic
6C2×#65244C211yesmaximal, characteristic
7C2×#65241C211yesmaximal, characteristic, complemented
8C2×#65236C211yesmaximal, characteristic, complemented
9C2×#65234C211yesmaximal, characteristic, complemented
10C2×#65229C211yesmaximal, characteristic, complemented
11C2×C4×#685C211yesmaximal, characteristic, complemented
12#10607621C2116yesmaximal, direct product factor
13C2×#64964C211yesmaximal, characteristic, complemented
14C2×#64962C211yesmaximal, characteristic, complemented
15C2×#64953C211yesmaximal, characteristic, complemented
16C2×#64953C211yesmaximal, characteristic, complemented
17C25×D5C2211yescharacteristic
18C23×C4×D5C2211yescharacteristic
19C23×C4×D5C2211yescharacteristic
20C23×Dic10C2211yescharacteristic, complemented
21C22×C5×C4⋊C4C2211yescharacteristic, complemented
22C22×C5×C22⋊C4C2211yescharacteristic
23C22×C5×C22⋊C4C2211yescharacteristic
24C22×C5×C22⋊C4C2211yescharacteristic
25C22×C42×C5C2211yescharacteristic, complemented
26C22×C22⋊Dic5C2211yescharacteristic
27C22×C22⋊Dic5C2211yescharacteristic
28C22×C22⋊Dic5C2211yescharacteristic
29C22×#685C2211yescharacteristic
30C22×#685C2211yescharacteristic
31C22×#685C2211yescharacteristic
32C22×#685C2211yescharacteristic
33C22×#685C2211yescharacteristic
34C22×#685C2211yescharacteristic
35C22×#685C2211yescharacteristic
36C22×#685C2211yescharacteristic
37C22×#685C2211yescharacteristic
38C22×#685C2211yescharacteristic
39C22×#683C2211yescharacteristic, complemented
40C22×#683C2211yescharacteristic, complemented
41C22×C4×Dic5C2211yescharacteristic, complemented
42C2×#4042—28no—
43C2×#4042C2218yescomplemented
44C2×D5×C22⋊C4—28no—
45C2×D5×C22⋊C4C2218yes—
46C5×#388C2218yescomplemented
47C2×C5×#95C2211yescharacteristic, complemented
48C2×C5×#95C2211yescharacteristic, complemented
49C2×#3963C2211yescharacteristic, complemented
50C2×#3963C2211yescharacteristic, complemented
51C2×#3963C2211yescharacteristic, complemented
52C2×#3963C2211yescharacteristic, complemented
53C2×#3963C2211yescharacteristic, complemented
54C2×#3963C2211yescharacteristic, complemented
55C2×#3963C2211yescharacteristic, complemented
56C2×#3963C2211yescharacteristic, complemented
57#65279C2218yescomplemented
58#65244C2218yes—
59#65244C2218yes—
60#65241C2218yescomplemented
61#65236C2218yescomplemented
62#65234C2218yescomplemented
63#65229C2218yescomplemented
64C4×#685C2218yescomplemented
65#64964C2218yescomplemented
66#64962C2218yescomplemented
67#64953C2218yescomplemented
68#64953C2218yescomplemented
69C2×#2561—51nomaximal, Sylow
70C25×C5C2311yescharacteristic
71C24×D5—24no—
72C24×D5—24no—
73C24×D5—24no—
74C24×D5—24no—
75C24×D5—24no—
76C24×D5—42no—
77C24×D5—42no—
78C24×D5C2311yescharacteristic
79C24×D5C2314yes—
80C24×D5C2311yescharacteristic
81C23×C4×C5C2311yescharacteristic
82C23×C4×C5C2311yescharacteristic
83C23×C4×C5C2311yescharacteristic
84C23×C4×C5C2311yescharacteristic
85C23×C4×C5C2311yescharacteristic
86C23×C4×C5C2311yescharacteristic
87C23×Dic5C2311yescharacteristic
88C23×Dic5C2311yescharacteristic
89C23×Dic5C2311yescharacteristic
90C23×Dic5C2311yescharacteristic
91C23×Dic5C2311yescharacteristic
92C23×Dic5C2311yescharacteristic
93C22×C4×D5—24no—
94C22×C4×D5—24no—
95C22×C4×D5—24no—
96C22×C4×D5—42no—
97C22×C4×D5—42no—
98C22×C4×D5D418yes—
99C22×C4×D5C2314yes—
100C22×C4×D5C2314yes—
101C22×Dic10—24no—
102C22×Dic10—42no—
103C22×Dic10—42no—
104C22×Dic10C2314yescomplemented
105C2×C5×C4⋊C4—24no—
106C2×C5×C4⋊C4C2314yescomplemented
107C2×C5×C22⋊C4—24no—
108C2×C5×C22⋊C4—24no—
109C2×C5×C22⋊C4—42no—
110C2×C5×C22⋊C4C2314yes—
111C2×C5×C22⋊C4C2314yes—
112C2×C5×C22⋊C4C2314yes—
113C2×C42×C5—42no—
114C2×C42×C5C2314yescomplemented
115C2×C22⋊Dic5—24no—
116C2×C22⋊Dic5—24no—
117C2×C22⋊Dic5—42no—
118C2×C22⋊Dic5C2314yes—
119C2×C22⋊Dic5C2314yes—
120C2×C22⋊Dic5C2314yes—
121C2×#685—24no—
122C2×#685—24no—
123C2×#685—24no—
124C2×#685—24no—
125C2×#685—24no—
126C2×#685—24no—
127C2×#685—24no—
128C2×#685—24no—
129C2×#685—42no—
130C2×#685—42no—
131C2×#685C2314yes—
132C2×#685C2314yes—
133C2×#685C2314yes—
134C2×#685C2314yes—
135C2×#685C2314yes—
136C2×#685C2314yes—
137C2×#685C2314yes—
138C2×#685C2314yes—
139C2×#685C2314yes—
140C2×#685C2314yes—
141C2×#683—24no—
142C2×#683—24no—
143C2×#683C2314yescomplemented
144C2×#683C2314yescomplemented
145C2×C4×Dic5—42no—
146C2×C4×Dic5C2314yescomplemented
147#4042—232no—
148D5×C22⋊C4—232no—
149C5×#95C2314yescomplemented
150C5×#95C2314yescomplemented
151#3963C2314yescomplemented
152#3963C2314yescomplemented
153#3963C2314yescomplemented
154#3963C2314yescomplemented
155#3963C2314yescomplemented
156#3963C2314yescomplemented
157#3963C2314yescomplemented
158#3963C2314yescomplemented
159C22×C22⋊Q8—51no—
160C23×C22⋊C4—51no—
161#2561—516no—
162C2×#397—51no—
163C2×#397—51no—
164C2×#393—51no—
165C2×#393—51no—
166C2×#388—51no—
167C2×#388—51no—
168C2×#388—51no—
169C2×#388D511yescharacteristic, complemented
170C2×#381—51no—
171C2×#381—51no—
172C2×#379—51no—
173C2×#379—51no—
174C2×C4×C22⋊C4—51no—
175C24×C5—22no—
176C24×C5—22no—
177C24×C5—22no—
178C24×C5—22no—
179C24×C5—22no—
180C24×C5—22no—
181C24×C5#4114yes—
182C24×C5C2412yes—
183C24×C5C2411yescharacteristic
184C23×D5—22no—
185C23×D5—22no—
186C23×D5—22no—
187C23×D5—22no—
188C23×D5—232no—
189C23×D5—22no—
190C23×D5—28no—
191C23×D5—22no—
192C23×D5—22no—
193C23×D5—22no—
194C23×D5—22no—
195C23×D5—22no—
196C23×D5—28no—
197C23×D5—28no—
198C23×D5—28no—
199C23×D5—28no—
200C23×D5—44no—
201C23×D5—44no—
202C23×D5—416no—
203C23×D5—416no—
204C23×D5—416no—
205C23×D5—416no—
206C23×D5—416no—
207C23×D5—416no—
208C23×D5C2×D414yes—
209C23×D5#4114yes—
210C23×D5#4114yes—
211C23×D5#4114yes—
212C23×D5C2412yes—
213C23×D5C2412yes—
214C22×C4×C5—22no—
215C22×C4×C5—22no—
216C22×C4×C5—22no—
217C22×C4×C5—22no—
218C22×C4×C5—22no—
219C22×C4×C5—22no—
220C22×C4×C5—22no—
221C22×C4×C5—22no—
222C22×C4×C5—22no—
223C22×C4×C5—22no—
224C22×C4×C5—22no—
225C22×C4×C5—22no—
226C22×C4×C5—22no—
227C22×C4×C5—22no—
228C22×C4×C5—22no—
229C22×C4×C5—22no—
230C22×C4×C5—22no—
231C22×C4×C5C2×D414yes—
232C22×C4×C5C2412yes—
233C22×C4×C5C2412yes—
234C22×C4×C5C2412yes—
235C22×C4×C5C2412yes—
236C22×C4×C5C2412yes—
237C22×C4×C5C2412yes—
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×Dic5—22no—
247C22×Dic5—22no—
248C22×Dic5—22no—
249C22×Dic5—22no—
250C22×Dic5—22no—
251C22×Dic5—22no—
252C22×Dic5—22no—
253C22×Dic5—22no—
254C22×Dic5—22no—
255C22×Dic5C2×D414yes—
256C22×Dic5C2412yes—
257C22×Dic5C2412yes—
258C22×Dic5C2412yes—
259C22×Dic5C2412yes—
260C22×Dic5C2412yes—
261C22×Dic5C2412yes—
262C2×C4×D5—28no—
263C2×C4×D5—28no—
264C2×C4×D5—28no—
265C2×C4×D5—416no—
266C2×C4×D5—44no—
267C2×C4×D5—44no—
268C2×C4×D5—416no—
269C2×C4×D5C2×D4116yes—
270C2×Dic10—28no—
271C2×Dic10—44no—
272C2×Dic10—44no—
273C2×Dic10—416no—
274C5×C4⋊C4—28no—
275C5×C22⋊C4—28no—
276C5×C22⋊C4—28no—
277C5×C22⋊C4—44no—
278C42×C5—44no—
279C22⋊Dic5—28no—
280C22⋊Dic5—28no—
281C22⋊Dic5—44no—
282#685—28no—
283#685—28no—
284#685—28no—
285#685—28no—
286#685—28no—
287#685—28no—
288#685—28no—
289#685—28no—
290#685—44no—
291#685—44no—
292#683—28no—
293#683—28no—
294C4×Dic5—44no—
295C26—51no—
296C23×Q8—51no—
297C24×C4—51no—
298C24×C4—51no—
299C2×C22⋊Q8—58no—
300C2×C22⋊Q8—108no—
301C22×C4⋊C4—51no—
302C22×C4⋊C4—51no—
303C22×C4⋊C4C2×D511yescharacteristic, complemented
304C22×C22⋊C4—51no—
305C22×C22⋊C4—51no—
306C22×C22⋊C4—51no—
307C22×C22⋊C4—51no—
308C22×C22⋊C4—51no—
309C22×C22⋊C4—51no—
310C22×C22⋊C4—51no—
311C22×C22⋊C4—51no—
312C22×C22⋊C4—51no—
313C22×C22⋊C4—51no—
314C22×C22⋊C4—51no—
315C22×C22⋊C4—51no—
316C22×C22⋊C4—51no—
317C22×C22⋊C4—58no—
318C22×C22⋊C4—108no—
319C22×C22⋊C4C2×D511yescharacteristic
320C22×C22⋊C4C2×D511yescharacteristic
321C22×C22⋊C4C2×D511yescharacteristic
322C22×C42—51no—
323C22×C42C2×D511yescharacteristic, complemented
324#397—58no—
325#397—58no—
326#393—58no—
327#393—58no—
328#388—58no—
329#388—58no—
330#388—58no—
331#388C2×D518yescomplemented
332#381—58no—
333#381—58no—
334#379—58no—
335#379—58no—
336C4×C22⋊C4—58no—
337C2×#95—51no—
338C2×#95—51no—
339C2×#95—51no—
340C2×#95—51no—
341C2×#95—51no—
342C2×#95—51no—
343C2×#95—51no—
344C2×#95—51no—
345C2×#95C2×D511yescharacteristic, complemented
346C2×#95C2×D511yescharacteristic, complemented
347C23×C5—28no—
348C23×C5—28no—
349C23×C5—28no—
350C23×C5—22no—
351C23×C5—22no—
352C23×C5—22no—
353C23×C5—22no—
354C23×C5—22no—
355C23×C5—22no—
356C23×C5—44no—
357C23×C5—44no—
358C23×C5—44no—
359C23×C5—44no—
360C23×C5C22×D412yes—
361C23×C5C2×#4114yes—
362C23×C5C2×#4112yes—
363C23×C5C2×#4112yes—
364C23×C5C2×#4112yes—
365C23×C5C2×#4112yes—
366C23×C5H(5,𝔽2)12yes—
367C23×C5H(5,𝔽2)12yes—
368C23×C5C2511yescharacteristic
369C22×D5—28no—
370C22×D5—28no—
371C22×D5—28no—
372C22×D5—28no—
373C22×D5—28no—
374C22×D5—28no—
375C22×D5—22no—
376C22×D5—22no—
377C22×D5—22no—
378C22×D5—22no—
379C22×D5—232no—
380C22×D5—28no—
381C22×D5—28no—
382C22×D5—28no—
383C22×D5—22no—
384C22×D5—22no—
385C22×D5—22no—
386C22×D5—22no—
387C22×D5—22no—
388C22×D5—22no—
389C22×D5—416no—
390C22×D5—416no—
391C22×D5—416no—
392C22×D5—416no—
393C22×D5—4128no—
394C22×D5—416no—
395C22×D5—44no—
396C22×D5—44no—
397C22×D5—44no—
398C22×D5—44no—
399C22×D5—416no—
400C22×D5#124116yes—
401C22×D5C22×D414yes—
402C22×D5C2×#4114yes—
403C22×D5C2×#4114yes—
404C22×D5C2×#4114yes—
405C2×C4×C5—28no—
406C2×C4×C5—22no—
407C2×C4×C5—22no—
408C2×C4×C5—22no—
409C2×C4×C5—22no—
410C2×C4×C5—22no—
411C2×C4×C5—22no—
412C2×C4×C5—22no—
413C2×C4×C5—22no—
414C2×C4×C5—22no—
415C2×C4×C5—22no—
416C2×C4×C5—22no—
417C2×C4×C5—22no—
418C2×C4×C5—22no—
419C2×C4×C5—22no—
420C2×C4×C5—22no—
421C2×C4×C5—22no—
422C2×C4×C5—22no—
423C2×C4×C5—44no—
424C2×C4×C5—44no—
425C2×C4×C5—44no—
426C2×C4×C5—44no—
427C2×C4×C5—44no—
428C2×C4×C5C22×D414yes—
429C2×Dic5—28no—
430C2×Dic5—22no—
431C2×Dic5—22no—
432C2×Dic5—22no—
433C2×Dic5—22no—
434C2×Dic5—22no—
435C2×Dic5—22no—
436C2×Dic5—22no—
437C2×Dic5—22no—
438C2×Dic5—22no—
439C2×Dic5—22no—
440C2×Dic5—22no—
441C2×Dic5—22no—
442C2×Dic5—22no—
443C2×Dic5—22no—
444C2×Dic5—22no—
445C2×Dic5—22no—
446C2×Dic5—22no—
447C2×Dic5—44no—
448C2×Dic5—44no—
449C2×Dic5—44no—
450C2×Dic5—44no—
451C2×Dic5—44no—
452C2×Dic5C22×D414yes—
453C4×D5—416no—
454C4×D5—416no—
455Dic10—416no—
456C25—51no—
457C25—51no—
458C25—54no—
459C25—104no—
460C25—104no—
461C25—104no—
462C25—104no—
463C25—104no—
464C25—202no—
465C25—202no—
466C25C22×D511yescharacteristic
467C22×Q8—54no—
468C22×Q8—104no—
469C22×Q8—202no—
470C22×Q8—202no—
471C23×C4—51no—
472C23×C4—58no—
473C23×C4—54no—
474C23×C4—51no—
475C23×C4—51no—
476C23×C4—51no—
477C23×C4—51no—
478C23×C4—51no—
479C23×C4—54no—
480C23×C4—104no—
481C23×C4—104no—
482C23×C4—104no—
483C23×C4—202no—
484C23×C4—202no—
485C23×C4C22×D511yescharacteristic
486C23×C4C22×D511yescharacteristic
487C23×C4C22×D511yescharacteristic
488C23×C4C22×D511yescharacteristic
489C23×C4C22×D511yescharacteristic
490C23×C4C22×D511yescharacteristic
491C22⋊Q8—1032no—
492C2×C4⋊C4—24no—
493C2×C4⋊C4—54no—
494C2×C4⋊C4—54no—
495C2×C4⋊C4—104no—
496C2×C4⋊C4—104no—
497C2×C4⋊C4C22×D514yescomplemented
498C2×C22⋊C4—24no—
499C2×C22⋊C4—24no—
500C2×C22⋊C4—42no—
501C2×C22⋊C4—54no—
502C2×C22⋊C4—54no—
503C2×C22⋊C4—54no—
504C2×C22⋊C4—54no—
505C2×C22⋊C4—54no—
506C2×C22⋊C4—54no—
507C2×C22⋊C4—54no—
508C2×C22⋊C4—54no—
509C2×C22⋊C4—54no—
510C2×C22⋊C4—54no—
511C2×C22⋊C4—54no—
512C2×C22⋊C4—54no—
513C2×C22⋊C4—54no—
514C2×C22⋊C4—1032no—
515C2×C22⋊C4—104no—
516C2×C22⋊C4—104no—
517C2×C22⋊C4—104no—
518C2×C22⋊C4—104no—
519C2×C22⋊C4—104no—
520C2×C22⋊C4—104no—
521C2×C22⋊C4—104no—
522C2×C22⋊C4—104no—
523C2×C22⋊C4—104no—
524C2×C22⋊C4—104no—
525C2×C22⋊C4—202no—
526C2×C22⋊C4—202no—
527C2×C22⋊C4—202no—
528C2×C22⋊C4C22×D514yes—
529C2×C22⋊C4C22×D514yes—
530C2×C22⋊C4C22×D514yes—
531C2×C42—42no—
532C2×C42—54no—
533C2×C42—202no—
534C2×C42C22×D514yescomplemented
535#95—54no—
536#95—54no—
537#95—54no—
538#95—54no—
539#95—54no—
540#95—54no—
541#95—54no—
542#95—54no—
543#95C22×D514yescomplemented
544#95C22×D514yescomplemented
545C22×C5—24no—
546C22×C5—24no—
547C22×C5—24no—
548C22×C5—416no—
549C22×C5—42no—
550C22×C5—42no—
551C22×C5—42no—
552C22×C5—42no—
553C22×C5#52514yes—
554C22×C5C2×#12414yes—
555C22×C5#53414yes—
556C22×C5#55114yes—
557C22×C5#55114yes—
558C22×C5#55114yes—
559C22×C5#55114yes—
560C22×C5C23×D411yescharacteristic
561C22×C5C22×#4111yescharacteristic
562C22×C5C22×#4111yescharacteristic
563C22×C5C22×#4111yescharacteristic
564C22×C5C22×#4111yescharacteristic
565C22×C5C2×H(5,𝔽2)11yescharacteristic
566C22×C5C2×H(5,𝔽2)11yescharacteristic
567C2×D5—232no—
568C2×D5—24no—
569C2×D5—24no—
570C2×D5—24no—
571C2×D5—24no—
572C2×D5—24no—
573C2×D5—24no—
574C2×D5—24no—
575C2×D5—24no—
576C2×D5—24no—
577C2×D5—464no—
578C2×D5—416no—
579C2×D5—42no—
580C2×D5—42no—
581C2×D5—42no—
582C2×D5—42no—
583C2×D5C2×#12418yes—
584C4×C5—24no—
585C4×C5—42no—
586C4×C5—42no—
587C4×C5—42no—
588C4×C5—42no—
589C4×C5—42no—
590Dic5—24no—
591Dic5—42no—
592Dic5—42no—
593Dic5—42no—
594Dic5—42no—
595Dic5—42no—
596C24—22no—
597C24—22no—
598C24—22no—
599C24—22no—
600C24—22no—
601C24—22no—
602C24—54no—
603C24—54no—
604C24—54no—
605C24—52no—
606C24—54no—
607C24—52no—
608C24—108no—
609C24—108no—
610C24—108no—
611C24—108no—
612C24—1032no—
613C24—102no—
614C24—102no—
615C24—102no—
616C24—102no—
617C24—108no—
618C24—102no—
619C24—102no—
620C24—102no—
621C24—102no—
622C24—102no—
623C24—102no—
624C24—204no—
625C24—204no—
626C24—2016no—
627C24—2016no—
628C24—2016no—
629C24—2016no—
630C24—2016no—
631C24—2016no—
632C24#70914yes—
633C24C23×D512yes—
634C24C23×D511yescharacteristic
635C2×Q8—108no—
636C2×Q8—204no—
637C2×Q8—204no—
638C2×Q8—2016no—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—22no—
642C22×C4—22no—
643C22×C4—22no—
644C22×C4—22no—
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—22no—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—54no—
657C22×C4—52no—
658C22×C4—516no—
659C22×C4—52no—
660C22×C4—52no—
661C22×C4—52no—
662C22×C4—52no—
663C22×C4—52no—
664C22×C4—108no—
665C22×C4—108no—
666C22×C4—108no—
667C22×C4—102no—
668C22×C4—102no—
669C22×C4—102no—
670C22×C4—102no—
671C22×C4—102no—
672C22×C4—102no—
673C22×C4—102no—
674C22×C4—102no—
675C22×C4—102no—
676C22×C4—102no—
677C22×C4—102no—
678C22×C4—102no—
679C22×C4—102no—
680C22×C4—102no—
681C22×C4—102no—
682C22×C4—102no—
683C22×C4—102no—
684C22×C4—2016no—
685C22×C4—204no—
686C22×C4—204no—
687C22×C4—2016no—
688C22×C4D4×D514yes—
689C22×C4C23×D512yes—
690C22×C4C23×D512yes—
691C22×C4C23×D512yes—
692C22×C4C23×D512yes—
693C22×C4C23×D512yes—
694C22×C4C23×D512yes—
695C4⋊C4—28no—
696C4⋊C4—108no—
697C4⋊C4—108no—
698C22⋊C4—28no—
699C22⋊C4—28no—
700C22⋊C4—44no—
701C22⋊C4—108no—
702C22⋊C4—108no—
703C22⋊C4—108no—
704C22⋊C4—108no—
705C22⋊C4—108no—
706C22⋊C4—108no—
707C22⋊C4—108no—
708C22⋊C4—108no—
709C22⋊C4—108no—
710C22⋊C4—108no—
711C22⋊C4—204no—
712C22⋊C4—204no—
713C22⋊C4—204no—
714C42—44no—
715C42—204no—
716C2×C5—44no—
717C2×C5#256118yescomplemented
718C2×C5C2×#52511yescharacteristic
719C2×C5C22×#12411yescharacteristic
720C2×C5C2×#53411yescharacteristic
721C2×C5C2×#55111yescharacteristic
722C2×C5C2×#55111yescharacteristic
723C2×C5C2×#55111yescharacteristic
724C2×C5C2×#55111yescharacteristic
725D5—28no—
726D5—44no—
727C23—28no—
728C23—28no—
729C23—28no—
730C23—22no—
731C23—22no—
732C23—22no—
733C23—22no—
734C23—22no—
735C23—22no—
736C23—44no—
737C23—44no—
738C23—44no—
739C23—44no—
740C23—516no—
741C23—54no—
742C23—54no—
743C23—54no—
744C23—54no—
745C23—1032no—
746C23—108no—
747C23—108no—
748C23—108no—
749C23—108no—
750C23—108no—
751C23—102no—
752C23—102no—
753C23—102no—
754C23—102no—
755C23—108no—
756C23—108no—
757C23—108no—
758C23—102no—
759C23—102no—
760C23—102no—
761C23—102no—
762C23—102no—
763C23—102no—
764C23—108no—
765C23—2016no—
766C23—2016no—
767C23—2016no—
768C23—2016no—
769C23—2016no—
770C23—20128no—
771C23—2016no—
772C23—204no—
773C23—204no—
774C23—204no—
775C23—204no—
776C23C2×#70914yes—
777C23C2×#70912yes—
778C23C2×D4×D512yes—
779C23#414412yes—
780C23D5×#4112yes—
781C23D5×#4112yes—
782C23D5×#4112yes—
783C23#414912yes—
784C23C24×D511yescharacteristic
785Q8—2016no—
786C2×C4—28no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—44no—
805C2×C4—44no—
806C2×C4—44no—
807C2×C4—44no—
808C2×C4—44no—
809C2×C4—54no—
810C2×C4—108no—
811C2×C4—102no—
812C2×C4—102no—
813C2×C4—102no—
814C2×C4—102no—
815C2×C4—102no—
816C2×C4—102no—
817C2×C4—102no—
818C2×C4—102no—
819C2×C4—102no—
820C2×C4—102no—
821C2×C4—102no—
822C2×C4—102no—
823C2×C4—102no—
824C2×C4—102no—
825C2×C4—102no—
826C2×C4—102no—
827C2×C4—102no—
828C2×C4—2016no—
829C2×C4—2016no—
830C2×C4—204no—
831C2×C4—204no—
832C2×C4—204no—
833C2×C4—204no—
834C2×C4—204no—
835C2×C4C2×D4×D514yes—
836C5C2×#256111yescharacteristic, complemented, Sylow
837C22—24no—
838C22—24no—
839C22—24no—
840C22—416no—
841C22—42no—
842C22—42no—
843C22—42no—
844C22—42no—
845C22—58no—
846C22—1032no—
847C22—104no—
848C22—104no—
849C22—104no—
850C22—104no—
851C22—104no—
852C22—104no—
853C22—104no—
854C22—104no—
855C22—104no—
856C22—2064no—
857C22—2016no—
858C22—202no—
859C22—202no—
860C22—202no—
861C22—202no—
862C22#6586114yes—
863C22#6588114yes—
864C22#6589014yes—
865C22#6593914yes—
866C22#6599314yes—
867C22D5×#12414yes—
868C22#6603914yes—
869C22C22×#70911yescharacteristic
870C22C22×D4×D511yescharacteristic
871C22C2×#414411yescharacteristic
872C22C2×D5×#4111yescharacteristic
873C22C2×D5×#4111yescharacteristic
874C22C2×D5×#4111yescharacteristic
875C22C2×#414911yescharacteristic
876C4—24no—
877C4—42no—
878C4—42no—
879C4—42no—
880C4—42no—
881C4—42no—
882C4—104no—
883C4—202no—
884C4—202no—
885C4—202no—
886C4—202no—
887C4—202no—
888C2—44no—
889C2—108no—
890C2—204no—
891C2#1060762118yesdirect product factor
892C2C2×#6586111yescharacteristic
893C2C2×#6588111yescharacteristic
894C2C2×#6589011yescharacteristic
895C2C2×#6593911yescharacteristic
896C2C2×#6599311yescharacteristic
897C2C2×D5×#12411yescharacteristic
898C2C2×#6603911yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC2×C5×#388C2
socleC24×C5C24
prime radicalC25×D5C22
hypercenterC2×#388D5
hypocenterC5C2×#2561
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
1. C22×#4042C2semidirect
3. C2×C5×#388C2semidirect
4. C2×#65279C2semidirect
7. C2×#65241C2semidirect
8. C2×#65236C2semidirect
9. C2×#65234C2semidirect
10. C2×#65229C2semidirect
11. C2×C4×#685C2semidirect
12. #10607621C2direct (N × H)
13. C2×#64964C2semidirect
14. C2×#64962C2semidirect
15. C2×#64953C2semidirect
16. C2×#64953C2semidirect
20. C23×Dic10C22semidirect
21. C22×C5×C4⋊C4C22semidirect
25. C22×C42×C5C22semidirect
39. C22×#683C22semidirect
40. C22×#683C22semidirect
41. C22×C4×Dic5C22semidirect
43. C2×#4042C22semidirect
46. C5×#388C22semidirect
47. C2×C5×#95C22semidirect
48. C2×C5×#95C22semidirect
49. C2×#3963C22semidirect
50. C2×#3963C22semidirect
51. C2×#3963C22semidirect
52. C2×#3963C22semidirect
53. C2×#3963C22semidirect
54. C2×#3963C22semidirect
55. C2×#3963C22semidirect
56. C2×#3963C22semidirect
57. #65279C22semidirect
60. #65241C22semidirect
61. #65236C22semidirect
62. #65234C22semidirect
63. #65229C22semidirect
64. C4×#685C22semidirect
65. #64964C22semidirect
66. #64962C22semidirect
67. #64953C22semidirect
68. #64953C22semidirect
104. C22×Dic10C23semidirect
106. C2×C5×C4⋊C4C23semidirect
114. C2×C42×C5C23semidirect
143. C2×#683C23semidirect
144. C2×#683C23semidirect
146. C2×C4×Dic5C23semidirect
149. C5×#95C23semidirect
150. C5×#95C23semidirect
151. #3963C23semidirect
152. #3963C23semidirect
153. #3963C23semidirect
154. #3963C23semidirect
155. #3963C23semidirect
156. #3963C23semidirect
157. #3963C23semidirect
158. #3963C23semidirect
169. C2×#388D5semidirect
303. C22×C4⋊C4C2×D5semidirect
323. C22×C42C2×D5semidirect
331. #388C2×D5semidirect
345. C2×#95C2×D5semidirect
346. C2×#95C2×D5semidirect
497. C2×C4⋊C4C22×D5semidirect
534. C2×C42C22×D5semidirect
543. #95C22×D5semidirect
544. #95C22×D5semidirect
717. C2×C5#2561semidirect
836. C5C2×#2561semidirect
891. C2#10607621direct (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×D5×C22⋊C42
C2×C5×#3882
C2×#652792
C2×#652442
C2×#652412
C2×#652362
C2×#652342
C2×#652292
C2×C4×#6852
#106076212
C2×#649642
C2×#649622
C2×#649532
C2×#25615