Finite Group Databasebeta

← C2×#10609213 #12266903

Subgroups — C2×#10609213 #12266903

Order 1280.

4102 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D5×C22⋊C4C211yesmaximal, characteristic
2C22×#4025C211yesmaximal, characteristic, complemented
3C2×C5×#397C211yesmaximal, characteristic, complemented
4C2×#65278C211yesmaximal, characteristic, complemented
5C2×#65279C211yesmaximal, characteristic, complemented
6C2×#65244C211yesmaximal, characteristic
7C2×#65244C211yesmaximal, characteristic
8C2×#65241C211yesmaximal, characteristic, complemented
9C2×#65234C211yesmaximal, characteristic, complemented
10#10609213C2116yesmaximal, direct product factor
11C2×#64964C211yesmaximal, characteristic, complemented
12C2×#64965C211yesmaximal, characteristic, complemented
13C2×#64957C211yesmaximal, characteristic, complemented
14C2×#64956C211yesmaximal, characteristic, complemented
15C2×#64959C211yesmaximal, characteristic, complemented
16C2×#64955C211yesmaximal, characteristic, complemented
17C25×D5C2211yescharacteristic
18C23×C4×D5C2211yescharacteristic
19C23×C4×D5C2211yescharacteristic
20C22×C5×C4⋊C4C2211yescharacteristic, complemented
21C22×C5×C22⋊C4C2211yescharacteristic
22C22×C5×C22⋊C4C2211yescharacteristic
23C22×C5×C22⋊C4C2211yescharacteristic
24C22×C22⋊Dic5C2211yescharacteristic
25C22×C22⋊Dic5C2211yescharacteristic
26C22×C22⋊Dic5C2211yescharacteristic
27C22×#685C2211yescharacteristic
28C22×#685C2211yescharacteristic
29C22×#685C2211yescharacteristic
30C22×#685C2211yescharacteristic
31C22×#685C2211yescharacteristic
32C22×#685C2211yescharacteristic
33C22×#685C2211yescharacteristic
34C22×#685C2211yescharacteristic
35C22×#685C2211yescharacteristic
36C22×#685C2211yescharacteristic
37C22×C4⋊Dic5C2211yescharacteristic, complemented
38C22×#683C2211yescharacteristic, complemented
39C22×#683C2211yescharacteristic, complemented
40C22×#683C2211yescharacteristic, complemented
41C22×#683C2211yescharacteristic, complemented
42C22×C4×Dic5C2211yescharacteristic, complemented
43C22×C4×Dic5C2211yescharacteristic, complemented
44C2×D5×C22⋊C4—28no—
45C2×D5×C22⋊C4C2218yes—
46C2×#4025—28no—
47C2×#4025C2218yescomplemented
48C5×#397C2218yescomplemented
49C2×C5×#95C2211yescharacteristic, complemented
50C2×C5×#95C2211yescharacteristic, complemented
51C2×C5×#95C2211yescharacteristic, complemented
52C2×#3963C2211yescharacteristic, complemented
53C2×#3963C2211yescharacteristic, complemented
54C2×#3963C2211yescharacteristic, complemented
55C2×#3963C2211yescharacteristic, complemented
56C2×#3963C2211yescharacteristic, complemented
57#65279C2218yescomplemented
58#65278C2218yescomplemented
59#65244C2218yes—
60#65244C2218yes—
61#65241C2218yescomplemented
62#65234C2218yescomplemented
63#64965C2218yescomplemented
64#64964C2218yescomplemented
65#64959C2218yescomplemented
66#64957C2218yescomplemented
67#64956C2218yescomplemented
68#64955C2218yescomplemented
69C2×#2480—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—24no—
97C22×C4×D5—42no—
98C22×C4×D5—42no—
99C22×C4×D5C2314yes—
100C22×C4×D5C2314yes—
101C2×C5×C4⋊C4—42no—
102C2×C5×C4⋊C4C2314yescomplemented
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×C22⋊Dic5—24no—
110C2×C22⋊Dic5—42no—
111C2×C22⋊Dic5D418yes—
112C2×C22⋊Dic5C2314yes—
113C2×C22⋊Dic5C2314yes—
114C2×C22⋊Dic5C2314yes—
115C2×#685—24no—
116C2×#685—24no—
117C2×#685—24no—
118C2×#685—24no—
119C2×#685—24no—
120C2×#685—24no—
121C2×#685—24no—
122C2×#685—24no—
123C2×#685—42no—
124C2×#685—42no—
125C2×#685C2314yes—
126C2×#685C2314yes—
127C2×#685C2314yes—
128C2×#685C2314yes—
129C2×#685C2314yes—
130C2×#685C2314yes—
131C2×#685C2314yes—
132C2×#685C2314yes—
133C2×#685C2314yes—
134C2×#685C2314yes—
135C2×C4⋊Dic5—24no—
136C2×C4⋊Dic5C2314yescomplemented
137C2×#683—24no—
138C2×#683—24no—
139C2×#683—42no—
140C2×#683—42no—
141C2×#683C2314yescomplemented
142C2×#683C2314yescomplemented
143C2×#683C2314yescomplemented
144C2×#683C2314yescomplemented
145C2×C4×Dic5—24no—
146C2×C4×Dic5—42no—
147C2×C4×Dic5C2314yescomplemented
148C2×C4×Dic5C2314yescomplemented
149D5×C22⋊C4—232no—
150#4025—232no—
151C5×#95C2314yescomplemented
152C5×#95C2314yescomplemented
153C5×#95C2314yescomplemented
154#3963C2314yescomplemented
155#3963C2314yescomplemented
156#3963C2314yescomplemented
157#3963C2314yescomplemented
158#3963C2314yescomplemented
159C22×#126—51no—
160C23×C22⋊C4—51no—
161#2480—516no—
162C2×#397—51no—
163C2×#397—51no—
164C2×#397D511yescharacteristic, complemented
165C2×#396—51no—
166C2×#388—51no—
167C2×#388—51no—
168C2×#388—51no—
169C2×#385—51no—
170C2×#385—51no—
171C2×#380—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×C5C2×D414yes—
182C24×C5C2412yes—
183C24×C5C2411yescharacteristic
184C23×D5—22no—
185C23×D5—22no—
186C23×D5—22no—
187C23×D5—22no—
188C23×D5—232no—
189C23×D5—28no—
190C23×D5—22no—
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×D5#4114yes—
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×C5—22no—
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×Dic5C2×D414yes—
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—28no—
266C2×C4×D5—44no—
267C2×C4×D5—44no—
268C2×C4×D5—416no—
269C2×C4×D5—416no—
270C5×C4⋊C4—44no—
271C5×C22⋊C4—28no—
272C5×C22⋊C4—28no—
273C5×C22⋊C4—44no—
274C22⋊Dic5—28no—
275C22⋊Dic5—44no—
276C22⋊Dic5C2×D4116yes—
277#685—28no—
278#685—28no—
279#685—28no—
280#685—28no—
281#685—28no—
282#685—28no—
283#685—28no—
284#685—28no—
285#685—44no—
286#685—44no—
287C4⋊Dic5—28no—
288#683—28no—
289#683—28no—
290#683—44no—
291#683—44no—
292C4×Dic5—28no—
293C4×Dic5—44no—
294C26—51no—
295C24×C4—51no—
296C24×C4—51no—
297C2×#126—58no—
298C2×#126—108no—
299C22×C4⋊C4—51no—
300C22×C4⋊C4—51no—
301C22×C4⋊C4—51no—
302C22×C4⋊C4—51no—
303C22×C4⋊C4—51no—
304C22×C4⋊C4C2×D511yescharacteristic, complemented
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—51no—
318C22×C22⋊C4—58no—
319C22×C22⋊C4—108no—
320C22×C22⋊C4C2×D511yescharacteristic
321C22×C22⋊C4C2×D511yescharacteristic
322C22×C22⋊C4C2×D511yescharacteristic
323C22×C42—51no—
324C22×C42—51no—
325#397—58no—
326#397—58no—
327#397C2×D518yescomplemented
328#396—58no—
329#388—58no—
330#388—58no—
331#388—58no—
332#385—58no—
333#385—58no—
334#380—58no—
335#379—58no—
336#379—58no—
337C4×C22⋊C4—58no—
338C2×#95—51no—
339C2×#95—51no—
340C2×#95—51no—
341C2×#95—51no—
342C2×#95—51no—
343C2×#95C2×D511yescharacteristic, complemented
344C2×#95C2×D511yescharacteristic, complemented
345C2×#95C2×D511yescharacteristic, complemented
346C23×C5—28no—
347C23×C5—28no—
348C23×C5—28no—
349C23×C5—22no—
350C23×C5—22no—
351C23×C5—22no—
352C23×C5—22no—
353C23×C5—22no—
354C23×C5—22no—
355C23×C5—44no—
356C23×C5—44no—
357C23×C5—44no—
358C23×C5—44no—
359C23×C5C22×D414yes—
360C23×C5C22×D412yes—
361C23×C5C2×#4112yes—
362C23×C5C2×#4112yes—
363C23×C5C2×#4112yes—
364C23×C5C2×#4112yes—
365C23×C5H(5,𝔽2)12yes—
366C23×C5H(5,𝔽2)12yes—
367C23×C5C2511yescharacteristic
368C22×D5—28no—
369C22×D5—28no—
370C22×D5—28no—
371C22×D5—28no—
372C22×D5—28no—
373C22×D5—28no—
374C22×D5—22no—
375C22×D5—22no—
376C22×D5—22no—
377C22×D5—22no—
378C22×D5—232no—
379C22×D5—28no—
380C22×D5—28no—
381C22×D5—28no—
382C22×D5—22no—
383C22×D5—22no—
384C22×D5—22no—
385C22×D5—22no—
386C22×D5—22no—
387C22×D5—22no—
388C22×D5—416no—
389C22×D5—416no—
390C22×D5—416no—
391C22×D5—416no—
392C22×D5—416no—
393C22×D5—4128no—
394C22×D5—44no—
395C22×D5—44no—
396C22×D5—44no—
397C22×D5—44no—
398C22×D5—416no—
399C22×D5#126116yescomplemented
400C22×D5C2×#4114yes—
401C22×D5C2×#4114yes—
402C22×D5C2×#4114yes—
403C22×D5C2×#4114yes—
404C2×C4×C5—22no—
405C2×C4×C5—22no—
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—44no—
423C2×C4×C5—44no—
424C2×C4×C5—44no—
425C2×C4×C5—44no—
426C2×C4×C5—44no—
427C2×C4×C5—44no—
428C2×Dic5—28no—
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—44no—
447C2×Dic5—44no—
448C2×Dic5—44no—
449C2×Dic5—44no—
450C2×Dic5C22×D414yes—
451C2×Dic5C22×D414yes—
452C4×D5—416no—
453C4×D5—416no—
454C25—51no—
455C25—51no—
456C25—54no—
457C25—104no—
458C25—104no—
459C25—104no—
460C25—104no—
461C25—104no—
462C25—202no—
463C25—202no—
464C25C22×D511yescharacteristic
465C23×C4—51no—
466C23×C4—51no—
467C23×C4—51no—
468C23×C4—51no—
469C23×C4—51no—
470C23×C4—51no—
471C23×C4—54no—
472C23×C4—54no—
473C23×C4—104no—
474C23×C4—104no—
475C23×C4—104no—
476C23×C4—104no—
477C23×C4—202no—
478C23×C4—202no—
479C23×C4C22×D511yescharacteristic
480C23×C4C22×D511yescharacteristic
481C23×C4C22×D511yescharacteristic
482C23×C4C22×D511yescharacteristic
483C23×C4C22×D511yescharacteristic
484C23×C4C22×D511yescharacteristic
485#126—1032no—
486C2×C4⋊C4—42no—
487C2×C4⋊C4—54no—
488C2×C4⋊C4—54no—
489C2×C4⋊C4—54no—
490C2×C4⋊C4—54no—
491C2×C4⋊C4—54no—
492C2×C4⋊C4—104no—
493C2×C4⋊C4—104no—
494C2×C4⋊C4—104no—
495C2×C4⋊C4—202no—
496C2×C4⋊C4—202no—
497C2×C4⋊C4C22×D514yescomplemented
498C2×C22⋊C4—24no—
499C2×C22⋊C4—24no—
500C2×C22⋊C4—42no—
501C2×C22⋊C4—58no—
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—54no—
515C2×C22⋊C4—1032no—
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—54no—
532C2×C42—54no—
533C2×C42—104no—
534C2×C42—202no—
535#95—54no—
536#95—54no—
537#95—54no—
538#95—54no—
539#95—54no—
540#95C22×D514yescomplemented
541#95C22×D514yescomplemented
542#95C22×D514yescomplemented
543C22×C5—24no—
544C22×C5—24no—
545C22×C5—24no—
546C22×C5—42no—
547C22×C5—42no—
548C22×C5—42no—
549C22×C5—42no—
550C22×C5—416no—
551C22×C5#52514yes—
552C22×C5C2×#12614yes—
553C22×C5#53814yes—
554C22×C5#54614yes—
555C22×C5#54614yes—
556C22×C5#55114yes—
557C22×C5#55114yes—
558C22×C5C23×D411yescharacteristic
559C22×C5C22×#4111yescharacteristic
560C22×C5C22×#4111yescharacteristic
561C22×C5C22×#4111yescharacteristic
562C22×C5C22×#4111yescharacteristic
563C22×C5C2×H(5,𝔽2)11yescharacteristic
564C22×C5C2×H(5,𝔽2)11yescharacteristic
565C2×D5—24no—
566C2×D5—24no—
567C2×D5—24no—
568C2×D5—24no—
569C2×D5—24no—
570C2×D5—24no—
571C2×D5—232no—
572C2×D5—24no—
573C2×D5—24no—
574C2×D5—24no—
575C2×D5—464no—
576C2×D5—42no—
577C2×D5—42no—
578C2×D5—42no—
579C2×D5—42no—
580C2×D5—416no—
581C2×D5C2×#12618yescomplemented
582C4×C5—42no—
583C4×C5—42no—
584C4×C5—42no—
585C4×C5—42no—
586C4×C5—42no—
587C4×C5—42no—
588Dic5—24no—
589Dic5—24no—
590Dic5—42no—
591Dic5—42no—
592Dic5—42no—
593Dic5—42no—
594C24—22no—
595C24—22no—
596C24—22no—
597C24—22no—
598C24—22no—
599C24—22no—
600C24—54no—
601C24—54no—
602C24—54no—
603C24—52no—
604C24—54no—
605C24—52no—
606C24—108no—
607C24—108no—
608C24—108no—
609C24—108no—
610C24—1032no—
611C24—102no—
612C24—102no—
613C24—102no—
614C24—102no—
615C24—108no—
616C24—102no—
617C24—102no—
618C24—102no—
619C24—102no—
620C24—102no—
621C24—102no—
622C24—204no—
623C24—204no—
624C24—2016no—
625C24—2016no—
626C24—2016no—
627C24—2016no—
628C24—2016no—
629C24—2016no—
630C24D4×D514yes—
631C24C23×D512yes—
632C24C23×D511yescharacteristic
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—22no—
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—54no—
652C22×C4—54no—
653C22×C4—52no—
654C22×C4—52no—
655C22×C4—52no—
656C22×C4—52no—
657C22×C4—52no—
658C22×C4—52no—
659C22×C4—108no—
660C22×C4—108no—
661C22×C4—108no—
662C22×C4—108no—
663C22×C4—102no—
664C22×C4—102no—
665C22×C4—102no—
666C22×C4—102no—
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—204no—
680C22×C4—204no—
681C22×C4—2016no—
682C22×C4—2016no—
683C22×C4C23×D512yes—
684C22×C4C23×D512yes—
685C22×C4C23×D512yes—
686C22×C4C23×D512yes—
687C22×C4C23×D512yes—
688C22×C4C23×D512yes—
689C4⋊C4—44no—
690C4⋊C4—108no—
691C4⋊C4—108no—
692C4⋊C4—108no—
693C4⋊C4—204no—
694C4⋊C4—204no—
695C22⋊C4—28no—
696C22⋊C4—28no—
697C22⋊C4—44no—
698C22⋊C4—516no—
699C22⋊C4—108no—
700C22⋊C4—108no—
701C22⋊C4—108no—
702C22⋊C4—108no—
703C22⋊C4—108no—
704C22⋊C4—108no—
705C22⋊C4—108no—
706C22⋊C4—108no—
707C22⋊C4—108no—
708C22⋊C4—204no—
709C22⋊C4—204no—
710C22⋊C4—204no—
711C42—108no—
712C42—204no—
713C2×C5—44no—
714C2×C5#248018yescomplemented
715C2×C5C2×#52511yescharacteristic
716C2×C5C22×#12611yescharacteristic
717C2×C5C2×#53811yescharacteristic
718C2×C5C2×#54611yescharacteristic
719C2×C5C2×#54611yescharacteristic
720C2×C5C2×#55111yescharacteristic
721C2×C5C2×#55111yescharacteristic
722D5—28no—
723D5—44no—
724C23—28no—
725C23—28no—
726C23—28no—
727C23—22no—
728C23—22no—
729C23—22no—
730C23—22no—
731C23—22no—
732C23—22no—
733C23—44no—
734C23—44no—
735C23—44no—
736C23—44no—
737C23—54no—
738C23—54no—
739C23—54no—
740C23—516no—
741C23—54no—
742C23—1032no—
743C23—108no—
744C23—108no—
745C23—108no—
746C23—108no—
747C23—108no—
748C23—102no—
749C23—102no—
750C23—102no—
751C23—102no—
752C23—108no—
753C23—108no—
754C23—108no—
755C23—102no—
756C23—102no—
757C23—102no—
758C23—102no—
759C23—102no—
760C23—102no—
761C23—108no—
762C23—2016no—
763C23—2016no—
764C23—2016no—
765C23—2016no—
766C23—2016no—
767C23—20128no—
768C23—2016no—
769C23—204no—
770C23—204no—
771C23—204no—
772C23—204no—
773C23C2×D4×D514yes—
774C23C2×D4×D512yes—
775C23#414412yes—
776C23D5×#4112yes—
777C23D5×#4112yes—
778C23D5×#4112yes—
779C23D5×#4112yes—
780C23#414912yes—
781C23C24×D511yescharacteristic
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
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—44no—
801C2×C4—44no—
802C2×C4—44no—
803C2×C4—44no—
804C2×C4—44no—
805C2×C4—44no—
806C2×C4—54no—
807C2×C4—54no—
808C2×C4—108no—
809C2×C4—108no—
810C2×C4—102no—
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—2016no—
827C2×C4—2016no—
828C2×C4—204no—
829C2×C4—204no—
830C2×C4—204no—
831C2×C4—204no—
832C5C2×#248011yescharacteristic, complemented, Sylow
833C22—24no—
834C22—24no—
835C22—24no—
836C22—42no—
837C22—416no—
838C22—42no—
839C22—42no—
840C22—42no—
841C22—58no—
842C22—104no—
843C22—104no—
844C22—104no—
845C22—1032no—
846C22—104no—
847C22—104no—
848C22—104no—
849C22—104no—
850C22—104no—
851C22—104no—
852C22—2064no—
853C22—202no—
854C22—2016no—
855C22—202no—
856C22—202no—
857C22—202no—
858C22#6594414yes—
859C22#6598814yes—
860C22#6599014yes—
861C22#6599314yes—
862C22#6601214yes—
863C22D5×#12614yes—
864C22#6603914yes—
865C22C22×D4×D511yescharacteristic
866C22C2×#414411yescharacteristic
867C22C2×D5×#4111yescharacteristic
868C22C2×D5×#4111yescharacteristic
869C22C2×D5×#4111yescharacteristic
870C22C2×D5×#4111yescharacteristic
871C22C2×#414911yescharacteristic
872C4—42no—
873C4—42no—
874C4—42no—
875C4—42no—
876C4—42no—
877C4—42no—
878C4—104no—
879C4—104no—
880C4—202no—
881C4—202no—
882C4—202no—
883C4—202no—
884C2—44no—
885C2—108no—
886C2—204no—
887C2#1060921318yesdirect product factor
888C2C2×#6594411yescharacteristic
889C2C2×#6599011yescharacteristic
890C2C2×#6598811yescharacteristic
891C2C2×#6599311yescharacteristic
892C2C2×#6601211yescharacteristic
893C2C2×D5×#12611yescharacteristic
894C2C2×#6603911yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC2×C5×#397C2
socleC24×C5C24
prime radicalC25×D5C22
hypercenterC2×#397D5
hypocenterC5C2×#2480
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#397

Complements

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

NH ≅ G/Ntype
2. C22×#4025C2semidirect
3. C2×C5×#397C2semidirect
4. C2×#65278C2semidirect
5. C2×#65279C2semidirect
8. C2×#65241C2semidirect
9. C2×#65234C2semidirect
10. #10609213C2direct (N × H)
11. C2×#64964C2semidirect
12. C2×#64965C2semidirect
13. C2×#64957C2semidirect
14. C2×#64956C2semidirect
15. C2×#64959C2semidirect
16. C2×#64955C2semidirect
20. C22×C5×C4⋊C4C22semidirect
37. C22×C4⋊Dic5C22semidirect
38. C22×#683C22semidirect
39. C22×#683C22semidirect
40. C22×#683C22semidirect
41. C22×#683C22semidirect
42. C22×C4×Dic5C22semidirect
43. C22×C4×Dic5C22semidirect
47. C2×#4025C22semidirect
48. C5×#397C22semidirect
49. C2×C5×#95C22semidirect
50. C2×C5×#95C22semidirect
51. C2×C5×#95C22semidirect
52. C2×#3963C22semidirect
53. C2×#3963C22semidirect
54. C2×#3963C22semidirect
55. C2×#3963C22semidirect
56. C2×#3963C22semidirect
57. #65279C22semidirect
58. #65278C22semidirect
61. #65241C22semidirect
62. #65234C22semidirect
63. #64965C22semidirect
64. #64964C22semidirect
65. #64959C22semidirect
66. #64957C22semidirect
67. #64956C22semidirect
68. #64955C22semidirect
102. C2×C5×C4⋊C4C23semidirect
136. C2×C4⋊Dic5C23semidirect
141. C2×#683C23semidirect
142. C2×#683C23semidirect
143. C2×#683C23semidirect
144. C2×#683C23semidirect
147. C2×C4×Dic5C23semidirect
148. C2×C4×Dic5C23semidirect
151. C5×#95C23semidirect
152. C5×#95C23semidirect
153. C5×#95C23semidirect
154. #3963C23semidirect
155. #3963C23semidirect
156. #3963C23semidirect
157. #3963C23semidirect
158. #3963C23semidirect
164. C2×#397D5semidirect
304. C22×C4⋊C4C2×D5semidirect
327. #397C2×D5semidirect
343. C2×#95C2×D5semidirect
344. C2×#95C2×D5semidirect
345. C2×#95C2×D5semidirect
399. C22×D5#126semidirect
497. C2×C4⋊C4C22×D5semidirect
540. #95C22×D5semidirect
541. #95C22×D5semidirect
542. #95C22×D5semidirect
581. C2×D5C2×#126semidirect
714. C2×C5#2480semidirect
832. C5C2×#2480semidirect
887. C2#10609213direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D5×C22⋊C42
C22×#40252
C2×C5×#3972
C2×#652782
C2×#652792
C2×#652442
C2×#652412
C2×#652342
#106092132
C2×#649642
C2×#649652
C2×#649572
C2×#649562
C2×#649592
C2×#649552
C2×#24805