Finite Group Databasebeta

← C2×#10614812 #12266905

Subgroups — C2×#10614812 #12266905

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×C5×#126C211yesmaximal, characteristic, complemented
2C22×D5×C22⋊C4C211yesmaximal, characteristic
3#10614812C2116yesmaximal, direct product factor
4C2×#65282C211yesmaximal, characteristic, complemented
5C2×#65283C211yesmaximal, characteristic, complemented
6C2×#65278C211yesmaximal, characteristic, complemented
7C2×#65278C211yesmaximal, characteristic, complemented
8C2×#65276C211yesmaximal, characteristic, complemented
9C2×#65279C211yesmaximal, characteristic, complemented
10C2×#65244C211yesmaximal, characteristic
11C2×#65244C211yesmaximal, characteristic
12C2×#65241C211yesmaximal, characteristic, complemented
13C2×#65241C211yesmaximal, characteristic, complemented
14C2×#65240C211yesmaximal, characteristic, complemented
15C2×#65229C211yesmaximal, characteristic, complemented
16C2×C4×#685C211yesmaximal, characteristic, complemented
17C25×D5C2211yescharacteristic
18C23×C4×D5C2211yescharacteristic
19C23×C4×D5C2211yescharacteristic
20C2×C5×#126—28no—
21C2×C5×#126C2218yescomplemented
22C22×C5×C4⋊C4C2211yescharacteristic, complemented
23C22×C5×C4⋊C4C2211yescharacteristic, complemented
24C22×C5×C4⋊C4C2211yescharacteristic, complemented
25C22×C5×C22⋊C4C2211yescharacteristic
26C22×C5×C22⋊C4C2211yescharacteristic
27C22×C5×C22⋊C4C2211yescharacteristic
28C22×C42×C5C2211yescharacteristic, complemented
29C22×C22⋊Dic5C2211yescharacteristic
30C22×C22⋊Dic5C2211yescharacteristic
31C22×C22⋊Dic5C2211yescharacteristic
32C22×#685C2211yescharacteristic
33C22×#685C2211yescharacteristic
34C22×#685C2211yescharacteristic
35C22×#685C2211yescharacteristic
36C22×#685C2211yescharacteristic
37C22×#685C2211yescharacteristic
38C22×#685C2211yescharacteristic
39C22×#685C2211yescharacteristic
40C22×#685C2211yescharacteristic
41C22×#685C2211yescharacteristic
42C22×C4⋊Dic5C2211yescharacteristic, complemented
43C22×#683C2211yescharacteristic, complemented
44C22×#683C2211yescharacteristic, complemented
45C22×C4×Dic5C2211yescharacteristic, complemented
46C2×D5×C22⋊C4—28no—
47C2×D5×C22⋊C4C2218yes—
48C2×#3963C2211yescharacteristic, complemented
49C2×#3963C2211yescharacteristic, complemented
50C2×#3963C2211yescharacteristic, complemented
51C2×#3963C2211yescharacteristic, complemented
52C2×#3963C2211yescharacteristic, complemented
53C2×#3963C2211yescharacteristic, complemented
54C2×#3963C2211yescharacteristic, complemented
55C2×#3963C2211yescharacteristic, complemented
56#65283C2218yescomplemented
57#65282C2218yescomplemented
58#65279C2218yescomplemented
59#65278C2218yescomplemented
60#65278C2218yescomplemented
61#65276C2218yescomplemented
62#65244C2218yes—
63#65244C2218yes—
64#65241C2218yescomplemented
65#65241C2218yescomplemented
66#65240C2218yescomplemented
67#65229C2218yescomplemented
68C4×#685C2218yescomplemented
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—
101C5×#126—232no—
102C2×C5×C4⋊C4—24no—
103C2×C5×C4⋊C4—24no—
104C2×C5×C4⋊C4—24no—
105C2×C5×C4⋊C4C2314yescomplemented
106C2×C5×C4⋊C4C2314yescomplemented
107C2×C5×C4⋊C4C2314yescomplemented
108C2×C5×C22⋊C4—24no—
109C2×C5×C22⋊C4—24no—
110C2×C5×C22⋊C4D418yes—
111C2×C5×C22⋊C4C2314yes—
112C2×C5×C22⋊C4C2314yes—
113C2×C5×C22⋊C4C2314yes—
114C2×C42×C5—24no—
115C2×C42×C5C2314yescomplemented
116C2×C22⋊Dic5—24no—
117C2×C22⋊Dic5—42no—
118C2×C22⋊Dic5—42no—
119C2×C22⋊Dic5C2314yes—
120C2×C22⋊Dic5C2314yes—
121C2×C22⋊Dic5C2314yes—
122C2×#685—24no—
123C2×#685—24no—
124C2×#685—24no—
125C2×#685—24no—
126C2×#685—24no—
127C2×#685—24no—
128C2×#685—24no—
129C2×#685—24no—
130C2×#685—42no—
131C2×#685—42no—
132C2×#685C2314yes—
133C2×#685C2314yes—
134C2×#685C2314yes—
135C2×#685C2314yes—
136C2×#685C2314yes—
137C2×#685C2314yes—
138C2×#685C2314yes—
139C2×#685C2314yes—
140C2×#685C2314yes—
141C2×#685C2314yes—
142C2×C4⋊Dic5—42no—
143C2×C4⋊Dic5C2314yescomplemented
144C2×#683—42no—
145C2×#683—42no—
146C2×#683C2314yescomplemented
147C2×#683C2314yescomplemented
148C2×C4×Dic5—42no—
149C2×C4×Dic5C2314yescomplemented
150D5×C22⋊C4—232no—
151#3963C2314yescomplemented
152#3963C2314yescomplemented
153#3963C2314yescomplemented
154#3963C2314yescomplemented
155#3963C2314yescomplemented
156#3963C2314yescomplemented
157#3963C2314yescomplemented
158#3963C2314yescomplemented
159C22×#126D511yescharacteristic, complemented
160C23×C22⋊C4—51no—
161#2480—516no—
162C2×#397—51no—
163C2×#397—51no—
164C2×#397—51no—
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×C5C2×D414yes—
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×Dic5—22no—
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—28no—
271C5×C4⋊C4—28no—
272C5×C4⋊C4—28no—
273C5×C22⋊C4—28no—
274C5×C22⋊C4—28no—
275C5×C22⋊C4C2×D4116yes—
276C42×C5—28no—
277C22⋊Dic5—28no—
278C22⋊Dic5—44no—
279C22⋊Dic5—44no—
280#685—28no—
281#685—28no—
282#685—28no—
283#685—28no—
284#685—28no—
285#685—28no—
286#685—28no—
287#685—28no—
288#685—44no—
289#685—44no—
290C4⋊Dic5—44no—
291#683—44no—
292#683—44no—
293C4×Dic5—44no—
294C26—51no—
295C24×C4—51no—
296C24×C4—51no—
297C2×#126—28no—
298C2×#126C2×D518yescomplemented
299C22×C4⋊C4—51no—
300C22×C4⋊C4—51no—
301C22×C4⋊C4—51no—
302C22×C4⋊C4C2×D511yescharacteristic, complemented
303C22×C4⋊C4C2×D511yescharacteristic, complemented
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×C42C2×D511yescharacteristic, complemented
325#397—58no—
326#397—58no—
327#397—58no—
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×#95—51no—
344C2×#95—51no—
345C2×#95—51no—
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—28no—
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—44no—
423C2×C4×C5—44no—
424C2×C4×C5—44no—
425C2×C4×C5—44no—
426C2×C4×C5C22×D414yes—
427C2×C4×C5C22×D414yes—
428C2×Dic5—22no—
429C2×Dic5—22no—
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×Dic5—44no—
451C2×Dic5—44no—
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—232no—
486C2×C4⋊C4—24no—
487C2×C4⋊C4—24no—
488C2×C4⋊C4—24no—
489C2×C4⋊C4—54no—
490C2×C4⋊C4—54no—
491C2×C4⋊C4—54no—
492C2×C4⋊C4—202no—
493C2×C4⋊C4—202no—
494C2×C4⋊C4—202no—
495C2×C4⋊C4C22×D514yescomplemented
496C2×C4⋊C4C22×D514yescomplemented
497C2×C4⋊C4C22×D514yescomplemented
498C2×C22⋊C4—24no—
499C2×C22⋊C4—24no—
500C2×C22⋊C4—54no—
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—104no—
514C2×C22⋊C4—104no—
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—1032no—
523C2×C22⋊C4—202no—
524C2×C22⋊C4—202no—
525C2×C22⋊C4—202no—
526C2×C22⋊C4—202no—
527C2×C22⋊C4C22⋊D518yes—
528C2×C22⋊C4C22×D514yes—
529C2×C22⋊C4C22×D514yes—
530C2×C22⋊C4C22×D514yes—
531C2×C42—24no—
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—
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—24no—
583C4×C5—24no—
584C4×C5—42no—
585C4×C5—42no—
586C4×C5—42no—
587C4×C5—42no—
588Dic5—42no—
589Dic5—42no—
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—102no—
616C24—102no—
617C24—102no—
618C24—102no—
619C24—102no—
620C24—108no—
621C24—102no—
622C24—204no—
623C24—204no—
624C24—2016no—
625C24—2016no—
626C24—2016no—
627C24—2016no—
628C24—2016no—
629C24—2016no—
630C24C2×C22⋊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—52no—
650C22×C4—52no—
651C22×C4—52no—
652C22×C4—52no—
653C22×C4—52no—
654C22×C4—52no—
655C22×C4—108no—
656C22×C4—108no—
657C22×C4—102no—
658C22×C4—102no—
659C22×C4—102no—
660C22×C4—102no—
661C22×C4—102no—
662C22×C4—102no—
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—108no—
676C22×C4—108no—
677C22×C4—204no—
678C22×C4—204no—
679C22×C4—2016no—
680C22×C4—2016no—
681C22×C4C2×C22⋊D514yes—
682C22×C4C2×C22⋊D514yes—
683C22×C4C23×D512yes—
684C22×C4C23×D512yes—
685C22×C4C23×D512yes—
686C22×C4C23×D512yes—
687C22×C4C23×D512yes—
688C22×C4C23×D512yes—
689C4⋊C4—28no—
690C4⋊C4—28no—
691C4⋊C4—28no—
692C4⋊C4—204no—
693C4⋊C4—204no—
694C4⋊C4—204no—
695C22⋊C4—28no—
696C22⋊C4—28no—
697C22⋊C4—108no—
698C22⋊C4—108no—
699C22⋊C4—108no—
700C22⋊C4—108no—
701C22⋊C4—108no—
702C22⋊C4—108no—
703C22⋊C4—108no—
704C22⋊C4—108no—
705C22⋊C4—108no—
706C22⋊C4—204no—
707C22⋊C4—204no—
708C22⋊C4—204no—
709C22⋊C4—204no—
710C22⋊C4C2×C22⋊D5116yes—
711C42—28no—
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—102no—
747C23—102no—
748C23—102no—
749C23—102no—
750C23—108no—
751C23—108no—
752C23—108no—
753C23—108no—
754C23—102no—
755C23—102no—
756C23—102no—
757C23—102no—
758C23—102no—
759C23—102no—
760C23—108no—
761C23—108no—
762C23—2016no—
763C23—2016no—
764C23—2016no—
765C23—2016no—
766C23—2016no—
767C23—20128no—
768C23—2016no—
769C23—204no—
770C23—204no—
771C23—204no—
772C23—204no—
773C23D5×#4112yes—
774C23D5×#4112yes—
775C23D5×#4112yes—
776C23D5×#4112yes—
777C23#414912yes—
778C23#414912yes—
779C23C22×C22⋊D514yes—
780C23C22×C22⋊D512yes—
781C23C24×D511yescharacteristic
782C2×C4—28no—
783C2×C4—28no—
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—102no—
805C2×C4—102no—
806C2×C4—102no—
807C2×C4—102no—
808C2×C4—102no—
809C2×C4—102no—
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—2016no—
823C2×C4—2016no—
824C2×C4—204no—
825C2×C4—204no—
826C2×C4—204no—
827C2×C4—204no—
828C2×C4—204no—
829C2×C4—204no—
830C2×C4C22×C22⋊D514yes—
831C2×C4C22×C22⋊D514yes—
832C5C2×#248011yescharacteristic, complemented, Sylow
833C22—24no—
834C22—24no—
835C22—24no—
836C22—416no—
837C22—42no—
838C22—42no—
839C22—42no—
840C22—42no—
841C22—58no—
842C22—1032no—
843C22—104no—
844C22—104no—
845C22—104no—
846C22—104no—
847C22—104no—
848C22—104no—
849C22—104no—
850C22—104no—
851C22—104no—
852C22—2064no—
853C22—2016no—
854C22—202no—
855C22—202no—
856C22—202no—
857C22—202no—
858C22D5×#12614yes—
859C22#6603814yes—
860C22#6603914yes—
861C22#6603914yes—
862C22#6616214yes—
863C22#6616314yes—
864C22#6616314yes—
865C22C2×D5×#4111yescharacteristic
866C22C2×D5×#4111yescharacteristic
867C22C2×D5×#4111yescharacteristic
868C22C2×D5×#4111yescharacteristic
869C22C2×#414911yescharacteristic
870C22C2×#414911yescharacteristic
871C22C23×C22⋊D511yescharacteristic
872C4—24no—
873C4—24no—
874C4—42no—
875C4—42no—
876C4—42no—
877C4—42no—
878C4—202no—
879C4—202no—
880C4—202no—
881C4—202no—
882C4—202no—
883C4—202no—
884C2—44no—
885C2—108no—
886C2—204no—
887C2#1061481218yesdirect product factor
888C2C2×D5×#12611yescharacteristic
889C2C2×#6603811yescharacteristic
890C2C2×#6603911yescharacteristic
891C2C2×#6603911yescharacteristic
892C2C2×#6616211yescharacteristic
893C2C2×#6616311yescharacteristic
894C2C2×#6616311yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC22×C5×#126C2
socleC24×C5C24
prime radicalC25×D5C22
hypercenterC22×#126D5
hypocenterC5C2×#2480
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C22×#126

Complements

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

NH ≅ G/Ntype
1. C22×C5×#126C2semidirect
3. #10614812C2direct (N × H)
4. C2×#65282C2semidirect
5. C2×#65283C2semidirect
6. C2×#65278C2semidirect
7. C2×#65278C2semidirect
8. C2×#65276C2semidirect
9. C2×#65279C2semidirect
12. C2×#65241C2semidirect
13. C2×#65241C2semidirect
14. C2×#65240C2semidirect
15. C2×#65229C2semidirect
16. C2×C4×#685C2semidirect
21. C2×C5×#126C22semidirect
22. C22×C5×C4⋊C4C22semidirect
23. C22×C5×C4⋊C4C22semidirect
24. C22×C5×C4⋊C4C22semidirect
28. C22×C42×C5C22semidirect
42. C22×C4⋊Dic5C22semidirect
43. C22×#683C22semidirect
44. C22×#683C22semidirect
45. C22×C4×Dic5C22semidirect
48. C2×#3963C22semidirect
49. C2×#3963C22semidirect
50. C2×#3963C22semidirect
51. C2×#3963C22semidirect
52. C2×#3963C22semidirect
53. C2×#3963C22semidirect
54. C2×#3963C22semidirect
55. C2×#3963C22semidirect
56. #65283C22semidirect
57. #65282C22semidirect
58. #65279C22semidirect
59. #65278C22semidirect
60. #65278C22semidirect
61. #65276C22semidirect
64. #65241C22semidirect
65. #65241C22semidirect
66. #65240C22semidirect
67. #65229C22semidirect
68. C4×#685C22semidirect
105. C2×C5×C4⋊C4C23semidirect
106. C2×C5×C4⋊C4C23semidirect
107. C2×C5×C4⋊C4C23semidirect
115. C2×C42×C5C23semidirect
143. C2×C4⋊Dic5C23semidirect
146. C2×#683C23semidirect
147. C2×#683C23semidirect
149. C2×C4×Dic5C23semidirect
151. #3963C23semidirect
152. #3963C23semidirect
153. #3963C23semidirect
154. #3963C23semidirect
155. #3963C23semidirect
156. #3963C23semidirect
157. #3963C23semidirect
158. #3963C23semidirect
159. C22×#126D5semidirect
298. C2×#126C2×D5semidirect
302. C22×C4⋊C4C2×D5semidirect
303. C22×C4⋊C4C2×D5semidirect
304. C22×C4⋊C4C2×D5semidirect
324. C22×C42C2×D5semidirect
399. C22×D5#126semidirect
495. C2×C4⋊C4C22×D5semidirect
496. C2×C4⋊C4C22×D5semidirect
497. C2×C4⋊C4C22×D5semidirect
534. C2×C42C22×D5semidirect
581. C2×D5C2×#126semidirect
714. C2×C5#2480semidirect
832. C5C2×#2480semidirect
887. C2#10614812direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C5×#1262
C22×D5×C22⋊C42
#106148122
C2×#652822
C2×#652832
C2×#652782
C2×#652762
C2×#652792
C2×#652442
C2×#652412
C2×#652402
C2×#652292
C2×C4×#6852
C2×#24805