Finite Group Databasebeta

← C2×#10609834 #12266759

Subgroups — C2×#10609834 #12266759

Order 1280.

4002 conjugacy classes of subgroups.

The subgroup lattice has 908 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D5×C4⋊C4C211yesmaximal, characteristic, complemented
2C22×#4039C211yesmaximal, characteristic, complemented
3C22×#4029C211yesmaximal, characteristic, complemented
4C22×#4030C211yesmaximal, characteristic
5C2×C5×#399C211yesmaximal, characteristic, complemented
6C2×#65282C211yesmaximal, characteristic, complemented
7C2×#65278C211yesmaximal, characteristic, complemented
8C2×#65278C211yesmaximal, characteristic, complemented
9C2×#65269C211yesmaximal, characteristic, complemented
10C2×#65248C211yesmaximal, characteristic, complemented
11C2×#65245C211yesmaximal, characteristic, complemented
12C2×#65245C211yesmaximal, characteristic, complemented
13C2×#65233C211yesmaximal, characteristic, complemented
14#10609834C2116yesmaximal, direct product factor
15C2×#64954C211yesmaximal, characteristic, complemented
16C2×#64942C211yesmaximal, characteristic, complemented
17C23×C22⋊D5C2211yescharacteristic
18C23×C22⋊D5C2211yescharacteristic
19C23×D20C2211yescharacteristic
20C23×C4×D5C2211yescharacteristic
21C23×C4×D5C2211yescharacteristic
22C23×C4×D5C2211yescharacteristic
23C23×C4×D5C2211yescharacteristic
24C22×C5×C4⋊C4C2211yescharacteristic
25C22×C5×C4⋊C4C2211yescharacteristic
26C22×C5×C4⋊C4C2211yescharacteristic
27C22×C5×C22⋊C4C2211yescharacteristic
28C22×C5×C22⋊C4C2211yescharacteristic
29C22×C5×C22⋊C4C2211yescharacteristic
30C22×C22⋊Dic5C2211yescharacteristic
31C22×C22⋊Dic5C2211yescharacteristic
32C22×#685C2211yescharacteristic
33C22×#685C2211yescharacteristic
34C22×#685C2211yescharacteristic
35C22×#685C2211yescharacteristic
36C22×#685C2211yescharacteristic
37C22×#685C2211yescharacteristic
38C22×C4⋊Dic5C2211yescharacteristic
39C22×#683C2211yescharacteristic
40C22×#683C2211yescharacteristic
41C22×#683C2211yescharacteristic
42C22×#683C2211yescharacteristic
43C22×C4×Dic5C2211yescharacteristic
44C2×#4039—28no—
45C2×#4039C2218yescomplemented
46C2×D5×C4⋊C4—28no—
47C2×D5×C4⋊C4C2218yescomplemented
48C2×#4030—28no—
49C2×#4030C2218yes—
50C2×#4029—28no—
51C2×#4029C2218yescomplemented
52C5×#399C2218yescomplemented
53C2×C5×#95C2211yescharacteristic
54C2×#3963C2211yescharacteristic
55C2×#3963C2211yescharacteristic
56C2×#3963C2211yescharacteristic
57C2×#3963C2211yescharacteristic
58C2×#3963C2211yescharacteristic
59C2×#3963C2211yescharacteristic
60C2×#3963C2211yescharacteristic
61#65282C2218yescomplemented
62#65278C2218yescomplemented
63#65278C2218yescomplemented
64#65269C2218yescomplemented
65#65248C2218yescomplemented
66#65245C2218yescomplemented
67#65245C2218yescomplemented
68#65233C2218yescomplemented
69#64954C2218yescomplemented
70#64942C2218yescomplemented
71C2×#2443—51nomaximal, Sylow
72C25×C5C2311yescharacteristic
73C24×D5C2311yescharacteristic
74C24×D5C2311yescharacteristic
75C23×C4×C5C2311yescharacteristic
76C23×C4×C5C2311yescharacteristic
77C23×C4×C5C2311yescharacteristic
78C23×C4×C5C2311yescharacteristic
79C23×C4×C5C2311yescharacteristic
80C23×C4×C5C2311yescharacteristic
81C22×C22⋊D5—24no—
82C22×C22⋊D5—24no—
83C22×C22⋊D5—24no—
84C22×C22⋊D5—24no—
85C22×C22⋊D5—24no—
86C22×C22⋊D5—42no—
87C22×C22⋊D5C2314yes—
88C22×C22⋊D5C2314yes—
89C23×Dic5C2311yescharacteristic
90C23×Dic5C2311yescharacteristic
91C23×Dic5C2311yescharacteristic
92C23×Dic5C2311yescharacteristic
93C23×Dic5C2311yescharacteristic
94C23×Dic5C2311yescharacteristic
95C22×D20—24no—
96C22×D20—24no—
97C22×D20D418yes—
98C22×D20C2314yes—
99C22×C4×D5—24no—
100C22×C4×D5—24no—
101C22×C4×D5—24no—
102C22×C4×D5—24no—
103C22×C4×D5—24no—
104C22×C4×D5—24no—
105C22×C4×D5—24no—
106C22×C4×D5—24no—
107C22×C4×D5—24no—
108C22×C4×D5—42no—
109C22×C4×D5—42no—
110C22×C4×D5—42no—
111C22×C4×D5C2314yes—
112C22×C4×D5C2314yes—
113C22×C4×D5C2314yes—
114C22×C4×D5C2314yes—
115C2×C5×C4⋊C4—24no—
116C2×C5×C4⋊C4—24no—
117C2×C5×C4⋊C4—42no—
118C2×C5×C4⋊C4C2314yes—
119C2×C5×C4⋊C4C2314yes—
120C2×C5×C4⋊C4C2314yes—
121C2×C5×C22⋊C4—24no—
122C2×C5×C22⋊C4—24no—
123C2×C5×C22⋊C4—42no—
124C2×C5×C22⋊C4C2314yes—
125C2×C5×C22⋊C4C2314yes—
126C2×C5×C22⋊C4C2314yes—
127C2×C22⋊Dic5—24no—
128C2×C22⋊Dic5—24no—
129C2×C22⋊Dic5C2314yes—
130C2×C22⋊Dic5C2314yes—
131C2×#685—24no—
132C2×#685—24no—
133C2×#685—24no—
134C2×#685—24no—
135C2×#685—24no—
136C2×#685—24no—
137C2×#685C2314yes—
138C2×#685C2314yes—
139C2×#685C2314yes—
140C2×#685C2314yes—
141C2×#685C2314yes—
142C2×#685C2314yes—
143C2×C4⋊Dic5D418yescomplemented
144C2×C4⋊Dic5C2314yes—
145C2×#683—24no—
146C2×#683—24no—
147C2×#683—24no—
148C2×#683—24no—
149C2×#683C2314yes—
150C2×#683C2314yes—
151C2×#683C2314yes—
152C2×#683C2314yes—
153C2×C4×Dic5—24no—
154C2×C4×Dic5C2314yes—
155#4039—232no—
156D5×C4⋊C4—232no—
157#4030—232no—
158#4029—232no—
159C5×#95C2314yes—
160#3963C2314yes—
161#3963C2314yes—
162#3963C2314yes—
163#3963C2314yes—
164#3963C2314yes—
165#3963C2314yes—
166#3963C2314yes—
167C22×#123—51no—
168C22×#121—51no—
169C22×C4×D4—51no—
170C23×C4⋊C4—51no—
171#2443—516no—
172C2×#399D511yescharacteristic, complemented
173C2×#398—51no—
174C2×#397—51no—
175C2×#394—51no—
176C2×#388—51no—
177C2×#387—51no—
178C2×#386—51no—
179C2×#386—51no—
180C2×#386—51no—
181C2×#385—51no—
182C2×#385—51no—
183C24×C5—22no—
184C24×C5—22no—
185C24×C5—22no—
186C24×C5—22no—
187C24×C5—22no—
188C24×C5—22no—
189C24×C5—22no—
190C24×C5C2412yes—
191C24×C5C2411yescharacteristic
192C23×D5—22no—
193C23×D5—22no—
194C23×D5—22no—
195C23×D5—22no—
196C23×D5—22no—
197C23×D5—22no—
198C23×D5—22no—
199C23×D5—22no—
200C23×D5—22no—
201C23×D5—22no—
202C23×D5C2×D414yes—
203C23×D5C2×D414yes—
204C23×D5#4114yes—
205C23×D5#4114yes—
206C23×D5C2412yes—
207C23×D5C2412yes—
208C22×C4×C5—22no—
209C22×C4×C5—22no—
210C22×C4×C5—22no—
211C22×C4×C5—22no—
212C22×C4×C5—22no—
213C22×C4×C5—22no—
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×C5C2×D414yes—
225C22×C4×C5C2×D414yes—
226C22×C4×C5C2412yes—
227C22×C4×C5C2412yes—
228C22×C4×C5C2412yes—
229C22×C4×C5C2412yes—
230C22×C4×C5C2412yes—
231C22×C4×C5C2412yes—
232C2×C22⋊D5—28no—
233C2×C22⋊D5—28no—
234C2×C22⋊D5—28no—
235C2×C22⋊D5—28no—
236C2×C22⋊D5—28no—
237C2×C22⋊D5—44no—
238C2×C22⋊D5—416no—
239C2×C22⋊D5—416no—
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×Dic5C2×D414yes—
257C22×Dic5#4114yes—
258C22×Dic5C2412yes—
259C22×Dic5C2412yes—
260C22×Dic5C2412yes—
261C22×Dic5C2412yes—
262C22×Dic5C2412yes—
263C22×Dic5C2412yes—
264C2×D20—232no—
265C2×D20—28no—
266C2×D20—28no—
267C2×D20C2×D4116yes—
268C2×C4×D5—232no—
269C2×C4×D5—28no—
270C2×C4×D5—28no—
271C2×C4×D5—28no—
272C2×C4×D5—28no—
273C2×C4×D5—28no—
274C2×C4×D5—28no—
275C2×C4×D5—28no—
276C2×C4×D5—28no—
277C2×C4×D5—28no—
278C2×C4×D5—44no—
279C2×C4×D5—44no—
280C2×C4×D5—44no—
281C2×C4×D5—416no—
282C2×C4×D5—416no—
283C2×C4×D5—416no—
284C5×C4⋊C4—28no—
285C5×C4⋊C4—28no—
286C5×C4⋊C4—44no—
287C5×C22⋊C4—28no—
288C5×C22⋊C4—28no—
289C5×C22⋊C4—44no—
290C22⋊Dic5—28no—
291C22⋊Dic5—28no—
292#685—28no—
293#685—28no—
294#685—28no—
295#685—28no—
296#685—28no—
297#685—28no—
298C4⋊Dic5C2×D4116yescomplemented
299#683—28no—
300#683—28no—
301#683—28no—
302#683—28no—
303C4×Dic5—28no—
304C23×D4—51no—
305C23×D4—51no—
306C23×D4—51no—
307C24×C4—51no—
308C24×C4—51no—
309C24×C4—51no—
310C24×C4—51no—
311C2×#123—58no—
312C2×#123—108no—
313C2×#121—58no—
314C2×#121—108no—
315C2×C4×D4—58no—
316C2×C4×D4—108no—
317C22×C4⋊C4—51no—
318C22×C4⋊C4—51no—
319C22×C4⋊C4—51no—
320C22×C4⋊C4—51no—
321C22×C4⋊C4—51no—
322C22×C4⋊C4—58no—
323C22×C4⋊C4—108no—
324C22×C4⋊C4C2×D511yescharacteristic
325C22×C4⋊C4C2×D511yescharacteristic
326C22×C4⋊C4C2×D511yescharacteristic
327C22×C22⋊C4—51no—
328C22×C22⋊C4—51no—
329C22×C22⋊C4—51no—
330C22×C22⋊C4—51no—
331C22×C22⋊C4—51no—
332C22×C22⋊C4—51no—
333C22×C22⋊C4—51no—
334C22×C22⋊C4—51no—
335C22×C22⋊C4C2×D511yescharacteristic
336C22×C22⋊C4C2×D511yescharacteristic
337C22×C22⋊C4C2×D511yescharacteristic
338C22×C42—51no—
339#399C2×D518yescomplemented
340#398—58no—
341#397—58no—
342#394—58no—
343#388—58no—
344#387—58no—
345#386—58no—
346#386—58no—
347#386—58no—
348#385—58no—
349#385—58no—
350C2×#95—51no—
351C2×#95—51no—
352C2×#95—51no—
353C2×#95—51no—
354C2×#95—51no—
355C2×#95—51no—
356C2×#95—51no—
357C2×#95C2×D511yescharacteristic
358C23×C5—22no—
359C23×C5—22no—
360C23×C5—22no—
361C23×C5—22no—
362C23×C5—22no—
363C23×C5—22no—
364C23×C5—22no—
365C23×C5—44no—
366C23×C5—44no—
367C23×C5—44no—
368C23×C5—44no—
369C23×C5—44no—
370C23×C5—44no—
371C23×C5—44no—
372C23×C5C22×D412yes—
373C23×C5C22×D412yes—
374C23×C5C2×#4112yes—
375C23×C5C2×#4112yes—
376C23×C5C2×#4112yes—
377C23×C5H(5,𝔽2)12yes—
378C23×C52−1+412yes—
379C23×C5C2511yescharacteristic
380C22×D5—28no—
381C22×D5—28no—
382C22×D5—28no—
383C22×D5—28no—
384C22×D5—28no—
385C22×D5—28no—
386C22×D5—22no—
387C22×D5—22no—
388C22×D5—22no—
389C22×D5—22no—
390C22×D5—28no—
391C22×D5—28no—
392C22×D5—28no—
393C22×D5—22no—
394C22×D5—22no—
395C22×D5—22no—
396C22×D5—22no—
397C22×D5—22no—
398C22×D5—22no—
399C22×D5—44no—
400C22×D5—44no—
401C22×D5—44no—
402C22×D5—44no—
403C22×D5#123116yescomplemented
404C22×D5C22×D414yes—
405C22×D5C22×D414yes—
406C22×D5C2×#4114yes—
407C22×D5C2×#4114yes—
408C2×C4×C5—28no—
409C2×C4×C5—28no—
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—22no—
424C2×C4×C5—22no—
425C2×C4×C5—22no—
426C2×C4×C5—44no—
427C2×C4×C5—44no—
428C2×C4×C5—44no—
429C2×C4×C5—44no—
430C2×C4×C5C22×D414yes—
431C2×C4×C5C22×D414yes—
432C22⋊D5—416no—
433C22⋊D5—416no—
434C2×Dic5—28no—
435C2×Dic5—28no—
436C2×Dic5—28no—
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—22no—
448C2×Dic5—22no—
449C2×Dic5—22no—
450C2×Dic5—22no—
451C2×Dic5—22no—
452C2×Dic5—44no—
453C2×Dic5—44no—
454C2×Dic5—44no—
455C2×Dic5C22×D414yes—
456C2×Dic5C22×D414yes—
457C2×Dic5C2×#4114yes—
458D20—232no—
459C4×D5—232no—
460C4×D5—416no—
461C4×D5—416no—
462C4×D5—416no—
463C25—51no—
464C25—51no—
465C25C22×D511yescharacteristic
466C22×D4—54no—
467C22×D4—54no—
468C22×D4—58no—
469C22×D4—54no—
470C22×D4—104no—
471C22×D4—104no—
472C22×D4—104no—
473C22×D4—104no—
474C22×D4—104no—
475C22×D4—104no—
476C22×D4—104no—
477C22×D4—202no—
478C23×C4—51no—
479C23×C4—51no—
480C23×C4—51no—
481C23×C4—51no—
482C23×C4—51no—
483C23×C4—51no—
484C23×C4—54no—
485C23×C4—54no—
486C23×C4—54no—
487C23×C4—54no—
488C23×C4—104no—
489C23×C4—104no—
490C23×C4—104no—
491C23×C4—104no—
492C23×C4—104no—
493C23×C4—104no—
494C23×C4—104no—
495C23×C4—104no—
496C23×C4—104no—
497C23×C4—202no—
498C23×C4—202no—
499C23×C4—202no—
500C23×C4C22×D511yescharacteristic
501C23×C4C22×D511yescharacteristic
502C23×C4C22×D511yescharacteristic
503C23×C4C22×D511yescharacteristic
504C23×C4C22×D511yescharacteristic
505C23×C4C22×D511yescharacteristic
506#123—1032no—
507#121—1032no—
508C4×D4—1032no—
509C2×C4⋊C4—24no—
510C2×C4⋊C4—24no—
511C2×C4⋊C4—42no—
512C2×C4⋊C4—58no—
513C2×C4⋊C4—54no—
514C2×C4⋊C4—54no—
515C2×C4⋊C4—54no—
516C2×C4⋊C4—54no—
517C2×C4⋊C4—54no—
518C2×C4⋊C4—1032no—
519C2×C4⋊C4—104no—
520C2×C4⋊C4—104no—
521C2×C4⋊C4—104no—
522C2×C4⋊C4—104no—
523C2×C4⋊C4C22×D514yes—
524C2×C4⋊C4C22×D514yes—
525C2×C4⋊C4C22×D514yes—
526C2×C22⋊C4—24no—
527C2×C22⋊C4—24no—
528C2×C22⋊C4—42no—
529C2×C22⋊C4—54no—
530C2×C22⋊C4—54no—
531C2×C22⋊C4—54no—
532C2×C22⋊C4—54no—
533C2×C22⋊C4—54no—
534C2×C22⋊C4—54no—
535C2×C22⋊C4—54no—
536C2×C22⋊C4—54no—
537C2×C22⋊C4—104no—
538C2×C22⋊C4—104no—
539C2×C22⋊C4—104no—
540C2×C22⋊C4—104no—
541C2×C22⋊C4—104no—
542C2×C22⋊C4—104no—
543C2×C22⋊C4—104no—
544C2×C22⋊C4—104no—
545C2×C22⋊C4C22×D514yes—
546C2×C22⋊C4C22×D514yes—
547C2×C22⋊C4C22×D514yes—
548C2×C42—54no—
549C2×C42—104no—
550#95—54no—
551#95—54no—
552#95—54no—
553#95—54no—
554#95—54no—
555#95—54no—
556#95—54no—
557#95C22×D514yes—
558C22×C5—42no—
559C22×C5—42no—
560C22×C5—42no—
561C22×C5—42no—
562C22×C5—42no—
563C22×C5—42no—
564C22×C5—42no—
565C22×C5—88no—
566C22×C5C2×#12314yes—
567C22×C5#52514yes—
568C22×C5#53914yes—
569C22×C5D4214yes—
570C22×C5#54714yes—
571C22×C5#54814yes—
572C22×C5#55314yes—
573C22×C5C23×D411yescharacteristic
574C22×C5C23×D411yescharacteristic
575C22×C5C22×#4111yescharacteristic
576C22×C5C22×#4111yescharacteristic
577C22×C5C22×#4111yescharacteristic
578C22×C5C2×H(5,𝔽2)11yescharacteristic
579C22×C5C2×2−1+411yescharacteristic
580C2×D5—24no—
581C2×D5—24no—
582C2×D5—24no—
583C2×D5—24no—
584C2×D5—24no—
585C2×D5—232no—
586C2×D5—24no—
587C2×D5—24no—
588C2×D5—24no—
589C2×D5—24no—
590C2×D5—42no—
591C2×D5—42no—
592C2×D5—42no—
593C2×D5—416no—
594C2×D5—42no—
595C2×D5C2×#12318yescomplemented
596C4×C5—24no—
597C4×C5—24no—
598C4×C5—42no—
599C4×C5—42no—
600C4×C5—42no—
601C4×C5—42no—
602Dic5—24no—
603Dic5—24no—
604Dic5—24no—
605Dic5—42no—
606Dic5—42no—
607Dic5—42no—
608C24—22no—
609C24—22no—
610C24—22no—
611C24—22no—
612C24—22no—
613C24—22no—
614C24—22no—
615C24—54no—
616C24—54no—
617C24—54no—
618C24—52no—
619C24—54no—
620C24—52no—
621C24—102no—
622C24—102no—
623C24—102no—
624C24—102no—
625C24—102no—
626C24—102no—
627C24—102no—
628C24—102no—
629C24—102no—
630C24—102no—
631C24C23×D512yes—
632C24C23×D511yescharacteristic
633C2×D4—516no—
634C2×D4—1032no—
635C2×D4—108no—
636C2×D4—108no—
637C2×D4—108no—
638C2×D4—108no—
639C2×D4—108no—
640C2×D4—108no—
641C2×D4—108no—
642C2×D4—204no—
643C2×D4—2016no—
644C2×D4—2016no—
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—22no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—54no—
662C22×C4—54no—
663C22×C4—54no—
664C22×C4—52no—
665C22×C4—52no—
666C22×C4—52no—
667C22×C4—52no—
668C22×C4—52no—
669C22×C4—52no—
670C22×C4—108no—
671C22×C4—108no—
672C22×C4—108no—
673C22×C4—108no—
674C22×C4—108no—
675C22×C4—1032no—
676C22×C4—108no—
677C22×C4—108no—
678C22×C4—108no—
679C22×C4—102no—
680C22×C4—102no—
681C22×C4—102no—
682C22×C4—102no—
683C22×C4—102no—
684C22×C4—102no—
685C22×C4—108no—
686C22×C4—102no—
687C22×C4—102no—
688C22×C4—102no—
689C22×C4—102no—
690C22×C4—102no—
691C22×C4—102no—
692C22×C4—102no—
693C22×C4—102no—
694C22×C4—102no—
695C22×C4—204no—
696C22×C4—204no—
697C22×C4—204no—
698C22×C4—2016no—
699C22×C4—2016no—
700C22×C4—2016no—
701C22×C4D4×D514yes—
702C22×C4D4×D514yes—
703C22×C4C23×D512yes—
704C22×C4C23×D512yes—
705C22×C4C23×D512yes—
706C22×C4C23×D512yes—
707C22×C4C23×D512yes—
708C22×C4C23×D512yes—
709C4⋊C4—28no—
710C4⋊C4—28no—
711C4⋊C4—44no—
712C4⋊C4—516no—
713C4⋊C4—108no—
714C4⋊C4—108no—
715C4⋊C4—108no—
716C4⋊C4—108no—
717C22⋊C4—28no—
718C22⋊C4—28no—
719C22⋊C4—44no—
720C22⋊C4—108no—
721C22⋊C4—108no—
722C22⋊C4—108no—
723C22⋊C4—108no—
724C22⋊C4—108no—
725C22⋊C4—108no—
726C22⋊C4—108no—
727C22⋊C4—108no—
728C42—108no—
729C2×C5—82no—
730C2×C5#244318yescomplemented
731C2×C5C22×#12311yescharacteristic
732C2×C5C2×#52511yescharacteristic
733C2×C5C2×#53911yescharacteristic
734C2×C5C2×D4211yescharacteristic
735C2×C5C2×#54711yescharacteristic
736C2×C5C2×#54811yescharacteristic
737C2×C5C2×#55311yescharacteristic
738D5—28no—
739D5—44no—
740C23—22no—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—22no—
745C23—22no—
746C23—22no—
747C23—44no—
748C23—44no—
749C23—44no—
750C23—44no—
751C23—44no—
752C23—44no—
753C23—44no—
754C23—516no—
755C23—54no—
756C23—54no—
757C23—54no—
758C23—54no—
759C23—108no—
760C23—108no—
761C23—108no—
762C23—108no—
763C23—108no—
764C23—108no—
765C23—102no—
766C23—102no—
767C23—102no—
768C23—102no—
769C23—108no—
770C23—108no—
771C23—108no—
772C23—102no—
773C23—102no—
774C23—102no—
775C23—102no—
776C23—102no—
777C23—102no—
778C23—204no—
779C23—204no—
780C23—204no—
781C23—204no—
782C23C2×D4×D512yes—
783C23C2×D4×D512yes—
784C23#414412yes—
785C23#414712yes—
786C23D5×#4112yes—
787C23D5×#4112yes—
788C23D5×#4112yes—
789C23C24×D511yescharacteristic
790D4—1032no—
791D4—2016no—
792D4—2016no—
793C2×C4—28no—
794C2×C4—28no—
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—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—44no—
812C2×C4—44no—
813C2×C4—44no—
814C2×C4—44no—
815C2×C4—54no—
816C2×C4—54no—
817C2×C4—54no—
818C2×C4—1032no—
819C2×C4—108no—
820C2×C4—108no—
821C2×C4—108no—
822C2×C4—102no—
823C2×C4—102no—
824C2×C4—102no—
825C2×C4—102no—
826C2×C4—102no—
827C2×C4—102no—
828C2×C4—102no—
829C2×C4—102no—
830C2×C4—102no—
831C2×C4—102no—
832C2×C4—102no—
833C2×C4—102no—
834C2×C4—102no—
835C2×C4—102no—
836C2×C4—102no—
837C2×C4—2016no—
838C2×C4—2016no—
839C2×C4—2016no—
840C2×C4—204no—
841C2×C4—204no—
842C2×C4—204no—
843C2×C4C2×D4×D514yes—
844C2×C4C2×D4×D514yes—
845C5C2×#244311yescharacteristic, complemented, Sylow
846C22—42no—
847C22—42no—
848C22—42no—
849C22—42no—
850C22—42no—
851C22—42no—
852C22—42no—
853C22—58no—
854C22—88no—
855C22—104no—
856C22—104no—
857C22—104no—
858C22—104no—
859C22—104no—
860C22—1032no—
861C22—104no—
862C22—104no—
863C22—104no—
864C22—104no—
865C22—202no—
866C22—202no—
867C22—202no—
868C22—202no—
869C22—2016no—
870C22#6596514yes—
871C22#6596714yes—
872C22#6597214yes—
873C22D5×#12314yes—
874C22#6599014yes—
875C22#6599514yes—
876C22#6605114yes—
877C22C22×D4×D511yescharacteristic
878C22C22×D4×D511yescharacteristic
879C22C2×#414411yescharacteristic
880C22C2×#414711yescharacteristic
881C22C2×D5×#4111yescharacteristic
882C22C2×D5×#4111yescharacteristic
883C22C2×D5×#4111yescharacteristic
884C4—24no—
885C4—24no—
886C4—42no—
887C4—42no—
888C4—42no—
889C4—42no—
890C4—104no—
891C4—104no—
892C4—104no—
893C4—202no—
894C4—202no—
895C4—202no—
896C2—82no—
897C2—108no—
898C2—204no—
899C2#1060983418yesdirect product factor
900C2C2×#6597211yescharacteristic
901C2C2×#6596511yescharacteristic
902C2C2×#6596711yescharacteristic
903C2C2×#6599011yescharacteristic
904C2C2×#6599511yescharacteristic
905C2C2×D5×#12311yescharacteristic
906C2C2×#6605111yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC2×C5×#399C2
socleC24×C5C24
prime radicalC22×#4030C2
hypercenterC2×#399D5
hypocenterC5C2×#2443
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#399

Complements

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

NH ≅ G/Ntype
1. C22×D5×C4⋊C4C2semidirect
2. C22×#4039C2semidirect
3. C22×#4029C2semidirect
5. C2×C5×#399C2semidirect
6. C2×#65282C2semidirect
7. C2×#65278C2semidirect
8. C2×#65278C2semidirect
9. C2×#65269C2semidirect
10. C2×#65248C2semidirect
11. C2×#65245C2semidirect
12. C2×#65245C2semidirect
13. C2×#65233C2semidirect
14. #10609834C2direct (N × H)
15. C2×#64954C2semidirect
16. C2×#64942C2semidirect
45. C2×#4039C22semidirect
47. C2×D5×C4⋊C4C22semidirect
51. C2×#4029C22semidirect
52. C5×#399C22semidirect
61. #65282C22semidirect
62. #65278C22semidirect
63. #65278C22semidirect
64. #65269C22semidirect
65. #65248C22semidirect
66. #65245C22semidirect
67. #65245C22semidirect
68. #65233C22semidirect
69. #64954C22semidirect
70. #64942C22semidirect
143. C2×C4⋊Dic5D4semidirect
172. C2×#399D5semidirect
298. C4⋊Dic5C2×D4semidirect
339. #399C2×D5semidirect
403. C22×D5#123semidirect
595. C2×D5C2×#123semidirect
730. C2×C5#2443semidirect
845. C5C2×#2443semidirect
899. C2#10609834direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D5×C4⋊C42
C22×#40392
C22×#40292
C22×#40302
C2×C5×#3992
C2×#652822
C2×#652782
C2×#652692
C2×#652482
C2×#652452
C2×#652332
#106098342
C2×#649542
C2×#649422
C2×#24435