Finite Group Databasebeta

← C2×#10614549 #12266822

Subgroups — C2×#10614549 #12266822

Order 1280.

3958 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×C5×C22⋊Q8C211yesmaximal, characteristic, complemented
2C22×#4092C211yesmaximal, characteristic, complemented
3C22×C4×C22⋊D5C211yesmaximal, characteristic, complemented
4C22×#4039C211yesmaximal, characteristic, complemented
5C2×#65520C211yesmaximal, characteristic, complemented
6C2×#65502C211yesmaximal, characteristic, complemented
7#10614549C2116yesmaximal, direct product factor
8C2×#65280C211yesmaximal, characteristic, complemented
9C2×#65278C211yesmaximal, characteristic, complemented
10C2×#65279C211yesmaximal, characteristic, complemented
11C2×#65267C211yesmaximal, characteristic, complemented
12C2×#65270C211yesmaximal, characteristic, complemented
13C2×#65249C211yesmaximal, characteristic
14C2×#65245C211yesmaximal, characteristic, complemented
15C2×#65250C211yesmaximal, characteristic, complemented
16C2×#65233C211yesmaximal, characteristic, complemented
17C23×C5×Q8C2211yescharacteristic
18C24×C4×C5C2211yescharacteristic
19C23×C22⋊D5C2211yescharacteristic
20C23×C22⋊D5C2211yescharacteristic
21C23×D20C2211yescharacteristic
22C23×C4×D5C2211yescharacteristic
23C23×C4×D5C2211yescharacteristic
24C2×C5×C22⋊Q8—28no—
25C2×C5×C22⋊Q8C2218yescomplemented
26C22×C5×C4⋊C4C2211yescharacteristic
27C22×C5×C4⋊C4C2211yescharacteristic
28C22×C5×C4⋊C4C2211yescharacteristic
29C22×C5×C22⋊C4C2211yescharacteristic
30C22×C5×C22⋊C4C2211yescharacteristic
31C22×C22⋊Dic5C2211yescharacteristic
32C22×C22⋊Dic5C2211yescharacteristic
33C2×#4092—28no—
34C2×#4092C2218yescomplemented
35C2×C4×C22⋊D5—28no—
36C2×C4×C22⋊D5C2218yescomplemented
37C22×#685C2211yescharacteristic
38C22×#685C2211yescharacteristic
39C22×#685C2211yescharacteristic
40C22×#685C2211yescharacteristic
41C22×#685C2211yescharacteristic
42C22×#685C2211yescharacteristic
43C22×#685C2211yescharacteristic
44C22×#685C2211yescharacteristic
45C22×C4⋊Dic5C2211yescharacteristic
46C22×#683C2211yescharacteristic
47C22×#683C2211yescharacteristic
48C22×C4×Dic5C2211yescharacteristic
49C22×C4×Dic5C2211yescharacteristic
50C2×#4039—28no—
51C2×#4039C2218yescomplemented
52#65520C2218yescomplemented
53#65502C2218yescomplemented
54C2×#3963C2211yescharacteristic
55C2×#3963C2211yescharacteristic
56C2×#3963C2211yescharacteristic
57C2×#3963C2211yescharacteristic
58C2×#3963C2211yescharacteristic
59C2×#3963C2211yescharacteristic
60C2×#3963C2211yescharacteristic
61C2×#3963C2211yescharacteristic
62#65280C2218yescomplemented
63#65279C2218yescomplemented
64#65278C2218yescomplemented
65#65270C2218yescomplemented
66#65267C2218yescomplemented
67#65250C2218yescomplemented
68#65249C2218yes—
69#65245C2218yescomplemented
70#65233C2218yescomplemented
71C2×#2463—51nomaximal, Sylow
72C25×C5C2311yescharacteristic
73C24×D5C2311yescharacteristic
74C24×D5C2311yescharacteristic
75C22×C5×Q8—24no—
76C22×C5×Q8—24no—
77C22×C5×Q8—42no—
78C22×C5×Q8C2314yes—
79C23×C4×C5—24no—
80C23×C4×C5—24no—
81C23×C4×C5—42no—
82C23×C4×C5C2311yescharacteristic
83C23×C4×C5C2311yescharacteristic
84C23×C4×C5C2314yes—
85C23×C4×C5C2311yescharacteristic
86C23×C4×C5C2311yescharacteristic
87C23×C4×C5C2311yescharacteristic
88C23×C4×C5C2311yescharacteristic
89C22×C22⋊D5—24no—
90C22×C22⋊D5—24no—
91C22×C22⋊D5—24no—
92C22×C22⋊D5—24no—
93C22×C22⋊D5—24no—
94C22×C22⋊D5—42no—
95C22×C22⋊D5C2314yes—
96C22×C22⋊D5C2314yes—
97C23×Dic5C2311yescharacteristic
98C23×Dic5C2311yescharacteristic
99C23×Dic5C2311yescharacteristic
100C23×Dic5C2311yescharacteristic
101C23×Dic5C2311yescharacteristic
102C23×Dic5C2311yescharacteristic
103C22×D20—24no—
104C22×D20—24no—
105C22×D20—24no—
106C22×D20C2314yes—
107C22×C4×D5—24no—
108C22×C4×D5—24no—
109C22×C4×D5—24no—
110C22×C4×D5—24no—
111C22×C4×D5—42no—
112C22×C4×D5—42no—
113C22×C4×D5C2314yes—
114C22×C4×D5C2314yes—
115C5×C22⋊Q8—232no—
116C2×C5×C4⋊C4—24no—
117C2×C5×C4⋊C4—24no—
118C2×C5×C4⋊C4D418yescomplemented
119C2×C5×C4⋊C4C2314yes—
120C2×C5×C4⋊C4C2314yes—
121C2×C5×C4⋊C4C2314yes—
122C2×C5×C22⋊C4—24no—
123C2×C5×C22⋊C4—24no—
124C2×C5×C22⋊C4C2314yes—
125C2×C5×C22⋊C4C2314yes—
126C2×C22⋊Dic5—24no—
127C2×C22⋊Dic5—24no—
128C2×C22⋊Dic5C2314yes—
129C2×C22⋊Dic5C2314yes—
130#4092—232no—
131C4×C22⋊D5—232no—
132C2×#685—24no—
133C2×#685—24no—
134C2×#685—24no—
135C2×#685—24no—
136C2×#685—24no—
137C2×#685—24no—
138C2×#685—24no—
139C2×#685—42no—
140C2×#685C2314yes—
141C2×#685C2314yes—
142C2×#685C2314yes—
143C2×#685C2314yes—
144C2×#685C2314yes—
145C2×#685C2314yes—
146C2×#685C2314yes—
147C2×#685C2314yes—
148C2×C4⋊Dic5—24no—
149C2×C4⋊Dic5C2314yes—
150C2×#683—24no—
151C2×#683D418yescomplemented
152C2×#683C2314yes—
153C2×#683C2314yes—
154C2×C4×Dic5—24no—
155C2×C4×Dic5—24no—
156C2×C4×Dic5C2314yes—
157C2×C4×Dic5C2314yes—
158#4039—232no—
159#3963C2314yes—
160#3963C2314yes—
161#3963C2314yes—
162#3963C2314yes—
163#3963C2314yes—
164#3963C2314yes—
165#3963C2314yes—
166#3963C2314yes—
167C22×C22⋊Q8—51no—
168C22×C22⋊Q8D511yescharacteristic, complemented
169C22×C4×D4—51no—
170C22×C4×D4—51no—
171#2463—516no—
172C2×#394—51no—
173C2×#394—51no—
174C2×#393—51no—
175C2×#392—51no—
176C2×#388—51no—
177C2×#388—51no—
178C2×#387—51no—
179C2×#387—51no—
180C2×#386—51no—
181C2×#386—51no—
182C2×#385—51no—
183C24×C5—22no—
184C24×C5—22no—
185C24×C5—22no—
186C24×C5—22no—
187C24×C5—22no—
188C24×C5—22no—
189C24×C5#4114yes—
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×D5—22no—
203C23×D5—22no—
204C23×D5#4114yes—
205C23×D5#4114yes—
206C23×D5C2412yes—
207C23×D5C2412yes—
208C2×C5×Q8—28no—
209C2×C5×Q8—28no—
210C2×C5×Q8—44no—
211C2×C5×Q8—416no—
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×C5—22no—
225C22×C4×C5—22no—
226C22×C4×C5—28no—
227C22×C4×C5—28no—
228C22×C4×C5—44no—
229C22×C4×C5—416no—
230C22×C4×C5C2×D414yes—
231C22×C4×C5C2×D414yes—
232C22×C4×C5C2×D414yes—
233C22×C4×C5C2×D414yes—
234C22×C4×C5C2412yes—
235C22×C4×C5C2412yes—
236C22×C4×C5C2412yes—
237C22×C4×C5C2412yes—
238C22×C4×C5C2412yes—
239C22×C4×C5C2412yes—
240C2×C22⋊D5—232no—
241C2×C22⋊D5—28no—
242C2×C22⋊D5—28no—
243C2×C22⋊D5—28no—
244C2×C22⋊D5—28no—
245C2×C22⋊D5—28no—
246C2×C22⋊D5—44no—
247C2×C22⋊D5—416no—
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×Dic5—22no—
257C22×Dic5—22no—
258C22×Dic5—22no—
259C22×Dic5—22no—
260C22×Dic5—22no—
261C22×Dic5—22no—
262C22×Dic5—22no—
263C22×Dic5—22no—
264C22×Dic5C2×D414yes—
265C22×Dic5C2×D414yes—
266C22×Dic5C2412yes—
267C22×Dic5C2412yes—
268C22×Dic5C2412yes—
269C22×Dic5C2412yes—
270C22×Dic5C2412yes—
271C22×Dic5C2412yes—
272C2×D20—232no—
273C2×D20—28no—
274C2×D20—28no—
275C2×D20—28no—
276C2×C4×D5—28no—
277C2×C4×D5—28no—
278C2×C4×D5—28no—
279C2×C4×D5—28no—
280C2×C4×D5—44no—
281C2×C4×D5—44no—
282C2×C4×D5—416no—
283C2×C4×D5—416no—
284C5×C4⋊C4—28no—
285C5×C4⋊C4—28no—
286C5×C4⋊C4C2×D4116yescomplemented
287C5×C22⋊C4—28no—
288C5×C22⋊C4—28no—
289C22⋊Dic5—28no—
290C22⋊Dic5—28no—
291#685—28no—
292#685—28no—
293#685—28no—
294#685—28no—
295#685—28no—
296#685—28no—
297#685—28no—
298#685—44no—
299C4⋊Dic5—28no—
300#683—28no—
301#683C2×D4116yescomplemented
302C4×Dic5—28no—
303C4×Dic5—28no—
304C23×Q8C2×D511yescharacteristic
305C23×D4—51no—
306C23×D4—51no—
307C23×D4—51no—
308C24×C4—51no—
309C24×C4—51no—
310C24×C4C2×D511yescharacteristic
311C2×C22⋊Q8—28no—
312C2×C22⋊Q8—58no—
313C2×C22⋊Q8—108no—
314C2×C22⋊Q8C2×D518yescomplemented
315C2×C4×D4—58no—
316C2×C4×D4—58no—
317C2×C4×D4—108no—
318C2×C4×D4—108no—
319C22×C4⋊C4—51no—
320C22×C4⋊C4—51no—
321C22×C4⋊C4—51no—
322C22×C4⋊C4C2×D511yescharacteristic
323C22×C4⋊C4C2×D511yescharacteristic
324C22×C4⋊C4C2×D511yescharacteristic
325C22×C22⋊C4—51no—
326C22×C22⋊C4—51no—
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×C42—51no—
338C22×C42—51no—
339#394—58no—
340#394—58no—
341#393—58no—
342#392—58no—
343#388—58no—
344#388—58no—
345#387—58no—
346#387—58no—
347#386—58no—
348#386—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×#95—51no—
358C23×C5—28no—
359C23×C5—28no—
360C23×C5—28no—
361C23×C5—22no—
362C23×C5—22no—
363C23×C5—22no—
364C23×C5—22no—
365C23×C5—22no—
366C23×C5—22no—
367C23×C5—44no—
368C23×C5—44no—
369C23×C5—44no—
370C23×C5—44no—
371C23×C5C22×D412yes—
372C23×C5C22×D412yes—
373C23×C5C2×#4114yes—
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—22no—
391C22×D5—22no—
392C22×D5—22no—
393C22×D5—22no—
394C22×D5—22no—
395C22×D5—22no—
396C22×D5—22no—
397C22×D5—22no—
398C22×D5—44no—
399C22×D5—44no—
400C22×D5—44no—
401C22×D5—44no—
402C22×D5—44no—
403C22×D5—44no—
404C22×D5—44no—
405C22×D5—44no—
406C22×D5C2×#4114yes—
407C22×D5C2×#4114yes—
408C5×Q8—416no—
409C2×C4×C5—28no—
410C2×C4×C5—28no—
411C2×C4×C5—28no—
412C2×C4×C5—28no—
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—22no—
427C2×C4×C5—416no—
428C2×C4×C5—44no—
429C2×C4×C5—44no—
430C2×C4×C5C22×D414yes—
431C2×C4×C5C22×D414yes—
432C2×C4×C5C22×D414yes—
433C2×C4×C5C22×D414yes—
434C22⋊D5—232no—
435C22⋊D5—416no—
436C2×Dic5—28no—
437C2×Dic5—28no—
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—22no—
453C2×Dic5—22no—
454C2×Dic5—44no—
455C2×Dic5—44no—
456C2×Dic5—44no—
457C2×Dic5—44no—
458C2×Dic5C22×D414yes—
459C2×Dic5C22×D414yes—
460D20—232no—
461C4×D5—416no—
462C4×D5—416no—
463C25—51no—
464C25—51no—
465C25C22×D511yescharacteristic
466C22×Q8—24no—
467C22×Q8—24no—
468C22×Q8—42no—
469C22×Q8C22×D514yes—
470C22×D4—54no—
471C22×D4—54no—
472C22×D4—54no—
473C22×D4—104no—
474C22×D4—104no—
475C22×D4—104no—
476C22×D4—104no—
477C22×D4—104no—
478C22×D4—104no—
479C22×D4—104no—
480C22×D4—104no—
481C22×D4—202no—
482C23×C4—24no—
483C23×C4—24no—
484C23×C4—42no—
485C23×C4—51no—
486C23×C4—51no—
487C23×C4—51no—
488C23×C4—51no—
489C23×C4—51no—
490C23×C4—51no—
491C23×C4—54no—
492C23×C4—54no—
493C23×C4—104no—
494C23×C4—104no—
495C23×C4—104no—
496C23×C4—104no—
497C23×C4—202no—
498C23×C4—202no—
499C23×C4C22×D511yescharacteristic
500C23×C4C22×D511yescharacteristic
501C23×C4C22×D514yes—
502C23×C4C22×D511yescharacteristic
503C23×C4C22×D511yescharacteristic
504C23×C4C22×D511yescharacteristic
505C23×C4C22×D511yescharacteristic
506C22⋊Q8—232no—
507C22⋊Q8—1032no—
508C4×D4—1032no—
509C4×D4—1032no—
510C2×C4⋊C4—24no—
511C2×C4⋊C4—24no—
512C2×C4⋊C4—58no—
513C2×C4⋊C4—54no—
514C2×C4⋊C4—54no—
515C2×C4⋊C4—54no—
516C2×C4⋊C4—104no—
517C2×C4⋊C4—104no—
518C2×C4⋊C4C22⋊D518yescomplemented
519C2×C4⋊C4C22×D514yes—
520C2×C4⋊C4C22×D514yes—
521C2×C4⋊C4C22×D514yes—
522C2×C22⋊C4—24no—
523C2×C22⋊C4—24no—
524C2×C22⋊C4—54no—
525C2×C22⋊C4—54no—
526C2×C22⋊C4—54no—
527C2×C22⋊C4—54no—
528C2×C22⋊C4—54no—
529C2×C22⋊C4—54no—
530C2×C22⋊C4—54no—
531C2×C22⋊C4—54no—
532C2×C22⋊C4—54no—
533C2×C22⋊C4—54no—
534C2×C22⋊C4—104no—
535C2×C22⋊C4—104no—
536C2×C22⋊C4—104no—
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—202no—
544C2×C22⋊C4C22×D514yes—
545C2×C22⋊C4C22×D514yes—
546C2×C42—54no—
547C2×C42—54no—
548C2×C42—104no—
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#95—54no—
558C22×C5—24no—
559C22×C5—24no—
560C22×C5—24no—
561C22×C5—42no—
562C22×C5—42no—
563C22×C5—42no—
564C22×C5—42no—
565C22×C5—416no—
566C22×C5#52514yes—
567C22×C5#52514yes—
568C22×C5#53914yes—
569C22×C5D4214yes—
570C22×C5#54814yes—
571C22×C5#54814yes—
572C22×C5#55114yes—
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—24no—
586C2×D5—42no—
587C2×D5—42no—
588C2×D5—42no—
589C2×D5—42no—
590C2×D5—42no—
591C2×D5—42no—
592C2×D5—42no—
593C2×D5—42no—
594C2×D5—416no—
595C2×D5—416no—
596C4×C5—24no—
597C4×C5—24no—
598C4×C5—24no—
599C4×C5—24no—
600C4×C5—42no—
601C4×C5—42no—
602Dic5—24no—
603Dic5—24no—
604Dic5—42no—
605Dic5—42no—
606Dic5—42no—
607Dic5—42no—
608C24—22no—
609C24—22no—
610C24—22no—
611C24—22no—
612C24—22no—
613C24—22no—
614C24—54no—
615C24—54no—
616C24—52no—
617C24—52no—
618C24—102no—
619C24—102no—
620C24—102no—
621C24—102no—
622C24—102no—
623C24—102no—
624C24—102no—
625C24—102no—
626C24—102no—
627C24—102no—
628C24—102no—
629C24—102no—
630C24#71314yes—
631C24C23×D512yes—
632C24C23×D511yescharacteristic
633C2×Q8—28no—
634C2×Q8—28no—
635C2×Q8—44no—
636C2×Q8—416no—
637C2×D4—108no—
638C2×D4—108no—
639C2×D4—1032no—
640C2×D4—108no—
641C2×D4—108no—
642C2×D4—1032no—
643C2×D4—108no—
644C2×D4—108no—
645C2×D4—108no—
646C2×D4—108no—
647C2×D4—204no—
648C2×D4—2016no—
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—22no—
662C22×C4—22no—
663C22×C4—28no—
664C22×C4—28no—
665C22×C4—44no—
666C22×C4—416no—
667C22×C4—54no—
668C22×C4—54no—
669C22×C4—52no—
670C22×C4—52no—
671C22×C4—52no—
672C22×C4—52no—
673C22×C4—52no—
674C22×C4—52no—
675C22×C4—108no—
676C22×C4—108no—
677C22×C4—102no—
678C22×C4—102no—
679C22×C4—102no—
680C22×C4—102no—
681C22×C4—102no—
682C22×C4—102no—
683C22×C4—102no—
684C22×C4—102no—
685C22×C4—102no—
686C22×C4—102no—
687C22×C4—102no—
688C22×C4—102no—
689C22×C4—102no—
690C22×C4—102no—
691C22×C4—102no—
692C22×C4—102no—
693C22×C4—108no—
694C22×C4—108no—
695C22×C4—204no—
696C22×C4—204no—
697C22×C4—2016no—
698C22×C4—2016no—
699C22×C4D4×D514yes—
700C22×C4C2×C22⋊D514yes—
701C22×C4C2×C22⋊D514yes—
702C22×C4C2×C22⋊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—516no—
712C4⋊C4—108no—
713C4⋊C4—108no—
714C4⋊C4C2×C22⋊D5116yescomplemented
715C22⋊C4—28no—
716C22⋊C4—28no—
717C22⋊C4—108no—
718C22⋊C4—108no—
719C22⋊C4—108no—
720C22⋊C4—108no—
721C22⋊C4—108no—
722C22⋊C4—108no—
723C22⋊C4—108no—
724C22⋊C4—108no—
725C22⋊C4—108no—
726C22⋊C4—204no—
727C42—108no—
728C42—108no—
729C2×C5—44no—
730C2×C5#246318yescomplemented
731C2×C5C2×#52511yescharacteristic
732C2×C5C2×#52511yescharacteristic
733C2×C5C2×#53911yescharacteristic
734C2×C5C2×D4211yescharacteristic
735C2×C5C2×#54811yescharacteristic
736C2×C5C2×#54811yescharacteristic
737C2×C5C2×#55111yescharacteristic
738D5—44no—
739D5—44no—
740C23—28no—
741C23—28no—
742C23—28no—
743C23—22no—
744C23—22no—
745C23—22no—
746C23—22no—
747C23—22no—
748C23—22no—
749C23—44no—
750C23—44no—
751C23—44no—
752C23—44no—
753C23—54no—
754C23—54no—
755C23—108no—
756C23—108no—
757C23—108no—
758C23—108no—
759C23—108no—
760C23—108no—
761C23—102no—
762C23—102no—
763C23—102no—
764C23—102no—
765C23—102no—
766C23—102no—
767C23—102no—
768C23—102no—
769C23—102no—
770C23—102no—
771C23—102no—
772C23—102no—
773C23—204no—
774C23—204no—
775C23—204no—
776C23—204no—
777C23—204no—
778C23—204no—
779C23—204no—
780C23—204no—
781C23C2×D4×D512yes—
782C23#414412yes—
783C23C2×#71314yes—
784C23C2×#71312yes—
785C23#414712yes—
786C23D5×#4112yes—
787C23D5×#4112yes—
788C23C22×C22⋊D512yes—
789C23C24×D511yescharacteristic
790Q8—416no—
791D4—1032no—
792D4—1032no—
793D4—2016no—
794C2×C4—28no—
795C2×C4—28no—
796C2×C4—28no—
797C2×C4—28no—
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—22no—
812C2×C4—416no—
813C2×C4—44no—
814C2×C4—44no—
815C2×C4—54no—
816C2×C4—54no—
817C2×C4—108no—
818C2×C4—108no—
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—102no—
829C2×C4—102no—
830C2×C4—102no—
831C2×C4—102no—
832C2×C4—102no—
833C2×C4—102no—
834C2×C4—102no—
835C2×C4—2016no—
836C2×C4—2016no—
837C2×C4—204no—
838C2×C4—204no—
839C2×C4—204no—
840C2×C4—204no—
841C2×C4C2×D4×D514yes—
842C2×C4C22×C22⋊D514yes—
843C2×C4C22×C22⋊D514yes—
844C2×C4C22×C22⋊D514yes—
845C5C2×#246311yescharacteristic, complemented, Sylow
846C22—24no—
847C22—24no—
848C22—24no—
849C22—42no—
850C22—416no—
851C22—42no—
852C22—42no—
853C22—42no—
854C22—104no—
855C22—104no—
856C22—104no—
857C22—104no—
858C22—104no—
859C22—104no—
860C22—202no—
861C22—202no—
862C22—202no—
863C22—202no—
864C22—202no—
865C22—2016no—
866C22—2016no—
867C22—202no—
868C22—202no—
869C22—202no—
870C22#6596114yes—
871C22#6596714yes—
872C22#6597114yes—
873C22#6597214yes—
874C22D4×C22⋊D514yes—
875C22#6615114yes—
876C22#6616214yes—
877C22C22×D4×D511yescharacteristic
878C22C2×#414411yescharacteristic
879C22C22×#71311yescharacteristic
880C22C2×#414711yescharacteristic
881C22C2×D5×#4111yescharacteristic
882C22C2×D5×#4111yescharacteristic
883C22C23×C22⋊D511yescharacteristic
884C4—24no—
885C4—24no—
886C4—24no—
887C4—24no—
888C4—42no—
889C4—42no—
890C4—104no—
891C4—104no—
892C4—202no—
893C4—202no—
894C4—202no—
895C4—202no—
896C2—44no—
897C2—204no—
898C2—204no—
899C2#1061454918yesdirect product factor
900C2C2×#6596111yescharacteristic
901C2C2×#6597211yescharacteristic
902C2C2×#6596711yescharacteristic
903C2C2×#6597111yescharacteristic
904C2C2×D4×C22⋊D511yescharacteristic
905C2C2×#6615111yescharacteristic
906C2C2×#6616211yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC22×C5×C22⋊Q8C2
socleC24×C5C24
prime radicalC2×#65249C2
hypercenterC22×C22⋊Q8D5
hypocenterC5C2×#2463
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C22×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C22×C5×C22⋊Q8C2semidirect
2. C22×#4092C2semidirect
3. C22×C4×C22⋊D5C2semidirect
4. C22×#4039C2semidirect
5. C2×#65520C2semidirect
6. C2×#65502C2semidirect
7. #10614549C2direct (N × H)
8. C2×#65280C2semidirect
9. C2×#65278C2semidirect
10. C2×#65279C2semidirect
11. C2×#65267C2semidirect
12. C2×#65270C2semidirect
14. C2×#65245C2semidirect
15. C2×#65250C2semidirect
16. C2×#65233C2semidirect
25. C2×C5×C22⋊Q8C22semidirect
34. C2×#4092C22semidirect
36. C2×C4×C22⋊D5C22semidirect
51. C2×#4039C22semidirect
52. #65520C22semidirect
53. #65502C22semidirect
62. #65280C22semidirect
63. #65279C22semidirect
64. #65278C22semidirect
65. #65270C22semidirect
66. #65267C22semidirect
67. #65250C22semidirect
69. #65245C22semidirect
70. #65233C22semidirect
118. C2×C5×C4⋊C4D4semidirect
151. C2×#683D4semidirect
168. C22×C22⋊Q8D5semidirect
286. C5×C4⋊C4C2×D4semidirect
301. #683C2×D4semidirect
314. C2×C22⋊Q8C2×D5semidirect
518. C2×C4⋊C4C22⋊D5semidirect
714. C4⋊C4C2×C22⋊D5semidirect
730. C2×C5#2463semidirect
845. C5C2×#2463semidirect
899. C2#10614549direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C5×C22⋊Q82
C22×#40922
C22×C4×C22⋊D52
C22×#40392
C2×#655202
C2×#655022
#106145492
C2×#652802
C2×#652782
C2×#652792
C2×#652672
C2×#652702
C2×#652492
C2×#652452
C2×#652502
C2×#652332
C2×#24635