Finite Group Databasebeta

← C2×#10614493 #12267941

Subgroups — C2×#10614493 #12267941

Order 1280.

3006 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C5×C22⋊Q8C211yesmaximal, characteristic
2C22×#4023C211yesmaximal, characteristic
3C2×#65518C211yesmaximal, characteristic, complemented
4C2×#65519C211yesmaximal, characteristic, complemented
5C2×#65499C211yesmaximal, characteristic
6C22×#3963C211yesmaximal, characteristic
7#10614493C2116yesmaximal, direct product factor
8C2×#65271C211yesmaximal, characteristic, complemented
9C2×#65273C211yesmaximal, characteristic, complemented
10C2×#65273C211yesmaximal, characteristic, complemented
11C2×#65262C211yesmaximal, characteristic, complemented
12C2×#65267C211yesmaximal, characteristic, complemented
13C2×#65267C211yesmaximal, characteristic, complemented
14C2×#65239C211yesmaximal, characteristic
15C2×#65232C211yesmaximal, characteristic
16C2×#65231C211yesmaximal, characteristic
17C23×C5×Q8C2211yescharacteristic
18C24×C4×C5C2211yescharacteristic
19C24×Dic5C2211yescharacteristic
20C24×Dic5C2211yescharacteristic
21C2×C5×C22⋊Q8—28no—
22C2×C5×C22⋊Q8C2218yes—
23C22×C5×C4⋊C4C2211yescharacteristic
24C22×C5×C4⋊C4C2211yescharacteristic
25C22×C5×C4⋊C4C2211yescharacteristic
26C22×C5×C22⋊C4C2211yescharacteristic
27C22×C5×C22⋊C4C2211yescharacteristic
28C22×C22⋊Dic5C2211yescharacteristic
29C22×C22⋊Dic5C2211yescharacteristic
30C22×C4⋊Dic5C2211yescharacteristic
31C22×C4⋊Dic5C2211yescharacteristic
32C22×#683C2211yescharacteristic
33C22×#683C2211yescharacteristic
34C22×#683C2211yescharacteristic
35C22×#683C2211yescharacteristic
36C22×#683C2211yescharacteristic
37C22×#683C2211yescharacteristic
38C22×C4×Dic5C2211yescharacteristic
39C22×C4×Dic5C2211yescharacteristic
40C2×#4023—28no—
41C2×#4023C2218yes—
42#65519C2218yescomplemented
43#65518C2218yescomplemented
44#65499C2218yes—
45C2×#3963C2211yescharacteristic
46C2×#3963C2211yescharacteristic
47C2×#3963C2211yescharacteristic
48C2×#3963C2211yescharacteristic
49C2×#3963C2211yescharacteristic
50C2×#3963C2211yescharacteristic
51C2×#3963C2211yescharacteristic
52C2×#3963C2211yescharacteristic
53C2×#3963C2211yescharacteristic
54C2×#3963C2211yescharacteristic
55C2×#3963C2211yescharacteristic
56C2×#3963C2211yescharacteristic
57C2×#3963C2211yescharacteristic
58C2×#3963C2211yescharacteristic
59C2×#3963C2218yes—
60#65273C2218yescomplemented
61#65273C2218yescomplemented
62#65271C2218yescomplemented
63#65267C2218yescomplemented
64#65267C2218yescomplemented
65#65262C2218yescomplemented
66#65239C2218yes—
67#65232C2218yes—
68#65231C2218yes—
69C2×#2438—51nomaximal, Sylow
70C25×C5C2311yescharacteristic
71C22×C5×Q8—24no—
72C22×C5×Q8—24no—
73C22×C5×Q8—42no—
74C22×C5×Q8C2314yes—
75C23×C4×C5—24no—
76C23×C4×C5—24no—
77C23×C4×C5—42no—
78C23×C4×C5C2311yescharacteristic
79C23×C4×C5C2311yescharacteristic
80C23×C4×C5C2311yescharacteristic
81C23×C4×C5C2314yes—
82C23×C4×C5C2311yescharacteristic
83C23×C4×C5C2311yescharacteristic
84C23×C4×C5C2311yescharacteristic
85C23×Dic5—24no—
86C23×Dic5—24no—
87C23×Dic5—24no—
88C23×Dic5—24no—
89C23×Dic5—42no—
90C23×Dic5Q818yescomplemented
91C23×Dic5C2311yescharacteristic
92C23×Dic5C2311yescharacteristic
93C23×Dic5C2311yescharacteristic
94C23×Dic5C2311yescharacteristic
95C23×Dic5C2311yescharacteristic
96C23×Dic5C2314yes—
97C23×Dic5C2311yescharacteristic
98C23×Dic5C2311yescharacteristic
99C23×Dic5C2314yes—
100C23×Dic5C2311yescharacteristic
101C5×C22⋊Q8—232no—
102C2×C5×C4⋊C4—24no—
103C2×C5×C4⋊C4—24no—
104C2×C5×C4⋊C4—24no—
105C2×C5×C4⋊C4C2314yes—
106C2×C5×C4⋊C4C2314yes—
107C2×C5×C4⋊C4C2314yes—
108C2×C5×C22⋊C4—24no—
109C2×C5×C22⋊C4D418yes—
110C2×C5×C22⋊C4C2314yes—
111C2×C5×C22⋊C4C2314yes—
112C2×C22⋊Dic5—24no—
113C2×C22⋊Dic5—24no—
114C2×C22⋊Dic5C2314yes—
115C2×C22⋊Dic5C2314yes—
116C2×C4⋊Dic5—24no—
117C2×C4⋊Dic5—42no—
118C2×C4⋊Dic5C2314yes—
119C2×C4⋊Dic5C2314yes—
120C2×#683—24no—
121C2×#683—24no—
122C2×#683—24no—
123C2×#683—24no—
124C2×#683—42no—
125C2×#683—42no—
126C2×#683C2314yes—
127C2×#683C2314yes—
128C2×#683C2314yes—
129C2×#683C2314yes—
130C2×#683C2314yes—
131C2×#683C2314yes—
132C2×C4×Dic5—24no—
133C2×C4×Dic5—24no—
134C2×C4×Dic5C2314yes—
135C2×C4×Dic5C2314yes—
136#4023—232no—
137#3963C2314yes—
138#3963C2314yes—
139#3963C2314yes—
140#3963C2314yes—
141#3963C2314yes—
142#3963C2314yes—
143#3963C2314yes—
144#3963C2314yes—
145#3963C2314yes—
146#3963C2314yes—
147#3963C2314yes—
148#3963C2314yes—
149#3963C2314yes—
150#3963C2314yes—
151C22×C22⋊Q8D511yescharacteristic
152C22×#117—51no—
153#2438—516no—
154C2×#400—51no—
155C2×#398—51no—
156C2×#398—51no—
157C2×#395—51no—
158C2×#391—51no—
159C2×#389—51no—
160C2×#387—51no—
161C2×#387—51no—
162C2×#385—51no—
163C2×#385—51no—
164C2×#381—51no—
165C2×#380—51no—
166C22×#95—51no—
167C24×C5—22no—
168C24×C5—22no—
169C24×C5—22no—
170C24×C5—22no—
171C24×C5C2×D414yes—
172C24×C5C2×Q814yes—
173C24×C5#4114yes—
174C24×C5C2412yes—
175C24×C5C2411yescharacteristic
176C2×C5×Q8—28no—
177C2×C5×Q8—28no—
178C2×C5×Q8—44no—
179C2×C5×Q8—416no—
180C22×C4×C5—22no—
181C22×C4×C5—22no—
182C22×C4×C5—22no—
183C22×C4×C5—22no—
184C22×C4×C5—22no—
185C22×C4×C5—22no—
186C22×C4×C5—22no—
187C22×C4×C5—22no—
188C22×C4×C5—22no—
189C22×C4×C5—28no—
190C22×C4×C5—22no—
191C22×C4×C5—22no—
192C22×C4×C5—22no—
193C22×C4×C5—22no—
194C22×C4×C5—22no—
195C22×C4×C5—22no—
196C22×C4×C5—28no—
197C22×C4×C5—44no—
198C22×C4×C5—416no—
199C22×C4×C5C2×D414yes—
200C22×C4×C5C2×D414yes—
201C22×C4×C5#4114yes—
202C22×C4×C5C2412yes—
203C22×C4×C5C2412yes—
204C22×C4×C5C2412yes—
205C22×C4×C5C2412yes—
206C22×C4×C5C2412yes—
207C22×C4×C5C2412yes—
208C22×Dic5—232no—
209C22×Dic5—28no—
210C22×Dic5—22no—
211C22×Dic5—22no—
212C22×Dic5—22no—
213C22×Dic5—22no—
214C22×Dic5—28no—
215C22×Dic5—22no—
216C22×Dic5—22no—
217C22×Dic5—22no—
218C22×Dic5—22no—
219C22×Dic5—22no—
220C22×Dic5—22no—
221C22×Dic5—28no—
222C22×Dic5—22no—
223C22×Dic5—22no—
224C22×Dic5—22no—
225C22×Dic5—22no—
226C22×Dic5—22no—
227C22×Dic5—22no—
228C22×Dic5—22no—
229C22×Dic5—22no—
230C22×Dic5—22no—
231C22×Dic5—22no—
232C22×Dic5—22no—
233C22×Dic5—28no—
234C22×Dic5—44no—
235C22×Dic5—416no—
236C22×Dic5C2×Q814yes—
237C22×Dic5C2×Q814yes—
238C22×Dic5C2×Q8116yescomplemented
239C22×Dic5#4114yes—
240C22×Dic5C2412yes—
241C22×Dic5C2412yes—
242C22×Dic5C2412yes—
243C22×Dic5C2412yes—
244C22×Dic5C2412yes—
245C22×Dic5C2412yes—
246C22×Dic5C2412yes—
247C22×Dic5C2412yes—
248C5×C4⋊C4—28no—
249C5×C4⋊C4—28no—
250C5×C4⋊C4—28no—
251C5×C22⋊C4—28no—
252C5×C22⋊C4C2×D4116yes—
253C22⋊Dic5—28no—
254C22⋊Dic5—28no—
255C4⋊Dic5—28no—
256C4⋊Dic5—44no—
257#683—28no—
258#683—28no—
259#683—28no—
260#683—28no—
261#683—44no—
262#683—44no—
263C4×Dic5—28no—
264C4×Dic5—28no—
265C23×Q8C2×D511yescharacteristic
266C24×C4—51no—
267C24×C4—51no—
268C24×C4C2×D511yescharacteristic
269C2×C22⋊Q8—28no—
270C2×C22⋊Q8C2×D518yes—
271C2×#117—58no—
272C2×#117—108no—
273C22×C4⋊C4—51no—
274C22×C4⋊C4—51no—
275C22×C4⋊C4—51no—
276C22×C4⋊C4—51no—
277C22×C4⋊C4—51no—
278C22×C4⋊C4—51no—
279C22×C4⋊C4—51no—
280C22×C4⋊C4—51no—
281C22×C4⋊C4C2×D511yescharacteristic
282C22×C4⋊C4C2×D511yescharacteristic
283C22×C4⋊C4C2×D511yescharacteristic
284C22×C22⋊C4—51no—
285C22×C22⋊C4—51no—
286C22×C22⋊C4C2×D511yescharacteristic
287C22×C22⋊C4C2×D511yescharacteristic
288C22×C42—51no—
289C22×C42—51no—
290#400—58no—
291#398—58no—
292#398—58no—
293#395—58no—
294#391—58no—
295#389—58no—
296#387—58no—
297#387—58no—
298#385—58no—
299#385—58no—
300#381—58no—
301#380—58no—
302C2×#95—51no—
303C2×#95—51no—
304C2×#95—51no—
305C2×#95—51no—
306C2×#95—51no—
307C2×#95—51no—
308C2×#95—51no—
309C2×#95—51no—
310C2×#95—51no—
311C2×#95—51no—
312C2×#95—58no—
313C2×#95—51no—
314C2×#95—51no—
315C2×#95—51no—
316C2×#95—51no—
317C23×C5—28no—
318C23×C5—28no—
319C23×C5—28no—
320C23×C5—28no—
321C23×C5—28no—
322C23×C5—28no—
323C23×C5—22no—
324C23×C5—22no—
325C23×C5—22no—
326C23×C5—22no—
327C23×C5C22⋊Q8116yes—
328C23×C5C22×D414yes—
329C23×C5C22×D412yes—
330C23×C5C22×Q814yes—
331C23×C5C22×Q812yes—
332C23×C5C2×#4112yes—
333C23×C5C2×#4114yes—
334C23×C5C2×#4112yes—
335C23×C5C2×#4112yes—
336C23×C5H(5,𝔽2)12yes—
337C23×C52−1+412yes—
338C23×C5C2511yescharacteristic
339C5×Q8—416no—
340C2×C4×C5—28no—
341C2×C4×C5—28no—
342C2×C4×C5—28no—
343C2×C4×C5—22no—
344C2×C4×C5—22no—
345C2×C4×C5—22no—
346C2×C4×C5—22no—
347C2×C4×C5—22no—
348C2×C4×C5—22no—
349C2×C4×C5—22no—
350C2×C4×C5—22no—
351C2×C4×C5—22no—
352C2×C4×C5—22no—
353C2×C4×C5—22no—
354C2×C4×C5—22no—
355C2×C4×C5—22no—
356C2×C4×C5—22no—
357C2×C4×C5—22no—
358C2×C4×C5—416no—
359C2×C4×C5—44no—
360C2×C4×C5—44no—
361C2×C4×C5—44no—
362C2×C4×C5C22×D414yes—
363C2×C4×C5C22×D414yes—
364C2×C4×C5C2×#4114yes—
365C2×Dic5—28no—
366C2×Dic5—28no—
367C2×Dic5—232no—
368C2×Dic5—28no—
369C2×Dic5—22no—
370C2×Dic5—22no—
371C2×Dic5—22no—
372C2×Dic5—22no—
373C2×Dic5—22no—
374C2×Dic5—22no—
375C2×Dic5—22no—
376C2×Dic5—22no—
377C2×Dic5—22no—
378C2×Dic5—22no—
379C2×Dic5—22no—
380C2×Dic5—22no—
381C2×Dic5—22no—
382C2×Dic5—22no—
383C2×Dic5—22no—
384C2×Dic5—22no—
385C2×Dic5—22no—
386C2×Dic5—22no—
387C2×Dic5—22no—
388C2×Dic5—22no—
389C2×Dic5—22no—
390C2×Dic5—416no—
391C2×Dic5—44no—
392C2×Dic5—44no—
393C2×Dic5—44no—
394C2×Dic5—44no—
395C2×Dic5—44no—
396C2×Dic5C22×Q814yes—
397C2×Dic5C22×Q814yes—
398C2×Dic5C2×#4114yes—
399C25C22×D511yescharacteristic
400C22×Q8—24no—
401C22×Q8—24no—
402C22×Q8—42no—
403C22×Q8C22×D514yes—
404C23×C4—24no—
405C23×C4—24no—
406C23×C4—42no—
407C23×C4—58no—
408C23×C4—54no—
409C23×C4—51no—
410C23×C4—51no—
411C23×C4—51no—
412C23×C4—51no—
413C23×C4—51no—
414C23×C4—51no—
415C23×C4—51no—
416C23×C4—51no—
417C23×C4—54no—
418C23×C4—104no—
419C23×C4—104no—
420C23×C4—104no—
421C23×C4—104no—
422C23×C4—202no—
423C23×C4C22×D511yescharacteristic
424C23×C4C22×D511yescharacteristic
425C23×C4C22×D511yescharacteristic
426C23×C4C22×D514yes—
427C23×C4C22×D511yescharacteristic
428C23×C4C22×D511yescharacteristic
429C23×C4C22×D511yescharacteristic
430C22⋊Q8—232no—
431#117—1032no—
432C2×C4⋊C4—24no—
433C2×C4⋊C4—24no—
434C2×C4⋊C4—24no—
435C2×C4⋊C4—54no—
436C2×C4⋊C4—54no—
437C2×C4⋊C4—54no—
438C2×C4⋊C4—54no—
439C2×C4⋊C4—54no—
440C2×C4⋊C4—54no—
441C2×C4⋊C4—54no—
442C2×C4⋊C4—54no—
443C2×C4⋊C4—104no—
444C2×C4⋊C4—104no—
445C2×C4⋊C4—104no—
446C2×C4⋊C4—104no—
447C2×C4⋊C4—104no—
448C2×C4⋊C4—202no—
449C2×C4⋊C4—202no—
450C2×C4⋊C4—202no—
451C2×C4⋊C4C22×D514yes—
452C2×C4⋊C4C22×D514yes—
453C2×C4⋊C4C22×D514yes—
454C2×C22⋊C4—24no—
455C2×C22⋊C4—54no—
456C2×C22⋊C4—54no—
457C2×C22⋊C4—104no—
458C2×C22⋊C4—104no—
459C2×C22⋊C4C22⋊D518yes—
460C2×C22⋊C4C22×D514yes—
461C2×C22⋊C4C22×D514yes—
462C2×C42—54no—
463C2×C42—54no—
464C2×C42—104no—
465C2×C42—104no—
466#95—54no—
467#95—54no—
468#95—54no—
469#95—54no—
470#95—54no—
471#95—54no—
472#95—54no—
473#95—54no—
474#95—54no—
475#95—54no—
476#95—54no—
477#95—54no—
478#95—54no—
479#95—54no—
480C22×C5—24no—
481C22×C5—24no—
482C22×C5—232no—
483C22×C5—24no—
484C22×C5—24no—
485C22×C5—24no—
486C22×C5—24no—
487C22×C5C2×C22⋊Q818yes—
488C22×C5C2×C22⋊Q814yes—
489C22×C5#53314yes—
490C22×C5#54414yes—
491C22×C5#54614yes—
492C22×C5#54714yes—
493C22×C5#55114yes—
494C22×C5#55214yes—
495C22×C5C23×D411yescharacteristic
496C22×C5C23×Q811yescharacteristic
497C22×C5C22×#4111yescharacteristic
498C22×C5C22×#4111yescharacteristic
499C22×C5C22×#4111yescharacteristic
500C22×C5C2×H(5,𝔽2)11yescharacteristic
501C22×C5C2×2−1+411yescharacteristic
502C4×C5—24no—
503C4×C5—24no—
504C4×C5—24no—
505C4×C5—42no—
506C4×C5—42no—
507C4×C5—42no—
508Dic5—24no—
509Dic5—24no—
510Dic5—24no—
511Dic5—42no—
512Dic5—42no—
513Dic5—42no—
514Dic5—42no—
515Dic5—42no—
516C24—22no—
517C24—22no—
518C24—22no—
519C24—22no—
520C24Q8×D514yes—
521C24#71314yes—
522C24C2×C22⋊D514yes—
523C24C23×D512yes—
524C24C23×D511yescharacteristic
525C2×Q8—28no—
526C2×Q8—28no—
527C2×Q8—44no—
528C2×Q8—416no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—28no—
545C22×C4—28no—
546C22×C4—44no—
547C22×C4—416no—
548C22×C4—54no—
549C22×C4—54no—
550C22×C4—516no—
551C22×C4—54no—
552C22×C4—52no—
553C22×C4—52no—
554C22×C4—52no—
555C22×C4—52no—
556C22×C4—52no—
557C22×C4—52no—
558C22×C4—52no—
559C22×C4—52no—
560C22×C4—108no—
561C22×C4—102no—
562C22×C4—108no—
563C22×C4—102no—
564C22×C4—102no—
565C22×C4—102no—
566C22×C4—102no—
567C22×C4—102no—
568C22×C4—108no—
569C22×C4—1032no—
570C22×C4—102no—
571C22×C4—102no—
572C22×C4—102no—
573C22×C4—102no—
574C22×C4—102no—
575C22×C4—102no—
576C22×C4—102no—
577C22×C4—108no—
578C22×C4—102no—
579C22×C4—102no—
580C22×C4—102no—
581C22×C4—102no—
582C22×C4—102no—
583C22×C4—102no—
584C22×C4—102no—
585C22×C4—102no—
586C22×C4—204no—
587C22×C4—2016no—
588C22×C4#71114yes—
589C22×C4C2×C22⋊D514yes—
590C22×C4C2×C22⋊D514yes—
591C22×C4C23×D512yes—
592C22×C4C23×D512yes—
593C22×C4C23×D512yes—
594C22×C4C23×D512yes—
595C22×C4C23×D512yes—
596C22×C4C23×D512yes—
597C4⋊C4—28no—
598C4⋊C4—28no—
599C4⋊C4—28no—
600C4⋊C4—108no—
601C4⋊C4—108no—
602C4⋊C4—108no—
603C4⋊C4—108no—
604C4⋊C4—108no—
605C4⋊C4—204no—
606C4⋊C4—204no—
607C4⋊C4—204no—
608C22⋊C4—28no—
609C22⋊C4—108no—
610C22⋊C4—108no—
611C22⋊C4C2×C22⋊D5116yes—
612C42—108no—
613C42—108no—
614C2×C5—28no—
615C2×C5#243818yescomplemented
616C2×C5C22×C22⋊Q811yescharacteristic
617C2×C5C2×#53311yescharacteristic
618C2×C5C2×#54411yescharacteristic
619C2×C5C2×#54611yescharacteristic
620C2×C5C2×#54711yescharacteristic
621C2×C5C2×#55111yescharacteristic
622C2×C5C2×#55211yescharacteristic
623C23—28no—
624C23—28no—
625C23—28no—
626C23—28no—
627C23—28no—
628C23—28no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23#4092116yes—
634C23C2×#71112yes—
635C23#414412yes—
636C23C2×Q8×D514yes—
637C23C2×Q8×D512yes—
638C23C2×#71314yes—
639C23C2×#71312yes—
640C23D5×#4112yes—
641C23#415012yes—
642C23C22×C22⋊D514yes—
643C23C22×C22⋊D512yes—
644C23C24×D511yescharacteristic
645Q8—416no—
646C2×C4—28no—
647C2×C4—28no—
648C2×C4—28no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—416no—
665C2×C4—44no—
666C2×C4—44no—
667C2×C4—44no—
668C2×C4—54no—
669C2×C4—54no—
670C2×C4—54no—
671C2×C4—1032no—
672C2×C4—108no—
673C2×C4—108no—
674C2×C4—108no—
675C2×C4—102no—
676C2×C4—102no—
677C2×C4—102no—
678C2×C4—102no—
679C2×C4—102no—
680C2×C4—102no—
681C2×C4—102no—
682C2×C4—102no—
683C2×C4—102no—
684C2×C4—102no—
685C2×C4—102no—
686C2×C4—102no—
687C2×C4—102no—
688C2×C4—102no—
689C2×C4—102no—
690C2×C4—102no—
691C2×C4—102no—
692C2×C4—102no—
693C2×C4—102no—
694C2×C4—102no—
695C2×C4—102no—
696C2×C4—2016no—
697C2×C4—204no—
698C2×C4—204no—
699C2×C4—204no—
700C2×C4—204no—
701C2×C4—204no—
702C2×C4C2×#71114yes—
703C2×C4C22×C22⋊D514yes—
704C2×C4C22×C22⋊D514yes—
705C5C2×#243811yescharacteristic, complemented, Sylow
706C22—24no—
707C22—24no—
708C22—24no—
709C22—24no—
710C22—24no—
711C22—232no—
712C22—24no—
713C22#6595614yes—
714C22#6595714yes—
715C22#6597114yes—
716C22#6597614yes—
717C22#6614014yes—
718C22C2×#409218yes—
719C22C2×#409214yes—
720C22#6615814yes—
721C22C22×#71111yescharacteristic
722C22C2×#414411yescharacteristic
723C22C22×Q8×D511yescharacteristic
724C22C22×#71311yescharacteristic
725C22C2×D5×#4111yescharacteristic
726C22C2×#415011yescharacteristic
727C22C23×C22⋊D511yescharacteristic
728C4—24no—
729C4—24no—
730C4—24no—
731C4—42no—
732C4—42no—
733C4—42no—
734C4—104no—
735C4—104no—
736C4—104no—
737C4—202no—
738C4—202no—
739C4—202no—
740C4—202no—
741C4—202no—
742C2—28no—
743C2#1061449318yesdirect product factor
744C2C2×#6595611yescharacteristic
745C2C2×#6595711yescharacteristic
746C2C2×#6597611yescharacteristic
747C2C2×#6597111yescharacteristic
748C2C2×#6614011yescharacteristic
749C2C22×#409211yescharacteristic
750C2C2×#6615811yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC22×C5×C22⋊Q8C2
socleC24×C5C24
prime radicalC25×C5C23
hypercenterC22×C22⋊Q8D5
hypocenterC5C2×#2438
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C22×C22⋊Q8

Complements

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

NH ≅ G/Ntype
3. C2×#65518C2semidirect
4. C2×#65519C2semidirect
7. #10614493C2direct (N × H)
8. C2×#65271C2semidirect
9. C2×#65273C2semidirect
10. C2×#65273C2semidirect
11. C2×#65262C2semidirect
12. C2×#65267C2semidirect
13. C2×#65267C2semidirect
42. #65519C22semidirect
43. #65518C22semidirect
60. #65273C22semidirect
61. #65273C22semidirect
62. #65271C22semidirect
63. #65267C22semidirect
64. #65267C22semidirect
65. #65262C22semidirect
90. C23×Dic5Q8semidirect
238. C22×Dic5C2×Q8semidirect
615. C2×C5#2438semidirect
705. C5C2×#2438semidirect
743. C2#10614493direct (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×#40232
C2×#655182
C2×#655192
C2×#654992
C22×#39632
#106144932
C2×#652712
C2×#652732
C2×#652622
C2×#652672
C2×#652392
C2×#652322
C2×#652312
C2×#24385