Finite Group Databasebeta

← C2×#10613906 #12266922

Subgroups — C2×#10613906 #12266922

Order 1280.

3114 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C5×C4⋊C4C211yesmaximal, characteristic, complemented
2C22×#4044C211yesmaximal, characteristic, complemented
3C2×#65502C211yesmaximal, characteristic
4C2×#65502C211yesmaximal, characteristic
5C2×#65502C211yesmaximal, characteristic
6C2×#65499C211yesmaximal, characteristic, complemented
7C2×#65501C211yesmaximal, characteristic, complemented
8C2×C4×C22⋊Dic5C211yesmaximal, characteristic, complemented
9C2×#65282C211yesmaximal, characteristic, complemented
10C2×#65283C211yesmaximal, characteristic, complemented
11#10613906C2116yesmaximal, direct product factor
12C2×#65271C211yesmaximal, characteristic, complemented
13C2×#65275C211yesmaximal, characteristic, complemented
14C2×#65279C211yesmaximal, characteristic, complemented
15C2×#65267C211yesmaximal, characteristic, complemented
16C2×#65270C211yesmaximal, characteristic, complemented
17C24×C4×C5C2211yescharacteristic
18C24×C4×C5C2211yescharacteristic
19C24×C4×C5C2211yescharacteristic
20C23×C22⋊D5C2211yescharacteristic
21C22×C5×C4⋊C4—28no—
22C22×C5×C4⋊C4C2211yescharacteristic
23C22×C5×C4⋊C4C2211yescharacteristic
24C22×C5×C4⋊C4C2211yescharacteristic
25C22×C5×C4⋊C4C2211yescharacteristic
26C22×C5×C4⋊C4C2218yescomplemented
27C22×C22⋊Dic5C2211yescharacteristic
28C22×C22⋊Dic5C2211yescharacteristic
29C22×C22⋊Dic5C2211yescharacteristic
30C22×#685C2211yescharacteristic
31C22×#685C2211yescharacteristic
32C22×#685C2211yescharacteristic
33C22×#685C2211yescharacteristic
34C22×#685C2211yescharacteristic
35C22×#685C2211yescharacteristic
36C22×C4⋊Dic5C2211yescharacteristic
37C22×C4⋊Dic5C2211yescharacteristic
38C22×#683C2211yescharacteristic
39C22×#683C2211yescharacteristic
40C22×C4×Dic5C2211yescharacteristic
41C22×C4×Dic5C2211yescharacteristic
42C2×#4044—28no—
43C2×#4044C2218yescomplemented
44#65502C2218yes—
45#65502C2218yes—
46#65502C2218yes—
47#65501C2218yescomplemented
48#65499C2218yescomplemented
49C4×C22⋊Dic5C2218yescomplemented
50C2×#3963C2211yescharacteristic
51C2×#3963C2211yescharacteristic
52C2×#3963C2211yescharacteristic
53C2×#3963C2211yescharacteristic
54C2×#3963C2211yescharacteristic
55C2×#3963C2211yescharacteristic
56C2×#3963C2211yescharacteristic
57C2×#3963C2211yescharacteristic
58C2×#3963C2211yescharacteristic
59C2×#3963C2211yescharacteristic
60C2×#3963C2211yescharacteristic
61C2×#3963C2211yescharacteristic
62#65283C2218yescomplemented
63#65282C2218yescomplemented
64#65279C2218yescomplemented
65#65275C2218yescomplemented
66#65271C2218yescomplemented
67#65270C2218yescomplemented
68#65267C2218yescomplemented
69C2×#2481—51nomaximal, Sylow
70C25×C5C2311yescharacteristic
71C24×D5C2311yescharacteristic
72C23×C4×C5—24no—
73C23×C4×C5—24no—
74C23×C4×C5—24no—
75C23×C4×C5—24no—
76C23×C4×C5—24no—
77C23×C4×C5—24no—
78C23×C4×C5—24no—
79C23×C4×C5—42no—
80C23×C4×C5—42no—
81C23×C4×C5C2311yescharacteristic
82C23×C4×C5C2311yescharacteristic
83C23×C4×C5C2314yes—
84C23×C4×C5C2314yes—
85C23×C4×C5C2314yes—
86C23×C4×C5C2311yescharacteristic
87C23×C4×C5C2311yescharacteristic
88C23×C4×C5C2311yescharacteristic
89C23×C4×C5C2311yescharacteristic
90C22×C22⋊D5—24no—
91C22×C22⋊D5—24no—
92C22×C22⋊D5—24no—
93C22×C22⋊D5C2314yes—
94C23×Dic5C2311yescharacteristic
95C23×Dic5C2311yescharacteristic
96C23×Dic5C2311yescharacteristic
97C23×Dic5C2311yescharacteristic
98C23×Dic5C2311yescharacteristic
99C23×Dic5C2311yescharacteristic
100C23×Dic5C2311yescharacteristic
101C2×C5×C4⋊C4—24no—
102C2×C5×C4⋊C4—24no—
103C2×C5×C4⋊C4—24no—
104C2×C5×C4⋊C4—232no—
105C2×C5×C4⋊C4D418yescomplemented
106C2×C5×C4⋊C4C2314yes—
107C2×C5×C4⋊C4C2314yes—
108C2×C5×C4⋊C4C2314yes—
109C2×C5×C4⋊C4C2314yes—
110C2×C22⋊Dic5—24no—
111C2×C22⋊Dic5—24no—
112C2×C22⋊Dic5—24no—
113C2×C22⋊Dic5C2314yes—
114C2×C22⋊Dic5C2314yes—
115C2×C22⋊Dic5C2314yes—
116C2×#685—24no—
117C2×#685—24no—
118C2×#685—24no—
119C2×#685—24no—
120C2×#685—42no—
121C2×#685—42no—
122C2×#685C2314yes—
123C2×#685C2314yes—
124C2×#685C2314yes—
125C2×#685C2314yes—
126C2×#685C2314yes—
127C2×#685C2314yes—
128C2×C4⋊Dic5—24no—
129C2×C4⋊Dic5—42no—
130C2×C4⋊Dic5C2314yes—
131C2×C4⋊Dic5C2314yes—
132C2×#683—24no—
133C2×#683—24no—
134C2×#683C2314yes—
135C2×#683C2314yes—
136C2×C4×Dic5—24no—
137C2×C4×Dic5—42no—
138C2×C4×Dic5C2314yes—
139C2×C4×Dic5C2314yes—
140#4044—232no—
141#3963C2314yes—
142#3963C2314yes—
143#3963C2314yes—
144#3963C2314yes—
145#3963C2314yes—
146#3963C2314yes—
147#3963C2314yes—
148#3963C2314yes—
149#3963C2314yes—
150#3963C2314yes—
151#3963C2314yes—
152#3963C2314yes—
153C22×#126—51no—
154C23×C4⋊C4D511yescharacteristic, complemented
155#2481—516no—
156C2×#400—51no—
157C2×#400—51no—
158C2×#397—51no—
159C2×#396—51no—
160C2×#388—51no—
161C2×#387—51no—
162C2×#387—51no—
163C2×#386—51no—
164C2×#386—51no—
165C2×#386—51no—
166C2×#385—51no—
167C2×#380—51no—
168C2×C4×C22⋊C4—51no—
169C24×C5—22no—
170C24×C5—22no—
171C24×C5—22no—
172C24×C5—22no—
173C24×C5#4114yes—
174C24×C5#4114yes—
175C24×C5#4114yes—
176C24×C5C2412yes—
177C24×C5C2411yescharacteristic
178C23×D5—22no—
179C23×D5—22no—
180C23×D5—22no—
181C23×D5—22no—
182C23×D5—22no—
183C23×D5—22no—
184C23×D5—22no—
185C23×D5C2412yes—
186C22×C4×C5—232no—
187C22×C4×C5—22no—
188C22×C4×C5—28no—
189C22×C4×C5—22no—
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—28no—
198C22×C4×C5—22no—
199C22×C4×C5—22no—
200C22×C4×C5—28no—
201C22×C4×C5—28no—
202C22×C4×C5—22no—
203C22×C4×C5—22no—
204C22×C4×C5—22no—
205C22×C4×C5—22no—
206C22×C4×C5—28no—
207C22×C4×C5—28no—
208C22×C4×C5—44no—
209C22×C4×C5—44no—
210C22×C4×C5—416no—
211C22×C4×C5—416no—
212C22×C4×C5C2×D414yes—
213C22×C4×C5C2×D414yes—
214C22×C4×C5C2×D414yes—
215C22×C4×C5#4114yes—
216C22×C4×C5C2412yes—
217C22×C4×C5C2412yes—
218C22×C4×C5C2412yes—
219C22×C4×C5C2412yes—
220C22×C4×C5C2412yes—
221C22×C4×C5C2412yes—
222C2×C22⋊D5—28no—
223C2×C22⋊D5—28no—
224C2×C22⋊D5—28no—
225C2×C22⋊D5—416no—
226C22×Dic5—22no—
227C22×Dic5—22no—
228C22×Dic5—22no—
229C22×Dic5—22no—
230C22×Dic5—22no—
231C22×Dic5—22no—
232C22×Dic5—22no—
233C22×Dic5—22no—
234C22×Dic5—22no—
235C22×Dic5—22no—
236C22×Dic5—22no—
237C22×Dic5—22no—
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×Dic5C2412yes—
248C22×Dic5C2412yes—
249C22×Dic5C2412yes—
250C22×Dic5C2412yes—
251C22×Dic5C2412yes—
252C22×Dic5C2412yes—
253C22×Dic5C2412yes—
254C5×C4⋊C4—28no—
255C5×C4⋊C4—28no—
256C5×C4⋊C4—28no—
257C5×C4⋊C4C2×D4116yescomplemented
258C22⋊Dic5—28no—
259C22⋊Dic5—28no—
260C22⋊Dic5—28no—
261#685—28no—
262#685—28no—
263#685—28no—
264#685—28no—
265#685—44no—
266#685—44no—
267C4⋊Dic5—28no—
268C4⋊Dic5—44no—
269#683—28no—
270#683—28no—
271C4×Dic5—28no—
272C4×Dic5—44no—
273C23×D4—51no—
274C24×C4C2×D511yescharacteristic
275C24×C4C2×D511yescharacteristic
276C24×C4C2×D511yescharacteristic
277C2×#126—58no—
278C2×#126—108no—
279C22×C4⋊C4—28no—
280C22×C4⋊C4—51no—
281C22×C4⋊C4—51no—
282C22×C4⋊C4—51no—
283C22×C4⋊C4—51no—
284C22×C4⋊C4C2×D511yescharacteristic
285C22×C4⋊C4C2×D511yescharacteristic
286C22×C4⋊C4C2×D511yescharacteristic
287C22×C4⋊C4C2×D511yescharacteristic
288C22×C4⋊C4C2×D518yescomplemented
289C22×C22⋊C4—51no—
290C22×C22⋊C4—51no—
291C22×C22⋊C4—51no—
292C22×C22⋊C4—51no—
293C22×C22⋊C4—51no—
294C22×C22⋊C4—51no—
295C22×C22⋊C4—51no—
296C22×C22⋊C4—51no—
297C22×C22⋊C4—51no—
298C22×C42—51no—
299C22×C42—51no—
300#400—58no—
301#400—58no—
302#397—58no—
303#396—58no—
304#388—58no—
305#387—58no—
306#387—58no—
307#386—58no—
308#386—58no—
309#386—58no—
310#385—58no—
311#380—58no—
312C4×C22⋊C4—58no—
313C2×#95—51no—
314C2×#95—51no—
315C2×#95—51no—
316C2×#95—51no—
317C2×#95—51no—
318C2×#95—51no—
319C2×#95—51no—
320C2×#95—51no—
321C2×#95—51no—
322C2×#95—51no—
323C2×#95—51no—
324C2×#95—51no—
325C23×C5—28no—
326C23×C5—28no—
327C23×C5—28no—
328C23×C5—28no—
329C23×C5—28no—
330C23×C5—28no—
331C23×C5—22no—
332C23×C5—22no—
333C23×C5—22no—
334C23×C5—22no—
335C23×C5#126116yescomplemented
336C23×C5C22×D412yes—
337C23×C5C2×#4114yes—
338C23×C5C2×#4112yes—
339C23×C5C2×#4112yes—
340C23×C5C2×#4114yes—
341C23×C5C2×#4112yes—
342C23×C5C2×#4114yes—
343C23×C5C2×#4112yes—
344C23×C5H(5,𝔽2)12yes—
345C23×C52−1+412yes—
346C23×C5C2511yescharacteristic
347C22×D5—22no—
348C22×D5—22no—
349C22×D5—22no—
350C22×D5—22no—
351C22×D5—22no—
352C22×D5—22no—
353C22×D5—22no—
354C22×D5—44no—
355C22×D5—44no—
356C22×D5—44no—
357C22×D5—44no—
358C22×D5—44no—
359C22×D5—44no—
360C22×D5—44no—
361C2×C4×C5—232no—
362C2×C4×C5—28no—
363C2×C4×C5—28no—
364C2×C4×C5—28no—
365C2×C4×C5—28no—
366C2×C4×C5—22no—
367C2×C4×C5—22no—
368C2×C4×C5—22no—
369C2×C4×C5—22no—
370C2×C4×C5—22no—
371C2×C4×C5—22no—
372C2×C4×C5—22no—
373C2×C4×C5—22no—
374C2×C4×C5—22no—
375C2×C4×C5—22no—
376C2×C4×C5—22no—
377C2×C4×C5—22no—
378C2×C4×C5—22no—
379C2×C4×C5—22no—
380C2×C4×C5—416no—
381C2×C4×C5—416no—
382C2×C4×C5—44no—
383C2×C4×C5—44no—
384C2×C4×C5C22×D414yes—
385C2×C4×C5C22×D414yes—
386C2×C4×C5C22×D414yes—
387C2×C4×C5C2×#4114yes—
388C22⋊D5—416no—
389C2×Dic5—22no—
390C2×Dic5—22no—
391C2×Dic5—22no—
392C2×Dic5—22no—
393C2×Dic5—22no—
394C2×Dic5—22no—
395C2×Dic5—22no—
396C2×Dic5—22no—
397C2×Dic5—22no—
398C2×Dic5—22no—
399C2×Dic5—22no—
400C2×Dic5—22no—
401C2×Dic5—22no—
402C2×Dic5—22no—
403C2×Dic5—22no—
404C2×Dic5—22no—
405C2×Dic5—22no—
406C2×Dic5—22no—
407C2×Dic5—22no—
408C2×Dic5—22no—
409C2×Dic5—22no—
410C2×Dic5—44no—
411C2×Dic5—44no—
412C2×Dic5—44no—
413C2×Dic5—44no—
414C2×Dic5—44no—
415C2×Dic5—44no—
416C2×Dic5—44no—
417C25—51no—
418C25C22×D511yescharacteristic
419C22×D4—54no—
420C22×D4—104no—
421C22×D4—104no—
422C22×D4—104no—
423C23×C4—24no—
424C23×C4—24no—
425C23×C4—24no—
426C23×C4—24no—
427C23×C4—24no—
428C23×C4—24no—
429C23×C4—24no—
430C23×C4—42no—
431C23×C4—42no—
432C23×C4—51no—
433C23×C4—51no—
434C23×C4—51no—
435C23×C4—51no—
436C23×C4—51no—
437C23×C4—51no—
438C23×C4—51no—
439C23×C4C22×D514yes—
440C23×C4C22×D511yescharacteristic
441C23×C4C22×D511yescharacteristic
442C23×C4C22×D514yes—
443C23×C4C22×D514yes—
444C23×C4C22×D511yescharacteristic
445C23×C4C22×D511yescharacteristic
446C23×C4C22×D511yescharacteristic
447C23×C4C22×D511yescharacteristic
448#126—1032no—
449C2×C4⋊C4—24no—
450C2×C4⋊C4—24no—
451C2×C4⋊C4—24no—
452C2×C4⋊C4—232no—
453C2×C4⋊C4—54no—
454C2×C4⋊C4—54no—
455C2×C4⋊C4—54no—
456C2×C4⋊C4—54no—
457C2×C4⋊C4—104no—
458C2×C4⋊C4—104no—
459C2×C4⋊C4—104no—
460C2×C4⋊C4—202no—
461C2×C4⋊C4C22⋊D518yescomplemented
462C2×C4⋊C4C22×D514yes—
463C2×C4⋊C4C22×D514yes—
464C2×C4⋊C4C22×D514yes—
465C2×C4⋊C4C22×D514yes—
466C2×C22⋊C4—54no—
467C2×C22⋊C4—54no—
468C2×C22⋊C4—54no—
469C2×C22⋊C4—54no—
470C2×C22⋊C4—54no—
471C2×C22⋊C4—54no—
472C2×C22⋊C4—54no—
473C2×C22⋊C4—54no—
474C2×C22⋊C4—54no—
475C2×C22⋊C4—104no—
476C2×C22⋊C4—104no—
477C2×C22⋊C4—104no—
478C2×C22⋊C4—104no—
479C2×C22⋊C4—104no—
480C2×C22⋊C4—104no—
481C2×C22⋊C4—104no—
482C2×C22⋊C4—202no—
483C2×C22⋊C4—202no—
484C2×C42—54no—
485C2×C42—54no—
486C2×C42—104no—
487C2×C42—202no—
488#95—54no—
489#95—54no—
490#95—54no—
491#95—54no—
492#95—54no—
493#95—54no—
494#95—54no—
495#95—54no—
496#95—54no—
497#95—54no—
498#95—54no—
499#95—54no—
500C22×C5—24no—
501C22×C5—24no—
502C22×C5—24no—
503C22×C5—24no—
504C22×C5—24no—
505C22×C5—24no—
506C22×C5—232no—
507C22×C5#52514yes—
508C22×C5C2×#12614yes—
509C22×C5C2×#12618yescomplemented
510C22×C5#53914yes—
511C22×C5#54614yes—
512C22×C5#54814yes—
513C22×C5#55214yes—
514C22×C5#55314yes—
515C22×C5C23×D411yescharacteristic
516C22×C5C22×#4111yescharacteristic
517C22×C5C22×#4111yescharacteristic
518C22×C5C22×#4111yescharacteristic
519C22×C5C22×#4111yescharacteristic
520C22×C5C2×H(5,𝔽2)11yescharacteristic
521C22×C5C2×2−1+411yescharacteristic
522C2×D5—42no—
523C2×D5—42no—
524C2×D5—42no—
525C2×D5—42no—
526C2×D5—42no—
527C2×D5—42no—
528C2×D5—42no—
529C2×D5—88no—
530C4×C5—24no—
531C4×C5—24no—
532C4×C5—24no—
533C4×C5—24no—
534C4×C5—42no—
535C4×C5—42no—
536Dic5—42no—
537Dic5—42no—
538Dic5—42no—
539Dic5—42no—
540Dic5—42no—
541Dic5—42no—
542Dic5—42no—
543C24—22no—
544C24—22no—
545C24—22no—
546C24—22no—
547C24—52no—
548C24—102no—
549C24—102no—
550C24—102no—
551C24—102no—
552C24—102no—
553C24—102no—
554C24—102no—
555C24#70914yes—
556C24#71114yes—
557C24#71314yes—
558C24C23×D512yes—
559C24C23×D511yescharacteristic
560C2×D4—108no—
561C2×D4—108no—
562C2×D4—108no—
563C2×D4—2016no—
564C22×C4—232no—
565C22×C4—28no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—28no—
575C22×C4—28no—
576C22×C4—28no—
577C22×C4—28no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—28no—
585C22×C4—28no—
586C22×C4—44no—
587C22×C4—44no—
588C22×C4—416no—
589C22×C4—416no—
590C22×C4—52no—
591C22×C4—52no—
592C22×C4—52no—
593C22×C4—52no—
594C22×C4—52no—
595C22×C4—52no—
596C22×C4—52no—
597C22×C4—102no—
598C22×C4—102no—
599C22×C4—102no—
600C22×C4—102no—
601C22×C4—102no—
602C22×C4—102no—
603C22×C4—102no—
604C22×C4—102no—
605C22×C4—102no—
606C22×C4—102no—
607C22×C4—102no—
608C22×C4—102no—
609C22×C4—102no—
610C22×C4—102no—
611C22×C4—102no—
612C22×C4—102no—
613C22×C4—102no—
614C22×C4—102no—
615C22×C4—102no—
616C22×C4—102no—
617C22×C4—102no—
618C22×C4#70914yes—
619C22×C4C2×C22⋊D514yes—
620C22×C4C2×C22⋊D514yes—
621C22×C4C2×C22⋊D514yes—
622C22×C4C23×D512yes—
623C22×C4C23×D512yes—
624C22×C4C23×D512yes—
625C22×C4C23×D512yes—
626C22×C4C23×D512yes—
627C22×C4C23×D512yes—
628C4⋊C4—28no—
629C4⋊C4—28no—
630C4⋊C4—28no—
631C4⋊C4—108no—
632C4⋊C4—108no—
633C4⋊C4—108no—
634C4⋊C4—204no—
635C4⋊C4C2×C22⋊D5116yescomplemented
636C22⋊C4—108no—
637C22⋊C4—108no—
638C22⋊C4—108no—
639C22⋊C4—108no—
640C22⋊C4—108no—
641C22⋊C4—108no—
642C22⋊C4—108no—
643C22⋊C4—204no—
644C22⋊C4—204no—
645C42—108no—
646C42—204no—
647C2×C5—28no—
648C2×C5#248118yescomplemented
649C2×C5C2×#52511yescharacteristic
650C2×C5C22×#12611yescharacteristic
651C2×C5C2×#53911yescharacteristic
652C2×C5C2×#54611yescharacteristic
653C2×C5C2×#54811yescharacteristic
654C2×C5C2×#55211yescharacteristic
655C2×C5C2×#55311yescharacteristic
656D5—82no—
657C23—28no—
658C23—28no—
659C23—28no—
660C23—28no—
661C23—28no—
662C23—28no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—102no—
668C23—102no—
669C23—102no—
670C23—102no—
671C23—102no—
672C23—102no—
673C23—102no—
674C23—204no—
675C23—204no—
676C23—204no—
677C23—204no—
678C23—204no—
679C23—204no—
680C23—204no—
681C23#4044116yescomplemented
682C23C2×#70914yes—
683C23C2×#70912yes—
684C23C2×#70912yes—
685C23C2×#71114yes—
686C23C2×#71112yes—
687C23#414412yes—
688C23C2×#71314yes—
689C23C2×#71312yes—
690C23#414712yes—
691C23C22×C22⋊D512yes—
692C23C24×D511yescharacteristic
693D4—2016no—
694C2×C4—232no—
695C2×C4—28no—
696C2×C4—28no—
697C2×C4—28no—
698C2×C4—28no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—416no—
714C2×C4—416no—
715C2×C4—44no—
716C2×C4—44no—
717C2×C4—102no—
718C2×C4—102no—
719C2×C4—102no—
720C2×C4—102no—
721C2×C4—102no—
722C2×C4—102no—
723C2×C4—102no—
724C2×C4—102no—
725C2×C4—102no—
726C2×C4—102no—
727C2×C4—102no—
728C2×C4—102no—
729C2×C4—102no—
730C2×C4—102no—
731C2×C4—102no—
732C2×C4—102no—
733C2×C4—102no—
734C2×C4—102no—
735C2×C4—102no—
736C2×C4—102no—
737C2×C4—102no—
738C2×C4—204no—
739C2×C4—204no—
740C2×C4—204no—
741C2×C4—204no—
742C2×C4—204no—
743C2×C4—204no—
744C2×C4—204no—
745C2×C4C2×#70914yes—
746C2×C4C22×C22⋊D514yes—
747C2×C4C22×C22⋊D514yes—
748C2×C4C22×C22⋊D514yes—
749C5C2×#248111yescharacteristic, complemented, Sylow
750C22—24no—
751C22—24no—
752C22—24no—
753C22—24no—
754C22—232no—
755C22—24no—
756C22—24no—
757C22—202no—
758C22—202no—
759C22—202no—
760C22—202no—
761C22—202no—
762C22—202no—
763C22—202no—
764C22—408no—
765C22C2×#404414yes—
766C22C2×#404418yescomplemented
767C22#6584714yes—
768C22#6584814yes—
769C22#6584914yes—
770C22#6612514yes—
771C22#6614014yes—
772C22#6615114yes—
773C22C22×#70911yescharacteristic
774C22C22×#70911yescharacteristic
775C22C22×#71111yescharacteristic
776C22C2×#414411yescharacteristic
777C22C22×#71311yescharacteristic
778C22C2×#414711yescharacteristic
779C22C23×C22⋊D511yescharacteristic
780C4—24no—
781C4—24no—
782C4—24no—
783C4—24no—
784C4—42no—
785C4—42no—
786C4—202no—
787C4—202no—
788C4—202no—
789C4—202no—
790C4—202no—
791C4—202no—
792C4—202no—
793C2—28no—
794C2—402no—
795C2#1061390618yesdirect product factor
796C2C22×#404411yescharacteristic
797C2C2×#6584711yescharacteristic
798C2C2×#6584911yescharacteristic
799C2C2×#6584811yescharacteristic
800C2C2×#6612511yescharacteristic
801C2C2×#6614011yescharacteristic
802C2C2×#6615111yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC23×C5×C4⋊C4C2
socleC24×C5C24
prime radicalC23×C22⋊D5C22
hypercenterC23×C4⋊C4D5
hypocenterC5C2×#2481
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C23×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C23×C5×C4⋊C4C2semidirect
2. C22×#4044C2semidirect
6. C2×#65499C2semidirect
7. C2×#65501C2semidirect
8. C2×C4×C22⋊Dic5C2semidirect
9. C2×#65282C2semidirect
10. C2×#65283C2semidirect
11. #10613906C2direct (N × H)
12. C2×#65271C2semidirect
13. C2×#65275C2semidirect
14. C2×#65279C2semidirect
15. C2×#65267C2semidirect
16. C2×#65270C2semidirect
26. C22×C5×C4⋊C4C22semidirect
43. C2×#4044C22semidirect
47. #65501C22semidirect
48. #65499C22semidirect
49. C4×C22⋊Dic5C22semidirect
62. #65283C22semidirect
63. #65282C22semidirect
64. #65279C22semidirect
65. #65275C22semidirect
66. #65271C22semidirect
67. #65270C22semidirect
68. #65267C22semidirect
105. C2×C5×C4⋊C4D4semidirect
154. C23×C4⋊C4D5semidirect
257. C5×C4⋊C4C2×D4semidirect
288. C22×C4⋊C4C2×D5semidirect
335. C23×C5#126semidirect
461. C2×C4⋊C4C22⋊D5semidirect
509. C22×C5C2×#126semidirect
635. C4⋊C4C2×C22⋊D5semidirect
648. C2×C5#2481semidirect
681. C23#4044semidirect
749. C5C2×#2481semidirect
766. C22C2×#4044semidirect
795. C2#10613906direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C5×C4⋊C42
C22×#40442
C2×#655022
C2×#654992
C2×#655012
C2×C4×C22⋊Dic52
C2×#652822
C2×#652832
#106139062
C2×#652712
C2×#652752
C2×#652792
C2×#652672
C2×#652702
C2×#24815