Finite Group Databasebeta

← C2×#10614813 #12266921

Subgroups — C2×#10614813 #12266921

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
1C22×C5×#126C211yesmaximal, characteristic, complemented
2C22×D5×C4⋊C4C211yesmaximal, characteristic, complemented
3#10614813C2116yesmaximal, direct product factor
4C2×#65278C211yesmaximal, characteristic, complemented
5C2×#65276C211yesmaximal, characteristic, complemented
6C2×#65271C211yesmaximal, characteristic, complemented
7C2×#65275C211yesmaximal, characteristic, complemented
8C2×#65270C211yesmaximal, characteristic, complemented
9C2×#65245C211yesmaximal, characteristic
10C2×#65245C211yesmaximal, characteristic
11C2×#65245C211yesmaximal, characteristic
12C2×#65242C211yesmaximal, characteristic, complemented
13C2×#65237C211yesmaximal, characteristic, complemented
14C2×#65234C211yesmaximal, characteristic, complemented
15C2×#65222C211yesmaximal, characteristic, complemented
16C2×C4×#685C211yesmaximal, characteristic, complemented
17C23×C22⋊D5C2211yescharacteristic
18C23×C4×D5C2211yescharacteristic
19C23×C4×D5C2211yescharacteristic
20C23×C4×D5C2211yescharacteristic
21C2×C5×#126—28no—
22C2×C5×#126C2218yescomplemented
23C22×C5×C4⋊C4C2211yescharacteristic
24C22×C5×C4⋊C4C2211yescharacteristic
25C22×C5×C4⋊C4C2211yescharacteristic
26C22×C5×C22⋊C4C2211yescharacteristic
27C22×C5×C22⋊C4C2211yescharacteristic
28C22×C5×C22⋊C4C2211yescharacteristic
29C22×C42×C5C2211yescharacteristic
30C22×C22⋊Dic5C2211yescharacteristic
31C22×C22⋊Dic5C2211yescharacteristic
32C22×C22⋊Dic5C2211yescharacteristic
33C22×#685C2211yescharacteristic
34C22×#685C2211yescharacteristic
35C22×#685C2211yescharacteristic
36C22×C4⋊Dic5C2211yescharacteristic
37C22×C4⋊Dic5C2211yescharacteristic
38C22×#683C2211yescharacteristic
39C22×#683C2211yescharacteristic
40C22×#683C2211yescharacteristic
41C22×C4×Dic5C2211yescharacteristic
42C2×D5×C4⋊C4—28no—
43C2×D5×C4⋊C4C2218yescomplemented
44C2×#3963C2211yescharacteristic
45C2×#3963C2211yescharacteristic
46C2×#3963C2211yescharacteristic
47C2×#3963C2211yescharacteristic
48C2×#3963C2211yescharacteristic
49C2×#3963C2211yescharacteristic
50C2×#3963C2211yescharacteristic
51C2×#3963C2211yescharacteristic
52C2×#3963C2211yescharacteristic
53C2×#3963C2211yescharacteristic
54C2×#3963C2211yescharacteristic
55C2×#3963C2211yescharacteristic
56#65278C2218yescomplemented
57#65276C2218yescomplemented
58#65275C2218yescomplemented
59#65271C2218yescomplemented
60#65270C2218yescomplemented
61#65245C2218yes—
62#65245C2218yes—
63#65245C2218yes—
64#65242C2218yescomplemented
65#65237C2218yescomplemented
66#65234C2218yescomplemented
67C4×#685C2218yescomplemented
68#65222C2218yescomplemented
69C2×#2481—51nomaximal, Sylow
70C25×C5C2311yescharacteristic
71C24×D5C2311yescharacteristic
72C23×C4×C5C2311yescharacteristic
73C23×C4×C5C2311yescharacteristic
74C23×C4×C5C2311yescharacteristic
75C23×C4×C5C2311yescharacteristic
76C23×C4×C5C2311yescharacteristic
77C23×C4×C5C2311yescharacteristic
78C22×C22⋊D5—24no—
79C22×C22⋊D5—24no—
80C22×C22⋊D5—24no—
81C22×C22⋊D5C2314yes—
82C23×Dic5C2311yescharacteristic
83C23×Dic5C2311yescharacteristic
84C23×Dic5C2311yescharacteristic
85C23×Dic5C2311yescharacteristic
86C23×Dic5C2311yescharacteristic
87C23×Dic5C2311yescharacteristic
88C23×Dic5C2311yescharacteristic
89C22×C4×D5—24no—
90C22×C4×D5—24no—
91C22×C4×D5—24no—
92C22×C4×D5—24no—
93C22×C4×D5—24no—
94C22×C4×D5—24no—
95C22×C4×D5—24no—
96C22×C4×D5—42no—
97C22×C4×D5—42no—
98C22×C4×D5C2314yes—
99C22×C4×D5C2314yes—
100C22×C4×D5C2314yes—
101C5×#126—232no—
102C2×C5×C4⋊C4—24no—
103C2×C5×C4⋊C4—24no—
104C2×C5×C4⋊C4D418yescomplemented
105C2×C5×C4⋊C4C2314yes—
106C2×C5×C4⋊C4C2314yes—
107C2×C5×C4⋊C4C2314yes—
108C2×C5×C22⋊C4—24no—
109C2×C5×C22⋊C4—24no—
110C2×C5×C22⋊C4—24no—
111C2×C5×C22⋊C4C2314yes—
112C2×C5×C22⋊C4C2314yes—
113C2×C5×C22⋊C4C2314yes—
114C2×C42×C5—24no—
115C2×C42×C5C2314yes—
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×#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×#683—24no—
135C2×#683C2314yes—
136C2×#683C2314yes—
137C2×#683C2314yes—
138C2×C4×Dic5—42no—
139C2×C4×Dic5C2314yes—
140D5×C4⋊C4—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×#126D511yescharacteristic, complemented
154C23×C4⋊C4—51no—
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—22no—
174C24×C5—22no—
175C24×C5—22no—
176C24×C5C2412yes—
177C24×C5C2411yescharacteristic
178C23×D5—22no—
179C23×D5—22no—
180C23×D5—22no—
181C23×D5—22no—
182C23×D5#4114yes—
183C23×D5#4114yes—
184C23×D5#4114yes—
185C23×D5C2412yes—
186C22×C4×C5—22no—
187C22×C4×C5—22no—
188C22×C4×C5—22no—
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—22no—
197C22×C4×C5—22no—
198C22×C4×C5—22no—
199C22×C4×C5—22no—
200C22×C4×C5—22no—
201C22×C4×C5C2×D414yes—
202C22×C4×C5C2×D414yes—
203C22×C4×C5C2×D414yes—
204C22×C4×C5C2412yes—
205C22×C4×C5C2412yes—
206C22×C4×C5C2412yes—
207C22×C4×C5C2412yes—
208C22×C4×C5C2412yes—
209C22×C4×C5C2412yes—
210C2×C22⋊D5—28no—
211C2×C22⋊D5—28no—
212C2×C22⋊D5—28no—
213C2×C22⋊D5—416no—
214C22×Dic5—22no—
215C22×Dic5—22no—
216C22×Dic5—22no—
217C22×Dic5—22no—
218C22×Dic5—22no—
219C22×Dic5—22no—
220C22×Dic5—22no—
221C22×Dic5—22no—
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—22no—
234C22×Dic5#4114yes—
235C22×Dic5C2412yes—
236C22×Dic5C2412yes—
237C22×Dic5C2412yes—
238C22×Dic5C2412yes—
239C22×Dic5C2412yes—
240C22×Dic5C2412yes—
241C22×Dic5C2412yes—
242C2×C4×D5—232no—
243C2×C4×D5—28no—
244C2×C4×D5—28no—
245C2×C4×D5—28no—
246C2×C4×D5—28no—
247C2×C4×D5—28no—
248C2×C4×D5—28no—
249C2×C4×D5—28no—
250C2×C4×D5—44no—
251C2×C4×D5—44no—
252C2×C4×D5—416no—
253C2×C4×D5—416no—
254C5×C4⋊C4—28no—
255C5×C4⋊C4—28no—
256C5×C4⋊C4C2×D4116yescomplemented
257C5×C22⋊C4—28no—
258C5×C22⋊C4—28no—
259C5×C22⋊C4—28no—
260C42×C5—28no—
261C22⋊Dic5—28no—
262C22⋊Dic5—44no—
263C22⋊Dic5—44no—
264#685—28no—
265#685—28no—
266#685—28no—
267C4⋊Dic5—28no—
268C4⋊Dic5—44no—
269#683—28no—
270#683—28no—
271#683—28no—
272C4×Dic5—44no—
273C23×D4—51no—
274C24×C4—51no—
275C24×C4—51no—
276C24×C4—51no—
277C2×#126—28no—
278C2×#126C2×D518yescomplemented
279C22×C4⋊C4—51no—
280C22×C4⋊C4—51no—
281C22×C4⋊C4—51no—
282C22×C4⋊C4—51no—
283C22×C4⋊C4—51no—
284C22×C4⋊C4—58no—
285C22×C4⋊C4—108no—
286C22×C4⋊C4C2×D511yescharacteristic
287C22×C4⋊C4C2×D511yescharacteristic
288C22×C4⋊C4C2×D511yescharacteristic
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⋊C4C2×D511yescharacteristic
296C22×C22⋊C4C2×D511yescharacteristic
297C22×C22⋊C4C2×D511yescharacteristic
298C22×C42—51no—
299C22×C42C2×D511yescharacteristic
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—22no—
326C23×C5—22no—
327C23×C5—22no—
328C23×C5—22no—
329C23×C5—22no—
330C23×C5—22no—
331C23×C5—22no—
332C23×C5—44no—
333C23×C5—44no—
334C23×C5—44no—
335C23×C5—44no—
336C23×C5—44no—
337C23×C5—44no—
338C23×C5—44no—
339C23×C5C22×D412yes—
340C23×C5C2×#4112yes—
341C23×C5C2×#4112yes—
342C23×C5C2×#4112yes—
343C23×C5C2×#4112yes—
344C23×C5H(5,𝔽2)12yes—
345C23×C52−1+412yes—
346C23×C5C2511yescharacteristic
347C22×D5—28no—
348C22×D5—28no—
349C22×D5—28no—
350C22×D5—28no—
351C22×D5—28no—
352C22×D5—28no—
353C22×D5—22no—
354C22×D5—22no—
355C22×D5—22no—
356C22×D5—22no—
357C22×D5#126116yescomplemented
358C22×D5C2×#4114yes—
359C22×D5C2×#4114yes—
360C22×D5C2×#4114yes—
361C2×C4×C5—28no—
362C2×C4×C5—28no—
363C2×C4×C5—28no—
364C2×C4×C5—22no—
365C2×C4×C5—22no—
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—44no—
380C2×C4×C5—44no—
381C2×C4×C5—44no—
382C2×C4×C5C22×D414yes—
383C2×C4×C5C22×D414yes—
384C2×C4×C5C22×D414yes—
385C22⋊D5—416no—
386C2×Dic5—28no—
387C2×Dic5—22no—
388C2×Dic5—22no—
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—44no—
408C2×Dic5—44no—
409C2×Dic5—44no—
410C2×Dic5—44no—
411C2×Dic5—44no—
412C2×Dic5—44no—
413C2×Dic5C2×#4114yes—
414C4×D5—232no—
415C4×D5—416no—
416C4×D5—416no—
417C25—51no—
418C25C22×D511yescharacteristic
419C22×D4—54no—
420C22×D4—104no—
421C22×D4—104no—
422C22×D4—104no—
423C23×C4—51no—
424C23×C4—51no—
425C23×C4—51no—
426C23×C4—51no—
427C23×C4—51no—
428C23×C4—51no—
429C23×C4—51no—
430C23×C4—54no—
431C23×C4—54no—
432C23×C4—54no—
433C23×C4—104no—
434C23×C4—104no—
435C23×C4—104no—
436C23×C4—104no—
437C23×C4—104no—
438C23×C4—104no—
439C23×C4—104no—
440C23×C4—202no—
441C23×C4—202no—
442C23×C4C22×D511yescharacteristic
443C23×C4C22×D511yescharacteristic
444C23×C4C22×D511yescharacteristic
445C23×C4C22×D511yescharacteristic
446C23×C4C22×D511yescharacteristic
447C23×C4C22×D511yescharacteristic
448#126—232no—
449C2×C4⋊C4—24no—
450C2×C4⋊C4—24no—
451C2×C4⋊C4—54no—
452C2×C4⋊C4—54no—
453C2×C4⋊C4—54no—
454C2×C4⋊C4—54no—
455C2×C4⋊C4—54no—
456C2×C4⋊C4—104no—
457C2×C4⋊C4—104no—
458C2×C4⋊C4—104no—
459C2×C4⋊C4—104no—
460C2×C4⋊C4—1032no—
461C2×C4⋊C4—202no—
462C2×C4⋊C4C22⋊D518yescomplemented
463C2×C4⋊C4C22×D514yes—
464C2×C4⋊C4C22×D514yes—
465C2×C4⋊C4C22×D514yes—
466C2×C22⋊C4—24no—
467C2×C22⋊C4—24no—
468C2×C22⋊C4—24no—
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—202no—
480C2×C22⋊C4—202no—
481C2×C22⋊C4C22×D514yes—
482C2×C22⋊C4C22×D514yes—
483C2×C22⋊C4C22×D514yes—
484C2×C42—24no—
485C2×C42—54no—
486C2×C42—202no—
487C2×C42C22×D514yes—
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—42no—
501C22×C5—42no—
502C22×C5—42no—
503C22×C5—42no—
504C22×C5—42no—
505C22×C5—42no—
506C22×C5—42no—
507C22×C5—88no—
508C22×C5#52514yes—
509C22×C5C2×#12614yes—
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—24no—
523C2×D5—24no—
524C2×D5—24no—
525C2×D5—24no—
526C2×D5—24no—
527C2×D5—24no—
528C2×D5—232no—
529C2×D5C2×#12618yescomplemented
530C4×C5—24no—
531C4×C5—24no—
532C4×C5—24no—
533C4×C5—42no—
534C4×C5—42no—
535C4×C5—42no—
536Dic5—24no—
537Dic5—42no—
538Dic5—42no—
539Dic5—42no—
540Dic5—42no—
541Dic5—42no—
542Dic5—42no—
543C24—22no—
544C24—22no—
545C24—22no—
546C24—22no—
547C24—22no—
548C24—22no—
549C24—22no—
550C24—54no—
551C24—54no—
552C24—54no—
553C24—52no—
554C24—102no—
555C24—102no—
556C24—102no—
557C24—102no—
558C24C23×D512yes—
559C24C23×D511yescharacteristic
560C2×D4—108no—
561C2×D4—108no—
562C2×D4—108no—
563C2×D4—2016no—
564C22×C4—22no—
565C22×C4—22no—
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—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—54no—
580C22×C4—52no—
581C22×C4—52no—
582C22×C4—52no—
583C22×C4—52no—
584C22×C4—52no—
585C22×C4—52no—
586C22×C4—52no—
587C22×C4—108no—
588C22×C4—108no—
589C22×C4—1032no—
590C22×C4—108no—
591C22×C4—108no—
592C22×C4—102no—
593C22×C4—102no—
594C22×C4—108no—
595C22×C4—102no—
596C22×C4—102no—
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—108no—
614C22×C4—108no—
615C22×C4—204no—
616C22×C4—204no—
617C22×C4—2016no—
618C22×C4—2016no—
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—108no—
631C4⋊C4—108no—
632C4⋊C4—108no—
633C4⋊C4—108no—
634C4⋊C4—204no—
635C4⋊C4C2×C22⋊D5116yescomplemented
636C22⋊C4—28no—
637C22⋊C4—28no—
638C22⋊C4—28no—
639C22⋊C4—108no—
640C22⋊C4—108no—
641C22⋊C4—108no—
642C22⋊C4—108no—
643C22⋊C4—204no—
644C22⋊C4—204no—
645C42—28no—
646C42—204no—
647C2×C5—82no—
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—28no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—22no—
664C23—44no—
665C23—44no—
666C23—44no—
667C23—44no—
668C23—44no—
669C23—44no—
670C23—44no—
671C23—54no—
672C23—54no—
673C23—54no—
674C23—516no—
675C23—108no—
676C23—108no—
677C23—108no—
678C23—102no—
679C23—102no—
680C23—102no—
681C23—102no—
682C23—108no—
683C23—108no—
684C23—108no—
685C23D5×#4112yes—
686C23D5×#4112yes—
687C23D5×#4112yes—
688C23D5×#4112yes—
689C23#414912yes—
690C23#415012yes—
691C23C22×C22⋊D512yes—
692C23C24×D511yescharacteristic
693D4—2016no—
694C2×C4—28no—
695C2×C4—28no—
696C2×C4—28no—
697C2×C4—22no—
698C2×C4—22no—
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—44no—
713C2×C4—44no—
714C2×C4—44no—
715C2×C4—54no—
716C2×C4—1032no—
717C2×C4—108no—
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—2016no—
739C2×C4—2016no—
740C2×C4—204no—
741C2×C4—204no—
742C2×C4—204no—
743C2×C4—204no—
744C2×C4—204no—
745C2×C4—204no—
746C2×C4C22×C22⋊D514yes—
747C2×C4C22×C22⋊D514yes—
748C2×C4C22×C22⋊D514yes—
749C5C2×#248111yescharacteristic, complemented, Sylow
750C22—42no—
751C22—42no—
752C22—42no—
753C22—42no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—58no—
758C22—88no—
759C22—1032no—
760C22—104no—
761C22—104no—
762C22—104no—
763C22—104no—
764C22—104no—
765C22—104no—
766C22D5×#12614yes—
767C22#6604114yes—
768C22#6604214yes—
769C22#6604314yes—
770C22#6616214yes—
771C22#6616314yes—
772C22#6616514yes—
773C22C2×D5×#4111yescharacteristic
774C22C2×D5×#4111yescharacteristic
775C22C2×D5×#4111yescharacteristic
776C22C2×D5×#4111yescharacteristic
777C22C2×#414911yescharacteristic
778C22C2×#415011yescharacteristic
779C22C23×C22⋊D511yescharacteristic
780C4—24no—
781C4—24no—
782C4—24no—
783C4—42no—
784C4—42no—
785C4—42no—
786C4—104no—
787C4—202no—
788C4—202no—
789C4—202no—
790C4—202no—
791C4—202no—
792C4—202no—
793C2—82no—
794C2—108no—
795C2#1061481318yesdirect product factor
796C2C2×#6604311yescharacteristic
797C2C2×D5×#12611yescharacteristic
798C2C2×#6604111yescharacteristic
799C2C2×#6604211yescharacteristic
800C2C2×#6616211yescharacteristic
801C2C2×#6616311yescharacteristic
802C2C2×#6616511yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC22×C5×#126C2
socleC24×C5C24
prime radicalC23×C22⋊D5C22
hypercenterC22×#126D5
hypocenterC5C2×#2481
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
2. C22×D5×C4⋊C4C2semidirect
3. #10614813C2direct (N × H)
4. C2×#65278C2semidirect
5. C2×#65276C2semidirect
6. C2×#65271C2semidirect
7. C2×#65275C2semidirect
8. C2×#65270C2semidirect
12. C2×#65242C2semidirect
13. C2×#65237C2semidirect
14. C2×#65234C2semidirect
15. C2×#65222C2semidirect
16. C2×C4×#685C2semidirect
22. C2×C5×#126C22semidirect
43. C2×D5×C4⋊C4C22semidirect
56. #65278C22semidirect
57. #65276C22semidirect
58. #65275C22semidirect
59. #65271C22semidirect
60. #65270C22semidirect
64. #65242C22semidirect
65. #65237C22semidirect
66. #65234C22semidirect
67. C4×#685C22semidirect
68. #65222C22semidirect
104. C2×C5×C4⋊C4D4semidirect
153. C22×#126D5semidirect
256. C5×C4⋊C4C2×D4semidirect
278. C2×#126C2×D5semidirect
357. C22×D5#126semidirect
462. C2×C4⋊C4C22⋊D5semidirect
529. C2×D5C2×#126semidirect
635. C4⋊C4C2×C22⋊D5semidirect
648. C2×C5#2481semidirect
749. C5C2×#2481semidirect
795. C2#10614813direct (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×C4⋊C42
#106148132
C2×#652782
C2×#652762
C2×#652712
C2×#652752
C2×#652702
C2×#652452
C2×#652422
C2×#652372
C2×#652342
C2×#652222
C2×C4×#6852
C2×#24815