Finite Group Databasebeta

← C2×#10607574 #12268000

Subgroups — C2×#10607574 #12268000

Order 1280.

3570 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D5×C4⋊C4C211yesmaximal, characteristic, complemented
2C22×#4029C211yesmaximal, characteristic
3C22×#4029C211yesmaximal, characteristic
4C22×#4018C211yesmaximal, characteristic, complemented
5C2×C5×#388C211yesmaximal, characteristic, complemented
6C2×#65261C211yesmaximal, characteristic, complemented
7C2×#65245C211yesmaximal, characteristic
8C2×#65237C211yesmaximal, characteristic, complemented
9C2×#65237C211yesmaximal, characteristic, complemented
10C2×#65234C211yesmaximal, characteristic, complemented
11C2×#65217C211yesmaximal, characteristic, complemented
12#10607574C2116yesmaximal, direct product factor
13C2×#64957C211yesmaximal, characteristic, complemented
14C2×#64953C211yesmaximal, characteristic, complemented
15C2×#64950C211yesmaximal, characteristic, complemented
16C2×#64946C211yesmaximal, characteristic, complemented
17C23×C22⋊D5C2211yescharacteristic
18C23×C4×D5C2211yescharacteristic
19C23×C4×D5C2211yescharacteristic
20C23×C4×D5C2211yescharacteristic
21C22×C5×C4⋊C4C2211yescharacteristic
22C22×C5×C22⋊C4C2211yescharacteristic
23C22×C5×C22⋊C4C2211yescharacteristic
24C22×C5×C22⋊C4C2211yescharacteristic
25C22×C42×C5C2211yescharacteristic
26C22×C22⋊Dic5C2211yescharacteristic
27C22×C22⋊Dic5C2211yescharacteristic
28C22×C22⋊Dic5C2211yescharacteristic
29C22×#685C2211yescharacteristic
30C22×#685C2211yescharacteristic
31C22×#685C2211yescharacteristic
32C22×C4⋊Dic5C2211yescharacteristic
33C22×C4⋊Dic5C2211yescharacteristic
34C22×C4⋊Dic5C2211yescharacteristic
35C22×C4⋊Dic5C2211yescharacteristic
36C22×#683C2211yescharacteristic
37C22×#683C2211yescharacteristic
38C22×#683C2211yescharacteristic
39C22×#683C2211yescharacteristic
40C22×#683C2211yescharacteristic
41C22×#683C2211yescharacteristic
42C22×#683C2211yescharacteristic
43C22×C4×Dic5C2211yescharacteristic
44C2×D5×C4⋊C4—28no—
45C2×D5×C4⋊C4C2218yescomplemented
46C2×#4029—28no—
47C2×#4029—28no—
48C2×#4029C2218yes—
49C2×#4029C2218yes—
50C2×#4018—28no—
51C2×#4018C2218yescomplemented
52C5×#388C2218yescomplemented
53C2×C5×#95C2211yescharacteristic
54C2×C5×#95C2211yescharacteristic
55C2×#3963C2211yescharacteristic
56C2×#3963C2211yescharacteristic
57C2×#3963C2211yescharacteristic
58C2×#3963C2211yescharacteristic
59C2×#3963C2211yescharacteristic
60C2×#3963C2211yescharacteristic
61#65261C2218yescomplemented
62#65245C2218yes—
63#65237C2218yescomplemented
64#65237C2218yescomplemented
65#65234C2218yescomplemented
66#65217C2218yescomplemented
67#64957C2218yescomplemented
68#64953C2218yescomplemented
69#64950C2218yescomplemented
70#64946C2218yescomplemented
71C2×#2413—51nomaximal, Sylow
72C25×C5C2311yescharacteristic
73C24×D5C2311yescharacteristic
74C23×C4×C5C2311yescharacteristic
75C23×C4×C5C2311yescharacteristic
76C23×C4×C5C2311yescharacteristic
77C23×C4×C5C2311yescharacteristic
78C23×C4×C5C2311yescharacteristic
79C23×C4×C5C2311yescharacteristic
80C22×C22⋊D5—24no—
81C22×C22⋊D5—24no—
82C22×C22⋊D5—24no—
83C22×C22⋊D5C2314yes—
84C23×Dic5C2311yescharacteristic
85C23×Dic5C2311yescharacteristic
86C23×Dic5C2311yescharacteristic
87C23×Dic5C2311yescharacteristic
88C23×Dic5C2311yescharacteristic
89C23×Dic5C2311yescharacteristic
90C23×Dic5C2311yescharacteristic
91C22×C4×D5—24no—
92C22×C4×D5—24no—
93C22×C4×D5—24no—
94C22×C4×D5—24no—
95C22×C4×D5—24no—
96C22×C4×D5—24no—
97C22×C4×D5—24no—
98C22×C4×D5—24no—
99C22×C4×D5D418yes—
100C22×C4×D5C2314yes—
101C22×C4×D5C2314yes—
102C22×C4×D5C2314yes—
103C2×C5×C4⋊C4—24no—
104C2×C5×C4⋊C4C2314yes—
105C2×C5×C22⋊C4—24no—
106C2×C5×C22⋊C4—24no—
107C2×C5×C22⋊C4—24no—
108C2×C5×C22⋊C4C2314yes—
109C2×C5×C22⋊C4C2314yes—
110C2×C5×C22⋊C4C2314yes—
111C2×C42×C5—24no—
112C2×C42×C5C2314yes—
113C2×C22⋊Dic5—24no—
114C2×C22⋊Dic5—24no—
115C2×C22⋊Dic5—24no—
116C2×C22⋊Dic5C2314yes—
117C2×C22⋊Dic5C2314yes—
118C2×C22⋊Dic5C2314yes—
119C2×#685—24no—
120C2×#685—24no—
121C2×#685D418yes—
122C2×#685C2314yes—
123C2×#685C2314yes—
124C2×#685C2314yes—
125C2×C4⋊Dic5—24no—
126C2×C4⋊Dic5—24no—
127C2×C4⋊Dic5—24no—
128C2×C4⋊Dic5—24no—
129C2×C4⋊Dic5C2314yes—
130C2×C4⋊Dic5C2314yes—
131C2×C4⋊Dic5C2314yes—
132C2×C4⋊Dic5C2314yes—
133C2×#683—24no—
134C2×#683—24no—
135C2×#683—24no—
136C2×#683—24no—
137C2×#683—24no—
138C2×#683—24no—
139C2×#683—24no—
140C2×#683C2314yes—
141C2×#683C2314yes—
142C2×#683C2314yes—
143C2×#683C2314yes—
144C2×#683C2314yes—
145C2×#683C2314yes—
146C2×#683C2314yes—
147C2×C4×Dic5—24no—
148C2×C4×Dic5C2314yes—
149D5×C4⋊C4—232no—
150#4029—232no—
151#4029—232no—
152#4018—232no—
153C5×#95C2314yes—
154C5×#95C2314yes—
155#3963C2314yes—
156#3963C2314yes—
157#3963C2314yes—
158#3963C2314yes—
159#3963C2314yes—
160#3963C2314yes—
161C22×#123—51no—
162C22×#123—51no—
163C22×#117—51no—
164C23×C4⋊C4—51no—
165#2413—516no—
166C2×#398—51no—
167C2×#398—51no—
168C2×#396—51no—
169C2×#396—51no—
170C2×#389—51no—
171C2×#389—51no—
172C2×#388—51no—
173C2×#388D511yescharacteristic, complemented
174C2×#386—51no—
175C2×#385—51no—
176C2×#381—51no—
177C24×C5—22no—
178C24×C5—22no—
179C24×C5—22no—
180C24×C5—22no—
181C24×C5—22no—
182C24×C5—22no—
183C24×C5—22no—
184C24×C5C2412yes—
185C24×C5C2411yescharacteristic
186C23×D5—22no—
187C23×D5—22no—
188C23×D5—22no—
189C23×D5—22no—
190C23×D5C2×D414yes—
191C23×D5C2×D414yes—
192C23×D5#4114yes—
193C23×D5C2412yes—
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×C5—22no—
202C22×C4×C5—22no—
203C22×C4×C5—22no—
204C22×C4×C5—22no—
205C22×C4×C5—22no—
206C22×C4×C5—22no—
207C22×C4×C5—22no—
208C22×C4×C5—22no—
209C22×C4×C5C2×D414yes—
210C22×C4×C5C2×D414yes—
211C22×C4×C5#4114yes—
212C22×C4×C5C2412yes—
213C22×C4×C5C2412yes—
214C22×C4×C5C2412yes—
215C22×C4×C5C2412yes—
216C22×C4×C5C2412yes—
217C22×C4×C5C2412yes—
218C2×C22⋊D5—28no—
219C2×C22⋊D5—28no—
220C2×C22⋊D5—28no—
221C2×C22⋊D5—416no—
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—22no—
235C22×Dic5—22no—
236C22×Dic5—22no—
237C22×Dic5—22no—
238C22×Dic5—22no—
239C22×Dic5—22no—
240C22×Dic5C2×D414yes—
241C22×Dic5C2×D414yes—
242C22×Dic5#4114yes—
243C22×Dic5C2412yes—
244C22×Dic5C2412yes—
245C22×Dic5C2412yes—
246C22×Dic5C2412yes—
247C22×Dic5C2412yes—
248C22×Dic5C2412yes—
249C22×Dic5C2412yes—
250C2×C4×D5—232no—
251C2×C4×D5—232no—
252C2×C4×D5—28no—
253C2×C4×D5—28no—
254C2×C4×D5—28no—
255C2×C4×D5—28no—
256C2×C4×D5—28no—
257C2×C4×D5—28no—
258C2×C4×D5—28no—
259C2×C4×D5—28no—
260C2×C4×D5—416no—
261C2×C4×D5C2×D4116yes—
262C5×C4⋊C4—28no—
263C5×C22⋊C4—28no—
264C5×C22⋊C4—28no—
265C5×C22⋊C4—28no—
266C42×C5—28no—
267C22⋊Dic5—28no—
268C22⋊Dic5—28no—
269C22⋊Dic5—28no—
270#685—28no—
271#685—28no—
272#685C2×D4116yes—
273C4⋊Dic5—28no—
274C4⋊Dic5—28no—
275C4⋊Dic5—28no—
276C4⋊Dic5—28no—
277#683—28no—
278#683—28no—
279#683—28no—
280#683—28no—
281#683—28no—
282#683—28no—
283#683—28no—
284C4×Dic5—28no—
285C23×D4—51no—
286C24×C4—51no—
287C24×C4—51no—
288C24×C4—51no—
289C2×#123—58no—
290C2×#123—58no—
291C2×#123—108no—
292C2×#123—108no—
293C2×#117—58no—
294C2×#117—108no—
295C22×C4⋊C4—51no—
296C22×C4⋊C4—51no—
297C22×C4⋊C4—51no—
298C22×C4⋊C4—51no—
299C22×C4⋊C4—51no—
300C22×C4⋊C4—51no—
301C22×C4⋊C4—51no—
302C22×C4⋊C4—51no—
303C22×C4⋊C4—51no—
304C22×C4⋊C4—51no—
305C22×C4⋊C4—51no—
306C22×C4⋊C4—58no—
307C22×C4⋊C4—108no—
308C22×C4⋊C4C2×D511yescharacteristic
309C22×C22⋊C4—51no—
310C22×C22⋊C4—51no—
311C22×C22⋊C4—51no—
312C22×C22⋊C4—51no—
313C22×C22⋊C4—51no—
314C22×C22⋊C4—51no—
315C22×C22⋊C4C2×D511yescharacteristic
316C22×C22⋊C4C2×D511yescharacteristic
317C22×C22⋊C4C2×D511yescharacteristic
318C22×C42—51no—
319C22×C42C2×D511yescharacteristic
320#398—58no—
321#398—58no—
322#396—58no—
323#396—58no—
324#389—58no—
325#389—58no—
326#388—58no—
327#388C2×D518yescomplemented
328#386—58no—
329#385—58no—
330#381—58no—
331C2×#95—51no—
332C2×#95—51no—
333C2×#95—51no—
334C2×#95—51no—
335C2×#95—51no—
336C2×#95—51no—
337C2×#95C2×D511yescharacteristic
338C2×#95C2×D511yescharacteristic
339C23×C5—22no—
340C23×C5—22no—
341C23×C5—22no—
342C23×C5—22no—
343C23×C5—22no—
344C23×C5—22no—
345C23×C5—22no—
346C23×C5—44no—
347C23×C5—44no—
348C23×C5—44no—
349C23×C5—44no—
350C23×C5—44no—
351C23×C5—44no—
352C23×C5—44no—
353C23×C5C22×D412yes—
354C23×C5C22×D412yes—
355C23×C5C2×#4112yes—
356C23×C5C2×#4112yes—
357C23×C5C2×#4112yes—
358C23×C52−1+412yes—
359C23×C52−1+412yes—
360C23×C5C2511yescharacteristic
361C22×D5—28no—
362C22×D5—28no—
363C22×D5—28no—
364C22×D5—28no—
365C22×D5—28no—
366C22×D5—28no—
367C22×D5—22no—
368C22×D5—22no—
369C22×D5—22no—
370C22×D5—22no—
371C22×D5#121116yes—
372C22×D5C22×D414yes—
373C22×D5C22×D414yes—
374C22×D5C2×#4114yes—
375C2×C4×C5—28no—
376C2×C4×C5—28no—
377C2×C4×C5—28no—
378C2×C4×C5—22no—
379C2×C4×C5—22no—
380C2×C4×C5—22no—
381C2×C4×C5—22no—
382C2×C4×C5—22no—
383C2×C4×C5—22no—
384C2×C4×C5—22no—
385C2×C4×C5—22no—
386C2×C4×C5—22no—
387C2×C4×C5—22no—
388C2×C4×C5—22no—
389C2×C4×C5—22no—
390C2×C4×C5—22no—
391C2×C4×C5—22no—
392C2×C4×C5—22no—
393C2×C4×C5—44no—
394C2×C4×C5—44no—
395C2×C4×C5—44no—
396C2×C4×C5C22×D414yes—
397C2×C4×C5C22×D414yes—
398C2×C4×C5C2×#4114yes—
399C22⋊D5—416no—
400C2×Dic5—28no—
401C2×Dic5—28no—
402C2×Dic5—28no—
403C2×Dic5—22no—
404C2×Dic5—22no—
405C2×Dic5—22no—
406C2×Dic5—22no—
407C2×Dic5—22no—
408C2×Dic5—22no—
409C2×Dic5—22no—
410C2×Dic5—22no—
411C2×Dic5—22no—
412C2×Dic5—22no—
413C2×Dic5—22no—
414C2×Dic5—22no—
415C2×Dic5—22no—
416C2×Dic5—22no—
417C2×Dic5—22no—
418C2×Dic5—22no—
419C2×Dic5—22no—
420C2×Dic5—22no—
421C2×Dic5—44no—
422C2×Dic5—44no—
423C2×Dic5—44no—
424C2×Dic5—44no—
425C2×Dic5C22×D414yes—
426C2×Dic5C22×D414yes—
427C2×Dic5C2×#4114yes—
428C4×D5—232no—
429C4×D5—232no—
430C4×D5—416no—
431C25—51no—
432C25C22×D511yescharacteristic
433C22×D4—54no—
434C22×D4—104no—
435C22×D4—104no—
436C22×D4—104no—
437C23×C4—51no—
438C23×C4—51no—
439C23×C4—51no—
440C23×C4—58no—
441C23×C4—54no—
442C23×C4—51no—
443C23×C4—51no—
444C23×C4—51no—
445C23×C4—51no—
446C23×C4—54no—
447C23×C4—54no—
448C23×C4—104no—
449C23×C4—104no—
450C23×C4—104no—
451C23×C4—104no—
452C23×C4—104no—
453C23×C4—104no—
454C23×C4—104no—
455C23×C4—104no—
456C23×C4C22×D511yescharacteristic
457C23×C4C22×D511yescharacteristic
458C23×C4C22×D511yescharacteristic
459C23×C4C22×D511yescharacteristic
460C23×C4C22×D511yescharacteristic
461C23×C4C22×D511yescharacteristic
462#123—1032no—
463#123—1032no—
464#117—1032no—
465C2×C4⋊C4—24no—
466C2×C4⋊C4—54no—
467C2×C4⋊C4—54no—
468C2×C4⋊C4—54no—
469C2×C4⋊C4—54no—
470C2×C4⋊C4—54no—
471C2×C4⋊C4—54no—
472C2×C4⋊C4—54no—
473C2×C4⋊C4—54no—
474C2×C4⋊C4—54no—
475C2×C4⋊C4—54no—
476C2×C4⋊C4—54no—
477C2×C4⋊C4—1032no—
478C2×C4⋊C4—104no—
479C2×C4⋊C4—104no—
480C2×C4⋊C4—104no—
481C2×C4⋊C4—104no—
482C2×C4⋊C4—104no—
483C2×C4⋊C4—104no—
484C2×C4⋊C4—104no—
485C2×C4⋊C4—104no—
486C2×C4⋊C4—104no—
487C2×C4⋊C4—104no—
488C2×C4⋊C4—104no—
489C2×C4⋊C4C22×D514yes—
490C2×C22⋊C4—24no—
491C2×C22⋊C4—24no—
492C2×C22⋊C4—24no—
493C2×C22⋊C4—58no—
494C2×C22⋊C4—54no—
495C2×C22⋊C4—54no—
496C2×C22⋊C4—54no—
497C2×C22⋊C4—54no—
498C2×C22⋊C4—54no—
499C2×C22⋊C4—54no—
500C2×C22⋊C4—104no—
501C2×C22⋊C4—104no—
502C2×C22⋊C4—104no—
503C2×C22⋊C4—104no—
504C2×C22⋊C4—104no—
505C2×C22⋊C4C22×D514yes—
506C2×C22⋊C4C22×D514yes—
507C2×C22⋊C4C22×D514yes—
508C2×C42—24no—
509C2×C42—54no—
510C2×C42—104no—
511C2×C42C22×D514yes—
512#95—54no—
513#95—54no—
514#95—54no—
515#95—54no—
516#95—54no—
517#95—54no—
518#95C22×D514yes—
519#95C22×D514yes—
520C22×C5—42no—
521C22×C5—42no—
522C22×C5—42no—
523C22×C5—42no—
524C22×C5—42no—
525C22×C5—42no—
526C22×C5—42no—
527C22×C5—88no—
528C22×C5C2×#12114yes—
529C22×C5#52514yes—
530C22×C5#53614yes—
531C22×C5#54714yes—
532C22×C5#54714yes—
533C22×C5#55214yes—
534C22×C5#55214yes—
535C22×C5C23×D411yescharacteristic
536C22×C5C23×D411yescharacteristic
537C22×C5C22×#4111yescharacteristic
538C22×C5C22×#4111yescharacteristic
539C22×C5C22×#4111yescharacteristic
540C22×C5C2×2−1+411yescharacteristic
541C22×C5C2×2−1+411yescharacteristic
542C2×D5—24no—
543C2×D5—232no—
544C2×D5—24no—
545C2×D5—24no—
546C2×D5—24no—
547C2×D5—24no—
548C2×D5—24no—
549C2×D5C2×#12118yes—
550C4×C5—24no—
551C4×C5—24no—
552C4×C5—24no—
553C4×C5—42no—
554C4×C5—42no—
555C4×C5—42no—
556Dic5—24no—
557Dic5—24no—
558Dic5—24no—
559Dic5—42no—
560Dic5—42no—
561Dic5—42no—
562Dic5—42no—
563C24—22no—
564C24—22no—
565C24—22no—
566C24—22no—
567C24—22no—
568C24—22no—
569C24—22no—
570C24—54no—
571C24—54no—
572C24—54no—
573C24—52no—
574C24—102no—
575C24—102no—
576C24—102no—
577C24—102no—
578C24C23×D512yes—
579C24C23×D511yescharacteristic
580C2×D4—108no—
581C2×D4—108no—
582C2×D4—108no—
583C2×D4—2016no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—54no—
600C22×C4—54no—
601C22×C4—54no—
602C22×C4—52no—
603C22×C4—52no—
604C22×C4—52no—
605C22×C4—516no—
606C22×C4—52no—
607C22×C4—52no—
608C22×C4—52no—
609C22×C4—52no—
610C22×C4—108no—
611C22×C4—108no—
612C22×C4—108no—
613C22×C4—1032no—
614C22×C4—108no—
615C22×C4—1032no—
616C22×C4—108no—
617C22×C4—108no—
618C22×C4—108no—
619C22×C4—102no—
620C22×C4—102no—
621C22×C4—102no—
622C22×C4—102no—
623C22×C4—102no—
624C22×C4—102no—
625C22×C4—108no—
626C22×C4—102no—
627C22×C4—102no—
628C22×C4—102no—
629C22×C4—102no—
630C22×C4—102no—
631C22×C4—102no—
632C22×C4—102no—
633C22×C4—102no—
634C22×C4—102no—
635C22×C4—102no—
636C22×C4—102no—
637C22×C4—102no—
638C22×C4—2016no—
639C22×C4#70914yes—
640C22×C4D4×D514yes—
641C22×C4D4×D514yes—
642C22×C4C23×D512yes—
643C22×C4C23×D512yes—
644C22×C4C23×D512yes—
645C22×C4C23×D512yes—
646C22×C4C23×D512yes—
647C22×C4C23×D512yes—
648C4⋊C4—28no—
649C4⋊C4—108no—
650C4⋊C4—108no—
651C4⋊C4—108no—
652C4⋊C4—108no—
653C4⋊C4—108no—
654C4⋊C4—108no—
655C4⋊C4—108no—
656C4⋊C4—108no—
657C4⋊C4—108no—
658C4⋊C4—108no—
659C4⋊C4—108no—
660C22⋊C4—28no—
661C22⋊C4—28no—
662C22⋊C4—28no—
663C22⋊C4—516no—
664C22⋊C4—108no—
665C22⋊C4—108no—
666C22⋊C4—108no—
667C22⋊C4—108no—
668C22⋊C4—108no—
669C42—28no—
670C42—108no—
671C2×C5—82no—
672C2×C5#241318yescomplemented
673C2×C5C22×#12111yescharacteristic
674C2×C5C2×#52511yescharacteristic
675C2×C5C2×#53611yescharacteristic
676C2×C5C2×#54711yescharacteristic
677C2×C5C2×#54711yescharacteristic
678C2×C5C2×#55211yescharacteristic
679C2×C5C2×#55211yescharacteristic
680D5—28no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—22no—
688C23—44no—
689C23—44no—
690C23—44no—
691C23—44no—
692C23—44no—
693C23—44no—
694C23—44no—
695C23—516no—
696C23—54no—
697C23—54no—
698C23—54no—
699C23—108no—
700C23—108no—
701C23—108no—
702C23—108no—
703C23—108no—
704C23—102no—
705C23—102no—
706C23—102no—
707C23—102no—
708C23—108no—
709C23C2×#70912yes—
710C23C2×D4×D512yes—
711C23C2×D4×D512yes—
712C23D5×#4112yes—
713C23D5×#4112yes—
714C23#415012yes—
715C23#415012yes—
716C23C24×D511yescharacteristic
717D4—2016no—
718C2×C4—28no—
719C2×C4—28no—
720C2×C4—28no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—44no—
737C2×C4—44no—
738C2×C4—44no—
739C2×C4—54no—
740C2×C4—54no—
741C2×C4—54no—
742C2×C4—1032no—
743C2×C4—1032no—
744C2×C4—108no—
745C2×C4—108no—
746C2×C4—108no—
747C2×C4—102no—
748C2×C4—102no—
749C2×C4—102no—
750C2×C4—102no—
751C2×C4—102no—
752C2×C4—102no—
753C2×C4—102no—
754C2×C4—102no—
755C2×C4—102no—
756C2×C4—102no—
757C2×C4—102no—
758C2×C4—102no—
759C2×C4—102no—
760C2×C4—102no—
761C2×C4—102no—
762C2×C4—102no—
763C2×C4—102no—
764C2×C4—102no—
765C2×C4—2016no—
766C2×C4—204no—
767C2×C4—204no—
768C2×C4—204no—
769C2×C4—204no—
770C2×C4C2×#70914yes—
771C2×C4C2×D4×D514yes—
772C2×C4C2×D4×D514yes—
773C5C2×#241311yescharacteristic, complemented, Sylow
774C22—42no—
775C22—42no—
776C22—42no—
777C22—42no—
778C22—42no—
779C22—42no—
780C22—42no—
781C22—58no—
782C22—88no—
783C22—104no—
784C22—104no—
785C22—104no—
786C22—104no—
787C22—104no—
788C22—104no—
789C22—1032no—
790C22#6586314yes—
791C22#6588114yes—
792C22#6588514yes—
793C22D5×#12114yes—
794C22#6598914yes—
795C22#6600914yes—
796C22#6604214yes—
797C22C22×#70911yescharacteristic
798C22C22×D4×D511yescharacteristic
799C22C22×D4×D511yescharacteristic
800C22C2×D5×#4111yescharacteristic
801C22C2×D5×#4111yescharacteristic
802C22C2×#415011yescharacteristic
803C22C2×#415011yescharacteristic
804C4—24no—
805C4—24no—
806C4—24no—
807C4—42no—
808C4—42no—
809C4—42no—
810C4—104no—
811C4—104no—
812C4—104no—
813C4—202no—
814C4—202no—
815C4—202no—
816C4—202no—
817C2—82no—
818C2—108no—
819C2#1060757418yesdirect product factor
820C2C2×#6586311yescharacteristic
821C2C2×#6588111yescharacteristic
822C2C2×#6588511yescharacteristic
823C2C2×D5×#12111yescharacteristic
824C2C2×#6598911yescharacteristic
825C2C2×#6600911yescharacteristic
826C2C2×#6604211yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC2×C5×#388C2
socleC24×C5C24
prime radicalC23×C22⋊D5C22
hypercenterC2×#388D5
hypocenterC5C2×#2413
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
1. C22×D5×C4⋊C4C2semidirect
4. C22×#4018C2semidirect
5. C2×C5×#388C2semidirect
6. C2×#65261C2semidirect
8. C2×#65237C2semidirect
9. C2×#65237C2semidirect
10. C2×#65234C2semidirect
11. C2×#65217C2semidirect
12. #10607574C2direct (N × H)
13. C2×#64957C2semidirect
14. C2×#64953C2semidirect
15. C2×#64950C2semidirect
16. C2×#64946C2semidirect
45. C2×D5×C4⋊C4C22semidirect
51. C2×#4018C22semidirect
52. C5×#388C22semidirect
61. #65261C22semidirect
63. #65237C22semidirect
64. #65237C22semidirect
65. #65234C22semidirect
66. #65217C22semidirect
67. #64957C22semidirect
68. #64953C22semidirect
69. #64950C22semidirect
70. #64946C22semidirect
173. C2×#388D5semidirect
327. #388C2×D5semidirect
672. C2×C5#2413semidirect
773. C5C2×#2413semidirect
819. C2#10607574direct (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×#40292
C22×#40182
C2×C5×#3882
C2×#652612
C2×#652452
C2×#652372
C2×#652342
C2×#652172
#106075742
C2×#649572
C2×#649532
C2×#649502
C2×#649462
C2×#24135