Finite Group Databasebeta

← #12065175

Subgroups — #12065175

Order 1280.

1738 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D5C211yesmaximal, characteristic
2C2×C5×#407C211yesmaximal, characteristic, complemented
3C2×#65496C211yesmaximal, characteristic, complemented
4#10600764C212yesmaximal, complemented
5#10600761C214yesmaximal, complemented
6#10600760C212yesmaximal, complemented
7#10600712C214yesmaximal, complemented
8C24×C4×C5C2211yescharacteristic
9C23×C22⋊D5C411yescharacteristic
10C23×C4×D5C411yescharacteristic
11C22×C5×M16—21no—
12C22×C22⋊Dic5C411yescharacteristic
13C2×C4×C22⋊D5—21no—
14C2×C4×C22⋊D5—21no—
15C2×C4×C22⋊D5—21no—
16C2×C4×C22⋊D5—21no—
17C2×C4×C22⋊D5—21no—
18C2×C4×C22⋊D5—21no—
19C2×C4×C22⋊D5—21no—
20C2×C4×C22⋊D5—21no—
21C2×C4×C22⋊D5C412yes—
22C2×C4×C22⋊D5C412yes—
23C2×C4×C22⋊D5C2212yes—
24C2×C4×C22⋊D5C2212yes—
25C22×#685C2211yescharacteristic
26C22×#683C2211yescharacteristic
27C22×C4×Dic5C411yescharacteristic
28C22×#681—21no—
29C5×#407—21no—
30C5×#407—21no—
31C5×#407C2212yes—
32C5×#407C2212yescomplemented
33C2×C5×C22⋊C8—21no—
34C2×C5×C22⋊C8C2212yescomplemented
35#65496—21no—
36#65496—21no—
37#65496C2212yes—
38#65496C2212yescomplemented
39C2×C22⋊#168—21no—
40C2×C22⋊#168C2212yescomplemented
41#64689C2218yescomplemented
42#64688C2218yescomplemented
43#17362—51nomaximal, Sylow
44C25×C5C2×C411yescharacteristic
45C24×D5C2×C411yescharacteristic
46C23×C4×C5—44no—
47C23×C4×C5C2×C411yescharacteristic
48C23×C4×C5C2×C411yescharacteristic
49C23×C4×C5C2×C411yescharacteristic
50C23×C4×C5D411yescharacteristic
51C23×C4×C5D411yescharacteristic
52C23×C4×C5D411yescharacteristic
53C23×C4×C5D411yescharacteristic
54C23×C4×C5D411yescharacteristic
55C23×C4×C5D411yescharacteristic
56C23×C4×C5D411yescharacteristic
57C23×C4×C5D411yescharacteristic
58C23×C4×C5C2311yescharacteristic
59C23×C4×C5C2311yescharacteristic
60C23×C4×C5C2311yescharacteristic
61C22×C22⋊D5—21no—
62C22×C22⋊D5—21no—
63C22×C22⋊D5—21no—
64C22×C22⋊D5—21no—
65C22×C22⋊D5—28no—
66C22×C22⋊D5C2×C412yes—
67C22×C22⋊D5C2×C412yes—
68C23×Dic5C2×C411yescharacteristic
69C23×Dic5C2×C411yescharacteristic
70C23×Dic5C2×C411yescharacteristic
71C22×C4×D5—21no—
72C22×C4×D5—21no—
73C22×C4×D5—21no—
74C22×C4×D5—21no—
75C22×C4×D5—44no—
76C22×C4×D5C2×C412yes—
77C22×C4×D5C2×C412yes—
78C2×C5×M16—22no—
79C2×C5×M16—22no—
80C2×C5×M16—44no—
81C22×C5×C8—22no—
82C2×C22⋊Dic5—21no—
83C2×C22⋊Dic5—21no—
84C2×C22⋊Dic5—21no—
85C2×C22⋊Dic5—21no—
86C2×C22⋊Dic5C2×C412yes—
87C2×C22⋊Dic5C2×C412yes—
88C4×C22⋊D5—22no—
89C4×C22⋊D5—22no—
90C4×C22⋊D5—22no—
91C4×C22⋊D5—22no—
92C4×C22⋊D5—22no—
93C4×C22⋊D5—22no—
94C4×C22⋊D5—22no—
95C4×C22⋊D5—22no—
96C4×C22⋊D5—22no—
97C4×C22⋊D5—22no—
98C4×C22⋊D5—22no—
99C4×C22⋊D5—22no—
100C4×C22⋊D5—22no—
101C4×C22⋊D5—22no—
102C4×C22⋊D5—22no—
103C4×C22⋊D5—22no—
104C2×#685—21no—
105C2×#685—21no—
106C2×#685—21no—
107C2×#685—21no—
108C2×#685C2×C412yes—
109C2×#685C2312yes—
110C2×#683—21no—
111C2×#683—21no—
112C2×#683—21no—
113C2×#683—21no—
114C2×#683C2×C412yes—
115C2×#683C2312yes—
116C2×C4×Dic5—21no—
117C2×C4×Dic5—21no—
118C2×C4×Dic5—21no—
119C2×C4×Dic5—21no—
120C2×C4×Dic5C2×C412yes—
121C2×C4×Dic5C2×C412yes—
122C2×#681—22no—
123C2×#681—22no—
124C2×#681—44no—
125C22×#168—22no—
126C5×C22⋊C8—22no—
127C5×C22⋊C8—22no—
128C5×C22⋊C8—22no—
129C5×C22⋊C8C2314yes—
130C22⋊#168—22no—
131C22⋊#168—22no—
132C22⋊#168—22no—
133C22⋊#168C2314yes—
134C22×C4×D4—51no—
135C2×#407—51no—
136C2×#407D511yescharacteristic, complemented
137#1465—54no—
138#1463—52no—
139#1462—52no—
140#1459—54no—
141C24×C5—24no—
142C24×C5—42no—
143C24×C5—42no—
144C24×C5C22⋊C411yescharacteristic
145C24×C5C22⋊C411yescharacteristic
146C24×C5C22⋊C411yescharacteristic
147C24×C5C22⋊C411yescharacteristic
148C24×C5C22×C411yescharacteristic
149C24×C5C22×C411yescharacteristic
150C24×C5C22×C411yescharacteristic
151C23×D5—21no—
152C23×D5—21no—
153C23×D5—24no—
154C23×D5—42no—
155C23×D5—42no—
156C23×D5C22×C412yes—
157C22×C4×C5—24no—
158C22×C4×C5—24no—
159C22×C4×C5—24no—
160C22×C4×C5—42no—
161C22×C4×C5—42no—
162C22×C4×C5—42no—
163C22×C4×C5—42no—
164C22×C4×C5—42no—
165C22×C4×C5—42no—
166C22×C4×C5—42no—
167C22×C4×C5—42no—
168C22×C4×C5—42no—
169C22×C4×C5—42no—
170C22×C4×C5—42no—
171C22×C4×C5C22⋊C411yescharacteristic
172C22×C4×C5C22⋊C411yescharacteristic
173C22×C4×C5C22⋊C411yescharacteristic
174C22×C4×C5C22⋊C411yescharacteristic
175C22×C4×C5C22⋊C411yescharacteristic
176C22×C4×C5C22⋊C411yescharacteristic
177C22×C4×C5C22⋊C411yescharacteristic
178C22×C4×C5C22⋊C411yescharacteristic
179C22×C4×C5C22⋊C411yescharacteristic
180C22×C4×C5C22⋊C411yescharacteristic
181C22×C4×C5C22⋊C411yescharacteristic
182C22×C4×C5C22⋊C411yescharacteristic
183C22×C4×C5C22×C411yescharacteristic
184C22×C4×C5C22×C411yescharacteristic
185C22×C4×C5C22×C411yescharacteristic
186C22×C4×C5C2×D411yescharacteristic
187C22×C4×C5C2×D411yescharacteristic
188C22×C4×C5C2×D411yescharacteristic
189C22×C4×C5C2×D411yescharacteristic
190C22×C4×C5C2×D411yescharacteristic
191C22×C4×C5C2×D411yescharacteristic
192C22×C4×C5C2×D411yescharacteristic
193C22×C4×C5C2×D411yescharacteristic
194C22×C4×C5C2×D411yescharacteristic
195C22×C4×C5C2×D411yescharacteristic
196C22×C4×C5C2×D411yescharacteristic
197C22×C4×C5C2×D411yescharacteristic
198C22×C4×C5C2411yescharacteristic
199C2×C22⋊D5—28no—
200C2×C22⋊D5—28no—
201C2×C22⋊D5—28no—
202C2×C22⋊D5—28no—
203C2×C22⋊D5—22no—
204C2×C22⋊D5—22no—
205C2×C22⋊D5—22no—
206C2×C22⋊D5—22no—
207C2×C22⋊D5—24no—
208C2×C22⋊D5—24no—
209C2×C22⋊D5—24no—
210C2×C22⋊D5M1618yescomplemented
211C22×Dic5—21no—
212C22×Dic5—21no—
213C22×Dic5—24no—
214C22×Dic5—21no—
215C22×Dic5—21no—
216C22×Dic5—21no—
217C22×Dic5—21no—
218C22×Dic5—42no—
219C22×Dic5—42no—
220C22×Dic5C22×C412yes—
221C22×Dic5C22×C412yes—
222C22×Dic5C22×C412yes—
223C2×C4×D5—22no—
224C2×C4×D5—22no—
225C2×C4×D5—22no—
226C2×C4×D5—22no—
227C2×C4×D5—44no—
228C2×C4×D5—44no—
229C2×C4×D5—44no—
230C2×C4×D5—44no—
231C2×C4×D5—44no—
232C2×C4×D5—44no—
233C5×M16—44no—
234C5×M16—44no—
235C2×C5×C8—24no—
236C2×C5×C8—44no—
237C22⋊Dic5—22no—
238C22⋊Dic5—22no—
239C22⋊Dic5—22no—
240C22⋊Dic5—22no—
241#685—22no—
242#685—22no—
243#685—22no—
244#685—22no—
245#683—22no—
246#683—22no—
247#683—22no—
248#683—22no—
249C4×Dic5—22no—
250C4×Dic5—22no—
251C4×Dic5—22no—
252C4×Dic5—22no—
253#681—44no—
254#681—44no—
255C2×#168—24no—
256C2×#168—44no—
257C23×D4—51no—
258C24×C4—51no—
259C24×C4C2×D511yescharacteristic
260C22×M16—21no—
261C22×M16—101no—
262C2×C4×D4—52no—
263C2×C4×D4—52no—
264C2×C4×D4—52no—
265C2×C4×D4—52no—
266C2×C4×D4—101no—
267C2×C4×D4—101no—
268C2×C4×D4—101no—
269C2×C4×D4—101no—
270C2×C4×D4—101no—
271C2×C4×D4—101no—
272C2×C4×D4—101no—
273C2×C4×D4—101no—
274C22×C4⋊C4—51no—
275C22×C22⋊C4—51no—
276C22×C22⋊C4—51no—
277C22×C42—51no—
278#407—21no—
279#407—21no—
280#407—52no—
281#407—52no—
282#407—101no—
283#407—101no—
284#407C2×D512yes—
285#407C2×D512yescomplemented
286C2×C22⋊C8—21no—
287C2×C22⋊C8—52no—
288C2×C22⋊C8—101no—
289C2×C22⋊C8C2×D512yescomplemented
290#324—58no—
291#323—58no—
292C23×C5—22no—
293C23×C5—22no—
294C23×C5—22no—
295C23×C5—22no—
296C23×C5—22no—
297C23×C5—22no—
298C23×C5—22no—
299C23×C5—22no—
300C23×C5—22no—
301C23×C5—22no—
302C23×C5—22no—
303C23×C5—22no—
304C23×C5—41no—
305C23×C5—41no—
306C23×C5—41no—
307C23×C5—41no—
308C23×C5—41no—
309C23×C5—41no—
310C23×C5—41no—
311C23×C5—41no—
312C23×C5—416no—
313C23×C5C2×C22⋊C411yescharacteristic
314C23×C5C2×C22⋊C411yescharacteristic
315C23×C5C2×C22⋊C411yescharacteristic
316C23×C5C2×C22⋊C411yescharacteristic
317C23×C5C2×C22⋊C411yescharacteristic
318C23×C5C2×C22⋊C411yescharacteristic
319C23×C5C2×M1614yes—
320C23×C5C23×C411yescharacteristic
321C22×D5—24no—
322C22×D5—24no—
323C22×D5—22no—
324C22×D5—22no—
325C22×D5—42no—
326C22×D5—416no—
327C22×D5—42no—
328C22×D5—42no—
329C22×D5—42no—
330C22×D5—42no—
331C22×D5—42no—
332C22×D5C2×M1614yescomplemented
333C2×C4×C5—22no—
334C2×C4×C5—22no—
335C2×C4×C5—22no—
336C2×C4×C5—22no—
337C2×C4×C5—22no—
338C2×C4×C5—22no—
339C2×C4×C5—22no—
340C2×C4×C5—22no—
341C2×C4×C5—22no—
342C2×C4×C5—22no—
343C2×C4×C5—22no—
344C2×C4×C5—22no—
345C2×C4×C5—22no—
346C2×C4×C5—22no—
347C2×C4×C5—22no—
348C2×C4×C5—41no—
349C2×C4×C5—41no—
350C2×C4×C5—41no—
351C2×C4×C5—41no—
352C2×C4×C5—41no—
353C2×C4×C5—41no—
354C2×C4×C5—41no—
355C2×C4×C5—41no—
356C2×C4×C5—41no—
357C2×C4×C5—41no—
358C2×C4×C5—41no—
359C2×C4×C5—41no—
360C2×C4×C5#9914yes—
361C2×C4×C5C2×C22⋊C411yescharacteristic
362C2×C4×C5C2×C22⋊C411yescharacteristic
363C2×C4×C5C2×C22⋊C411yescharacteristic
364C2×C4×C5C2×C22⋊C411yescharacteristic
365C2×C4×C5C2×C22⋊C411yescharacteristic
366C2×C4×C5C2×C22⋊C411yescharacteristic
367C2×C4×C5C22×D411yescharacteristic
368C2×C4×C5C22×D411yescharacteristic
369C22⋊D5—28no—
370C22⋊D5—28no—
371C22⋊D5—28no—
372C22⋊D5—28no—
373C2×Dic5—24no—
374C2×Dic5—24no—
375C2×Dic5—22no—
376C2×Dic5—22no—
377C2×Dic5—22no—
378C2×Dic5—22no—
379C2×Dic5—42no—
380C2×Dic5—42no—
381C2×Dic5—42no—
382C2×Dic5—42no—
383C2×Dic5—42no—
384C2×Dic5—42no—
385C2×Dic5C2×M1614yescomplemented
386C4×D5—44no—
387C4×D5—44no—
388C4×D5—44no—
389C4×D5—44no—
390C5×C8—44no—
391#168—44no—
392C25—51no—
393C25C4×D511yescharacteristic
394C22×D4—52no—
395C22×D4—52no—
396C22×D4—108no—
397C22×D4—101no—
398C22×D4—101no—
399C22×D4—101no—
400C22×D4—101no—
401C23×C4—44no—
402C23×C4—51no—
403C23×C4—51no—
404C23×C4—51no—
405C23×C4—52no—
406C23×C4—52no—
407C23×C4—101no—
408C23×C4—101no—
409C23×C4—101no—
410C23×C4—101no—
411C23×C4—204no—
412C23×C4C4×D511yescharacteristic
413C23×C4C4×D511yescharacteristic
414C23×C4C4×D511yescharacteristic
415C23×C4D2011yescharacteristic
416C23×C4D2011yescharacteristic
417C23×C4D2011yescharacteristic
418C23×C4D2011yescharacteristic
419C23×C4C22⋊D511yescharacteristic
420C23×C4C22⋊D511yescharacteristic
421C23×C4C22⋊D511yescharacteristic
422C23×C4C22⋊D511yescharacteristic
423C23×C4C22×D511yescharacteristic
424C23×C4C22×D511yescharacteristic
425C23×C4C22×D511yescharacteristic
426C2×M16—22no—
427C2×M16—22no—
428C2×M16—44no—
429C2×M16—102no—
430C2×M16—102no—
431C2×M16—204no—
432C22×C8—22no—
433C22×C8—102no—
434C4×D4—102no—
435C4×D4—102no—
436C4×D4—102no—
437C4×D4—102no—
438C4×D4—102no—
439C4×D4—102no—
440C4×D4—102no—
441C4×D4—102no—
442C4×D4—102no—
443C4×D4—102no—
444C4×D4—102no—
445C4×D4—102no—
446C4×D4—102no—
447C4×D4—102no—
448C4×D4—102no—
449C4×D4—102no—
450C2×C4⋊C4—52no—
451C2×C4⋊C4—52no—
452C2×C4⋊C4—101no—
453C2×C4⋊C4—101no—
454C2×C4⋊C4—101no—
455C2×C4⋊C4—101no—
456C2×C22⋊C4—52no—
457C2×C22⋊C4—52no—
458C2×C22⋊C4—52no—
459C2×C22⋊C4—52no—
460C2×C22⋊C4—101no—
461C2×C22⋊C4—101no—
462C2×C22⋊C4—101no—
463C2×C22⋊C4—101no—
464C2×C22⋊C4—101no—
465C2×C22⋊C4—101no—
466C2×C22⋊C4—101no—
467C2×C22⋊C4—101no—
468C2×C42—52no—
469C2×C42—52no—
470C2×C42—101no—
471C2×C42—101no—
472C2×C42—101no—
473C2×C42—101no—
474C22⋊C8—22no—
475C22⋊C8—22no—
476C22⋊C8—22no—
477C22⋊C8—54no—
478C22⋊C8—102no—
479C22⋊C8—102no—
480C22⋊C8—102no—
481C22⋊C8C22×D514yes—
482C22×C5—28no—
483C22×C5—21no—
484C22×C5—21no—
485C22×C5—21no—
486C22×C5—21no—
487C22×C5—21no—
488C22×C5—21no—
489C22×C5—21no—
490C22×C5—21no—
491C22×C5—21no—
492C22×C5—21no—
493C22×C5—21no—
494C22×C5—21no—
495C22×C5—21no—
496C22×C5—21no—
497C22×C5—21no—
498C22×C5—21no—
499C22×C5—44no—
500C22×C5—44no—
501C22×C5—44no—
502C22×C5—44no—
503C22×C5—44no—
504C22×C5—44no—
505C22×C5#40712yes—
506C22×C5#40712yes—
507C22×C5C2×#9912yes—
508C22×C5#41312yes—
509C22×C5C22×C22⋊C411yescharacteristic
510C22×C5C22×M1612yes—
511C2×D5—24no—
512C2×D5—44no—
513C2×D5—48no—
514C2×D5—48no—
515C2×D5—42no—
516C2×D5—42no—
517C2×D5—44no—
518C4×C5—21no—
519C4×C5—21no—
520C4×C5—21no—
521C4×C5—21no—
522C4×C5—21no—
523C4×C5—21no—
524C4×C5C2×#9912yes—
525C4×C5C2×#9912yes—
526Dic5—24no—
527Dic5—42no—
528Dic5—42no—
529C24—24no—
530C24—42no—
531C24—42no—
532C24—52no—
533C24—104no—
534C24—101no—
535C24—101no—
536C24—202no—
537C24—202no—
538C24#68511yescharacteristic
539C24#68511yescharacteristic
540C24#68511yescharacteristic
541C24#68511yescharacteristic
542C24C2×C4×D511yescharacteristic
543C24C2×C4×D511yescharacteristic
544C24C2×C4×D511yescharacteristic
545C2×D4—58no—
546C2×D4—104no—
547C2×D4—104no—
548C2×D4—108no—
549C2×D4—108no—
550C2×D4—108no—
551C2×D4—108no—
552C2×D4—104no—
553C2×D4—102no—
554C2×D4—102no—
555C2×D4—102no—
556C2×D4—102no—
557C22×C4—24no—
558C22×C4—24no—
559C22×C4—24no—
560C22×C4—42no—
561C22×C4—42no—
562C22×C4—42no—
563C22×C4—42no—
564C22×C4—42no—
565C22×C4—42no—
566C22×C4—42no—
567C22×C4—42no—
568C22×C4—42no—
569C22×C4—42no—
570C22×C4—42no—
571C22×C4—52no—
572C22×C4—52no—
573C22×C4—52no—
574C22×C4—104no—
575C22×C4—101no—
576C22×C4—101no—
577C22×C4—101no—
578C22×C4—101no—
579C22×C4—101no—
580C22×C4—101no—
581C22×C4—102no—
582C22×C4—102no—
583C22×C4—102no—
584C22×C4—102no—
585C22×C4—204no—
586C22×C4—204no—
587C22×C4—204no—
588C22×C4—204no—
589C22×C4—204no—
590C22×C4—204no—
591C22×C4—202no—
592C22×C4—202no—
593C22×C4#68511yescharacteristic
594C22×C4#68511yescharacteristic
595C22×C4#68511yescharacteristic
596C22×C4#68511yescharacteristic
597C22×C4#68511yescharacteristic
598C22×C4#68511yescharacteristic
599C22×C4#68511yescharacteristic
600C22×C4#68511yescharacteristic
601C22×C4#68511yescharacteristic
602C22×C4#68511yescharacteristic
603C22×C4#68511yescharacteristic
604C22×C4#68511yescharacteristic
605C22×C4C2×C4×D511yescharacteristic
606C22×C4C2×C4×D511yescharacteristic
607C22×C4C2×C4×D511yescharacteristic
608C22×C4C2×D2011yescharacteristic
609C22×C4C2×D2011yescharacteristic
610C22×C4C2×D2011yescharacteristic
611C22×C4C2×D2011yescharacteristic
612C22×C4C2×D2011yescharacteristic
613C22×C4C2×D2011yescharacteristic
614C22×C4C2×C22⋊D511yescharacteristic
615C22×C4C2×C22⋊D511yescharacteristic
616C22×C4C2×C22⋊D511yescharacteristic
617C22×C4C2×C22⋊D511yescharacteristic
618C22×C4C2×C22⋊D511yescharacteristic
619C22×C4C2×C22⋊D511yescharacteristic
620C22×C4C23×D511yescharacteristic
621M16—44no—
622M16—44no—
623M16—204no—
624M16—204no—
625C2×C8—24no—
626C2×C8—44no—
627C2×C8—104no—
628C2×C8—204no—
629C4⋊C4—102no—
630C4⋊C4—102no—
631C4⋊C4—102no—
632C4⋊C4—102no—
633C22⋊C4—102no—
634C22⋊C4—102no—
635C22⋊C4—102no—
636C22⋊C4—102no—
637C22⋊C4—102no—
638C22⋊C4—102no—
639C22⋊C4—102no—
640C22⋊C4—102no—
641C42—102no—
642C42—102no—
643C42—102no—
644C42—102no—
645C2×C5—22no—
646C2×C5—22no—
647C2×C5—22no—
648C2×C5—22no—
649C2×C5—22no—
650C2×C5—41no—
651C2×C5—41no—
652C2×C5C2×#40711yescharacteristic
653C2×C5C22×#9911yescharacteristic
654C2×C5C2×#41311yescharacteristic
655D5—44no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—416no—
677C23—54no—
678C23—104no—
679C23—104no—
680C23—102no—
681C23—102no—
682C23—202no—
683C23—202no—
684C23—202no—
685C23—2016no—
686C23—202no—
687C23—202no—
688C23—202no—
689C23D5×M1614yes—
690C23C2×#68511yescharacteristic
691C23C2×#68511yescharacteristic
692C23C2×#68511yescharacteristic
693C23C2×#68511yescharacteristic
694C23C2×#68511yescharacteristic
695C23C2×#68511yescharacteristic
696C23C22×C4×D511yescharacteristic
697D4—108no—
698D4—108no—
699D4—108no—
700D4—108no—
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—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—54no—
729C2×C4—104no—
730C2×C4—104no—
731C2×C4—102no—
732C2×C4—102no—
733C2×C4—102no—
734C2×C4—102no—
735C2×C4—204no—
736C2×C4—204no—
737C2×C4—202no—
738C2×C4—202no—
739C2×C4—202no—
740C2×C4—202no—
741C2×C4—204no—
742C2×C4—204no—
743C2×C4—202no—
744C2×C4—202no—
745C2×C4#393814yes—
746C2×C4C2×#68511yescharacteristic
747C2×C4C2×#68511yescharacteristic
748C2×C4C2×#68511yescharacteristic
749C2×C4C2×#68511yescharacteristic
750C2×C4C2×#68511yescharacteristic
751C2×C4C2×#68511yescharacteristic
752C2×C4C22×D2011yescharacteristic
753C2×C4C22×C22⋊D511yescharacteristic
754C8—44no—
755C8—204no—
756C5#1736211yescharacteristic, complemented, Sylow
757C22—28no—
758C22—21no—
759C22—21no—
760C22—21no—
761C22—21no—
762C22—21no—
763C22—21no—
764C22—21no—
765C22—21no—
766C22—21no—
767C22—21no—
768C22—21no—
769C22—21no—
770C22—21no—
771C22—21no—
772C22—21no—
773C22—21no—
774C22—44no—
775C22—44no—
776C22—44no—
777C22—44no—
778C22—44no—
779C22—44no—
780C22—104no—
781C22—204no—
782C22—204no—
783C22—208no—
784C22—208no—
785C22—202no—
786C22—202no—
787C22C2×#393812yes—
788C22#6541512yes—
789C22#6541512yes—
790C22#6542112yes—
791C22C2×D5×M1612yes—
792C22C22×#68511yescharacteristic
793C4—21no—
794C4—21no—
795C4—21no—
796C4—21no—
797C4—21no—
798C4—21no—
799C4—104no—
800C4—202no—
801C4—202no—
802C4C2×#393812yes—
803C4C2×#393812yes—
804C2—22no—
805C2—22no—
806C2—22no—
807C2—22no—
808C2—22no—
809C2—41no—
810C2—41no—
811C2—204no—
812C2C22×#393811yescharacteristic
813C2C2×#6541511yescharacteristic
814C2C2×#6542111yescharacteristic
subgroupG/H
centerC2×C4C2×#685
commutatorC23×C5C23×C4
FrattiniC22×C4C23×D5
FittingC2×C5×#407C2
socleC22×C5C22×C22⋊C4
prime radicalC23×C22⋊D5C4
cosocleC22×C4×C5C24
hypercenterC2×#407D5
hypocenterC5#17362
LCSG ▷ C23×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C24×C4 ◁ C2×#407

Complements

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

NH ≅ G/Ntype
2. C2×C5×#407C2semidirect
3. C2×#65496C2semidirect
4. #10600764C2semidirect
5. #10600761C2semidirect
6. #10600760C2semidirect
7. #10600712C2semidirect
32. C5×#407C22semidirect
34. C2×C5×C22⋊C8C22semidirect
38. #65496C22semidirect
40. C2×C22⋊#168C22semidirect
41. #64689C22semidirect
42. #64688C22semidirect
136. C2×#407D5semidirect
210. C2×C22⋊D5M16semidirect
285. #407C2×D5semidirect
289. C2×C22⋊C8C2×D5semidirect
332. C22×D5C2×M16semidirect
385. C2×Dic5C2×M16semidirect
756. C5#17362semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D52
C2×C5×#4072
C2×#654962
#106007642
#106007612
#106007602
#106007122
#173625