Finite Group Databasebeta

← #12121428

Subgroups — #12121428

Order 1280.

1098 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C5×C4⋊C8C211yesmaximal, characteristic, complemented
2C2×#65400C211yesmaximal, characteristic, complemented
3C2×C8×C22⋊D5C211yesmaximal, characteristic, complemented
4C4×#4076C211yesmaximal, characteristic
5C2×#65125C211yesmaximal, characteristic, complemented
6#10602768C211yesmaximal, characteristic, complemented
7#10602768C211yesmaximal, characteristic, complemented
8#10602322C211yesmaximal, characteristic, complemented
9#10601271C211yesmaximal, characteristic, complemented
10#10601270C211yesmaximal, characteristic, complemented
11#10601264C211yesmaximal, characteristic, complemented
12#10601262C211yesmaximal, characteristic, complemented
13#10601260C211yesmaximal, characteristic, complemented
14#10601243C211yesmaximal, characteristic, complemented
15#10601242C211yesmaximal, characteristic, complemented
16C23×C5×C8C2211yescharacteristic
17C23×C5×C8C2211yescharacteristic
18C22×C42×C5C2211yescharacteristic
19C2×#4076C411yescharacteristic
20C2×C4×C22⋊D5C2211yescharacteristic
21C2×C4×C22⋊D5C2211yescharacteristic
22C22×#676C2211yescharacteristic
23C22×C8×D5C2211yescharacteristic
24C2×C4×D20C2211yescharacteristic
25C2×C5×C4⋊C8—24no—
26C2×C5×C4⋊C8C2211yescharacteristic
27C2×C5×C4⋊C8C2211yescharacteristic
28C2×C5×C4⋊C8C2211yescharacteristic
29C2×C5×C4⋊C8C2211yescharacteristic
30#65502C411yescharacteristic
31#65502C411yescharacteristic
32#65501C411yescharacteristic
33C2×C22⋊#168C2211yescharacteristic
34C2×C22⋊#168C2211yescharacteristic
35#65400—24no—
36C8×C22⋊D5—24no—
37C2×#3952C2211yescharacteristic
38C2×#3952C2211yescharacteristic
39C2×#3952C2211yescharacteristic
40C2×#3952C2211yescharacteristic
41C2×#3952C2211yescharacteristic
42C2×#3952C2211yescharacteristic
43C2×#3947C2211yescharacteristic
44C2×#3946C2211yescharacteristic
45C2×#3946C2211yescharacteristic
46C2×C8×Dic5C2211yescharacteristic
47#65229C411yescharacteristic
48#65229C411yescharacteristic
49#65228C411yescharacteristic
50C4×#685C2211yescharacteristic
51C4×#685C2211yescharacteristic
52C4×C4⋊Dic5C2211yescharacteristic
53#65217C411yescharacteristic
54C2×#3935C2211yescharacteristic
55C2×#3935C2211yescharacteristic
56#65125—24no—
57#64770C2211yescharacteristic
58#64770C2211yescharacteristic
59#64770C2211yescharacteristic
60#64770C2211yescharacteristic
61#64744C2211yescharacteristic
62#64744C2211yescharacteristic
63#22987—51nomaximal, Sylow
64C23×C4×C5C2×C411yescharacteristic
65C23×C4×C5C2×C411yescharacteristic
66C23×C4×C5C2311yescharacteristic
67C22×C22⋊D5C2×C411yescharacteristic
68C22×C22⋊D5C2×C411yescharacteristic
69C22×D20C2×C411yescharacteristic
70C22×C4×D5C2311yescharacteristic
71C22×C4×D5C2311yescharacteristic
72C22×C5×C8—22no—
73C22×C5×C8—22no—
74C22×C5×C8—22no—
75C22×C5×C8—22no—
76C22×C5×C8—41no—
77C22×C5×C8—41no—
78C22×C5×C8C2311yescharacteristic
79C22×C5×C8C2311yescharacteristic
80C22×C5×C8C2311yescharacteristic
81C22×C5×C8C2311yescharacteristic
82C2×C42×C5—22no—
83C2×C42×C5—22no—
84C2×C42×C5C2×C411yescharacteristic
85C2×C42×C5C2×C411yescharacteristic
86C2×C42×C5C2311yescharacteristic
87C2×C42×C5C2311yescharacteristic
88C2×C22⋊Dic5C2×C411yescharacteristic
89C2×C22⋊Dic5C2×C411yescharacteristic
90#4076—24no—
91C4×C22⋊D5—22no—
92C4×C22⋊D5—22no—
93C4×C22⋊D5—22no—
94C4×C22⋊D5—22no—
95C2×#685C2×C411yescharacteristic
96C2×#685C2×C411yescharacteristic
97C2×#685C2×C411yescharacteristic
98C2×#685C2×C411yescharacteristic
99C2×#685C2×C411yescharacteristic
100C2×#685C2×C411yescharacteristic
101C2×#685C2×C411yescharacteristic
102C2×#685C2×C411yescharacteristic
103C2×C4⋊Dic5C2×C411yescharacteristic
104C2×C4⋊Dic5C2×C411yescharacteristic
105C2×C4⋊Dic5C2×C411yescharacteristic
106C2×#683C2×C411yescharacteristic
107C2×#683C2×C411yescharacteristic
108C2×C4×Dic5C2311yescharacteristic
109C2×C4×Dic5C2311yescharacteristic
110C22×#168C2311yescharacteristic
111C22×#168C2311yescharacteristic
112C22×#168C2311yescharacteristic
113C22×#168C2311yescharacteristic
114C2×#676—22no—
115C2×#676—22no—
116C2×#676—41no—
117C2×C8×D5—22no—
118C2×C8×D5—22no—
119C2×C8×D5—41no—
120C4×D20—22no—
121C4×D20—22no—
122C5×C4⋊C8—22no—
123C5×C4⋊C8—22no—
124C5×C4⋊C8—22no—
125C5×C4⋊C8D414yescomplemented
126#3963C2×C411yescharacteristic
127#3963C2×C411yescharacteristic
128#3963C2×C411yescharacteristic
129#3963C2×C411yescharacteristic
130#3963C2×C411yescharacteristic
131#3963C2×C411yescharacteristic
132C22⋊#168—22no—
133C22⋊#168D414yescomplemented
134#3952—22no—
135#3952—22no—
136#3952—22no—
137#3952—22no—
138#3952—41no—
139#3952—41no—
140#3947—22no—
141#3946—22no—
142#3946—22no—
143C8×Dic5—22no—
144#3935—22no—
145#3935—22no—
146C2×#435—51no—
147C2×#435—51no—
148C2×C8×D4—51no—
149C22×C4⋊C8D511yescharacteristic, complemented
150C4×#121—51no—
151#1955—51no—
152#1940—51no—
153#1924—51no—
154#1923—51no—
155#1869—51no—
156#1869—51no—
157#1851—51no—
158#1850—51no—
159#1771—51no—
160#1749—51no—
161C24×C5C22×C411yescharacteristic
162C23×D5C22×C411yescharacteristic
163C23×D5C22×C411yescharacteristic
164C22×C4×C5—22no—
165C22×C4×C5—22no—
166C22×C4×C5—22no—
167C22×C4×C5—21no—
168C22×C4×C5—21no—
169C22×C4×C5—21no—
170C22×C4×C5—21no—
171C22×C4×C5—22no—
172C22×C4×C5—22no—
173C22×C4×C5—41no—
174C22×C4×C5C22×C411yescharacteristic
175C22×C4×C5C22×C411yescharacteristic
176C22×C4×C5C22×C411yescharacteristic
177C22×C4×C5C22×C411yescharacteristic
178C22×C4×C5C22×C411yescharacteristic
179C22×C4×C5C2×D412yes—
180C22×C4×C5#4112yes—
181C22×C4×C5C2411yescharacteristic
182C2×C22⋊D5—22no—
183C2×C22⋊D5—22no—
184C2×C22⋊D5—22no—
185C2×C22⋊D5—22no—
186C2×C22⋊D5—22no—
187C2×C22⋊D5M1614yescomplemented
188C22×Dic5C22×C411yescharacteristic
189C22×Dic5C22×C411yescharacteristic
190C22×Dic5C22×C411yescharacteristic
191C22×Dic5C22×C411yescharacteristic
192C22×Dic5C22×C411yescharacteristic
193C22×Dic5C22×C411yescharacteristic
194C2×D20—22no—
195C2×D20—22no—
196C2×D20—41no—
197C2×C4×D5—21no—
198C2×C4×D5—21no—
199C2×C4×D5—21no—
200C2×C4×D5—21no—
201C2×C4×D5—21no—
202C2×C4×D5—21no—
203C2×C4×D5—21no—
204C2×C4×D5—21no—
205C2×C4×D5—21no—
206C2×C4×D5—21no—
207C2×C4×D5—21no—
208C2×C4×D5—21no—
209C2×C5×C8—21no—
210C2×C5×C8—21no—
211C2×C5×C8—21no—
212C2×C5×C8—21no—
213C2×C5×C8—21no—
214C2×C5×C8—21no—
215C2×C5×C8—21no—
216C2×C5×C8—21no—
217C2×C5×C8—21no—
218C2×C5×C8—21no—
219C2×C5×C8—44no—
220C2×C5×C8—44no—
221C2×C5×C8C2×D412yes—
222C2×C5×C8C2×D412yes—
223C42×C5—22no—
224C42×C5—22no—
225C42×C5—21no—
226C42×C5—21no—
227C42×C5C2×D412yes—
228C42×C5#4112yes—
229C22⋊Dic5—22no—
230C22⋊Dic5—22no—
231#685—22no—
232#685—22no—
233#685—22no—
234#685—22no—
235#685—22no—
236#685—22no—
237#685—22no—
238#685—22no—
239C4⋊Dic5—22no—
240C4⋊Dic5—22no—
241C4⋊Dic5—41no—
242#683—22no—
243#683—22no—
244C4×Dic5—21no—
245C4×Dic5—21no—
246C4×Dic5—21no—
247C4×Dic5—21no—
248C2×#168—21no—
249C2×#168—21no—
250C2×#168—21no—
251C2×#168—21no—
252C2×#168—21no—
253C2×#168—21no—
254C2×#168—21no—
255C2×#168—21no—
256C2×#168—21no—
257C2×#168—21no—
258C2×#168C2×D412yes—
259C2×#168C2×D412yes—
260#676—44no—
261C8×D5—44no—
262C22×M16—51no—
263C23×C8—51no—
264C23×C8C2×D511yescharacteristic
265C23×C8C2×D511yescharacteristic
266C2×#121—51no—
267C2×C4×D4—51no—
268C2×C4×D4—51no—
269C2×C4×D4—51no—
270C22×C42C2×D511yescharacteristic
271#435—104no—
272#435—104no—
273C8×D4—104no—
274C2×C4⋊C8—24no—
275C2×C4⋊C8—51no—
276C2×C4⋊C8—51no—
277C2×C4⋊C8C2×D511yescharacteristic
278C2×C4⋊C8C2×D511yescharacteristic
279C2×C4⋊C8C2×D511yescharacteristic
280C2×C4⋊C8C2×D511yescharacteristic
281C2×C22⋊C8—51no—
282C2×C22⋊C8—51no—
283C2×C22⋊C8—51no—
284C2×C22⋊C8—51no—
285C2×C22⋊C8—51no—
286C2×C22⋊C8—51no—
287C2×C22⋊C8—51no—
288C2×C22⋊C8—51no—
289C2×#97—51no—
290C2×#97—51no—
291C2×#97—51no—
292C2×C4×C8—51no—
293#390—51no—
294#389—51no—
295#388—51no—
296#388—51no—
297#386—51no—
298#386—51no—
299#380—51no—
300C4×C4⋊C4—51no—
301C4×C22⋊C4—51no—
302C4×C22⋊C4—51no—
303#336—51no—
304#336—51no—
305#336—51no—
306#336—51no—
307#336—51no—
308#336—51no—
309C23×C5—21no—
310C23×C5—21no—
311C23×C5—21no—
312C23×C5—21no—
313C23×C5C4×D412yes—
314C23×C5C2×M1612yes—
315C23×C5#13112yes—
316C23×C5C23×C411yescharacteristic
317C22×D5—21no—
318C22×D5—21no—
319C22×D5—21no—
320C22×D5—21no—
321C22×D5—21no—
322C22×D5—21no—
323C22×D5—21no—
324C22×D5—21no—
325C22×D5—21no—
326C22×D5—21no—
327C22×D5—21no—
328C22×D5—21no—
329C22×D5—21no—
330C22×D5C2×M1612yes—
331C2×C4×C5—28no—
332C2×C4×C5—21no—
333C2×C4×C5—21no—
334C2×C4×C5—21no—
335C2×C4×C5—21no—
336C2×C4×C5—21no—
337C2×C4×C5—21no—
338C2×C4×C5—21no—
339C2×C4×C5—21no—
340C2×C4×C5—22no—
341C2×C4×C5—22no—
342C2×C4×C5—22no—
343C2×C4×C5—22no—
344C2×C4×C5—21no—
345C2×C4×C5—21no—
346C2×C4×C5—21no—
347C2×C4×C5—44no—
348C2×C4×C5C4×D412yes—
349C2×C4×C5C4×D412yes—
350C2×C4×C5C4×D412yes—
351C2×C4×C5#13112yes—
352C2×C4×C5C22×D411yescharacteristic
353C2×C4×C5C22×D411yescharacteristic
354C2×C4×C5C2×#4111yescharacteristic
355C2×C4×C5C2×#4111yescharacteristic
356C2×C4×C5H(5,𝔽2)11yescharacteristic
357C2×C4×C52−1+411yescharacteristic
358C22⋊D5—28no—
359C22⋊D5—44no—
360C2×Dic5—21no—
361C2×Dic5—21no—
362C2×Dic5—21no—
363C2×Dic5—21no—
364C2×Dic5—21no—
365C2×Dic5—21no—
366C2×Dic5—21no—
367C2×Dic5—21no—
368C2×Dic5—21no—
369C2×Dic5—21no—
370C2×Dic5—21no—
371C2×Dic5—21no—
372C2×Dic5—21no—
373C2×Dic5—21no—
374C2×Dic5—21no—
375C2×Dic5—21no—
376C2×Dic5—21no—
377C2×Dic5C2×M1612yes—
378D20—44no—
379C4×D5—41no—
380C4×D5—41no—
381C4×D5—41no—
382C4×D5—41no—
383C4×D5—41no—
384C4×D5—41no—
385C4×D5—41no—
386C4×D5—41no—
387C5×C8—22no—
388C5×C8—22no—
389C5×C8—41no—
390C5×C8—41no—
391#168—22no—
392#168—22no—
393#168—41no—
394#168—41no—
395C22×D4—51no—
396C22×D4—51no—
397C22×D4—51no—
398C23×C4—51no—
399C23×C4—51no—
400C23×C4C4×D511yescharacteristic
401C23×C4C4×D511yescharacteristic
402C23×C4C22×D511yescharacteristic
403C2×M16—102no—
404C2×M16—102no—
405C2×M16—201no—
406C22×C8—22no—
407C22×C8—22no—
408C22×C8—22no—
409C22×C8—22no—
410C22×C8—41no—
411C22×C8—41no—
412C22×C8—51no—
413C22×C8—51no—
414C22×C8—51no—
415C22×C8—51no—
416C22×C8—102no—
417C22×C8—102no—
418C22×C8—201no—
419C22×C8C22×D511yescharacteristic
420C22×C8C22×D511yescharacteristic
421C22×C8C22×D511yescharacteristic
422C22×C8C22×D511yescharacteristic
423#121—104no—
424C4×D4—102no—
425C4×D4—102no—
426C4×D4—102no—
427C4×D4—102no—
428C4×D4—102no—
429C4×D4—102no—
430C2×C4⋊C4—51no—
431C2×C4⋊C4—51no—
432C2×C4⋊C4—51no—
433C2×C4⋊C4—51no—
434C2×C4⋊C4—51no—
435C2×C22⋊C4—51no—
436C2×C22⋊C4—51no—
437C2×C22⋊C4—51no—
438C2×C22⋊C4—51no—
439C2×C22⋊C4—51no—
440C2×C22⋊C4—51no—
441C2×C22⋊C4—51no—
442C2×C22⋊C4—51no—
443C2×C22⋊C4—51no—
444C2×C22⋊C4—51no—
445C2×C42—22no—
446C2×C42—22no—
447C2×C42—51no—
448C2×C42—51no—
449C2×C42C4×D511yescharacteristic
450C2×C42C4×D511yescharacteristic
451C2×C42C22×D511yescharacteristic
452C2×C42C22×D511yescharacteristic
453C4⋊C8—22no—
454C4⋊C8—22no—
455C4⋊C8—22no—
456C4⋊C8—102no—
457C4⋊C8—102no—
458C4⋊C8C22⋊D514yescomplemented
459C22⋊C8—54no—
460C22⋊C8—102no—
461C22⋊C8—102no—
462C22⋊C8—102no—
463C22⋊C8—102no—
464C22⋊C8—102no—
465C22⋊C8—201no—
466C22⋊C8—201no—
467#97—102no—
468#97—102no—
469#97—102no—
470C4×C8—102no—
471#95—51no—
472#95—51no—
473#95—51no—
474#95—51no—
475#95—51no—
476#95—51no—
477C22×C5—22no—
478C22×C5—22no—
479C22×C5—22no—
480C22×C5—22no—
481C22×C5—22no—
482C22×C5—22no—
483C22×C5#43514yescomplemented
484C22×C5C2×C4×D411yescharacteristic
485C22×C5C2×C4×D411yescharacteristic
486C22×C5#52011yescharacteristic
487C22×C5C22×M1611yescharacteristic
488C22×C5C2×#13111yescharacteristic
489C22×C5C2×#13111yescharacteristic
490C22×C5#56811yescharacteristic
491C2×D5—22no—
492C2×D5—22no—
493C2×D5—22no—
494C2×D5—41no—
495C2×D5—41no—
496C2×D5—41no—
497C2×D5—41no—
498C2×D5—41no—
499C2×D5—41no—
500C2×D5—41no—
501C2×D5—41no—
502C2×D5—41no—
503C2×D5—41no—
504C2×D5—41no—
505C4×C5—22no—
506C4×C5—22no—
507C4×C5—22no—
508C4×C5—22no—
509C4×C5—41no—
510C4×C5D4211yescharacteristic
511C4×C5#54711yescharacteristic
512C4×C5#54811yescharacteristic
513C4×C5#55311yescharacteristic
514Dic5—22no—
515Dic5—41no—
516Dic5—41no—
517Dic5—41no—
518Dic5—41no—
519Dic5—41no—
520C24—51no—
521C24—51no—
522C24C2×C4×D511yescharacteristic
523C2×D4—54no—
524C2×D4—102no—
525C2×D4—102no—
526C2×D4—102no—
527C2×D4—102no—
528C2×D4—102no—
529C2×D4—102no—
530C2×D4—102no—
531C2×D4—201no—
532C22×C4—22no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—41no—
542C22×C4—51no—
543C22×C4—51no—
544C22×C4—51no—
545C22×C4—51no—
546C22×C4—51no—
547C22×C4—51no—
548C22×C4—101no—
549C22×C4—101no—
550C22×C4—101no—
551C22×C4—101no—
552C22×C4—101no—
553C22×C4—101no—
554C22×C4—101no—
555C22×C4—101no—
556C22×C4—101no—
557C22×C4—101no—
558C22×C4—101no—
559C22×C4—101no—
560C22×C4C2×C4×D511yescharacteristic
561C22×C4C2×C4×D511yescharacteristic
562C22×C4C2×C4×D511yescharacteristic
563C22×C4C2×C4×D511yescharacteristic
564C22×C4C2×C4×D511yescharacteristic
565C22×C4D4×D512yes—
566C22×C4#71312yes—
567C22×C4C23×D511yescharacteristic
568M16—204no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—44no—
580C2×C8—44no—
581C2×C8—52no—
582C2×C8—52no—
583C2×C8—101no—
584C2×C8—101no—
585C2×C8—101no—
586C2×C8—101no—
587C2×C8—101no—
588C2×C8—101no—
589C2×C8—101no—
590C2×C8—101no—
591C2×C8—101no—
592C2×C8—101no—
593C2×C8—204no—
594C2×C8C2×C22⋊D512yes—
595C2×C8C2×C22⋊D512yes—
596C4⋊C4—102no—
597C4⋊C4—102no—
598C4⋊C4—102no—
599C4⋊C4—102no—
600C4⋊C4—201no—
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—
611C42—21no—
612C42—21no—
613C42—22no—
614C42—22no—
615C42—101no—
616C42—101no—
617C42—101no—
618C42—101no—
619C42#70912yes—
620C42C2×C22⋊D512yes—
621C2×C5—24no—
622C2×C5#236111yescharacteristic
623C2×C5C2×#43511yescharacteristic
624C2×C5#292911yescharacteristic
625C2×C5D4×M1611yescharacteristic
626C2×C5#293511yescharacteristic
627C2×C5#299011yescharacteristic
628C2×C5#299211yescharacteristic
629D5—42no—
630D5—81no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—52no—
636C23—101no—
637C23—101no—
638C23—101no—
639C23—101no—
640C23—101no—
641C23—101no—
642C23—101no—
643C23—101no—
644C23—101no—
645C23—101no—
646C23—101no—
647C23—101no—
648C23—101no—
649C23#403912yes—
650C23#404712yes—
651C23D5×M1612yes—
652C23C22×C4×D511yescharacteristic
653D4—108no—
654D4—204no—
655D4—204no—
656C2×C4—28no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—44no—
673C2×C4—52no—
674C2×C4—101no—
675C2×C4—101no—
676C2×C4—101no—
677C2×C4—101no—
678C2×C4—101no—
679C2×C4—101no—
680C2×C4—101no—
681C2×C4—101no—
682C2×C4—101no—
683C2×C4—101no—
684C2×C4—101no—
685C2×C4—101no—
686C2×C4—101no—
687C2×C4—101no—
688C2×C4—101no—
689C2×C4—101no—
690C2×C4—101no—
691C2×C4—201no—
692C2×C4—201no—
693C2×C4—201no—
694C2×C4—201no—
695C2×C4—201no—
696C2×C4—201no—
697C2×C4—201no—
698C2×C4—201no—
699C2×C4#403912yes—
700C2×C4#404712yes—
701C2×C4C4×C22⋊D512yes—
702C2×C4C4×C22⋊D512yes—
703C2×C4C2×#70911yescharacteristic
704C2×C4C2×D4×D511yescharacteristic
705C2×C4#414411yescharacteristic
706C2×C4C2×#71311yescharacteristic
707C2×C4#414711yescharacteristic
708C2×C4C22×C22⋊D511yescharacteristic
709C8—22no—
710C8—22no—
711C8—41no—
712C8—41no—
713C8—102no—
714C8—102no—
715C8—201no—
716C8—201no—
717C5#2298711yescharacteristic, complemented, Sylow
718C22—22no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—22no—
724C22—102no—
725C22—102no—
726C22—102no—
727C22—201no—
728C22—201no—
729C22—201no—
730C22—201no—
731C22—201no—
732C22—201no—
733C22—201no—
734C22—201no—
735C22—201no—
736C22—201no—
737C22—201no—
738C22#6512514yescomplemented
739C22C2×#403911yescharacteristic
740C22#6583811yescharacteristic
741C22C2×#404711yescharacteristic
742C22C2×#404711yescharacteristic
743C22C2×D5×M1611yescharacteristic
744C22#6607911yescharacteristic
745C22C2×C4×C22⋊D511yescharacteristic
746C4—22no—
747C4—22no—
748C4—22no—
749C4—22no—
750C4—41no—
751C4—102no—
752C4—201no—
753C4—201no—
754C4—201no—
755C4—201no—
756C4—201no—
757C4#6584111yescharacteristic
758C4#6584811yescharacteristic
759C4D4×C22⋊D511yescharacteristic
760C4#6615111yescharacteristic
761C2—24no—
762C2—202no—
763C2—401no—
764C2C2×#6512511yescharacteristic
765C2#1061073511yescharacteristic
766C2#1061074611yescharacteristic
767C2#1061074711yescharacteristic
768C2#1061389411yescharacteristic
769C2#1061546511yescharacteristic
770C2M16×C22⋊D511yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D5
commutator, socleC23×C5C23×C4
FittingC22×C5×C4⋊C8C2
prime radicalC2×#4076C4
cosocleC22×C4×C5C24
hypercenterC22×C4⋊C8D5
hypocenterC5#22987
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C22×C4 ◁ C22×C4⋊C8

Complements

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

NH ≅ G/Ntype
1. C22×C5×C4⋊C8C2semidirect
2. C2×#65400C2semidirect
3. C2×C8×C22⋊D5C2semidirect
5. C2×#65125C2semidirect
6. #10602768C2semidirect
7. #10602768C2semidirect
8. #10602322C2semidirect
9. #10601271C2semidirect
10. #10601270C2semidirect
11. #10601264C2semidirect
12. #10601262C2semidirect
13. #10601260C2semidirect
14. #10601243C2semidirect
15. #10601242C2semidirect
125. C5×C4⋊C8D4semidirect
133. C22⋊#168D4semidirect
149. C22×C4⋊C8D5semidirect
187. C2×C22⋊D5M16semidirect
458. C4⋊C8C22⋊D5semidirect
483. C22×C5#435semidirect
717. C5#22987semidirect
738. C22#65125semidirect

Maximal subgroups

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

subgroupindex
C22×C5×C4⋊C82
C2×#654002
C2×C8×C22⋊D52
C4×#40762
C2×#651252
#106027682
#106023222
#106012712
#106012702
#106012642
#106012622
#106012602
#106012432
#106012422
#229875