Finite Group Databasebeta

← #12110399

Subgroups — #12110399

Order 1280.

1156 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#4099C211yesmaximal, characteristic
2C2×#65496C211yesmaximal, characteristic, complemented
3C2×#65018C211yesmaximal, characteristic, complemented
4C5×#1779C211yesmaximal, characteristic, complemented
5#10600751C211yesmaximal, characteristic, complemented
6#10600751C211yesmaximal, characteristic, complemented
7#10600746C211yesmaximal, characteristic, complemented
8#10600744C211yesmaximal, characteristic, complemented
9#10600742C211yesmaximal, characteristic, complemented
10#10600710C211yesmaximal, characteristic, complemented
11#10600709C211yesmaximal, characteristic, complemented
12#10600707C211yesmaximal, characteristic, complemented
13#10600706C211yesmaximal, characteristic, complemented
14#10600706C211yesmaximal, characteristic, complemented
15#10600705C211yesmaximal, characteristic, complemented
16C24×C4×C5C2211yescharacteristic
17C2×#4099C411yescharacteristic
18C2×C4×C22⋊D5C2211yescharacteristic
19C2×C4×C22⋊D5C2211yescharacteristic
20C2×C4×C22⋊D5C2211yescharacteristic
21C22×#681C2211yescharacteristic
22C22×#681C2211yescharacteristic
23C22×#676C2211yescharacteristic, complemented
24C2×C5×C22⋊C8C2211yescharacteristic
25C2×C5×C22⋊C8C2211yescharacteristic
26C2×C5×C22⋊C8C2211yescharacteristic
27C2×C5×C22⋊C8C2211yescharacteristic
28C2×C5×C22⋊C8C2211yescharacteristic
29C2×C5×C22⋊C8C2211yescharacteristic
30#65536C411yescharacteristic
31#65502C411yescharacteristic
32#65502C411yescharacteristic
33#65502C411yescharacteristic
34#65499C411yescharacteristic
35#65499C411yescharacteristic
36#65499C411yescharacteristic
37C4×C22⋊Dic5C2211yescharacteristic
38C4×C22⋊Dic5C2211yescharacteristic
39C4×C22⋊Dic5C2211yescharacteristic
40#65496—24no—
41C2×C22⋊#168C2211yescharacteristic
42C2×C22⋊#168C2211yescharacteristic
43C2×C22⋊#168C2211yescharacteristic
44C2×C22⋊#168C2211yescharacteristic
45C2×#3952C2211yescharacteristic, complemented
46C2×#3952C2211yescharacteristic, complemented
47C2×#3952C2211yescharacteristic, complemented
48C2×#3947C2211yescharacteristic, complemented
49C2×#3946C2211yescharacteristic, complemented
50C2×#3946C2211yescharacteristic, complemented
51C2×#3946C2211yescharacteristic, complemented
52C2×C8×Dic5C2211yescharacteristic, complemented
53C2×C8×Dic5C2211yescharacteristic, complemented
54#65018—24no—
55#64770C2211yescharacteristic, complemented
56#64770C2211yescharacteristic, complemented
57#64770C2211yescharacteristic, complemented
58#64770C2211yescharacteristic, complemented
59#64770C2211yescharacteristic, complemented
60#64770C2211yescharacteristic, complemented
61#22038—51nomaximal, Sylow
62C25×C5C2×C411yescharacteristic
63C23×C4×C5—22no—
64C23×C4×C5—22no—
65C23×C4×C5—41no—
66C23×C4×C5—41no—
67C23×C4×C5—41no—
68C23×C4×C5—41no—
69C23×C4×C5C2×C411yescharacteristic
70C23×C4×C5C2×C411yescharacteristic
71C23×C4×C5C2×C411yescharacteristic
72C23×C4×C5C2311yescharacteristic
73C23×C4×C5C2311yescharacteristic
74C23×C4×C5C2311yescharacteristic
75C22×C22⋊D5C2×C411yescharacteristic
76C22×C22⋊D5C2×C411yescharacteristic
77C22×C22⋊D5C2×C411yescharacteristic
78C22×C4×D5C2311yescharacteristic
79C22×C5×C8C2311yescharacteristic
80C22×C5×C8C2311yescharacteristic
81C22×C5×C8C2311yescharacteristic
82C22×C5×C8C2311yescharacteristic
83#4099—24no—
84C2×C22⋊Dic5C2×C411yescharacteristic
85C2×C22⋊Dic5C2×C411yescharacteristic
86C2×C22⋊Dic5C2×C411yescharacteristic
87C2×C22⋊Dic5C2×C411yescharacteristic
88C2×C22⋊Dic5C2×C411yescharacteristic
89C2×C22⋊Dic5C2×C411yescharacteristic
90C2×C22⋊Dic5C2×C411yescharacteristic
91C2×C22⋊Dic5C2×C411yescharacteristic
92C2×C22⋊Dic5C2×C411yescharacteristic
93C4×C22⋊D5—22no—
94C4×C22⋊D5—22no—
95C4×C22⋊D5—41no—
96C4×C22⋊D5—41no—
97C4×C22⋊D5—41no—
98C4×C22⋊D5—41no—
99C2×#685C2×C411yescharacteristic
100C2×#685C2×C411yescharacteristic
101C2×#685C2×C411yescharacteristic
102C2×#683C2×C411yescharacteristic
103C2×#683C2×C411yescharacteristic
104C2×#683C2×C411yescharacteristic
105C2×C4×Dic5C2311yescharacteristic
106C2×C4×Dic5C2311yescharacteristic
107C2×C4×Dic5C2311yescharacteristic
108C2×#681—22no—
109C2×#681—41no—
110C2×#681—41no—
111C2×#681—41no—
112C2×#681—41no—
113C2×#681D414yescomplemented
114C22×#168C2311yescharacteristic
115C22×#168C2311yescharacteristic
116C22×#168C2311yescharacteristic
117C22×#168C2311yescharacteristic
118C2×#676—22no—
119C2×#676—41no—
120C2×#676—41no—
121C5×C22⋊C8—22no—
122C5×C22⋊C8—22no—
123C5×C22⋊C8—41no—
124C5×C22⋊C8—41no—
125C5×C22⋊C8—41no—
126C5×C22⋊C8—41no—
127#3963C2×C411yescharacteristic
128#3963C2×C411yescharacteristic
129#3963C2×C411yescharacteristic
130#3963C2×C411yescharacteristic
131#3963C2×C411yescharacteristic
132#3963C2×C411yescharacteristic
133C22⋊#168—22no—
134C22⋊#168—22no—
135C22⋊#168—22no—
136C22⋊#168—22no—
137#3952—22no—
138#3952—41no—
139#3952—41no—
140#3947—41no—
141#3946—22no—
142#3946—41no—
143#3946—41no—
144C8×Dic5—22no—
145C8×Dic5—41no—
146C2×#436—51no—
147C2×#407—51no—
148C4×#120—51no—
149#1955—51no—
150#1954—51no—
151#1924—51no—
152#1923—51no—
153#1923—51no—
154#1923—51no—
155#1870—51no—
156#1870—51no—
157#1870—51no—
158#1851—51no—
159#1779D511yescharacteristic, complemented
160#1753—51no—
161C24×C5—22no—
162C24×C5—22no—
163C24×C5—22no—
164C24×C5—41no—
165C24×C5—41no—
166C24×C5—41no—
167C24×C5—41no—
168C24×C5C22×C411yescharacteristic
169C24×C5C22×C411yescharacteristic
170C24×C5C22×C411yescharacteristic
171C23×D5C22×C411yescharacteristic
172C22×C4×C5—21no—
173C22×C4×C5—21no—
174C22×C4×C5—21no—
175C22×C4×C5—21no—
176C22×C4×C5—22no—
177C22×C4×C5—22no—
178C22×C4×C5—22no—
179C22×C4×C5—21no—
180C22×C4×C5—21no—
181C22×C4×C5—21no—
182C22×C4×C5—21no—
183C22×C4×C5—21no—
184C22×C4×C5—21no—
185C22×C4×C5—21no—
186C22×C4×C5—21no—
187C22×C4×C5—21no—
188C22×C4×C5—21no—
189C22×C4×C5—21no—
190C22×C4×C5—21no—
191C22×C4×C5—41no—
192C22×C4×C5—41no—
193C22×C4×C5—41no—
194C22×C4×C5—41no—
195C22×C4×C5—41no—
196C22×C4×C5—41no—
197C22×C4×C5—44no—
198C22×C4×C5—44no—
199C22×C4×C5—44no—
200C22×C4×C5—44no—
201C22×C4×C5C22×C411yescharacteristic
202C22×C4×C5C22×C411yescharacteristic
203C22×C4×C5C22×C411yescharacteristic
204C22×C4×C5C2×D412yes—
205C22×C4×C5#4112yes—
206C22×C4×C5C2411yescharacteristic
207C2×C22⋊D5—22no—
208C2×C22⋊D5—22no—
209C2×C22⋊D5—22no—
210C2×C22⋊D5—22no—
211C2×C22⋊D5—22no—
212C2×C22⋊D5—41no—
213C2×C22⋊D5—41no—
214C2×C22⋊D5—41no—
215C2×C22⋊D5—41no—
216C22×Dic5C22×C411yescharacteristic
217C22×Dic5C22×C411yescharacteristic
218C22×Dic5C22×C411yescharacteristic
219C22×Dic5C22×C411yescharacteristic
220C22×Dic5C22×C411yescharacteristic
221C22×Dic5C22×C411yescharacteristic
222C22×Dic5C22×C411yescharacteristic
223C2×C4×D5—21no—
224C2×C4×D5—21no—
225C2×C4×D5—21no—
226C2×C4×D5—21no—
227C2×C4×D5—21no—
228C2×C4×D5—21no—
229C2×C5×C8—21no—
230C2×C5×C8—21no—
231C2×C5×C8—21no—
232C2×C5×C8—21no—
233C2×C5×C8—21no—
234C2×C5×C8—21no—
235C2×C5×C8—21no—
236C2×C5×C8—21no—
237C2×C5×C8—21no—
238C2×C5×C8—21no—
239C2×C5×C8—21no—
240C2×C5×C8—21no—
241C22⋊Dic5—22no—
242C22⋊Dic5—22no—
243C22⋊Dic5—22no—
244C22⋊Dic5—22no—
245C22⋊Dic5—41no—
246C22⋊Dic5—41no—
247C22⋊Dic5—41no—
248C22⋊Dic5—41no—
249C22⋊Dic5M1614yescomplemented
250#685—22no—
251#685—41no—
252#685—41no—
253#683—22no—
254#683—41no—
255#683—41no—
256C4×Dic5—21no—
257C4×Dic5—21no—
258C4×Dic5—21no—
259C4×Dic5—21no—
260C4×Dic5—21no—
261C4×Dic5—21no—
262#681—44no—
263#681—44no—
264C2×#168—21no—
265C2×#168—21no—
266C2×#168—21no—
267C2×#168—21no—
268C2×#168—21no—
269C2×#168—21no—
270C2×#168—21no—
271C2×#168—21no—
272C2×#168—21no—
273C2×#168—21no—
274C2×#168C2×D412yes—
275C2×#168C2×D412yes—
276#676—44no—
277C24×C4C2×D511yescharacteristic
278C22×M16—51no—
279C22×M16—51no—
280C22×M16—51no—
281C2×#120—51no—
282C2×C4×D4—51no—
283C2×C4×D4—51no—
284C2×C4×D4—51no—
285#436—104no—
286C2×C4⋊C8—51no—
287C2×C4⋊C8—51no—
288C2×C4⋊C8—51no—
289#407—104no—
290C2×C22⋊C8—51no—
291C2×C22⋊C8—51no—
292C2×C22⋊C8—51no—
293C2×C22⋊C8—51no—
294C2×C22⋊C8—51no—
295C2×C22⋊C8—51no—
296C2×C22⋊C8—51no—
297C2×C22⋊C8C2×D511yescharacteristic
298C2×C22⋊C8C2×D511yescharacteristic
299C2×C22⋊C8C2×D511yescharacteristic
300C2×C22⋊C8C2×D511yescharacteristic
301C2×C22⋊C8C2×D511yescharacteristic
302C2×C22⋊C8C2×D511yescharacteristic
303C2×#97—51no—
304C2×C4×C8—51no—
305C2×C4×C8—51no—
306#386—51no—
307#386—51no—
308#386—51no—
309#385—51no—
310#385—51no—
311#385—51no—
312#379—51no—
313C4×C22⋊C4—51no—
314C4×C22⋊C4—51no—
315C4×C22⋊C4—51no—
316#336—51no—
317#336—51no—
318#336—51no—
319#336—51no—
320#336—51no—
321#336—51no—
322C23×C5—21no—
323C23×C5—21no—
324C23×C5—21no—
325C23×C5—21no—
326C23×C5—21no—
327C23×C5—21no—
328C23×C5—21no—
329C23×C5—21no—
330C23×C5—21no—
331C23×C5—21no—
332C23×C5—21no—
333C23×C5—21no—
334C23×C5—21no—
335C23×C5—21no—
336C23×C5—21no—
337C23×C5—21no—
338C23×C5—21no—
339C23×C5—21no—
340C23×C5—44no—
341C23×C5—44no—
342C23×C5—44no—
343C23×C5—44no—
344C23×C5—44no—
345C23×C5—44no—
346C23×C5—44no—
347C23×C5C4×D412yes—
348C23×C5C2×M1612yes—
349C23×C5#13112yes—
350C23×C5C23×C411yescharacteristic
351C22×D5—21no—
352C22×D5—21no—
353C22×D5—21no—
354C22×D5—21no—
355C22×D5—21no—
356C22×D5—21no—
357C22×D5—21no—
358C2×C4×C5—21no—
359C2×C4×C5—21no—
360C2×C4×C5—22no—
361C2×C4×C5—22no—
362C2×C4×C5—22no—
363C2×C4×C5—22no—
364C2×C4×C5—21no—
365C2×C4×C5—21no—
366C2×C4×C5—21no—
367C2×C4×C5—21no—
368C2×C4×C5—21no—
369C2×C4×C5—21no—
370C2×C4×C5—44no—
371C2×C4×C5—44no—
372C2×C4×C5—44no—
373C2×C4×C5—41no—
374C2×C4×C5—41no—
375C2×C4×C5—41no—
376C2×C4×C5—41no—
377C2×C4×C5—41no—
378C2×C4×C5—41no—
379C2×C4×C5—41no—
380C2×C4×C5—41no—
381C2×C4×C5C4×D412yes—
382C2×C4×C5C22×D411yescharacteristic
383C2×C4×C5C2×#4111yescharacteristic
384C2×C4×C5H(5,𝔽2)11yescharacteristic
385C2×C4×C5H(5,𝔽2)11yescharacteristic
386C2×C4×C5H(5,𝔽2)11yescharacteristic
387C2×C4×C5H(5,𝔽2)11yescharacteristic
388C22⋊D5—44no—
389C22⋊D5—44no—
390C22⋊D5—44no—
391C2×Dic5—21no—
392C2×Dic5—21no—
393C2×Dic5—21no—
394C2×Dic5—21no—
395C2×Dic5—21no—
396C2×Dic5—21no—
397C2×Dic5—21no—
398C2×Dic5—21no—
399C2×Dic5—21no—
400C2×Dic5—21no—
401C2×Dic5—21no—
402C2×Dic5—21no—
403C2×Dic5—21no—
404C2×Dic5—21no—
405C2×Dic5—21no—
406C2×Dic5—21no—
407C2×Dic5—21no—
408C2×Dic5—21no—
409C2×Dic5—21no—
410C2×Dic5C2×M1612yes—
411C2×Dic5C2×M1612yes—
412C4×D5—41no—
413C4×D5—41no—
414C4×D5—41no—
415C4×D5—41no—
416C5×C8—41no—
417C5×C8—41no—
418C5×C8—41no—
419C5×C8—41no—
420#168—22no—
421#168—22no—
422#168—41no—
423#168—41no—
424C25C4×D511yescharacteristic
425C22×D4—51no—
426C22×D4—51no—
427C22×D4—51no—
428C23×C4—22no—
429C23×C4—22no—
430C23×C4—41no—
431C23×C4—41no—
432C23×C4—41no—
433C23×C4—41no—
434C23×C4—51no—
435C23×C4C4×D511yescharacteristic
436C23×C4C4×D511yescharacteristic
437C23×C4C4×D511yescharacteristic
438C23×C4C22×D511yescharacteristic
439C23×C4C22×D511yescharacteristic
440C23×C4C22×D511yescharacteristic
441C2×M16—54no—
442C2×M16—102no—
443C2×M16—102no—
444C2×M16—201no—
445C2×M16—201no—
446C2×M16—201no—
447C2×M16—201no—
448C2×M16—201no—
449C2×M16—201no—
450C22×C8—51no—
451C22×C8—51no—
452C22×C8—51no—
453C22×C8—51no—
454C22×C8C22×D511yescharacteristic
455C22×C8C22×D511yescharacteristic
456C22×C8C22×D511yescharacteristic
457C22×C8C22×D511yescharacteristic
458#120—104no—
459C4×D4—102no—
460C4×D4—102no—
461C4×D4—201no—
462C4×D4—201no—
463C4×D4—201no—
464C4×D4—201no—
465C2×C4⋊C4—51no—
466C2×C4⋊C4—51no—
467C2×C4⋊C4—51no—
468C2×C22⋊C4—51no—
469C2×C22⋊C4—51no—
470C2×C22⋊C4—51no—
471C2×C22⋊C4—51no—
472C2×C22⋊C4—51no—
473C2×C22⋊C4—51no—
474C2×C22⋊C4—51no—
475C2×C22⋊C4—51no—
476C2×C22⋊C4—51no—
477C2×C22⋊C4—51no—
478C2×C22⋊C4—51no—
479C2×C22⋊C4—51no—
480C2×C42—51no—
481C2×C42—51no—
482C2×C42—51no—
483C4⋊C8—102no—
484C4⋊C8—201no—
485C4⋊C8—201no—
486C22⋊C8—22no—
487C22⋊C8—22no—
488C22⋊C8—41no—
489C22⋊C8—41no—
490C22⋊C8—41no—
491C22⋊C8—41no—
492C22⋊C8—102no—
493C22⋊C8—102no—
494C22⋊C8—102no—
495C22⋊C8—102no—
496C22⋊C8—102no—
497C22⋊C8—201no—
498C22⋊C8—201no—
499#97—201no—
500C4×C8—102no—
501C4×C8—201no—
502#95—51no—
503#95—51no—
504#95—51no—
505#95—51no—
506#95—51no—
507#95—51no—
508C22×C5—22no—
509C22×C5—22no—
510C22×C5—22no—
511C22×C5—22no—
512C22×C5—22no—
513C22×C5—22no—
514C22×C5—22no—
515C22×C5—22no—
516C22×C5—22no—
517C22×C5—416no—
518C22×C5—41no—
519C22×C5—41no—
520C22×C5—41no—
521C22×C5—41no—
522C22×C5—41no—
523C22×C5—41no—
524C22×C5—41no—
525C22×C5—41no—
526C22×C5—41no—
527C22×C5—41no—
528C22×C5—41no—
529C22×C5—41no—
530C22×C5C2×C4×D411yescharacteristic
531C22×C5#51811yescharacteristic
532C22×C5#51811yescharacteristic
533C22×C5C22×M1611yescharacteristic
534C22×C5C2×#13111yescharacteristic
535C22×C5#56811yescharacteristic
536C22×C5#56811yescharacteristic
537C2×D5—41no—
538C2×D5—41no—
539C2×D5—41no—
540C2×D5—41no—
541C2×D5—41no—
542C2×D5—41no—
543C2×D5—41no—
544C4×C5—22no—
545C4×C5—41no—
546C4×C5—41no—
547C4×C5#53411yescharacteristic
548C4×C5#53511yescharacteristic
549C4×C5#53811yescharacteristic
550C4×C5#53811yescharacteristic
551Dic5—22no—
552Dic5—22no—
553Dic5—41no—
554Dic5—41no—
555Dic5—41no—
556Dic5—41no—
557Dic5—41no—
558C24—22no—
559C24—22no—
560C24—22no—
561C24—41no—
562C24—41no—
563C24—41no—
564C24—41no—
565C24—51no—
566C24C2×C4×D511yescharacteristic
567C24C2×C4×D511yescharacteristic
568C24C2×C4×D511yescharacteristic
569C2×D4—102no—
570C2×D4—102no—
571C2×D4—102no—
572C2×D4—102no—
573C2×D4—102no—
574C2×D4—201no—
575C2×D4—201no—
576C2×D4—201no—
577C2×D4—201no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—22no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—41no—
598C22×C4—41no—
599C22×C4—41no—
600C22×C4—41no—
601C22×C4—41no—
602C22×C4—41no—
603C22×C4—44no—
604C22×C4—44no—
605C22×C4—44no—
606C22×C4—44no—
607C22×C4—51no—
608C22×C4—51no—
609C22×C4—51no—
610C22×C4—51no—
611C22×C4—51no—
612C22×C4—51no—
613C22×C4—51no—
614C22×C4—101no—
615C22×C4—101no—
616C22×C4—101no—
617C22×C4—101no—
618C22×C4—101no—
619C22×C4—101no—
620C22×C4C2×C4×D511yescharacteristic
621C22×C4C2×C4×D511yescharacteristic
622C22×C4C2×C4×D511yescharacteristic
623C22×C4D4×D512yes—
624C22×C4#71112yes—
625C22×C4C23×D511yescharacteristic
626M16—204no—
627M16—204no—
628M16—204no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—52no—
642C2×C8—52no—
643C2×C8—101no—
644C2×C8—101no—
645C2×C8—101no—
646C2×C8—101no—
647C2×C8—101no—
648C2×C8—101no—
649C2×C8—101no—
650C2×C8—101no—
651C2×C8—101no—
652C2×C8—101no—
653C4⋊C4—102no—
654C4⋊C4—201no—
655C4⋊C4—201no—
656C22⋊C4—54no—
657C22⋊C4—102no—
658C22⋊C4—102no—
659C22⋊C4—102no—
660C22⋊C4—102no—
661C22⋊C4—102no—
662C22⋊C4—201no—
663C22⋊C4—201no—
664C22⋊C4—201no—
665C22⋊C4—201no—
666C22⋊C4—201no—
667C22⋊C4—201no—
668C42—101no—
669C42—101no—
670C42—101no—
671C42—101no—
672C42—101no—
673C42—101no—
674C2×C5—42no—
675C2×C5—42no—
676C2×C5—42no—
677C2×C5#232111yescharacteristic
678C2×C5#293311yescharacteristic
679C2×C5D4×M1611yescharacteristic
680C2×C5#297411yescharacteristic
681C2×C5#297511yescharacteristic
682C2×C5#297611yescharacteristic
683C2×C5#297811yescharacteristic
684D5—81no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—44no—
704C23—44no—
705C23—44no—
706C23—44no—
707C23—44no—
708C23—44no—
709C23—44no—
710C23—101no—
711C23—101no—
712C23—101no—
713C23—101no—
714C23—101no—
715C23—101no—
716C23—101no—
717C23#402712yes—
718C23#404712yes—
719C23D5×M1612yes—
720C23C22×C4×D511yescharacteristic
721D4—204no—
722D4—204no—
723D4—204no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—44no—
737C2×C4—44no—
738C2×C4—44no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—52no—
748C2×C4—52no—
749C2×C4—101no—
750C2×C4—101no—
751C2×C4—101no—
752C2×C4—101no—
753C2×C4—101no—
754C2×C4—101no—
755C2×C4—101no—
756C2×C4—101no—
757C2×C4—101no—
758C2×C4—101no—
759C2×C4—101no—
760C2×C4—101no—
761C2×C4—101no—
762C2×C4—101no—
763C2×C4—101no—
764C2×C4—101no—
765C2×C4—101no—
766C2×C4—101no—
767C2×C4—101no—
768C2×C4—201no—
769C2×C4—201no—
770C2×C4—201no—
771C2×C4—201no—
772C2×C4#402712yes—
773C2×C4C2×D4×D511yescharacteristic
774C2×C4C2×#71111yescharacteristic
775C2×C4#414411yescharacteristic
776C2×C4#414411yescharacteristic
777C2×C4#414411yescharacteristic
778C2×C4#414411yescharacteristic
779C8—41no—
780C8—41no—
781C8—41no—
782C8—41no—
783C8—102no—
784C8—102no—
785C8—201no—
786C8—201no—
787C5#2203811yescharacteristic, complemented, Sylow
788C22—22no—
789C22—22no—
790C22—22no—
791C22—22no—
792C22—22no—
793C22—22no—
794C22—22no—
795C22—22no—
796C22—22no—
797C22—416no—
798C22—41no—
799C22—41no—
800C22—41no—
801C22—41no—
802C22—41no—
803C22—41no—
804C22—41no—
805C22—41no—
806C22—41no—
807C22—41no—
808C22—41no—
809C22—41no—
810C22—201no—
811C22—201no—
812C22—201no—
813C22—201no—
814C22—201no—
815C22—201no—
816C22—201no—
817C22C2×#402711yescharacteristic
818C22#6582011yescharacteristic
819C22#6582011yescharacteristic
820C22C2×#404711yescharacteristic
821C22C2×D5×M1611yescharacteristic
822C22#6607911yescharacteristic
823C22#6607911yescharacteristic
824C4—22no—
825C4—41no—
826C4—41no—
827C4—102no—
828C4—102no—
829C4—201no—
830C4—201no—
831C4—201no—
832C4—201no—
833C4—201no—
834C4#6592311yescharacteristic
835C4#6592611yescharacteristic
836C4#6592711yescharacteristic
837C4#6592711yescharacteristic
838C2—42no—
839C2—42no—
840C2—42no—
841C2—401no—
842C2#1060555211yescharacteristic
843C2#1061032711yescharacteristic
844C2#1061033411yescharacteristic
845C2#1061033511yescharacteristic
846C2#1061035911yescharacteristic
847C2#1061036511yescharacteristic
848C2#1061036711yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D5
commutator, socleC23×C5C23×C4
FittingC5×#1779C2
prime radicalC2×#4099C4
cosocleC22×C4×C5C24
hypercenter#1779D5
hypocenterC5#22038
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C22×C4 ◁ #1779

Complements

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

NH ≅ G/Ntype
2. C2×#65496C2semidirect
3. C2×#65018C2semidirect
4. C5×#1779C2semidirect
5. #10600751C2semidirect
6. #10600751C2semidirect
7. #10600746C2semidirect
8. #10600744C2semidirect
9. #10600742C2semidirect
10. #10600710C2semidirect
11. #10600709C2semidirect
12. #10600707C2semidirect
13. #10600706C2semidirect
14. #10600706C2semidirect
15. #10600705C2semidirect
23. C22×#676C22semidirect
45. C2×#3952C22semidirect
46. C2×#3952C22semidirect
47. C2×#3952C22semidirect
48. C2×#3947C22semidirect
49. C2×#3946C22semidirect
50. C2×#3946C22semidirect
51. C2×#3946C22semidirect
52. C2×C8×Dic5C22semidirect
53. C2×C8×Dic5C22semidirect
55. #64770C22semidirect
56. #64770C22semidirect
57. #64770C22semidirect
58. #64770C22semidirect
59. #64770C22semidirect
60. #64770C22semidirect
113. C2×#681D4semidirect
159. #1779D5semidirect
249. C22⋊Dic5M16semidirect
787. C5#22038semidirect

Maximal subgroups

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

subgroupindex
C4×#40992
C2×#654962
C2×#650182
C5×#17792
#106007512
#106007462
#106007442
#106007422
#106007102
#106007092
#106007072
#106007062
#106007052
#220385