Finite Group Databasebeta

← #12108946

Subgroups — #12108946

Order 1280.

1128 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65872C211yesmaximal, characteristic
2C2×#65128C211yesmaximal, characteristic, complemented
3C2×#64998C211yesmaximal, characteristic, complemented
4C5×#1955C211yesmaximal, characteristic, complemented
5#10602407C211yesmaximal, characteristic, complemented
6#10601265C211yesmaximal, characteristic, complemented
7#10600751C211yesmaximal, characteristic, complemented
8#10600751C211yesmaximal, characteristic, complemented
9#10600750C211yesmaximal, characteristic, complemented
10#10600750C211yesmaximal, characteristic, complemented
11#10600702C211yesmaximal, characteristic, complemented
12#10600702C211yesmaximal, characteristic, complemented
13#10600701C211yesmaximal, characteristic, complemented
14#10600701C211yesmaximal, characteristic, complemented
15#10600631C211yesmaximal, characteristic, complemented
16C2×C4×C5×D4C2211yescharacteristic
17C2×#4085C411yescharacteristic
18C2×#4081C411yescharacteristic
19C2×C4×C22⋊D5C2211yescharacteristic
20C2×C4×C22⋊D5C2211yescharacteristic
21C2×#4072C2211yescharacteristic
22C22×C4×Dic5C2211yescharacteristic
23C22×#676C2211yescharacteristic
24C22×C8×D5C2211yescharacteristic
25#65872—24no—
26#65872—24no—
27C2×#4044C411yescharacteristic
28C2×#4035C411yescharacteristic
29C2×#4032C411yescharacteristic
30C2×#4031C411yescharacteristic
31C2×#4025C411yescharacteristic
32C2×#4024C411yescharacteristic
33C2×#4018C2211yescharacteristic
34C2×C4×Dic10C2211yescharacteristic
35C2×C5×C4⋊C8C2211yescharacteristic
36C2×C5×C22⋊C8C2211yescharacteristic
37C2×C5×C22⋊C8C2211yescharacteristic
38C2×C5×C22⋊C8C2211yescharacteristic
39C2×C5×C22⋊C8C2211yescharacteristic
40C2×C5×#97C2211yescharacteristic
41C2×C22⋊#168C2211yescharacteristic
42C2×C22⋊#168C2211yescharacteristic
43C2×C22⋊#168C2211yescharacteristic
44C2×C22⋊#168C2211yescharacteristic
45C2×#3952C2211yescharacteristic
46C2×#3952C2211yescharacteristic
47C2×#3946C2211yescharacteristic
48C2×#3946C2211yescharacteristic
49C2×#3946C2211yescharacteristic
50C2×#3946C2211yescharacteristic
51C2×C4⋊#168C2211yescharacteristic
52C2×C4×#168C2211yescharacteristic
53#65128—24no—
54#64998—24no—
55#64770C2211yescharacteristic
56#64770C2211yescharacteristic
57#64770C2211yescharacteristic
58#64770C2211yescharacteristic
59#64770C2211yescharacteristic
60#64770C2211yescharacteristic
61#64770C2211yescharacteristic
62#64770C2211yescharacteristic
63#21855—51nomaximal, Sylow
64C22×C5×D4C2×C411yescharacteristic
65C23×C4×C5C2311yescharacteristic
66C23×C4×C5C2311yescharacteristic
67C22×C22⋊D5C2×C411yescharacteristic
68C22×C22⋊D5C2×C411yescharacteristic
69C23×Dic5C2×C411yescharacteristic
70C23×Dic5C2×C411yescharacteristic
71C22×C4×D5C2311yescharacteristic
72C22×Dic10C2×C411yescharacteristic
73C22×C5×C8C2311yescharacteristic
74C22×C5×C8C2311yescharacteristic
75C22×C5×C8C2311yescharacteristic
76C22×C5×C8C2311yescharacteristic
77C4×C5×D4—22no—
78C4×C5×D4—22no—
79C2×C5×C4⋊C4C2×C411yescharacteristic
80C2×C5×C22⋊C4C2×C411yescharacteristic
81C2×C5×C22⋊C4C2×C411yescharacteristic
82C2×C42×C5C2311yescharacteristic
83C2×C22⋊Dic5C2×C411yescharacteristic
84C2×C22⋊Dic5C2×C411yescharacteristic
85C2×C22⋊Dic5C2×C411yescharacteristic
86C2×C22⋊Dic5C2×C411yescharacteristic
87#4085—24no—
88#4081—24no—
89C4×C22⋊D5—22no—
90C4×C22⋊D5—22no—
91C4×C22⋊D5—22no—
92C4×C22⋊D5—22no—
93C2×#685C2×C411yescharacteristic
94C2×#685C2×C411yescharacteristic
95C2×#685C2×C411yescharacteristic
96C2×#685C2×C411yescharacteristic
97#4072—22no—
98#4072—22no—
99C2×C4⋊Dic5C2×C411yescharacteristic
100C2×C4⋊Dic5C2×C411yescharacteristic
101C2×C4⋊Dic5C2×C411yescharacteristic
102C2×#683C2×C411yescharacteristic
103C2×#683C2×C411yescharacteristic
104C2×#683C2×C411yescharacteristic
105C2×#683C2×C411yescharacteristic
106C2×#683C2×C411yescharacteristic
107C2×#683C2×C411yescharacteristic
108C2×C4×Dic5—22no—
109C2×C4×Dic5—22no—
110C2×C4×Dic5C2×C411yescharacteristic
111C2×C4×Dic5C2×C411yescharacteristic
112C2×C4×Dic5C2311yescharacteristic
113C2×C4×Dic5C2311yescharacteristic
114C2×C4×Dic5C2311yescharacteristic
115C22×#168C2311yescharacteristic
116C22×#168C2311yescharacteristic
117C22×#168C2311yescharacteristic
118C22×#168C2311yescharacteristic
119C2×#676—22no—
120C2×#676—41no—
121C2×#676—41no—
122C2×C8×D5—22no—
123C2×C8×D5—41no—
124C2×C8×D5—41no—
125#4044—24no—
126#4035—24no—
127#4032—24no—
128#4031—24no—
129#4025—24no—
130#4024—24no—
131#4018D414yes—
132#4018D414yes—
133C4×Dic10—22no—
134C4×Dic10—22no—
135C5×C4⋊C8—22no—
136C5×C22⋊C8—41no—
137C5×C22⋊C8—41no—
138C5×C22⋊C8—41no—
139C5×C22⋊C8—41no—
140C5×#97—22no—
141C22⋊#168—41no—
142C22⋊#168—41no—
143C22⋊#168—41no—
144C22⋊#168—41no—
145#3952—22no—
146#3952—22no—
147#3946—22no—
148#3946—22no—
149#3946—22no—
150#3946—22no—
151C4⋊#168—22no—
152C4×#168—22no—
153C2×#529—51no—
154C2×#433—51no—
155C2×#424—51no—
156#1985—51no—
157#1984—51no—
158#1955D511yescharacteristic, complemented
159#1954—51no—
160#1870—51no—
161#1870—51no—
162#1869—51no—
163#1869—51no—
164#1798—51no—
165#1798—51no—
166#1797—51no—
167#1797—51no—
168C24×C5C22×C411yescharacteristic
169C24×C5C22×C411yescharacteristic
170C23×D5C22×C411yescharacteristic
171C2×C5×D4—22no—
172C2×C5×D4—22no—
173C2×C5×D4—41no—
174C22×C4×C5—21no—
175C22×C4×C5—21no—
176C22×C4×C5—21no—
177C22×C4×C5—21no—
178C22×C4×C5—21no—
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×C5C22×C411yescharacteristic
187C22×C4×C5C22×C411yescharacteristic
188C22×C4×C5C22×C411yescharacteristic
189C22×C4×C5C22×C411yescharacteristic
190C22×C4×C5C2411yescharacteristic
191C2×C22⋊D5—22no—
192C2×C22⋊D5—22no—
193C2×C22⋊D5—22no—
194C2×C22⋊D5—22no—
195C2×C22⋊D5—41no—
196C2×C22⋊D5—41no—
197C22×Dic5—22no—
198C22×Dic5—22no—
199C22×Dic5—22no—
200C22×Dic5—22no—
201C22×Dic5—41no—
202C22×Dic5—41no—
203C22×Dic5C22×C411yescharacteristic
204C22×Dic5C22×C411yescharacteristic
205C22×Dic5C22×C411yescharacteristic
206C22×Dic5C22×C411yescharacteristic
207C22×Dic5C22×C411yescharacteristic
208C22×Dic5C22×C411yescharacteristic
209C22×Dic5C22×C411yescharacteristic
210C2×C4×D5—21no—
211C2×C4×D5—21no—
212C2×C4×D5—21no—
213C2×C4×D5—21no—
214C2×C4×D5C2×D412yes—
215C2×C4×D5C2×D412yes—
216C2×Dic10—22no—
217C2×Dic10—22no—
218C2×Dic10—41no—
219C2×C5×C8—21no—
220C2×C5×C8—21no—
221C2×C5×C8—21no—
222C2×C5×C8—21no—
223C2×C5×C8—21no—
224C2×C5×C8—21no—
225C2×C5×C8—21no—
226C2×C5×C8—21no—
227C2×C5×C8—21no—
228C2×C5×C8—21no—
229C2×C5×C8—21no—
230C2×C5×C8—21no—
231C5×C4⋊C4—22no—
232C5×C22⋊C4—22no—
233C5×C22⋊C4—22no—
234C42×C5C2×D412yes—
235C42×C5C2×D412yes—
236C22⋊Dic5—22no—
237C22⋊Dic5—22no—
238C22⋊Dic5—22no—
239C22⋊Dic5—22no—
240#685—22no—
241#685—22no—
242#685C22⋊C414yes—
243#685C22⋊C414yes—
244C4⋊Dic5—22no—
245C4⋊Dic5—22no—
246C4⋊Dic5—22no—
247#683—22no—
248#683—22no—
249#683—22no—
250#683—22no—
251#683C22⋊C414yes—
252#683C22⋊C414yes—
253C4×Dic5—21no—
254C4×Dic5—21no—
255C4×Dic5—21no—
256C4×Dic5—21no—
257C4×Dic5—22no—
258C4×Dic5—22no—
259C4×Dic5C2×D412yes—
260C4×Dic5C2×D412yes—
261C2×#168—21no—
262C2×#168—21no—
263C2×#168—21no—
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—
273#676—44no—
274C8×D5—44no—
275C22×M16—51no—
276C23×C8—51no—
277#529—104no—
278#529—104no—
279C2×#126—51no—
280C2×#126—51no—
281C2×#125—51no—
282C2×#124—51no—
283C2×#123—51no—
284C2×#123—51no—
285C2×C22⋊Q8—51no—
286C2×#121—51no—
287C2×C4×Q8—51no—
288C2×C4×D4—51no—
289C2×C4×D4—51no—
290C2×C4×D4C2×D511yescharacteristic
291C2×#117—51no—
292C2×#117—51no—
293C22×C42—51no—
294#433—104no—
295#424—104no—
296C2×C4⋊C8—51no—
297C2×C4⋊C8—51no—
298C2×C4⋊C8—51no—
299C2×C4⋊C8—51no—
300C2×C4⋊C8—51no—
301C2×C4⋊C8C2×D511yescharacteristic
302C2×C22⋊C8—51no—
303C2×C22⋊C8—51no—
304C2×C22⋊C8—51no—
305C2×C22⋊C8—51no—
306C2×C22⋊C8—51no—
307C2×C22⋊C8—51no—
308C2×C22⋊C8C2×D511yescharacteristic
309C2×C22⋊C8C2×D511yescharacteristic
310C2×C22⋊C8C2×D511yescharacteristic
311C2×C22⋊C8C2×D511yescharacteristic
312C2×#97C2×D511yescharacteristic
313C2×C4×C8—51no—
314#336—51no—
315#336—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#13112yes—
336C23×C5C23×C411yescharacteristic
337C22×D5—21no—
338C22×D5—21no—
339C22×D5—21no—
340C22×D5—21no—
341C22×D5—21no—
342C22×D5—21no—
343C22×D5C2×C22⋊C412yes—
344C5×D4—44no—
345C2×C4×C5—21no—
346C2×C4×C5—21no—
347C2×C4×C5—21no—
348C2×C4×C5—21no—
349C2×C4×C5—21no—
350C2×C4×C5—21no—
351C2×C4×C5—21no—
352C2×C4×C5—21no—
353C2×C4×C5—21no—
354C2×C4×C5—21no—
355C2×C4×C5—41no—
356C2×C4×C5—41no—
357C2×C4×C5—41no—
358C2×C4×C5—41no—
359C2×C4×C5—41no—
360C2×C4×C5—41no—
361C2×C4×C5—41no—
362C2×C4×C5—41no—
363C2×C4×C5C2×C22⋊C412yes—
364C2×C4×C5C2×C22⋊C412yes—
365C2×C4×C5C22×D411yescharacteristic
366C2×C4×C5C22×D411yescharacteristic
367C2×C4×C5H(5,𝔽2)11yescharacteristic
368C2×C4×C5H(5,𝔽2)11yescharacteristic
369C2×C4×C52−1+411yescharacteristic
370C2×C4×C52−1+411yescharacteristic
371C22⋊D5—44no—
372C22⋊D5—44no—
373C2×Dic5—21no—
374C2×Dic5—21no—
375C2×Dic5—21no—
376C2×Dic5—21no—
377C2×Dic5—21no—
378C2×Dic5—21no—
379C2×Dic5—21no—
380C2×Dic5—21no—
381C2×Dic5—21no—
382C2×Dic5—21no—
383C2×Dic5—21no—
384C2×Dic5—21no—
385C2×Dic5—21no—
386C2×Dic5—21no—
387C2×Dic5—21no—
388C2×Dic5—21no—
389C2×Dic5—21no—
390C2×Dic5—44no—
391C2×Dic5—44no—
392C2×Dic5C2×C22⋊C412yes—
393C2×Dic5C2×C22⋊C412yes—
394C2×Dic5C2×C22⋊C412yes—
395C2×Dic5#13112yes—
396C4×D5—22no—
397C4×D5—22no—
398C4×D5—22no—
399C4×D5—22no—
400Dic10—44no—
401C5×C8—41no—
402C5×C8—41no—
403C5×C8—41no—
404C5×C8—41no—
405#168—41no—
406#168—41no—
407#168—41no—
408#168—41no—
409C22×Q8—51no—
410C22×D4—51no—
411C22×D4—51no—
412C22×D4C4×D511yescharacteristic
413C23×C4—51no—
414C23×C4—51no—
415C23×C4—51no—
416C23×C4C22×D511yescharacteristic
417C23×C4C22×D511yescharacteristic
418C2×M16—102no—
419C2×M16—201no—
420C2×M16—201no—
421C22×C8—51no—
422C22×C8—51no—
423C22×C8—51no—
424C22×C8—51no—
425C22×C8—102no—
426C22×C8—201no—
427C22×C8—201no—
428C22×C8C22×D511yescharacteristic
429C22×C8C22×D511yescharacteristic
430C22×C8C22×D511yescharacteristic
431C22×C8C22×D511yescharacteristic
432#126—104no—
433#126—104no—
434#125—104no—
435#124—104no—
436#123—104no—
437#123—104no—
438C22⋊Q8—104no—
439#121—104no—
440C4×Q8—102no—
441C4×Q8—102no—
442C4×D4—22no—
443C4×D4—22no—
444C4×D4—102no—
445C4×D4—102no—
446C4×D4—102no—
447C4×D4—102no—
448#117—54no—
449#117—54no—
450#117—102no—
451#117—102no—
452C2×C4⋊C4—51no—
453C2×C4⋊C4—51no—
454C2×C4⋊C4—51no—
455C2×C4⋊C4—51no—
456C2×C4⋊C4—51no—
457C2×C4⋊C4—51no—
458C2×C4⋊C4—51no—
459C2×C4⋊C4—51no—
460C2×C4⋊C4—51no—
461C2×C4⋊C4C4×D511yescharacteristic
462C2×C22⋊C4—51no—
463C2×C22⋊C4—51no—
464C2×C22⋊C4—51no—
465C2×C22⋊C4—51no—
466C2×C22⋊C4—51no—
467C2×C22⋊C4—51no—
468C2×C22⋊C4—51no—
469C2×C22⋊C4—51no—
470C2×C22⋊C4C4×D511yescharacteristic
471C2×C22⋊C4C4×D511yescharacteristic
472C2×C42—51no—
473C2×C42—51no—
474C2×C42—51no—
475C2×C42—51no—
476C2×C42—51no—
477C2×C42—102no—
478C2×C42—102no—
479C2×C42C22×D511yescharacteristic
480C4⋊C8—22no—
481C4⋊C8—102no—
482C4⋊C8—102no—
483C4⋊C8—102no—
484C4⋊C8—102no—
485C4⋊C8—102no—
486C22⋊C8—41no—
487C22⋊C8—41no—
488C22⋊C8—41no—
489C22⋊C8—41no—
490C22⋊C8—102no—
491C22⋊C8—102no—
492C22⋊C8—201no—
493C22⋊C8—201no—
494C22⋊C8—201no—
495C22⋊C8—201no—
496#97—22no—
497C4×C8—102no—
498C22×C5—22no—
499C22×C5—22no—
500C22×C5—22no—
501C22×C5—41no—
502C22×C5—41no—
503C22×C5—41no—
504C22×C5—41no—
505C22×C5—41no—
506C22×C5—41no—
507C22×C5—41no—
508C22×C5—41no—
509C22×C5—41no—
510C22×C5—41no—
511C22×C5—41no—
512C22×C5C22×C22⋊C411yescharacteristic
513C22×C5#52011yescharacteristic
514C22×C5#52011yescharacteristic
515C22×C5C2×#13111yescharacteristic
516C22×C5C2×#13111yescharacteristic
517C22×C5#56811yescharacteristic
518C22×C5#56811yescharacteristic
519C2×D5—22no—
520C2×D5—22no—
521C2×D5—22no—
522C2×D5—41no—
523C2×D5—41no—
524C2×D5—41no—
525C2×D5—41no—
526C4×C5—22no—
527C4×C5—22no—
528C4×C5—41no—
529C4×C5—41no—
530C4×C5#53511yescharacteristic
531C4×C5#53611yescharacteristic
532C4×C5#53711yescharacteristic
533C4×C5#53711yescharacteristic
534Dic5—22no—
535Dic5—22no—
536Dic5—22no—
537Dic5—22no—
538Dic5—41no—
539Dic5—41no—
540Dic5—41no—
541C24—51no—
542C24C2×C4×D511yescharacteristic
543C24C2×C4×D511yescharacteristic
544C2×Q8—102no—
545C2×Q8—102no—
546C2×Q8—201no—
547C2×D4—22no—
548C2×D4—22no—
549C2×D4—41no—
550C2×D4—102no—
551C2×D4—102no—
552C2×D4—102no—
553C2×D4—102no—
554C2×D4—201no—
555C2×D4—201no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—51no—
569C22×C4—51no—
570C22×C4—51no—
571C22×C4—51no—
572C22×C4—52no—
573C22×C4—52no—
574C22×C4—51no—
575C22×C4—51no—
576C22×C4—51no—
577C22×C4—102no—
578C22×C4—102no—
579C22×C4—102no—
580C22×C4—101no—
581C22×C4—101no—
582C22×C4—101no—
583C22×C4—101no—
584C22×C4—102no—
585C22×C4—201no—
586C22×C4—201no—
587C22×C4C2×C4×D511yescharacteristic
588C22×C4C2×C4×D511yescharacteristic
589C22×C4C2×C4×D511yescharacteristic
590C22×C4C2×C4×D511yescharacteristic
591C22×C4C23×D511yescharacteristic
592M16—204no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—101no—
606C2×C8—101no—
607C2×C8—101no—
608C2×C8—101no—
609C2×C8—101no—
610C2×C8—101no—
611C2×C8—101no—
612C2×C8—101no—
613C2×C8—101no—
614C2×C8—101no—
615C2×C8—101no—
616C2×C8—101no—
617C2×C8—204no—
618C4⋊C4—22no—
619C4⋊C4—54no—
620C4⋊C4—54no—
621C4⋊C4—102no—
622C4⋊C4—102no—
623C4⋊C4—102no—
624C4⋊C4—102no—
625C4⋊C4—102no—
626C4⋊C4—102no—
627C4⋊C4—102no—
628C22⋊C4—22no—
629C22⋊C4—22no—
630C22⋊C4—54no—
631C22⋊C4—54no—
632C22⋊C4—102no—
633C22⋊C4—102no—
634C22⋊C4—102no—
635C22⋊C4—102no—
636C22⋊C4—102no—
637C22⋊C4—102no—
638C42—52no—
639C42—52no—
640C42—102no—
641C42—102no—
642C42—101no—
643C42—101no—
644C42—101no—
645C42—101no—
646C42D4×D512yes—
647C42D4×D512yes—
648C2×C5—42no—
649C2×C5—81no—
650C2×C5#231111yescharacteristic
651C2×C5#288011yescharacteristic
652C2×C5#288011yescharacteristic
653C2×C5#299211yescharacteristic
654C2×C5#299311yescharacteristic
655C2×C5#299411yescharacteristic
656C2×C5#299511yescharacteristic
657D5—42no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—52no—
672C23—101no—
673C23—101no—
674C23—101no—
675C23—101no—
676C23—101no—
677C23—101no—
678C23#405312yes—
679C23C22×C4×D511yescharacteristic
680Q8—204no—
681D4—44no—
682D4—204no—
683D4—204no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—52no—
703C2×C4—52no—
704C2×C4—52no—
705C2×C4—52no—
706C2×C4—101no—
707C2×C4—101no—
708C2×C4—101no—
709C2×C4—101no—
710C2×C4—101no—
711C2×C4—101no—
712C2×C4—101no—
713C2×C4—101no—
714C2×C4—102no—
715C2×C4—102no—
716C2×C4—102no—
717C2×C4—102no—
718C2×C4—101no—
719C2×C4—101no—
720C2×C4—101no—
721C2×C4—101no—
722C2×C4—101no—
723C2×C4—101no—
724C2×C4—101no—
725C2×C4—101no—
726C2×C4—101no—
727C2×C4—204no—
728C2×C4—204no—
729C2×C4D5×C22⋊C412yes—
730C2×C4D5×C22⋊C412yes—
731C2×C4C2×D4×D511yescharacteristic
732C2×C4C2×D4×D511yescharacteristic
733C2×C4#414411yescharacteristic
734C2×C4#414411yescharacteristic
735C2×C4#415011yescharacteristic
736C2×C4#415011yescharacteristic
737C8—41no—
738C8—41no—
739C8—41no—
740C8—41no—
741C8—201no—
742C8—201no—
743C8—201no—
744C8—201no—
745C5#2185511yescharacteristic, complemented, Sylow
746C22—22no—
747C22—22no—
748C22—22no—
749C22—41no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—102no—
761C22—102no—
762C22—102no—
763C22—201no—
764C22—201no—
765C22—201no—
766C22—201no—
767C22C2×D5×C22⋊C411yescharacteristic
768C22#6588011yescharacteristic
769C22#6588011yescharacteristic
770C22C2×#405311yescharacteristic
771C22#6607911yescharacteristic
772C22D5×#13111yescharacteristic
773C22#6608411yescharacteristic
774C4—22no—
775C4—22no—
776C4—41no—
777C4—41no—
778C4—102no—
779C4—102no—
780C4—102no—
781C4—102no—
782C4—201no—
783C4—201no—
784C4—201no—
785C4#6594211yescharacteristic
786C4#6594211yescharacteristic
787C4#6600911yescharacteristic
788C4#6604911yescharacteristic
789C2—42no—
790C2—81no—
791C2—202no—
792C2#1060802511yescharacteristic
793C2#1061036211yescharacteristic
794C2#1061039411yescharacteristic
795C2#1061119411yescharacteristic
796C2#1061119611yescharacteristic
797C2#1061119711yescharacteristic
798C2#1061119811yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D5
commutator, socleC23×C5C23×C4
FittingC5×#1955C2
prime radicalC2×#4085C4
cosocleC22×C4×C5C24
hypercenter#1955D5
hypocenterC5#21855
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C22×C4 ◁ #1955

Complements

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

NH ≅ G/Ntype
2. C2×#65128C2semidirect
3. C2×#64998C2semidirect
4. C5×#1955C2semidirect
5. #10602407C2semidirect
6. #10601265C2semidirect
7. #10600751C2semidirect
8. #10600751C2semidirect
9. #10600750C2semidirect
10. #10600750C2semidirect
11. #10600702C2semidirect
12. #10600702C2semidirect
13. #10600701C2semidirect
14. #10600701C2semidirect
15. #10600631C2semidirect
158. #1955D5semidirect
745. C5#21855semidirect

Maximal subgroups

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

subgroupindex
C2×#658722
C2×#651282
C2×#649982
C5×#19552
#106024072
#106012652
#106007512
#106007502
#106007022
#106007012
#106006312
#218555