Finite Group Databasebeta

← #12097111

Subgroups — #12097111

Order 1280.

1738 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65879C211yesmaximal, characteristic
2C2×#65059C211yesmaximal, characteristic
3C2×D5×#102C211yesmaximal, characteristic
4C2×#64997C211yesmaximal, characteristic, complemented
5#10605481C211yesmaximal, characteristic, complemented
6C5×#1762C211yesmaximal, characteristic, complemented
7C4×#3964C211yesmaximal, characteristic, complemented
8#10600945C211yesmaximal, characteristic, complemented
9Dic5×#102C211yesmaximal, characteristic, complemented
10#10600605C211yesmaximal, characteristic, complemented
11C4×#3941C211yesmaximal, characteristic, complemented
12#10599660C211yesmaximal, characteristic, complemented
13#10599659C211yesmaximal, characteristic, complemented
14#10599575C211yesmaximal, characteristic, complemented
15#10599573C211yesmaximal, characteristic, complemented
16C22×D4×D5C2211yescharacteristic
17C2×C4×C5×D4C2211yescharacteristic
18C2×D4×Dic5C2211yescharacteristic
19C2×C4×C22⋊D5—21no—
20C22×#685—21no—
21C22×#676C2211yescharacteristic
22C22×C8×D5C2211yescharacteristic
23#65879—24no—
24#65879C418yescomplemented
25C2×#4039C2211yescharacteristic
26C2×#4038C2211yescharacteristic
27C2×#4038C2211yescharacteristic
28C2×D5×C4⋊C4C2211yescharacteristic
29C2×#4027—21no—
30C2×D5×C22⋊C4—21no—
31C2×C4×D20C2211yescharacteristic
32C2×#4018C2211yescharacteristic
33C2×C5×#102C2211yescharacteristic
34C2×C5×#102C2211yescharacteristic
35C2×C5×#97C2211yescharacteristic, complemented
36C4×C5×C4⋊C4C2211yescharacteristic, complemented
37C2×#3964C2211yescharacteristic
38C2×#3964C2211yescharacteristic
39C2×#3953C2211yescharacteristic
40C2×#3953C2211yescharacteristic
41C2×#3947C2211yescharacteristic, complemented
42C2×C8×Dic5C2211yescharacteristic, complemented
43C4⋊C4×Dic5C2211yescharacteristic, complemented
44C4⋊C4×Dic5C2211yescharacteristic, complemented
45C2×#3941C2211yescharacteristic
46C2×#3941C2211yescharacteristic
47C4×#685—21no—
48C4×C4⋊Dic5C2211yescharacteristic, complemented
49C4×#683—21no—
50C2×C4×#168C2211yescharacteristic, complemented
51#65059C418yescomplemented
52D5×#102C418yescomplemented
53#64997—24no—
54#64955—21no—
55#64938—21no—
56C5×#340C2211yescharacteristic, complemented
57C5×#340C2211yescharacteristic, complemented
58#64771C2211yescharacteristic, complemented
59#64771C2211yescharacteristic, complemented
60#64749C2211yescharacteristic, complemented
61#64749C2211yescharacteristic, complemented
62#64749C2211yescharacteristic, complemented
63#64749C2211yescharacteristic, complemented
64#20416—51nomaximal, Sylow
65C24×D5—21no—
66C22×C5×D4C2311yescharacteristic
67C23×C4×C5—21no—
68C22×C22⋊D5—21no—
69C23×Dic5—21no—
70C2×D4×D5—22no—
71C2×D4×D5—22no—
72C2×D4×D5—22no—
73C2×D4×D5C2×C414yes—
74C2×D4×D5C2×C414yes—
75C2×D4×D5C2×C414yes—
76C22×D20C2311yescharacteristic
77C22×C4×D5—21no—
78C22×C4×D5—21no—
79C22×C4×D5—21no—
80C22×C4×D5C2311yescharacteristic
81C22×C5×C8C2311yescharacteristic
82C22×C5×C8C2311yescharacteristic
83C4×C5×D4—22no—
84C4×C5×D4C2×C414yescomplemented
85C2×C5×C4⋊C4C2311yescharacteristic
86C2×C5×C4⋊C4C2311yescharacteristic
87C2×C5×C4⋊C4C2311yescharacteristic
88C2×C5×C22⋊C4—21no—
89C2×C42×C5—21no—
90C2×C42×C5C2311yescharacteristic
91C2×C22⋊Dic5—21no—
92D4×Dic5—22no—
93D4×Dic5C2×C414yescomplemented
94C4×C22⋊D5—28no—
95C2×#685—21no—
96C2×#685—21no—
97C2×#685—21no—
98C2×#685—21no—
99C2×#685—28no—
100C2×#685D411yescharacteristic
101C2×#685D411yescharacteristic
102C2×C4⋊Dic5C2311yescharacteristic
103C2×C4⋊Dic5C2311yescharacteristic
104C2×C4⋊Dic5C2311yescharacteristic
105C2×#683—21no—
106C2×#683D411yescharacteristic
107C2×#683D411yescharacteristic
108C2×C4×Dic5—21no—
109C2×C4×Dic5—21no—
110C2×C4×Dic5—21no—
111C2×C4×Dic5—21no—
112C2×C4×Dic5—21no—
113C2×C4×Dic5C2311yescharacteristic
114C22×#168C2311yescharacteristic
115C22×#168C2311yescharacteristic
116C2×#676—22no—
117C2×#676—22no—
118C2×#676C2×C414yescomplemented
119C2×C8×D5—22no—
120C2×C8×D5—22no—
121C2×C8×D5C2×C414yescomplemented
122#4039—22no—
123#4039C2×C414yescomplemented
124#4038—22no—
125#4038—22no—
126#4038C2×C414yes—
127#4038C2×C414yescomplemented
128D5×C4⋊C4—22no—
129D5×C4⋊C4C2×C414yescomplemented
130#4027—28no—
131D5×C22⋊C4—28no—
132C4×D20—22no—
133C4×D20C2×C414yescomplemented
134#4018C2×C414yes—
135#4018D414yes—
136C5×#102C2×C414yescomplemented
137C5×#102C2×C414yescomplemented
138C5×#97—22no—
139C5×#95—21no—
140#3964C2×C414yescomplemented
141#3964C2×C414yescomplemented
142#3963—21no—
143#3963—21no—
144#3963—21no—
145#3953C2×C414yescomplemented
146#3953C2×C414yescomplemented
147#3947—22no—
148C8×Dic5—22no—
149#3941C2×C414yescomplemented
150#3941C2×C414yescomplemented
151C4×#168—22no—
152C2×#518—51no—
153C2×#418—51no—
154C22×#102—51no—
155C2×#405—51no—
156#2274—51no—
157#1762—51no—
158#1762—51no—
159#1762—51no—
160#1762D511yescharacteristic, complemented
161C4×#102—51no—
162C4×#102—51no—
163C4×#102—51no—
164C4×#102—51no—
165#1736—51no—
166#1735—51no—
167C24×C5—21no—
168C23×D5—21no—
169C23×D5—24no—
170C23×D5—24no—
171C23×D5—24no—
172C23×D5—81no—
173C23×D5—81no—
174C23×D5—81no—
175C23×D5—81no—
176C23×D5C2×D411yescharacteristic
177C2×C5×D4—21no—
178C2×C5×D4—21no—
179C2×C5×D4—21no—
180C2×C5×D4C22×C412yes—
181C2×C5×D4C22×C412yes—
182C2×C5×D4C22×C412yes—
183C22×C4×C5—21no—
184C22×C4×C5—21no—
185C22×C4×C5—21no—
186C22×C4×C5—24no—
187C22×C4×C5—81no—
188C22×C4×C5—81no—
189C22×C4×C5C2×D411yescharacteristic
190C22×C4×C5C2×D411yescharacteristic
191C22×C4×C5C2411yescharacteristic
192C2×C22⋊D5—24no—
193C2×C22⋊D5—24no—
194C2×C22⋊D5—24no—
195C22×Dic5—21no—
196C22×Dic5—21no—
197C22×Dic5—21no—
198C22×Dic5—24no—
199C22×Dic5—81no—
200C22×Dic5—81no—
201C22×Dic5C2×D411yescharacteristic
202C22×Dic5C2×D411yescharacteristic
203C22×Dic5C2×D411yescharacteristic
204D4×D5—28no—
205D4×D5—28no—
206D4×D5—28no—
207D4×D5C42116yescomplemented
208C2×D20—21no—
209C2×D20—21no—
210C2×D20—21no—
211C2×D20C22×C412yes—
212C2×D20C22×C412yes—
213C2×D20C22×C412yes—
214C2×C4×D5—24no—
215C2×C4×D5—24no—
216C2×C4×D5—24no—
217C2×C4×D5—81no—
218C2×C4×D5—81no—
219C2×C4×D5—81no—
220C2×C4×D5—81no—
221C2×C4×D5—81no—
222C2×C4×D5—81no—
223C2×C4×D5C22×C412yes—
224C2×C4×D5C22×C412yes—
225C2×C4×D5C22×C412yes—
226C2×C4×D5C2×D412yes—
227C2×C4×D5#4112yes—
228C2×C4×D5#4112yes—
229C2×C5×C8—21no—
230C2×C5×C8—21no—
231C2×C5×C8—21no—
232C2×C5×C8—21no—
233C2×C5×C8C22×C412yes—
234C2×C5×C8C22×C412yes—
235C5×C4⋊C4—21no—
236C5×C4⋊C4—21no—
237C5×C4⋊C4—21no—
238C5×C4⋊C4C22×C412yes—
239C5×C4⋊C4C22×C412yes—
240C5×C4⋊C4C22×C412yes—
241C5×C22⋊C4—24no—
242C42×C5—81no—
243C42×C5C22×C412yes—
244C42×C5C2×D412yes—
245C22⋊Dic5—24no—
246#685—24no—
247#685—24no—
248#685—24no—
249#685—24no—
250#685C22⋊C414yes—
251#685C22⋊C414yes—
252C4⋊Dic5—21no—
253C4⋊Dic5—21no—
254C4⋊Dic5—21no—
255C4⋊Dic5C22×C412yes—
256C4⋊Dic5C22×C412yes—
257C4⋊Dic5C22×C412yes—
258#683—24no—
259#683C22⋊C414yes—
260#683C22⋊C414yes—
261C4×Dic5—24no—
262C4×Dic5—24no—
263C4×Dic5—81no—
264C4×Dic5—81no—
265C4×Dic5—81no—
266C4×Dic5C22×C412yes—
267C4×Dic5C2×D412yes—
268C2×#168—21no—
269C2×#168—21no—
270C2×#168—21no—
271C2×#168—21no—
272C2×#168C22×C412yes—
273C2×#168C22×C412yes—
274#676—28no—
275C8×D5—28no—
276C23×D4—51no—
277C22×M16—51no—
278C23×C8—51no—
279#518—58no—
280#518—104no—
281C2×C4×D4—51no—
282C2×C4×D4—51no—
283C2×C4×D4—51no—
284C2×C4×D4—101no—
285C2×C4×D4—101no—
286C2×C4×D4C2×D511yescharacteristic
287C2×#117—51no—
288C2×#117—51no—
289C2×#117—51no—
290C22×C4⋊C4—51no—
291C22×C22⋊C4—101no—
292C22×C22⋊C4—101no—
293#418—58no—
294C2×#102—51no—
295C2×#102—51no—
296C2×#102—51no—
297C2×#102—51no—
298C2×#102—51no—
299C2×#102—51no—
300C2×#102—58no—
301C2×#102C2×D511yescharacteristic
302C2×#102C2×D511yescharacteristic
303#405—104no—
304C2×#97—51no—
305C2×#97C2×D511yescharacteristic, complemented
306C2×C4×C8—51no—
307C2×C4×C8—51no—
308C4×C4⋊C4—51no—
309C4×C4⋊C4—51no—
310C4×C4⋊C4—51no—
311C4×C4⋊C4—101no—
312C4×C4⋊C4—101no—
313C4×C4⋊C4C2×D511yescharacteristic, complemented
314C4×C22⋊C4—101no—
315C4×C22⋊C4—101no—
316#340—51no—
317#340—51no—
318#340—51no—
319#340—51no—
320#340—51no—
321#340—51no—
322#340C2×D511yescharacteristic, complemented
323#340C2×D511yescharacteristic, complemented
324C23×C5—22no—
325C23×C5—22no—
326C23×C5—22no—
327C23×C5—41no—
328C23×C5—41no—
329C23×C5—41no—
330C23×C5—41no—
331C23×C5C22×D411yescharacteristic
332C22×D5—21no—
333C22×D5—21no—
334C22×D5—21no—
335C22×D5—21no—
336C22×D5—22no—
337C22×D5—22no—
338C22×D5—22no—
339C22×D5—216no—
340C22×D5—41no—
341C22×D5—41no—
342C22×D5—41no—
343C22×D5—41no—
344C22×D5—84no—
345C22×D5—84no—
346C22×D5—84no—
347C22×D5—84no—
348C22×D5—84no—
349C22×D5—84no—
350C22×D5C2×C22⋊C412yes—
351C22×D5C4×D412yes—
352C22×D5C4×D412yes—
353C5×D4—22no—
354C5×D4—22no—
355C5×D4—22no—
356C5×D4C2×C4214yes—
357C2×C4×C5—21no—
358C2×C4×C5—21no—
359C2×C4×C5—21no—
360C2×C4×C5—21no—
361C2×C4×C5—22no—
362C2×C4×C5—22no—
363C2×C4×C5—22no—
364C2×C4×C5—41no—
365C2×C4×C5—41no—
366C2×C4×C5—41no—
367C2×C4×C5—41no—
368C2×C4×C5—41no—
369C2×C4×C5—41no—
370C2×C4×C5—84no—
371C2×C4×C5C2×C22⋊C412yes—
372C2×C4×C5C2×C22⋊C412yes—
373C2×C4×C5C23×C411yescharacteristic
374C2×C4×C5C23×C411yescharacteristic
375C2×C4×C5C23×C411yescharacteristic
376C2×C4×C5C22×D411yescharacteristic
377C2×C4×C5C2×#4111yescharacteristic
378C2×C4×C5C2×#4111yescharacteristic
379C22⋊D5—216no—
380C2×Dic5—21no—
381C2×Dic5—21no—
382C2×Dic5—21no—
383C2×Dic5—21no—
384C2×Dic5—22no—
385C2×Dic5—22no—
386C2×Dic5—22no—
387C2×Dic5—41no—
388C2×Dic5—41no—
389C2×Dic5—41no—
390C2×Dic5—41no—
391C2×Dic5—41no—
392C2×Dic5—41no—
393C2×Dic5—84no—
394C2×Dic5C2×C22⋊C412yes—
395C2×Dic5C2×C22⋊C412yes—
396C2×Dic5C2×C22⋊C412yes—
397C2×Dic5C4×D412yes—
398C2×Dic5C4×D412yes—
399D20—22no—
400D20—22no—
401D20—22no—
402D20C2×C4214yes—
403C4×D5—84no—
404C4×D5—84no—
405C4×D5—84no—
406C4×D5C2×C4214yes—
407C4×D5#11714yes—
408C4×D5C4×D414yes—
409C4×D5C4×D414yes—
410C5×C8—22no—
411C5×C8—22no—
412#168—22no—
413#168—22no—
414C25—101no—
415C22×D4—54no—
416C22×D4—54no—
417C22×D4—54no—
418C22×D4—51no—
419C22×D4—102no—
420C22×D4—102no—
421C22×D4—102no—
422C22×D4—101no—
423C22×D4C22×D511yescharacteristic
424C23×C4—21no—
425C23×C4—51no—
426C23×C4—101no—
427C23×C4—101no—
428C23×C4—101no—
429C23×C4—101no—
430C2×M16—54no—
431C2×M16—102no—
432C2×M16—102no—
433C22×C8—51no—
434C22×C8—51no—
435C22×C8—54no—
436C22×C8—102no—
437C22×C8—102no—
438C22×C8C22×D511yescharacteristic
439C22×C8C22×D511yescharacteristic
440C4×D4—22no—
441C4×D4—54no—
442C4×D4—54no—
443C4×D4—54no—
444C4×D4—102no—
445C4×D4—102no—
446C4×D4—108no—
447C4×D4—108no—
448C4×D4—102no—
449C4×D4C4×D514yescomplemented
450#117—54no—
451#117—54no—
452#117—54no—
453#117—54no—
454#117—102no—
455#117—102no—
456C2×C4⋊C4—51no—
457C2×C4⋊C4—51no—
458C2×C4⋊C4—51no—
459C2×C4⋊C4—51no—
460C2×C4⋊C4—51no—
461C2×C4⋊C4—54no—
462C2×C4⋊C4—102no—
463C2×C4⋊C4—101no—
464C2×C4⋊C4C22×D511yescharacteristic
465C2×C4⋊C4C22×D511yescharacteristic
466C2×C4⋊C4C22×D511yescharacteristic
467C2×C22⋊C4—21no—
468C2×C22⋊C4—51no—
469C2×C22⋊C4—51no—
470C2×C22⋊C4—108no—
471C2×C22⋊C4—108no—
472C2×C22⋊C4—101no—
473C2×C22⋊C4—101no—
474C2×C22⋊C4—101no—
475C2×C22⋊C4—101no—
476C2×C22⋊C4—101no—
477C2×C42—21no—
478C2×C42—51no—
479C2×C42—101no—
480C2×C42—101no—
481C2×C42—101no—
482C2×C42—101no—
483C2×C42—101no—
484C2×C42C22×D511yescharacteristic
485#102—54no—
486#102—54no—
487#102—54no—
488#102—54no—
489#102—54no—
490#102—54no—
491#102C4×D514yescomplemented
492#102C4×D514yescomplemented
493#97—22no—
494#97—102no—
495C4×C8—102no—
496C4×C8—102no—
497#95—21no—
498#95—101no—
499#95—101no—
500#95—101no—
501C22×C5—24no—
502C22×C5—42no—
503C22×C5—42no—
504C22×C5—42no—
505C22×C5—42no—
506C22×C5—42no—
507C22×C5—42no—
508C22×C5C22×C22⋊C411yescharacteristic
509C22×C5C2×C4×D411yescharacteristic
510C22×C5C2×C4×D411yescharacteristic
511C22×C5#57611yescharacteristic
512C22×C5#57611yescharacteristic
513C22×C5#57711yescharacteristic
514C22×C5#57711yescharacteristic
515C2×D5—22no—
516C2×D5—22no—
517C2×D5—22no—
518C2×D5—22no—
519C2×D5—22no—
520C2×D5—22no—
521C2×D5—24no—
522C2×D5—42no—
523C2×D5—42no—
524C2×D5—42no—
525C2×D5—42no—
526C2×D5—42no—
527C2×D5—42no—
528C2×D5—816no—
529C2×D5C4×C22⋊C414yes—
530C4×C5—22no—
531C4×C5—22no—
532C4×C5—42no—
533C4×C5—42no—
534C4×C5—42no—
535C4×C5C22×C4211yescharacteristic
536C4×C5C2×#11711yescharacteristic
537C4×C5C2×C4×D411yescharacteristic
538C4×C5C2×C4×D411yescharacteristic
539Dic5—22no—
540Dic5—22no—
541Dic5—42no—
542Dic5—42no—
543Dic5—42no—
544Dic5C4×C22⋊C414yes—
545C24—21no—
546C24—51no—
547C24—104no—
548C24—104no—
549C24—104no—
550C24—101no—
551C24—401no—
552C24—401no—
553C24—401no—
554C24—401no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—516no—
559C2×D4—52no—
560C2×D4—52no—
561C2×D4—52no—
562C2×D4—108no—
563C2×D4—108no—
564C2×D4—108no—
565C2×D4—104no—
566C2×D4—104no—
567C2×D4—104no—
568C2×D4—101no—
569C2×D4—101no—
570C2×D4—101no—
571C2×D4C2×C4×D512yes—
572C2×D4C2×C4×D512yes—
573C2×D4C2×C4×D512yes—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—24no—
578C22×C4—51no—
579C22×C4—52no—
580C22×C4—52no—
581C22×C4—52no—
582C22×C4—52no—
583C22×C4—52no—
584C22×C4—52no—
585C22×C4—51no—
586C22×C4—51no—
587C22×C4—81no—
588C22×C4—81no—
589C22×C4—104no—
590C22×C4—104no—
591C22×C4—104no—
592C22×C4—101no—
593C22×C4—101no—
594C22×C4—101no—
595C22×C4—104no—
596C22×C4—401no—
597C22×C4—401no—
598C22×C4—401no—
599C22×C4—401no—
600C22×C4—401no—
601C22×C4—401no—
602C22×C4—401no—
603C22×C4—401no—
604C22×C4D4×D511yescharacteristic
605C22×C4D4×D511yescharacteristic
606C22×C4C23×D511yescharacteristic
607M16—108no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—52no—
613C2×C8—52no—
614C2×C8—108no—
615C2×C8—101no—
616C2×C8—101no—
617C2×C8—101no—
618C2×C8—101no—
619C2×C8C2×C4×D512yes—
620C2×C8C2×C4×D512yes—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—54no—
625C4⋊C4—54no—
626C4⋊C4—52no—
627C4⋊C4—52no—
628C4⋊C4—52no—
629C4⋊C4—104no—
630C4⋊C4—101no—
631C4⋊C4—101no—
632C4⋊C4—101no—
633C4⋊C4C2×C4×D512yes—
634C4⋊C4C2×C4×D512yes—
635C4⋊C4C2×C4×D512yes—
636C22⋊C4—24no—
637C22⋊C4—54no—
638C22⋊C4—54no—
639C22⋊C4—104no—
640C22⋊C4—104no—
641C22⋊C4—104no—
642C22⋊C4—104no—
643C22⋊C4—104no—
644C42—52no—
645C42—52no—
646C42—81no—
647C42—104no—
648C42—104no—
649C42—401no—
650C42—401no—
651C42—401no—
652C42C2×C4×D512yes—
653C42D4×D512yes—
654C2×C5—44no—
655C2×C5C2×C4×C22⋊C411yescharacteristic
656C2×C5#289711yescharacteristic
657C2×C5#289711yescharacteristic
658C2×C5#294611yescharacteristic
659C2×C5#294611yescharacteristic
660C2×C5#294811yescharacteristic
661C2×C5#294911yescharacteristic
662D5—24no—
663D5—44no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—52no—
672C23—52no—
673C23—52no—
674C23—1016no—
675C23—101no—
676C23—101no—
677C23—101no—
678C23—101no—
679C23—102no—
680C23—102no—
681C23—102no—
682C23—201no—
683C23—201no—
684C23—201no—
685C23—201no—
686C23—404no—
687C23—404no—
688C23—404no—
689C23—404no—
690C23—404no—
691C23—404no—
692C23C2×D4×D511yescharacteristic
693D4—22no—
694D4—22no—
695D4—22no—
696D4—54no—
697D4—1016no—
698D4—102no—
699D4—102no—
700D4—102no—
701D4C42×D514yes—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—52no—
716C2×C4—52no—
717C2×C4—52no—
718C2×C4—54no—
719C2×C4—54no—
720C2×C4—54no—
721C2×C4—54no—
722C2×C4—52no—
723C2×C4—52no—
724C2×C4—84no—
725C2×C4—101no—
726C2×C4—101no—
727C2×C4—101no—
728C2×C4—101no—
729C2×C4—102no—
730C2×C4—102no—
731C2×C4—102no—
732C2×C4—201no—
733C2×C4—201no—
734C2×C4—201no—
735C2×C4—201no—
736C2×C4—201no—
737C2×C4—201no—
738C2×C4—404no—
739C2×C4—404no—
740C2×C4—404no—
741C2×C4—404no—
742C2×C4D5×C22⋊C412yes—
743C2×C4D5×C22⋊C412yes—
744C2×C4C22×C4×D511yescharacteristic
745C2×C4C22×C4×D511yescharacteristic
746C2×C4C22×C4×D511yescharacteristic
747C2×C4C2×D4×D511yescharacteristic
748C2×C4D5×#4111yescharacteristic
749C2×C4D5×#4111yescharacteristic
750C8—22no—
751C8—22no—
752C8—102no—
753C8—102no—
754C5#2041611yescharacteristic, complemented, Sylow
755C22—24no—
756C22—42no—
757C22—42no—
758C22—42no—
759C22—42no—
760C22—42no—
761C22—42no—
762C22—54no—
763C22—102no—
764C22—102no—
765C22—102no—
766C22—102no—
767C22—102no—
768C22—102no—
769C22—104no—
770C22—202no—
771C22—202no—
772C22—202no—
773C22—202no—
774C22—202no—
775C22—202no—
776C22—4016no—
777C22C2×D5×C22⋊C411yescharacteristic
778C22C4×D4×D511yescharacteristic
779C22C4×D4×D511yescharacteristic
780C22#6610811yescharacteristic
781C22#6610811yescharacteristic
782C22#6610911yescharacteristic
783C22#6611211yescharacteristic
784C4—22no—
785C4—22no—
786C4—42no—
787C4—42no—
788C4—42no—
789C4—54no—
790C4—102no—
791C4—102no—
792C4—202no—
793C4—202no—
794C4—202no—
795C4C2×C42×D511yescharacteristic
796C4D5×#11711yescharacteristic
797C4C4×D4×D511yescharacteristic
798C4C4×D4×D511yescharacteristic
799C2—44no—
800C2—104no—
801C2—204no—
802C2C4×D5×C22⋊C411yescharacteristic
803C2#1061061311yescharacteristic
804C2#1061065611yescharacteristic
805C2#1061150611yescharacteristic
806C2#1061150811yescharacteristic
807C2#1061159711yescharacteristic
808C2#1061159811yescharacteristic
subgroupG/H
centerC23C2×D4×D5
commutatorC4×C5C22×C42
FrattiniC22×C4C23×D5
FittingC5×#1762C2
socleC23×C5C22×D4
prime radicalC22×D4×D5C22
cosocleC22×C4×C5C24
hypercenter#1762D5
hypocenterC5#20416
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1762

Complements

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

NH ≅ G/Ntype
4. C2×#64997C2semidirect
5. #10605481C2semidirect
6. C5×#1762C2semidirect
7. C4×#3964C2semidirect
8. #10600945C2semidirect
9. Dic5×#102C2semidirect
10. #10600605C2semidirect
11. C4×#3941C2semidirect
12. #10599660C2semidirect
13. #10599659C2semidirect
14. #10599575C2semidirect
15. #10599573C2semidirect
24. #65879C4semidirect
35. C2×C5×#97C22semidirect
36. C4×C5×C4⋊C4C22semidirect
41. C2×#3947C22semidirect
42. C2×C8×Dic5C22semidirect
43. C4⋊C4×Dic5C22semidirect
44. C4⋊C4×Dic5C22semidirect
48. C4×C4⋊Dic5C22semidirect
50. C2×C4×#168C22semidirect
51. #65059C4semidirect
52. D5×#102C4semidirect
56. C5×#340C22semidirect
57. C5×#340C22semidirect
58. #64771C22semidirect
59. #64771C22semidirect
60. #64749C22semidirect
61. #64749C22semidirect
62. #64749C22semidirect
63. #64749C22semidirect
84. C4×C5×D4C2×C4semidirect
93. D4×Dic5C2×C4semidirect
118. C2×#676C2×C4semidirect
121. C2×C8×D5C2×C4semidirect
123. #4039C2×C4semidirect
127. #4038C2×C4semidirect
129. D5×C4⋊C4C2×C4semidirect
133. C4×D20C2×C4semidirect
136. C5×#102C2×C4semidirect
137. C5×#102C2×C4semidirect
140. #3964C2×C4semidirect
141. #3964C2×C4semidirect
145. #3953C2×C4semidirect
146. #3953C2×C4semidirect
149. #3941C2×C4semidirect
150. #3941C2×C4semidirect
160. #1762D5semidirect
207. D4×D5C42semidirect
305. C2×#97C2×D5semidirect
313. C4×C4⋊C4C2×D5semidirect
322. #340C2×D5semidirect
323. #340C2×D5semidirect
449. C4×D4C4×D5semidirect
491. #102C4×D5semidirect
492. #102C4×D5semidirect
754. C5#20416semidirect

Maximal subgroups

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

subgroupindex
C2×#658792
C2×#650592
C2×D5×#1022
C2×#649972
#106054812
C5×#17622
C4×#39642
#106009452
Dic5×#1022
#106006052
C4×#39412
#105996602
#105996592
#105995752
#105995732
#204165