Finite Group Databasebeta

← #12027140

Subgroups — #12027140

Order 1280.

1202 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65267C211yesmaximal, characteristic
2C2×#64942C211yesmaximal, characteristic
3C2×#64940C211yesmaximal, characteristic
4C5×#1444C211yesmaximal, characteristic
5#10602360C211yesmaximal, characteristic
6#10602360C211yesmaximal, characteristic
7#10602357C211yesmaximal, characteristic
8#10602356C211yesmaximal, characteristic
9#10602356C211yesmaximal, characteristic
10#10600216C211yesmaximal, characteristic
11#10600210C211yesmaximal, characteristic
12#10600203C211yesmaximal, characteristic
13#10600200C211yesmaximal, characteristic
14#10600196C211yesmaximal, characteristic
15#10600194C211yesmaximal, characteristic
16C22×C5×C4⋊C4C2211yescharacteristic
17C22×C5×C4⋊C4C2211yescharacteristic
18C22×C5×C4⋊C4C2211yescharacteristic
19C22×C4⋊Dic5C2211yescharacteristic
20C22×C4⋊Dic5C2211yescharacteristic
21C22×#683C2211yescharacteristic
22C22×C4×Dic5C2211yescharacteristic
23C22×C4×Dic5C2211yescharacteristic
24C22×C4×Dic5C2211yescharacteristic
25C2×C5×#95C2211yescharacteristic
26C2×C5×#95C2211yescharacteristic
27C2×C5×#95C2211yescharacteristic
28C2×C5×#95C2211yescharacteristic
29C2×#3963C2211yescharacteristic
30C2×#3963C2211yescharacteristic
31C2×#3963C2211yescharacteristic
32C2×#3963C2211yescharacteristic
33C2×#3963C2211yescharacteristic
34C2×#3963C2211yescharacteristic
35C2×#3963C2211yescharacteristic
36C2×#3963C2211yescharacteristic
37C2×#3963C2211yescharacteristic
38C2×#3963C2211yescharacteristic
39C2×#3963C2211yescharacteristic
40C2×#3963C2211yescharacteristic
41C2×#3963C2211yescharacteristic
42C2×#3963C2211yescharacteristic
43C2×#3963C2211yescharacteristic
44C2×#3963C2211yescharacteristic
45C2×#3963C2211yescharacteristic
46C2×#3963C2211yescharacteristic
47C2×#3963C2211yescharacteristic
48C2×#3963C2211yescharacteristic
49C2×#3963C2211yescharacteristic
50C2×#3963C2211yescharacteristic
51#65267—24no—
52#64942C418yescomplemented
53#64940—24no—
54#14395—51nomaximal, Sylow
55C23×C4×C5C2311yescharacteristic
56C23×C4×C5C2311yescharacteristic
57C23×C4×C5C2311yescharacteristic
58C23×C4×C5C2311yescharacteristic
59C23×C4×C5C2311yescharacteristic
60C23×C4×C5C2311yescharacteristic
61C23×C4×C5C2311yescharacteristic
62C23×Dic5C2311yescharacteristic
63C23×Dic5C2311yescharacteristic
64C23×Dic5C2311yescharacteristic
65C23×Dic5C2311yescharacteristic
66C23×Dic5C2311yescharacteristic
67C23×Dic5C2311yescharacteristic
68C23×Dic5C2311yescharacteristic
69C23×Dic5C2311yescharacteristic
70C2×C5×C4⋊C4—22no—
71C2×C5×C4⋊C4—22no—
72C2×C5×C4⋊C4—22no—
73C2×C5×C4⋊C4—22no—
74C2×C5×C4⋊C4—41no—
75C2×C5×C4⋊C4—41no—
76C2×C5×C4⋊C4—41no—
77C2×C5×C4⋊C4—41no—
78C2×C5×C4⋊C4—41no—
79C2×C4⋊Dic5—22no—
80C2×C4⋊Dic5—22no—
81C2×C4⋊Dic5—22no—
82C2×C4⋊Dic5—22no—
83C2×C4⋊Dic5—41no—
84C2×C4⋊Dic5C2×C414yes—
85C2×#683—22no—
86C2×#683—22no—
87C2×#683C2×C414yes—
88C2×C4×Dic5—22no—
89C2×C4×Dic5—22no—
90C2×C4×Dic5—22no—
91C2×C4×Dic5—22no—
92C2×C4×Dic5—22no—
93C2×C4×Dic5—22no—
94C2×C4×Dic5—41no—
95C2×C4×Dic5—41no—
96C2×C4×Dic5C2×C414yes—
97C5×#95—22no—
98C5×#95—22no—
99C5×#95—41no—
100C5×#95C2×C414yes—
101#3963—22no—
102#3963—22no—
103#3963—22no—
104#3963—22no—
105#3963—22no—
106#3963—22no—
107#3963—22no—
108#3963—22no—
109#3963—22no—
110#3963—41no—
111#3963—41no—
112#3963—41no—
113#3963—41no—
114#3963—41no—
115#3963—41no—
116#3963—41no—
117#3963—41no—
118#3963—41no—
119#3963C2×C414yes—
120#3963C2×C414yes—
121#3963C2×C414yes—
122#3963D414yes—
123C2×#387—51no—
124C2×#387—51no—
125C2×#383—51no—
126#1445—51no—
127#1444D511yescharacteristic
128#1443—51no—
129#1442—51no—
130#1442—51no—
131#1441—51no—
132#1436—51no—
133#1436—51no—
134C4⋊#95—51no—
135C4⋊#95—51no—
136#1434—51no—
137#1434—51no—
138C24×C5C2411yescharacteristic
139C22×C4×C5—21no—
140C22×C4×C5—21no—
141C22×C4×C5—21no—
142C22×C4×C5—21no—
143C22×C4×C5—21no—
144C22×C4×C5—21no—
145C22×C4×C5—21no—
146C22×C4×C5—21no—
147C22×C4×C5—21no—
148C22×C4×C5—21no—
149C22×C4×C5—21no—
150C22×C4×C5—21no—
151C22×C4×C5—21no—
152C22×C4×C5—21no—
153C22×C4×C5—21no—
154C22×C4×C5—21no—
155C22×C4×C5—21no—
156C22×C4×C5—21no—
157C22×C4×C5—21no—
158C22×C4×C5—21no—
159C22×C4×C5—21no—
160C22×C4×C5—21no—
161C22×C4×C5—21no—
162C22×C4×C5—21no—
163C22×C4×C5—21no—
164C22×C4×C5—21no—
165C22×C4×C5—21no—
166C22×C4×C5—21no—
167C22×C4×C5—21no—
168C22×C4×C5—21no—
169C22×C4×C5—21no—
170C22×C4×C5—21no—
171C22×C4×C5—21no—
172C22×C4×C5—21no—
173C22×C4×C5—21no—
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×C5C22×C412yes—
181C22×C4×C5C22×C412yes—
182C22×C4×C5C22×C412yes—
183C22×C4×C5C2×D412yes—
184C22×C4×C5#4112yes—
185C22×C4×C5#4112yes—
186C22×C4×C5#4112yes—
187C22×C4×C5#4112yes—
188C22×Dic5—21no—
189C22×Dic5—21no—
190C22×Dic5—21no—
191C22×Dic5—21no—
192C22×Dic5—21no—
193C22×Dic5—21no—
194C22×Dic5—21no—
195C22×Dic5—21no—
196C22×Dic5—21no—
197C22×Dic5—21no—
198C22×Dic5—21no—
199C22×Dic5—21no—
200C22×Dic5—21no—
201C22×Dic5—21no—
202C22×Dic5—21no—
203C22×Dic5—21no—
204C22×Dic5—21no—
205C22×Dic5—21no—
206C22×Dic5—21no—
207C22×Dic5—21no—
208C22×Dic5—21no—
209C22×Dic5—21no—
210C22×Dic5—21no—
211C22×Dic5—21no—
212C22×Dic5—21no—
213C22×Dic5—21no—
214C22×Dic5—21no—
215C22×Dic5—21no—
216C22×Dic5—21no—
217C22×Dic5—21no—
218C22×Dic5—21no—
219C22×Dic5—21no—
220C22×Dic5—21no—
221C22×Dic5—21no—
222C22×Dic5—21no—
223C22×Dic5—21no—
224C22×Dic5—21no—
225C22×Dic5—21no—
226C22×Dic5—21no—
227C22×Dic5—21no—
228C22×Dic5—21no—
229C22×Dic5—21no—
230C22×Dic5—21no—
231C22×Dic5—21no—
232C22×Dic5—21no—
233C22×Dic5—21no—
234C22×Dic5—21no—
235C22×Dic5—21no—
236C22×Dic5—21no—
237C22×Dic5C22×C412yes—
238C22×Dic5C22×C412yes—
239C22×Dic5C22×C412yes—
240C22×Dic5C22×C412yes—
241C22×Dic5C2×D412yes—
242C22×Dic5C2×D412yes—
243C22×Dic5#4112yes—
244C5×C4⋊C4—44no—
245C5×C4⋊C4—44no—
246C5×C4⋊C4—44no—
247C4⋊Dic5—28no—
248C4⋊Dic5—44no—
249#683—28no—
250C4×Dic5—28no—
251C4×Dic5—44no—
252C4×Dic5—44no—
253C22×C4⋊C4—51no—
254C22×C4⋊C4—51no—
255C22×C4⋊C4—51no—
256C22×C4⋊C4C2×D511yescharacteristic
257C22×C4⋊C4C2×D511yescharacteristic
258C22×C4⋊C4C2×D511yescharacteristic
259C22×C42—51no—
260C22×C42—51no—
261C22×C42—51no—
262#387—58no—
263#387—104no—
264#383—104no—
265C2×#95—51no—
266C2×#95—51no—
267C2×#95—51no—
268C2×#95—51no—
269C2×#95—51no—
270C2×#95—51no—
271C2×#95—51no—
272C2×#95—51no—
273C2×#95—51no—
274C2×#95—51no—
275C2×#95—51no—
276C2×#95—51no—
277C2×#95—51no—
278C2×#95—51no—
279C2×#95—51no—
280C2×#95—51no—
281C2×#95—51no—
282C2×#95—51no—
283C2×#95—51no—
284C2×#95—51no—
285C2×#95—51no—
286C2×#95—51no—
287C2×#95C2×D511yescharacteristic
288C2×#95C2×D511yescharacteristic
289C2×#95C2×D511yescharacteristic
290C2×#95C2×D511yescharacteristic
291C23×C5C23×C411yescharacteristic
292C23×C5C22×D411yescharacteristic
293C23×C5C2×#4111yescharacteristic
294C23×C5C2×#4111yescharacteristic
295C23×C5C2×#4111yescharacteristic
296C23×C5C2×#4111yescharacteristic
297C23×C5C2×#4111yescharacteristic
298C23×C5H(5,𝔽2)11yescharacteristic
299C23×C5H(5,𝔽2)11yescharacteristic
300C23×C5H(5,𝔽2)11yescharacteristic
301C23×C52−1+411yescharacteristic
302C23×C52−1+411yescharacteristic
303C23×C52−1+411yescharacteristic
304C23×C52−1+411yescharacteristic
305C23×C52−1+411yescharacteristic
306C2×C4×C5—22no—
307C2×C4×C5—22no—
308C2×C4×C5—22no—
309C2×C4×C5—22no—
310C2×C4×C5—22no—
311C2×C4×C5—22no—
312C2×C4×C5—22no—
313C2×C4×C5—22no—
314C2×C4×C5—22no—
315C2×C4×C5—22no—
316C2×C4×C5—22no—
317C2×C4×C5—22no—
318C2×C4×C5—22no—
319C2×C4×C5—22no—
320C2×C4×C5—22no—
321C2×C4×C5—22no—
322C2×C4×C5—22no—
323C2×C4×C5—22no—
324C2×C4×C5—41no—
325C2×C4×C5—41no—
326C2×C4×C5—41no—
327C2×C4×C5—41no—
328C2×C4×C5—41no—
329C2×C4×C5—41no—
330C2×C4×C5—41no—
331C2×C4×C5—41no—
332C2×C4×C5—41no—
333C2×C4×C5—41no—
334C2×C4×C5—41no—
335C2×C4×C5—41no—
336C2×C4×C5—41no—
337C2×C4×C5—41no—
338C2×C4×C5—41no—
339C2×C4×C5—41no—
340C2×C4×C5—41no—
341C2×C4×C5—41no—
342C2×C4×C5—41no—
343C2×C4×C5—41no—
344C2×C4×C5—41no—
345C2×C4×C5—41no—
346C2×C4×C5—41no—
347C2×C4×C5—41no—
348C2×C4×C5—41no—
349C2×C4×C5—41no—
350C2×C4×C5—41no—
351C2×C4×C5—41no—
352C2×C4×C5—41no—
353C2×C4×C5#11714yes—
354C2×C4×C5C4×D414yes—
355C2×Dic5—22no—
356C2×Dic5—22no—
357C2×Dic5—22no—
358C2×Dic5—22no—
359C2×Dic5—22no—
360C2×Dic5—22no—
361C2×Dic5—22no—
362C2×Dic5—22no—
363C2×Dic5—22no—
364C2×Dic5—22no—
365C2×Dic5—22no—
366C2×Dic5—22no—
367C2×Dic5—22no—
368C2×Dic5—22no—
369C2×Dic5—22no—
370C2×Dic5—22no—
371C2×Dic5—22no—
372C2×Dic5—22no—
373C2×Dic5—22no—
374C2×Dic5—22no—
375C2×Dic5—22no—
376C2×Dic5—41no—
377C2×Dic5—41no—
378C2×Dic5—41no—
379C2×Dic5—41no—
380C2×Dic5—41no—
381C2×Dic5—41no—
382C2×Dic5—41no—
383C2×Dic5—41no—
384C2×Dic5—41no—
385C2×Dic5—41no—
386C2×Dic5—41no—
387C2×Dic5—41no—
388C2×Dic5—41no—
389C2×Dic5—41no—
390C2×Dic5—41no—
391C2×Dic5—41no—
392C2×Dic5—41no—
393C2×Dic5—41no—
394C2×Dic5—41no—
395C2×Dic5—41no—
396C2×Dic5—41no—
397C2×Dic5—41no—
398C2×Dic5—41no—
399C2×Dic5—41no—
400C2×Dic5—41no—
401C2×Dic5—41no—
402C2×Dic5—41no—
403C2×Dic5—41no—
404C2×Dic5—41no—
405C2×Dic5—41no—
406C2×Dic5—41no—
407C2×Dic5—41no—
408C2×Dic5—41no—
409C2×Dic5—41no—
410C2×Dic5—41no—
411C23×C4—51no—
412C23×C4—51no—
413C23×C4—51no—
414C23×C4—51no—
415C23×C4—51no—
416C23×C4—51no—
417C23×C4—51no—
418C23×C4—51no—
419C23×C4C22×D511yescharacteristic
420C23×C4C22×D511yescharacteristic
421C23×C4C22×D511yescharacteristic
422C23×C4C22×D511yescharacteristic
423C23×C4C22×D511yescharacteristic
424C23×C4C22×D511yescharacteristic
425C23×C4C22×D511yescharacteristic
426C2×C4⋊C4—22no—
427C2×C4⋊C4—22no—
428C2×C4⋊C4—22no—
429C2×C4⋊C4—22no—
430C2×C4⋊C4—41no—
431C2×C4⋊C4—41no—
432C2×C4⋊C4—41no—
433C2×C4⋊C4—41no—
434C2×C4⋊C4—41no—
435C2×C4⋊C4—54no—
436C2×C4⋊C4—54no—
437C2×C4⋊C4—102no—
438C2×C4⋊C4—102no—
439C2×C4⋊C4—102no—
440C2×C4⋊C4—102no—
441C2×C4⋊C4—102no—
442C2×C4⋊C4—102no—
443C2×C4⋊C4—201no—
444C2×C42—54no—
445C2×C42—102no—
446C2×C42—102no—
447C2×C42—102no—
448C2×C42—102no—
449C2×C42—102no—
450C2×C42—102no—
451C2×C42—201no—
452C2×C42—201no—
453#95—22no—
454#95—22no—
455#95—41no—
456#95—54no—
457#95—54no—
458#95—54no—
459#95—54no—
460#95—102no—
461#95—102no—
462#95—102no—
463#95—102no—
464#95—102no—
465#95—102no—
466#95—102no—
467#95—102no—
468#95—102no—
469#95—201no—
470#95—201no—
471#95—201no—
472#95—201no—
473#95—201no—
474#95—201no—
475#95—201no—
476#95—201no—
477#95—201no—
478#95C4×D514yes—
479C22×C5C2×#11711yescharacteristic
480C22×C5C2×C4×D411yescharacteristic
481C22×C5C4×#4111yescharacteristic
482C22×C5#51911yescharacteristic
483C22×C5#52011yescharacteristic
484C22×C5#52011yescharacteristic
485C22×C5#52011yescharacteristic
486C22×C5#53611yescharacteristic
487C22×C5#53711yescharacteristic
488C22×C5#53911yescharacteristic
489C22×C5#53911yescharacteristic
490C22×C5#54111yescharacteristic
491C22×C5#54111yescharacteristic
492C22×C5#54111yescharacteristic
493C22×C5#54111yescharacteristic
494C22×C5#54111yescharacteristic
495C22×C5#54211yescharacteristic
496C22×C5#54211yescharacteristic
497C22×C5#54211yescharacteristic
498C22×C5#54611yescharacteristic
499C22×C5#54711yescharacteristic
500C22×C5#54711yescharacteristic
501C22×C5#55011yescharacteristic
502C22×C5#55111yescharacteristic
503C22×C5#55111yescharacteristic
504C22×C5#55111yescharacteristic
505C22×C5#55211yescharacteristic
506C22×C5#55211yescharacteristic
507C22×C5#55211yescharacteristic
508C22×C5#55511yescharacteristic
509C22×C5#55611yescharacteristic
510C22×C5#56011yescharacteristic
511C22×C5#56311yescharacteristic
512C22×C5#56311yescharacteristic
513C22×C5#56311yescharacteristic
514C4×C5—24no—
515C4×C5—24no—
516C4×C5—42no—
517C4×C5—42no—
518C4×C5—81no—
519C4×C5—81no—
520C4×C5—81no—
521Dic5—42no—
522Dic5—42no—
523Dic5—42no—
524Dic5—42no—
525Dic5—42no—
526Dic5—42no—
527Dic5—42no—
528Dic5—81no—
529C24C23×D511yescharacteristic
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
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—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—52no—
572C22×C4—52no—
573C22×C4—52no—
574C22×C4—52no—
575C22×C4—52no—
576C22×C4—52no—
577C22×C4—52no—
578C22×C4—101no—
579C22×C4—101no—
580C22×C4—101no—
581C22×C4—101no—
582C22×C4—101no—
583C22×C4—101no—
584C22×C4—101no—
585C22×C4—101no—
586C22×C4—101no—
587C22×C4—101no—
588C22×C4—101no—
589C22×C4—101no—
590C22×C4—101no—
591C22×C4—101no—
592C22×C4—101no—
593C22×C4—101no—
594C22×C4—101no—
595C22×C4—101no—
596C22×C4—101no—
597C22×C4—101no—
598C22×C4—101no—
599C22×C4—101no—
600C22×C4—101no—
601C22×C4—101no—
602C22×C4—101no—
603C22×C4—101no—
604C22×C4—101no—
605C22×C4—101no—
606C22×C4—101no—
607C22×C4—101no—
608C22×C4—101no—
609C22×C4—101no—
610C22×C4—101no—
611C22×C4—101no—
612C22×C4—101no—
613C22×C4—101no—
614C22×C4—101no—
615C22×C4—101no—
616C22×C4—101no—
617C22×C4—101no—
618C22×C4—101no—
619C22×C4—101no—
620C22×C4—101no—
621C22×C4—101no—
622C22×C4—101no—
623C22×C4—101no—
624C22×C4—101no—
625C22×C4—101no—
626C22×C4—101no—
627C22×C4C2×C4×D512yes—
628C22×C4C2×C4×D512yes—
629C22×C4C2×C4×D512yes—
630C22×C4D4×D512yes—
631C22×C4#71112yes—
632C22×C4#71112yes—
633C22×C4#71312yes—
634C22×C4#71312yes—
635C4⋊C4—44no—
636C4⋊C4—44no—
637C4⋊C4—44no—
638C4⋊C4—108no—
639C4⋊C4—108no—
640C4⋊C4—204no—
641C42—108no—
642C42—204no—
643C42—204no—
644C2×C5#232011yescharacteristic
645C2×C5#232311yescharacteristic
646C2×C5#233611yescharacteristic
647C2×C5#234311yescharacteristic
648C2×C5#235411yescharacteristic
649C2×C5#235911yescharacteristic
650C2×C5#238311yescharacteristic
651C2×C5#269811yescharacteristic
652C2×C5#270511yescharacteristic
653C2×C5#272111yescharacteristic
654C2×C5#272211yescharacteristic
655C2×C5#273711yescharacteristic
656C2×C5#275811yescharacteristic
657C2×C5#276211yescharacteristic
658C2×C5#276911yescharacteristic
659C23C22×C4×D511yescharacteristic
660C23C2×D4×D511yescharacteristic
661C23C2×#71111yescharacteristic
662C23C2×#71111yescharacteristic
663C23#414411yescharacteristic
664C23#414411yescharacteristic
665C23#414411yescharacteristic
666C23C2×#71311yescharacteristic
667C23C2×#71311yescharacteristic
668C23#414711yescharacteristic
669C23#414711yescharacteristic
670C23D5×#4111yescharacteristic
671C23#415011yescharacteristic
672C23#415011yescharacteristic
673C23#415011yescharacteristic
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—41no—
693C2×C4—41no—
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—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—102no—
722C2×C4—102no—
723C2×C4—102no—
724C2×C4—102no—
725C2×C4—102no—
726C2×C4—102no—
727C2×C4—102no—
728C2×C4—102no—
729C2×C4—102no—
730C2×C4—102no—
731C2×C4—102no—
732C2×C4—102no—
733C2×C4—102no—
734C2×C4—102no—
735C2×C4—102no—
736C2×C4—102no—
737C2×C4—102no—
738C2×C4—102no—
739C2×C4—102no—
740C2×C4—102no—
741C2×C4—102no—
742C2×C4—201no—
743C2×C4—201no—
744C2×C4—201no—
745C2×C4—201no—
746C2×C4—201no—
747C2×C4—201no—
748C2×C4—201no—
749C2×C4—201no—
750C2×C4—201no—
751C2×C4—201no—
752C2×C4—201no—
753C2×C4—201no—
754C2×C4—201no—
755C2×C4—201no—
756C2×C4—201no—
757C2×C4—201no—
758C2×C4—201no—
759C2×C4—201no—
760C2×C4—201no—
761C2×C4—201no—
762C2×C4—201no—
763C2×C4—201no—
764C2×C4—201no—
765C2×C4—201no—
766C2×C4—201no—
767C2×C4—201no—
768C2×C4—201no—
769C2×C4—201no—
770C2×C4—201no—
771C2×C4—201no—
772C2×C4—201no—
773C2×C4—201no—
774C2×C4—201no—
775C2×C4—201no—
776C2×C4—201no—
777C2×C4#403814yes—
778C2×C4#403914yes—
779C5#1439511yescharacteristic, complemented, Sylow
780C22C2×#403811yescharacteristic
781C22C2×#403911yescharacteristic
782C22#6583811yescharacteristic
783C22C4×#71111yescharacteristic
784C22#6588011yescharacteristic
785C22#6588011yescharacteristic
786C22#6590611yescharacteristic
787C22#6592111yescharacteristic
788C22#6592511yescharacteristic
789C22#6592911yescharacteristic
790C22#6593611yescharacteristic
791C22#6593711yescharacteristic
792C22#6594211yescharacteristic
793C22#6595911yescharacteristic
794C22#6596211yescharacteristic
795C22#6597111yescharacteristic
796C22#6597111yescharacteristic
797C22#6597211yescharacteristic
798C22#6597611yescharacteristic
799C22#6597611yescharacteristic
800C22#6598011yescharacteristic
801C22#6598011yescharacteristic
802C22#6598411yescharacteristic
803C22#6598511yescharacteristic
804C22#6598911yescharacteristic
805C22#6603011yescharacteristic
806C22#6603111yescharacteristic
807C22#6603111yescharacteristic
808C22#6605211yescharacteristic
809C22#6606011yescharacteristic
810C22#6606511yescharacteristic
811C22#6606611yescharacteristic
812C22#6606711yescharacteristic
813C22#6606711yescharacteristic
814C22#6606811yescharacteristic
815C4—24no—
816C4—24no—
817C4—42no—
818C4—42no—
819C4—81no—
820C4—81no—
821C4—81no—
822C4—202no—
823C4—202no—
824C4—202no—
825C4—202no—
826C4—202no—
827C4—202no—
828C4—202no—
829C4—401no—
830C2#1060605511yescharacteristic
831C2#1060612311yescharacteristic
832C2#1060612611yescharacteristic
833C2#1060613411yescharacteristic
834C2#1060770111yescharacteristic
835C2#1060770911yescharacteristic
836C2#1060792811yescharacteristic
837C2#1060845511yescharacteristic
838C2#1060895711yescharacteristic
839C2#1060899711yescharacteristic
840C2#1060900011yescharacteristic
841C2#1060959511yescharacteristic
842C2#1060961111yescharacteristic
843C2#1060962311yescharacteristic
844C2#1060980011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D5
commutatorC23×C5C23×C4
FittingC5×#1444C2
socle, prime radical, cosocleC24×C5C24
hypercenter#1444D5
hypocenterC5#14395
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ #1444

Complements

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

NH ≅ G/Ntype
52. #64942C4semidirect
779. C5#14395semidirect

Maximal subgroups

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

subgroupindex
C2×#652672
C2×#649422
C2×#649402
C5×#14442
#106023602
#106023572
#106023562
#106002162
#106002102
#106002032
#106002002
#106001962
#106001942
#143955