Finite Group Databasebeta

← #12026014

Subgroups — #12026014

Order 1280.

1102 conjugacy classes of subgroups.

The subgroup lattice has 830 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64943C211yesmaximal, characteristic
2C5×#1442C211yesmaximal, characteristic
3#10602359C211yesmaximal, characteristic
4#10602357C211yesmaximal, characteristic
5#10600214C211yesmaximal, characteristic
6#10600211C211yesmaximal, characteristic
7#10600210C211yesmaximal, characteristic
8#10600209C211yesmaximal, characteristic
9#10600207C211yesmaximal, characteristic
10#10600207C211yesmaximal, characteristic
11#10600200C211yesmaximal, characteristic
12#10600200C211yesmaximal, characteristic
13#10600198C211yesmaximal, characteristic
14#10600195C211yesmaximal, characteristic
15Dic5×#95C211yesmaximal, characteristic
16C22×C5×C4⋊C4C2211yescharacteristic
17C22×C4⋊Dic5C2211yescharacteristic
18C22×#683C2211yescharacteristic
19C22×#683C2211yescharacteristic
20C22×C4×Dic5C2211yescharacteristic
21C22×C4×Dic5C2211yescharacteristic
22C22×C4×Dic5C2211yescharacteristic
23C2×C5×#95C2211yescharacteristic
24C2×C5×#95C2211yescharacteristic
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#64943C418yescomplemented
52#14294—51nomaximal, Sylow
53C23×C4×C5C2311yescharacteristic
54C23×C4×C5C2311yescharacteristic
55C23×C4×C5C2311yescharacteristic
56C23×C4×C5C2311yescharacteristic
57C23×C4×C5C2311yescharacteristic
58C23×C4×C5C2311yescharacteristic
59C23×C4×C5C2311yescharacteristic
60C23×Dic5C2311yescharacteristic
61C23×Dic5C2311yescharacteristic
62C23×Dic5C2311yescharacteristic
63C23×Dic5C2311yescharacteristic
64C23×Dic5C2311yescharacteristic
65C23×Dic5C2311yescharacteristic
66C23×Dic5C2311yescharacteristic
67C23×Dic5C2311yescharacteristic
68C2×C5×C4⋊C4—22no—
69C2×C5×C4⋊C4—41no—
70C2×C5×C4⋊C4—41no—
71C2×C4⋊Dic5—22no—
72C2×C4⋊Dic5—22no—
73C2×C4⋊Dic5C2×C414yes—
74C2×#683—22no—
75C2×#683—41no—
76C2×#683—41no—
77C2×#683—41no—
78C2×#683—41no—
79C2×#683C2×C414yes—
80C2×C4×Dic5—22no—
81C2×C4×Dic5—22no—
82C2×C4×Dic5—41no—
83C2×C4×Dic5—41no—
84C2×C4×Dic5—41no—
85C2×C4×Dic5—41no—
86C2×C4×Dic5—41no—
87C2×C4×Dic5—41no—
88C2×C4×Dic5C2×C414yes—
89C5×#95—22no—
90C5×#95—22no—
91C5×#95—22no—
92C5×#95—41no—
93C5×#95—41no—
94C5×#95C2×C414yes—
95#3963—22no—
96#3963—22no—
97#3963—22no—
98#3963—22no—
99#3963—22no—
100#3963—22no—
101#3963—22no—
102#3963—22no—
103#3963—22no—
104#3963—41no—
105#3963—41no—
106#3963—41no—
107#3963—41no—
108#3963—41no—
109#3963—41no—
110#3963—41no—
111#3963—41no—
112#3963—41no—
113#3963—41no—
114#3963C2×C414yes—
115#3963C2×C414yes—
116#3963C2×C414yes—
117C2×#387—51no—
118#1445—51no—
119#1443—51no—
120#1443—51no—
121#1443—51no—
122#1442—51no—
123#1442—51no—
124#1442D511yescharacteristic
125#1441—51no—
126#1436—51no—
127#1436—51no—
128#1436—51no—
129#1436—51no—
130#1434—51no—
131C4×#95—51no—
132C24×C5C2411yescharacteristic
133C22×C4×C5—21no—
134C22×C4×C5—21no—
135C22×C4×C5—21no—
136C22×C4×C5—21no—
137C22×C4×C5—21no—
138C22×C4×C5—21no—
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×C5C22×C412yes—
178C22×C4×C5C22×C412yes—
179C22×C4×C5C22×C412yes—
180C22×C4×C5#4112yes—
181C22×C4×C5#4112yes—
182C22×Dic5—21no—
183C22×Dic5—21no—
184C22×Dic5—21no—
185C22×Dic5—21no—
186C22×Dic5—21no—
187C22×Dic5—21no—
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×Dic5C22×C412yes—
231C22×Dic5C22×C412yes—
232C22×Dic5C22×C412yes—
233C22×Dic5C22×C412yes—
234C22×Dic5#4112yes—
235C22×Dic5#4112yes—
236C22×Dic5#4112yes—
237C22×Dic5#4112yes—
238C5×C4⋊C4—44no—
239C4⋊Dic5—28no—
240#683—44no—
241#683—44no—
242C4×Dic5—44no—
243C4×Dic5—44no—
244C4×Dic5—44no—
245C22×C4⋊C4—51no—
246C22×C4⋊C4—51no—
247C22×C4⋊C4—51no—
248C22×C4⋊C4C2×D511yescharacteristic
249C22×C42—51no—
250C22×C42—51no—
251C22×C42—51no—
252#387—58no—
253C2×#95—51no—
254C2×#95—51no—
255C2×#95—51no—
256C2×#95—51no—
257C2×#95—51no—
258C2×#95—51no—
259C2×#95—51no—
260C2×#95—51no—
261C2×#95—51no—
262C2×#95—51no—
263C2×#95—51no—
264C2×#95—51no—
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×#95C2×D511yescharacteristic
276C2×#95C2×D511yescharacteristic
277C2×#95C2×D511yescharacteristic
278C2×#95C2×D511yescharacteristic
279C2×#95C2×D511yescharacteristic
280C2×#95C2×D511yescharacteristic
281C23×C5C23×C411yescharacteristic
282C23×C5C2×#4111yescharacteristic
283C23×C5C2×#4111yescharacteristic
284C23×C5C2×#4111yescharacteristic
285C23×C5C2×#4111yescharacteristic
286C23×C5C2×#4111yescharacteristic
287C23×C5C2×#4111yescharacteristic
288C23×C5H(5,𝔽2)11yescharacteristic
289C23×C5H(5,𝔽2)11yescharacteristic
290C23×C5H(5,𝔽2)11yescharacteristic
291C23×C5H(5,𝔽2)11yescharacteristic
292C23×C52−1+411yescharacteristic
293C23×C52−1+411yescharacteristic
294C23×C52−1+411yescharacteristic
295C23×C52−1+411yescharacteristic
296C2×C4×C5—22no—
297C2×C4×C5—22no—
298C2×C4×C5—22no—
299C2×C4×C5—22no—
300C2×C4×C5—22no—
301C2×C4×C5—22no—
302C2×C4×C5—22no—
303C2×C4×C5—22no—
304C2×C4×C5—22no—
305C2×C4×C5—22no—
306C2×C4×C5—22no—
307C2×C4×C5—22no—
308C2×C4×C5—22no—
309C2×C4×C5—22no—
310C2×C4×C5—22no—
311C2×C4×C5—41no—
312C2×C4×C5—41no—
313C2×C4×C5—41no—
314C2×C4×C5—41no—
315C2×C4×C5—41no—
316C2×C4×C5—41no—
317C2×C4×C5—41no—
318C2×C4×C5—41no—
319C2×C4×C5—41no—
320C2×C4×C5—41no—
321C2×C4×C5—41no—
322C2×C4×C5—41no—
323C2×C4×C5—41no—
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×Dic5—22no—
346C2×Dic5—22no—
347C2×Dic5—22no—
348C2×Dic5—22no—
349C2×Dic5—22no—
350C2×Dic5—22no—
351C2×Dic5—22no—
352C2×Dic5—22no—
353C2×Dic5—22no—
354C2×Dic5—22no—
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—41no—
367C2×Dic5—41no—
368C2×Dic5—41no—
369C2×Dic5—41no—
370C2×Dic5—41no—
371C2×Dic5—41no—
372C2×Dic5—41no—
373C2×Dic5—41no—
374C2×Dic5—41no—
375C2×Dic5—41no—
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#11714yes—
401C23×C4—51no—
402C23×C4—51no—
403C23×C4—51no—
404C23×C4—51no—
405C23×C4—51no—
406C23×C4—51no—
407C23×C4—51no—
408C23×C4—51no—
409C23×C4C22×D511yescharacteristic
410C23×C4C22×D511yescharacteristic
411C23×C4C22×D511yescharacteristic
412C23×C4C22×D511yescharacteristic
413C23×C4C22×D511yescharacteristic
414C23×C4C22×D511yescharacteristic
415C23×C4C22×D511yescharacteristic
416C2×C4⋊C4—22no—
417C2×C4⋊C4—41no—
418C2×C4⋊C4—41no—
419C2×C4⋊C4—54no—
420C2×C4⋊C4—54no—
421C2×C4⋊C4—102no—
422C2×C4⋊C4—102no—
423C2×C4⋊C4—102no—
424C2×C4⋊C4—201no—
425C2×C4⋊C4—201no—
426C2×C4⋊C4—201no—
427C2×C4⋊C4—201no—
428C2×C42—54no—
429C2×C42—102no—
430C2×C42—102no—
431C2×C42—201no—
432C2×C42—201no—
433C2×C42—201no—
434C2×C42—201no—
435C2×C42—201no—
436C2×C42—201no—
437#95—22no—
438#95—22no—
439#95—22no—
440#95—41no—
441#95—41no—
442#95—54no—
443#95—54no—
444#95—54no—
445#95—102no—
446#95—102no—
447#95—102no—
448#95—102no—
449#95—102no—
450#95—102no—
451#95—102no—
452#95—102no—
453#95—102no—
454#95—201no—
455#95—201no—
456#95—201no—
457#95—201no—
458#95—201no—
459#95—201no—
460#95—201no—
461#95—201no—
462#95—201no—
463#95—201no—
464#95C4×D514yes—
465C22×C5C2×#11711yescharacteristic
466C22×C5C4×#4111yescharacteristic
467C22×C5C4×#4111yescharacteristic
468C22×C5#51811yescharacteristic
469C22×C5#51911yescharacteristic
470C22×C5#52011yescharacteristic
471C22×C5#52011yescharacteristic
472C22×C5#52911yescharacteristic
473C22×C5#52911yescharacteristic
474C22×C5#52911yescharacteristic
475C22×C5#52911yescharacteristic
476C22×C5#53811yescharacteristic
477C22×C5#53811yescharacteristic
478C22×C5#53811yescharacteristic
479C22×C5#53811yescharacteristic
480C22×C5#53911yescharacteristic
481C22×C5#53911yescharacteristic
482C22×C5#53911yescharacteristic
483C22×C5#53911yescharacteristic
484C22×C5#53911yescharacteristic
485C22×C5#53911yescharacteristic
486C22×C5#53911yescharacteristic
487C22×C5#53911yescharacteristic
488C22×C5#54011yescharacteristic
489C22×C5#54111yescharacteristic
490C22×C5#54111yescharacteristic
491C22×C5#54111yescharacteristic
492C22×C5#54111yescharacteristic
493C22×C5#54111yescharacteristic
494C22×C5#54211yescharacteristic
495C22×C5#54211yescharacteristic
496C22×C5#54211yescharacteristic
497C22×C5#54211yescharacteristic
498C22×C5#54211yescharacteristic
499C22×C5#54211yescharacteristic
500C4×C5—42no—
501C4×C5—42no—
502C4×C5—42no—
503C4×C5—42no—
504C4×C5—42no—
505C4×C5—81no—
506C4×C5—81no—
507Dic5—24no—
508Dic5—42no—
509Dic5—42no—
510Dic5—42no—
511Dic5—42no—
512Dic5—42no—
513Dic5—81no—
514Dic5—81no—
515C24C23×D511yescharacteristic
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
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—52no—
561C22×C4—52no—
562C22×C4—52no—
563C22×C4—52no—
564C22×C4—52no—
565C22×C4—52no—
566C22×C4—52no—
567C22×C4—52no—
568C22×C4—101no—
569C22×C4—101no—
570C22×C4—101no—
571C22×C4—101no—
572C22×C4—101no—
573C22×C4—101no—
574C22×C4—101no—
575C22×C4—101no—
576C22×C4—101no—
577C22×C4—101no—
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×C4C2×C4×D512yes—
617C22×C4C2×C4×D512yes—
618C22×C4C2×C4×D512yes—
619C22×C4#71112yes—
620C22×C4#71112yes—
621C4⋊C4—44no—
622C4⋊C4—108no—
623C4⋊C4—204no—
624C4⋊C4—204no—
625C42—204no—
626C42—204no—
627C42—204no—
628C2×C5#229811yescharacteristic
629C2×C5#231811yescharacteristic
630C2×C5#232011yescharacteristic
631C2×C5#233211yescharacteristic
632C2×C5#233411yescharacteristic
633C2×C5#233511yescharacteristic
634C2×C5#233611yescharacteristic
635C2×C5#264911yescharacteristic
636C2×C5#265011yescharacteristic
637C2×C5#265211yescharacteristic
638C2×C5#265211yescharacteristic
639C2×C5#265311yescharacteristic
640C2×C5#265411yescharacteristic
641C2×C5#265511yescharacteristic
642C2×C5#265511yescharacteristic
643C23C22×C4×D511yescharacteristic
644C23C2×#71111yescharacteristic
645C23C2×#71111yescharacteristic
646C23#414411yescharacteristic
647C23#414411yescharacteristic
648C23#414711yescharacteristic
649C23#414711yescharacteristic
650C23D5×#4111yescharacteristic
651C23D5×#4111yescharacteristic
652C23D5×#4111yescharacteristic
653C23D5×#4111yescharacteristic
654C23#414911yescharacteristic
655C23#414911yescharacteristic
656C23#415011yescharacteristic
657C23#415011yescharacteristic
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
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—54no—
708C2×C4—102no—
709C2×C4—102no—
710C2×C4—102no—
711C2×C4—102no—
712C2×C4—102no—
713C2×C4—102no—
714C2×C4—102no—
715C2×C4—102no—
716C2×C4—102no—
717C2×C4—102no—
718C2×C4—102no—
719C2×C4—102no—
720C2×C4—102no—
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—201no—
730C2×C4—201no—
731C2×C4—201no—
732C2×C4—201no—
733C2×C4—201no—
734C2×C4—201no—
735C2×C4—201no—
736C2×C4—201no—
737C2×C4—201no—
738C2×C4—201no—
739C2×C4—201no—
740C2×C4—201no—
741C2×C4—201no—
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—
763C5#1429411yescharacteristic, complemented, Sylow
764C22#6583811yescharacteristic
765C22#6585011yescharacteristic
766C22D5×#11711yescharacteristic
767C22C4×#71111yescharacteristic
768C22C4×#71111yescharacteristic
769C22#6587911yescharacteristic
770C22#6590811yescharacteristic
771C22#6592711yescharacteristic
772C22#6593411yescharacteristic
773C22#6593711yescharacteristic
774C22#6595111yescharacteristic
775C22#6595911yescharacteristic
776C22#6597211yescharacteristic
777C22#6597211yescharacteristic
778C22#6597411yescharacteristic
779C22#6597711yescharacteristic
780C22#6598311yescharacteristic
781C22#6599111yescharacteristic
782C22#6599711yescharacteristic
783C22#6599911yescharacteristic
784C22#6599911yescharacteristic
785C22#6600311yescharacteristic
786C22#6600311yescharacteristic
787C22#6600311yescharacteristic
788C22#6601411yescharacteristic
789C22#6602611yescharacteristic
790C22#6602611yescharacteristic
791C22#6603011yescharacteristic
792C22#6603011yescharacteristic
793C22#6603011yescharacteristic
794C22#6603811yescharacteristic
795C22#6604011yescharacteristic
796C22#6604111yescharacteristic
797C22#6604111yescharacteristic
798C22#6606511yescharacteristic
799C4—42no—
800C4—42no—
801C4—42no—
802C4—42no—
803C4—42no—
804C4—81no—
805C4—81no—
806C4—104no—
807C4—202no—
808C4—202no—
809C4—202no—
810C4—202no—
811C4—202no—
812C4—401no—
813C4—401no—
814C2#1060588211yescharacteristic
815C2#1060612111yescharacteristic
816C2#1060667611yescharacteristic
817C2#1060669011yescharacteristic
818C2#1060718211yescharacteristic
819C2#1060719511yescharacteristic
820C2#1060770611yescharacteristic
821C2#1060854711yescharacteristic
822C2#1060872311yescharacteristic
823C2#1060928311yescharacteristic
824C2#1060956511yescharacteristic
825C2#1060956611yescharacteristic
826C2#1060995411yescharacteristic
827C2#1060995511yescharacteristic
828C2#1060995711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D5
commutatorC23×C5C23×C4
FittingC5×#1442C2
socle, prime radical, cosocleC24×C5C24
hypercenter#1442D5
hypocenterC5#14294
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ #1442

Complements

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

NH ≅ G/Ntype
51. #64943C4semidirect
763. C5#14294semidirect

Maximal subgroups

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

subgroupindex
C2×#649432
C5×#14422
#106023592
#106023572
#106002142
#106002112
#106002102
#106002092
#106002072
#106002002
#106001982
#106001952
Dic5×#952
#142945