Finite Group Databasebeta

← #12022763

Subgroups — #12022763

Order 1280.

2054 conjugacy classes of subgroups.

The subgroup lattice has 942 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#4034C211yesmaximal, characteristic
2C22×C4×Dic10C211yesmaximal, characteristic
3C2×#64935C211yesmaximal, characteristic
4C2×#64935C211yesmaximal, characteristic
5C2×#64935C211yesmaximal, characteristic
6C5×#1436C211yesmaximal, characteristic
7#10602358C211yesmaximal, characteristic
8#10602329C211yesmaximal, characteristic
9#10600204C211yesmaximal, characteristic
10#10600203C211yesmaximal, characteristic
11#10600202C211yesmaximal, characteristic
12#10600200C211yesmaximal, characteristic
13#10600199C211yesmaximal, characteristic
14#10600197C211yesmaximal, characteristic
15Dic5×#95C211yesmaximal, characteristic
16C23×Dic10C2211yescharacteristic
17C23×Dic10C2211yescharacteristic
18C22×C5×C4⋊C4C2211yescharacteristic
19C22×C42×C5C2211yescharacteristic
20C22×C4⋊Dic5C2211yescharacteristic
21C22×C4⋊Dic5C2211yescharacteristic
22C22×#683C2211yescharacteristic
23C22×#683C2211yescharacteristic
24C22×#683C2211yescharacteristic
25C22×#683C2211yescharacteristic
26C22×#683C2211yescharacteristic
27C22×C4×Dic5C2211yescharacteristic
28C22×C4×Dic5C2211yescharacteristic
29C22×C4×Dic5C2211yescharacteristic
30C22×C4×Dic5C2211yescharacteristic
31C2×#4034—24no—
32C2×#4034—24no—
33C2×#4034C418yescomplemented
34C2×C4×Dic10—24no—
35C2×C4×Dic10—24no—
36C2×C4×Dic10—24no—
37C2×C5×#95C2211yescharacteristic
38C2×C5×#95C2211yescharacteristic
39C2×C5×#95C2211yescharacteristic
40C2×C5×#95C2211yescharacteristic
41C2×C5×#95C2211yescharacteristic
42C2×#3963C2211yescharacteristic
43C2×#3963C2211yescharacteristic
44C2×#3963C2211yescharacteristic
45C2×#3963C2211yescharacteristic
46C2×#3963C2211yescharacteristic
47C2×#3963C2211yescharacteristic
48C2×#3963C2211yescharacteristic
49C2×#3963C2211yescharacteristic
50C2×#3963C2211yescharacteristic
51C2×#3963C2211yescharacteristic
52C2×#3963C2211yescharacteristic
53C2×#3963C2211yescharacteristic
54C2×#3963C2211yescharacteristic
55C2×#3963C2211yescharacteristic
56C2×#3963C2211yescharacteristic
57#64935—24no—
58#64935—24no—
59#64935—24no—
60#14024—51nomaximal, Sylow
61C23×C4×C5C2311yescharacteristic
62C23×C4×C5C2311yescharacteristic
63C23×C4×C5C2311yescharacteristic
64C23×C4×C5C2311yescharacteristic
65C23×C4×C5C2311yescharacteristic
66C23×C4×C5C2311yescharacteristic
67C23×C4×C5C2311yescharacteristic
68C23×Dic5C2311yescharacteristic
69C23×Dic5C2311yescharacteristic
70C23×Dic5C2311yescharacteristic
71C23×Dic5C2311yescharacteristic
72C23×Dic5C2311yescharacteristic
73C23×Dic5C2311yescharacteristic
74C23×Dic5C2311yescharacteristic
75C23×Dic5C2311yescharacteristic
76C22×Dic10—22no—
77C22×Dic10—22no—
78C22×Dic10—22no—
79C22×Dic10—22no—
80C22×Dic10—22no—
81C22×Dic10—22no—
82C22×Dic10—22no—
83C22×Dic10—22no—
84C22×Dic10—22no—
85C22×Dic10—22no—
86C22×Dic10C2×C414yes—
87C22×Dic10C2×C414yes—
88C22×Dic10D414yes—
89C22×Dic10D414yes—
90C2×C5×C4⋊C4—22no—
91C2×C5×C4⋊C4—22no—
92C2×C5×C4⋊C4C2×C414yes—
93C2×C42×C5—22no—
94C2×C42×C5—22no—
95C2×C42×C5—22no—
96C2×C4⋊Dic5—22no—
97C2×C4⋊Dic5—22no—
98C2×C4⋊Dic5—22no—
99C2×C4⋊Dic5—22no—
100C2×C4⋊Dic5—22no—
101C2×C4⋊Dic5C2×C414yes—
102C2×#683—22no—
103C2×#683—22no—
104C2×#683—22no—
105C2×#683—22no—
106C2×#683—22no—
107C2×#683—22no—
108C2×#683—22no—
109C2×#683—22no—
110C2×#683—22no—
111C2×#683—22no—
112C2×#683—22no—
113C2×#683—22no—
114C2×#683C2×C414yes—
115C2×#683C2×C414yes—
116C2×#683D414yes—
117C2×C4×Dic5—22no—
118C2×C4×Dic5—22no—
119C2×C4×Dic5—22no—
120C2×C4×Dic5—22no—
121C2×C4×Dic5—22no—
122C2×C4×Dic5—22no—
123C2×C4×Dic5—22no—
124C2×C4×Dic5—22no—
125C2×C4×Dic5—22no—
126C2×C4×Dic5—22no—
127C2×C4×Dic5C2×C414yes—
128C2×C4×Dic5D414yes—
129#4034—232no—
130C4×Dic10—232no—
131C5×#95—22no—
132C5×#95—22no—
133C5×#95—22no—
134C5×#95—22no—
135C5×#95Q814yescomplemented
136#3963—22no—
137#3963—22no—
138#3963—22no—
139#3963—22no—
140#3963—22no—
141#3963—22no—
142#3963—22no—
143#3963—22no—
144#3963—22no—
145#3963—22no—
146#3963—22no—
147#3963—22no—
148#3963—22no—
149#3963—22no—
150#3963Q814yescomplemented
151C22×C4⋊Q8—51no—
152C22×C4×Q8—51no—
153C2×#391—51no—
154C2×#391—51no—
155C2×#391—51no—
156#1441—51no—
157#1441—51no—
158#1441—51no—
159#1441—51no—
160#1436—51no—
161#1436—51no—
162#1436—51no—
163#1436D511yescharacteristic
164C4⋊#95—51no—
165C4×#95—51no—
166C24×C5C2411yescharacteristic
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×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—21no—
192C22×C4×C5—21no—
193C22×C4×C5—21no—
194C22×C4×C5—21no—
195C22×C4×C5—21no—
196C22×C4×C5—21no—
197C22×C4×C5—21no—
198C22×C4×C5—21no—
199C22×C4×C5—21no—
200C22×C4×C5—21no—
201C22×C4×C5—21no—
202C22×C4×C5—21no—
203C22×C4×C5—21no—
204C22×C4×C5C22×C412yes—
205C22×C4×C5C22×C412yes—
206C22×C4×C5C22×C412yes—
207C22×C4×C5C2×D412yes—
208C22×C4×C5C2×D412yes—
209C22×C4×C5C2×D412yes—
210C22×C4×C5C2×D412yes—
211C22×C4×C5C2×Q812yes—
212C22×C4×C5C2×Q812yes—
213C22×C4×C5C2×Q812yes—
214C22×C4×C5C2×Q812yes—
215C22×C4×C5#4112yes—
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×Dic5—21no—
238C22×Dic5—21no—
239C22×Dic5—21no—
240C22×Dic5—21no—
241C22×Dic5—21no—
242C22×Dic5—21no—
243C22×Dic5—21no—
244C22×Dic5—21no—
245C22×Dic5—21no—
246C22×Dic5—21no—
247C22×Dic5—21no—
248C22×Dic5—21no—
249C22×Dic5—21no—
250C22×Dic5—21no—
251C22×Dic5—21no—
252C22×Dic5—21no—
253C22×Dic5—21no—
254C22×Dic5—21no—
255C22×Dic5C22×C412yes—
256C22×Dic5C22×C412yes—
257C22×Dic5C22×C412yes—
258C22×Dic5C22×C412yes—
259C22×Dic5C2×D412yes—
260C22×Dic5C2×D412yes—
261C22×Dic5C2×D412yes—
262C22×Dic5C2×D412yes—
263C22×Dic5C2×D412yes—
264C22×Dic5C2×D412yes—
265C22×Dic5C2×D412yes—
266C22×Dic5C2×D412yes—
267C22×Dic5C2×Q812yes—
268C22×Dic5C2×Q812yes—
269C22×Dic5#4112yes—
270C22×Dic5#4112yes—
271C22×Dic5#4112yes—
272C2×Dic10—28no—
273C2×Dic10—28no—
274C2×Dic10—28no—
275C2×Dic10—28no—
276C2×Dic10—28no—
277C2×Dic10—28no—
278C2×Dic10—28no—
279C2×Dic10—28no—
280C2×Dic10—28no—
281C2×Dic10—44no—
282C2×Dic10—44no—
283C2×Dic10—44no—
284C2×Dic10—44no—
285C2×Dic10C22⋊C4116yes—
286C5×C4⋊C4—28no—
287C42×C5—28no—
288C4⋊Dic5—28no—
289C4⋊Dic5—28no—
290#683—28no—
291#683—28no—
292#683—28no—
293#683—28no—
294#683—44no—
295C4×Dic5—28no—
296C4×Dic5—28no—
297C4×Dic5—28no—
298C4×Dic5—44no—
299C23×Q8—51no—
300C23×Q8—51no—
301C2×C4⋊Q8—58no—
302C2×C4⋊Q8—104no—
303C2×C4⋊Q8—104no—
304C2×C4×Q8—104no—
305C2×C4×Q8—104no—
306C2×C4×Q8—104no—
307C22×C4⋊C4—51no—
308C22×C4⋊C4—51no—
309C22×C4⋊C4—51no—
310C22×C4⋊C4—51no—
311C22×C4⋊C4—51no—
312C22×C4⋊C4—51no—
313C22×C4⋊C4—51no—
314C22×C4⋊C4C2×D511yescharacteristic
315C22×C42—51no—
316C22×C42—51no—
317C22×C42—51no—
318C22×C42—51no—
319C22×C42C2×D511yescharacteristic
320#391—104no—
321#391—104no—
322#391—104no—
323C2×#95—51no—
324C2×#95—51no—
325C2×#95—51no—
326C2×#95—51no—
327C2×#95—51no—
328C2×#95—51no—
329C2×#95—51no—
330C2×#95—51no—
331C2×#95—51no—
332C2×#95—51no—
333C2×#95—51no—
334C2×#95—51no—
335C2×#95—51no—
336C2×#95—51no—
337C2×#95—51no—
338C2×#95C2×D511yescharacteristic
339C2×#95C2×D511yescharacteristic
340C2×#95C2×D511yescharacteristic
341C2×#95C2×D511yescharacteristic
342C2×#95C2×D511yescharacteristic
343C23×C5C23×C411yescharacteristic
344C23×C5C22×D411yescharacteristic
345C23×C5C22×D411yescharacteristic
346C23×C5C22×D411yescharacteristic
347C23×C5C22×D411yescharacteristic
348C23×C5C22×Q811yescharacteristic
349C23×C5C22×Q811yescharacteristic
350C23×C5C2×#4111yescharacteristic
351C23×C5C2×#4111yescharacteristic
352C23×C5C2×#4111yescharacteristic
353C23×C5C2×#4111yescharacteristic
354C23×C52−1+411yescharacteristic
355C23×C52−1+411yescharacteristic
356C23×C52−1+411yescharacteristic
357C23×C52−1+411yescharacteristic
358C2×C4×C5—22no—
359C2×C4×C5—22no—
360C2×C4×C5—22no—
361C2×C4×C5—22no—
362C2×C4×C5—22no—
363C2×C4×C5—22no—
364C2×C4×C5—22no—
365C2×C4×C5—22no—
366C2×C4×C5—22no—
367C2×C4×C5—22no—
368C2×C4×C5—22no—
369C2×C4×C5—22no—
370C2×C4×C5—22no—
371C2×C4×C5—22no—
372C2×C4×C5—22no—
373C2×C4×C5—22no—
374C2×C4×C5—22no—
375C2×C4×C5—22no—
376C2×C4×C5—22no—
377C2×C4×C5—22no—
378C2×C4×C5—22no—
379C2×C4×C5—22no—
380C2×C4×C5—22no—
381C2×C4×C5—22no—
382C2×C4×C5—22no—
383C2×C4×C5—22no—
384C2×C4×C5—22no—
385C2×C4×C5—41no—
386C2×C4×C5—41no—
387C2×C4×C5—41no—
388C2×C4×C5—41no—
389C2×C4×C5—41no—
390C2×C4×C5—41no—
391C2×C4×C5—41no—
392C2×C4×C5—41no—
393C2×C4×C5—41no—
394C2×C4×C5—41no—
395C2×C4×C5—41no—
396C2×C4×C5—41no—
397C2×C4×C5—41no—
398C2×C4×C5—41no—
399C2×C4×C5—41no—
400C2×C4×C5—41no—
401C2×C4×C5—41no—
402C2×C4×C5—41no—
403C2×C4×C5—41no—
404C2×C4×C5C2×C22⋊C414yes—
405C2×C4×C5C4×Q814yescomplemented
406C2×C4×C5C4⋊Q814yescomplemented
407C2×Dic5—22no—
408C2×Dic5—22no—
409C2×Dic5—22no—
410C2×Dic5—22no—
411C2×Dic5—22no—
412C2×Dic5—22no—
413C2×Dic5—22no—
414C2×Dic5—22no—
415C2×Dic5—22no—
416C2×Dic5—22no—
417C2×Dic5—22no—
418C2×Dic5—22no—
419C2×Dic5—22no—
420C2×Dic5—22no—
421C2×Dic5—22no—
422C2×Dic5—22no—
423C2×Dic5—22no—
424C2×Dic5—22no—
425C2×Dic5—22no—
426C2×Dic5—22no—
427C2×Dic5—22no—
428C2×Dic5—22no—
429C2×Dic5—22no—
430C2×Dic5—22no—
431C2×Dic5—41no—
432C2×Dic5—41no—
433C2×Dic5—41no—
434C2×Dic5—41no—
435C2×Dic5—41no—
436C2×Dic5—41no—
437C2×Dic5—41no—
438C2×Dic5—41no—
439C2×Dic5—41no—
440C2×Dic5—41no—
441C2×Dic5—41no—
442C2×Dic5—41no—
443C2×Dic5—41no—
444C2×Dic5—41no—
445C2×Dic5—41no—
446C2×Dic5—41no—
447C2×Dic5—41no—
448C2×Dic5—41no—
449C2×Dic5—41no—
450C2×Dic5—41no—
451C2×Dic5—41no—
452C2×Dic5—41no—
453C2×Dic5—41no—
454C2×Dic5C2×C22⋊C414yes—
455C2×Dic5C2×C22⋊C414yes—
456C2×Dic5C4×D414yes—
457C2×Dic5C4×D414yes—
458C2×Dic5C4×Q814yescomplemented
459C2×Dic5#12014yes—
460C2×Dic5#12114yes—
461C2×Dic5#12114yes—
462C2×Dic5#12314yes—
463Dic10—232no—
464Dic10—416no—
465C22×Q8—54no—
466C22×Q8—54no—
467C22×Q8—54no—
468C22×Q8—54no—
469C22×Q8—102no—
470C22×Q8—102no—
471C22×Q8—102no—
472C22×Q8—102no—
473C22×Q8—102no—
474C22×Q8—102no—
475C22×Q8—102no—
476C22×Q8—102no—
477C22×Q8—102no—
478C22×Q8—102no—
479C23×C4—51no—
480C23×C4—51no—
481C23×C4—51no—
482C23×C4—51no—
483C23×C4—51no—
484C23×C4—51no—
485C23×C4—51no—
486C23×C4—51no—
487C23×C4C22×D511yescharacteristic
488C23×C4C22×D511yescharacteristic
489C23×C4C22×D511yescharacteristic
490C23×C4C22×D511yescharacteristic
491C23×C4C22×D511yescharacteristic
492C23×C4C22×D511yescharacteristic
493C23×C4C22×D511yescharacteristic
494C4⋊Q8—1032no—
495C4×Q8—1032no—
496C2×C4⋊C4—22no—
497C2×C4⋊C4—22no—
498C2×C4⋊C4—54no—
499C2×C4⋊C4—54no—
500C2×C4⋊C4—54no—
501C2×C4⋊C4—54no—
502C2×C4⋊C4—102no—
503C2×C4⋊C4—102no—
504C2×C4⋊C4—102no—
505C2×C4⋊C4—102no—
506C2×C4⋊C4—102no—
507C2×C4⋊C4—102no—
508C2×C4⋊C4—102no—
509C2×C4⋊C4—102no—
510C2×C4⋊C4—102no—
511C2×C4⋊C4—102no—
512C2×C4⋊C4—102no—
513C2×C4⋊C4—102no—
514C2×C4⋊C4—102no—
515C2×C4⋊C4—102no—
516C2×C4⋊C4—102no—
517C2×C4⋊C4—102no—
518C2×C4⋊C4—102no—
519C2×C4⋊C4C4×D514yes—
520C2×C42—22no—
521C2×C42—22no—
522C2×C42—22no—
523C2×C42—54no—
524C2×C42—54no—
525C2×C42—102no—
526C2×C42—102no—
527C2×C42—102no—
528C2×C42—102no—
529C2×C42—102no—
530C2×C42—102no—
531C2×C42—102no—
532C2×C42—102no—
533C2×C42—102no—
534C2×C42—102no—
535#95—22no—
536#95—22no—
537#95—22no—
538#95—22no—
539#95—54no—
540#95—102no—
541#95—102no—
542#95—102no—
543#95—102no—
544#95—102no—
545#95—102no—
546#95—102no—
547#95—102no—
548#95—102no—
549#95—102no—
550#95—102no—
551#95—102no—
552#95—102no—
553#95—102no—
554#95Dic1014yescomplemented
555C22×C5C22×C22⋊C411yescharacteristic
556C22×C5C2×C4×D411yescharacteristic
557C22×C5C2×C4×D411yescharacteristic
558C22×C5C2×C4×Q811yescharacteristic
559C22×C5C2×C4×Q811yescharacteristic
560C22×C5#51911yescharacteristic
561C22×C5#51911yescharacteristic
562C22×C5C2×#12011yescharacteristic
563C22×C5C2×#12111yescharacteristic
564C22×C5C2×#12111yescharacteristic
565C22×C5C2×#12311yescharacteristic
566C22×C5C2×C4⋊Q811yescharacteristic
567C22×C5#53211yescharacteristic
568C22×C5#53311yescharacteristic
569C22×C5#53311yescharacteristic
570C22×C5#53611yescharacteristic
571C22×C5#53611yescharacteristic
572C22×C5#54111yescharacteristic
573C22×C5#54111yescharacteristic
574C22×C5#54711yescharacteristic
575C22×C5#54711yescharacteristic
576C22×C5#54811yescharacteristic
577C22×C5#54811yescharacteristic
578C22×C5#54811yescharacteristic
579C22×C5#54811yescharacteristic
580C22×C5D4×Q811yescharacteristic
581C22×C5D4×Q811yescharacteristic
582C22×C5D4×Q811yescharacteristic
583C22×C5D4×Q811yescharacteristic
584C22×C5D4×Q811yescharacteristic
585C22×C5D4×Q811yescharacteristic
586C22×C5#55611yescharacteristic
587C22×C5#55611yescharacteristic
588C22×C5#55711yescharacteristic
589C22×C5#55711yescharacteristic
590C4×C5—24no—
591C4×C5—24no—
592C4×C5—24no—
593C4×C5—42no—
594C4×C5—42no—
595C4×C5—42no—
596C4×C5—81no—
597Dic5—24no—
598Dic5—24no—
599Dic5—42no—
600Dic5—42no—
601Dic5—42no—
602Dic5—42no—
603Dic5—81no—
604Dic5#38618yes—
605C24C23×D511yescharacteristic
606C2×Q8—516no—
607C2×Q8—108no—
608C2×Q8—108no—
609C2×Q8—108no—
610C2×Q8—108no—
611C2×Q8—108no—
612C2×Q8—108no—
613C2×Q8—108no—
614C2×Q8—108no—
615C2×Q8—108no—
616C2×Q8—204no—
617C2×Q8—204no—
618C2×Q8—204no—
619C2×Q8—204no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—52no—
658C22×C4—52no—
659C22×C4—52no—
660C22×C4—52no—
661C22×C4—52no—
662C22×C4—52no—
663C22×C4—52no—
664C22×C4—52no—
665C22×C4—52no—
666C22×C4—52no—
667C22×C4—52no—
668C22×C4—52no—
669C22×C4—52no—
670C22×C4—52no—
671C22×C4—52no—
672C22×C4—52no—
673C22×C4—52no—
674C22×C4—101no—
675C22×C4—101no—
676C22×C4—101no—
677C22×C4—101no—
678C22×C4—101no—
679C22×C4—101no—
680C22×C4—101no—
681C22×C4—101no—
682C22×C4—101no—
683C22×C4—101no—
684C22×C4—101no—
685C22×C4—101no—
686C22×C4—101no—
687C22×C4—101no—
688C22×C4—101no—
689C22×C4—101no—
690C22×C4—101no—
691C22×C4—101no—
692C22×C4—101no—
693C22×C4—101no—
694C22×C4—101no—
695C22×C4—101no—
696C22×C4—101no—
697C22×C4—101no—
698C22×C4—101no—
699C22×C4—101no—
700C22×C4—101no—
701C22×C4—101no—
702C22×C4—101no—
703C22×C4—101no—
704C22×C4—101no—
705C22×C4—101no—
706C22×C4—101no—
707C22×C4—101no—
708C22×C4—101no—
709C22×C4—101no—
710C22×C4—101no—
711C22×C4—101no—
712C22×C4—101no—
713C22×C4C2×Dic1012yes—
714C22×C4C2×Dic1012yes—
715C22×C4C2×Dic1012yes—
716C22×C4C2×C4×D512yes—
717C22×C4C2×C4×D512yes—
718C22×C4C2×C4×D512yes—
719C22×C4#70912yes—
720C22×C4D4×D512yes—
721C22×C4D4×D512yes—
722C22×C4D4×D512yes—
723C22×C4D4×D512yes—
724C22×C4Q8×D512yes—
725C4⋊C4—28no—
726C4⋊C4—108no—
727C4⋊C4—108no—
728C4⋊C4—108no—
729C4⋊C4—108no—
730C4⋊C4—108no—
731C4⋊C4—108no—
732C4⋊C4—204no—
733C42—28no—
734C42—108no—
735C42—108no—
736C42—108no—
737C42—204no—
738C2×C5C2×#38611yescharacteristic
739C2×C5C4×C4⋊Q811yescharacteristic
740C2×C5#232711yescharacteristic
741C2×C5Q8×C22⋊C411yescharacteristic
742C2×C5Q8×C22⋊C411yescharacteristic
743C2×C5#236511yescharacteristic
744C2×C5#236511yescharacteristic
745C2×C5#242911yescharacteristic
746C2×C5#242911yescharacteristic
747C2×C5#243211yescharacteristic
748C2×C5#243411yescharacteristic
749C2×C5#244611yescharacteristic
750C2×C5#244611yescharacteristic
751C2×C5#254511yescharacteristic
752C2×C5#254611yescharacteristic
753C23C22×Dic1011yescharacteristic
754C23C22×C4×D511yescharacteristic
755C23C2×#70911yescharacteristic
756C23C2×D4×D511yescharacteristic
757C23C2×D4×D511yescharacteristic
758C23C2×D4×D511yescharacteristic
759C23C2×D4×D511yescharacteristic
760C23C2×Q8×D511yescharacteristic
761C23#414711yescharacteristic
762C23D5×#4111yescharacteristic
763C23D5×#4111yescharacteristic
764C23D5×#4111yescharacteristic
765C23#415011yescharacteristic
766C23#415011yescharacteristic
767C23#415011yescharacteristic
768Q8—1032no—
769Q8—2016no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—54no—
817C2×C4—54no—
818C2×C4—54no—
819C2×C4—54no—
820C2×C4—54no—
821C2×C4—54no—
822C2×C4—54no—
823C2×C4—54no—
824C2×C4—54no—
825C2×C4—102no—
826C2×C4—102no—
827C2×C4—102no—
828C2×C4—102no—
829C2×C4—102no—
830C2×C4—102no—
831C2×C4—102no—
832C2×C4—102no—
833C2×C4—102no—
834C2×C4—102no—
835C2×C4—102no—
836C2×C4—102no—
837C2×C4—102no—
838C2×C4—102no—
839C2×C4—102no—
840C2×C4—102no—
841C2×C4—102no—
842C2×C4—102no—
843C2×C4—102no—
844C2×C4—102no—
845C2×C4—102no—
846C2×C4—102no—
847C2×C4—102no—
848C2×C4—102no—
849C2×C4—201no—
850C2×C4—201no—
851C2×C4—201no—
852C2×C4—201no—
853C2×C4—201no—
854C2×C4—201no—
855C2×C4—201no—
856C2×C4—201no—
857C2×C4—201no—
858C2×C4—201no—
859C2×C4—201no—
860C2×C4—201no—
861C2×C4—201no—
862C2×C4—201no—
863C2×C4—201no—
864C2×C4—201no—
865C2×C4—201no—
866C2×C4—201no—
867C2×C4—201no—
868C2×C4—201no—
869C2×C4—201no—
870C2×C4—201no—
871C2×C4—201no—
872C2×C4C4×Dic1014yescomplemented
873C2×C4D5×C22⋊C414yes—
874C2×C4#403414yescomplemented
875C5#1402411yescharacteristic, complemented, Sylow
876C22C2×C4×Dic1011yescharacteristic
877C22C2×D5×C22⋊C411yescharacteristic
878C22C2×#403411yescharacteristic
879C22#6584111yescharacteristic
880C22#6585011yescharacteristic
881C22#6585111yescharacteristic
882C22#6586711yescharacteristic
883C22D4×Dic1011yescharacteristic
884C22D4×Dic1011yescharacteristic
885C22D4×Dic1011yescharacteristic
886C22C4×D4×D511yescharacteristic
887C22C4×D4×D511yescharacteristic
888C22#6588211yescharacteristic
889C22#6588611yescharacteristic
890C22#6588611yescharacteristic
891C22#6590311yescharacteristic
892C22C4×Q8×D511yescharacteristic
893C22#6590611yescharacteristic
894C22#6591211yescharacteristic
895C22D5×#12011yescharacteristic
896C22D5×#12111yescharacteristic
897C22D5×#12111yescharacteristic
898C22#6596211yescharacteristic
899C22#6596611yescharacteristic
900C22#6596611yescharacteristic
901C22#6596711yescharacteristic
902C22#6598211yescharacteristic
903C22D5×#12311yescharacteristic
904C22#6598911yescharacteristic
905C22#6601111yescharacteristic
906C22#6601911yescharacteristic
907C22#6603011yescharacteristic
908C22#6603511yescharacteristic
909C22#6603611yescharacteristic
910C22#6606111yescharacteristic
911C4—24no—
912C4—24no—
913C4—24no—
914C4—42no—
915C4—42no—
916C4—42no—
917C4—58no—
918C4—81no—
919C4—104no—
920C4—104no—
921C4—202no—
922C4—202no—
923C4—202no—
924C4—202no—
925C4—401no—
926C2C22⋊C4×Dic1011yescharacteristic
927C2C4×#403411yescharacteristic
928C2#1060538311yescharacteristic
929C2#1060614211yescharacteristic
930C2#1060614311yescharacteristic
931C2D5×#38611yescharacteristic
932C2#1060667911yescharacteristic
933C2#1060669811yescharacteristic
934C2#1060671611yescharacteristic
935C2#1060671711yescharacteristic
936C2#1060723111yescharacteristic
937C2#1060732411yescharacteristic
938C2#1060772711yescharacteristic
939C2#1060779111yescharacteristic
940C2#1060834511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D5
commutatorC23×C5C23×C4
FittingC5×#1436C2
socle, prime radical, cosocleC24×C5C24
hypercenter#1436D5
hypocenterC5#14024
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
33. C2×#4034C4semidirect
135. C5×#95Q8semidirect
150. #3963Q8semidirect
405. C2×C4×C5C4×Q8semidirect
406. C2×C4×C5C4⋊Q8semidirect
458. C2×Dic5C4×Q8semidirect
554. #95Dic10semidirect
872. C2×C4C4×Dic10semidirect
874. C2×C4#4034semidirect
875. C5#14024semidirect

Maximal subgroups

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

subgroupindex
C22×#40342
C22×C4×Dic102
C2×#649352
C5×#14362
#106023582
#106023292
#106002042
#106002032
#106002022
#106002002
#106001992
#106001972
Dic5×#952
#140245