Finite Group Databasebeta

← #12004580

Subgroups — #12004580

Order 1280.

1518 conjugacy classes of subgroups.

The subgroup lattice has 874 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#4038C211yesmaximal, characteristic
2C22×#3952C211yesmaximal, characteristic
3C2×#65276C211yesmaximal, characteristic
4C2×C5×#340C211yesmaximal, characteristic, complemented
5C2×#64771C211yesmaximal, characteristic, complemented
6C2×#64749C211yesmaximal, characteristic, complemented
7C2×#64749C211yesmaximal, characteristic, complemented
8C23×C4×D5C2211yescharacteristic
9C23×C5×C8C2211yescharacteristic
10C22×C5×C4⋊C4C2211yescharacteristic
11C22×C5×C4⋊C4C2211yescharacteristic
12C22×#685—21no—
13C22×#685—21no—
14C22×C4⋊Dic5C2211yescharacteristic
15C22×C4⋊Dic5C2211yescharacteristic
16C22×C4×Dic5—21no—
17C23×#168C2211yescharacteristic
18C2×#4038—22no—
19C2×#4038—22no—
20C2×#4038—22no—
21C2×#4038—22no—
22C2×#4038—22no—
23C2×#4038C414yescomplemented
24C2×#3963—21no—
25C2×#3952—22no—
26C2×#3952—22no—
27C2×#3952C414yescomplemented
28#65276—22no—
29#65276C414yescomplemented
30C5×#340—22no—
31#64771—22no—
32#64749—22no—
33#64749—22no—
34#10731—51nomaximal, Sylow
35C24×D5D411yescharacteristic
36C23×C4×C5—21no—
37C23×C4×C5—21no—
38C23×C4×C5C2311yescharacteristic
39C23×Dic5—21no—
40C23×Dic5—21no—
41C23×Dic5D411yescharacteristic
42C22×C4×D5—21no—
43C22×C4×D5—21no—
44C22×C4×D5—21no—
45C22×C4×D5—21no—
46C22×C4×D5—21no—
47C22×C4×D5—21no—
48C22×C4×D5—21no—
49C22×C4×D5—21no—
50C22×C4×D5C2×C412yes—
51C22×C4×D5C2×C412yes—
52C22×C4×D5C2×C412yes—
53C22×C4×D5D412yes—
54C22×C4×D5D412yes—
55C22×C4×D5Q812yes—
56C22×C5×C8—21no—
57C22×C5×C8—21no—
58C22×C5×C8—21no—
59C22×C5×C8—21no—
60C22×C5×C8—21no—
61C22×C5×C8—21no—
62C22×C5×C8C2×C412yes—
63C2×C5×C4⋊C4—21no—
64C2×C5×C4⋊C4—21no—
65C2×C5×C4⋊C4—21no—
66C2×C5×C4⋊C4—21no—
67C2×C5×C4⋊C4—21no—
68C2×C5×C4⋊C4—21no—
69C2×C5×C4⋊C4—21no—
70C2×C5×C4⋊C4—21no—
71C2×C5×C4⋊C4C2×C412yes—
72C2×C5×C4⋊C4C2×C412yes—
73C2×C5×C4⋊C4D412yes—
74C2×C5×C4⋊C4D412yes—
75C2×#685—24no—
76C2×#685—24no—
77C2×#685—24no—
78C2×#685—24no—
79C2×#685—42no—
80C2×#685—42no—
81C2×C4⋊Dic5—21no—
82C2×C4⋊Dic5—21no—
83C2×C4⋊Dic5—21no—
84C2×C4⋊Dic5—21no—
85C2×C4⋊Dic5—21no—
86C2×C4⋊Dic5—21no—
87C2×C4⋊Dic5—21no—
88C2×C4⋊Dic5—21no—
89C2×C4⋊Dic5C2×C412yes—
90C2×C4⋊Dic5C2×C412yes—
91C2×C4⋊Dic5D412yes—
92C2×C4⋊Dic5D412yes—
93C2×C4×Dic5—24no—
94C2×C4×Dic5—24no—
95C2×C4×Dic5—24no—
96C22×#168—21no—
97C22×#168—21no—
98C22×#168—21no—
99C22×#168—21no—
100C22×#168—21no—
101C22×#168—21no—
102C22×#168C2×C412yes—
103#4038—28no—
104#4038—28no—
105#4038—28no—
106#4038—28no—
107#3963—24no—
108#3952—28no—
109C22×#117—51no—
110C22×C22⋊C8—51no—
111C2×#380—51no—
112C2×#340—51no—
113C2×#340—51no—
114C2×#340—51no—
115C2×#340D511yescharacteristic, complemented
116C24×C5C2×D411yescharacteristic
117C23×D5—21no—
118C23×D5—21no—
119C23×D5—21no—
120C23×D5—21no—
121C23×D5—21no—
122C23×D5—21no—
123C23×D5—21no—
124C23×D5—21no—
125C23×D5—21no—
126C23×D5—21no—
127C23×D5—21no—
128C23×D5—21no—
129C23×D5C22⋊C412yes—
130C23×D5C22⋊C412yes—
131C23×D5C4⋊C412yes—
132C22×C4×C5—22no—
133C22×C4×C5—22no—
134C22×C4×C5—22no—
135C22×C4×C5—22no—
136C22×C4×C5—41no—
137C22×C4×C5—41no—
138C22×C4×C5—41no—
139C22×C4×C5—41no—
140C22×C4×C5—41no—
141C22×C4×C5—41no—
142C22×C4×C5—41no—
143C22×C4×C5—41no—
144C22×C4×C5—41no—
145C22×C4×C5—41no—
146C22×C4×C5C22×C411yescharacteristic
147C22×C4×C5C22×C411yescharacteristic
148C22×C4×C5C22×C411yescharacteristic
149C22×C4×C5C2×D411yescharacteristic
150C22×C4×C5C2×D411yescharacteristic
151C22×C4×C5C2×D411yescharacteristic
152C22×C4×C5C2×D411yescharacteristic
153C22×C4×C5C2×D411yescharacteristic
154C22×C4×C5C2×D411yescharacteristic
155C22×C4×C5C2×Q811yescharacteristic
156C22×C4×C5#4111yescharacteristic
157C22×C4×C5#4111yescharacteristic
158C22×C4×C5#4111yescharacteristic
159C22×C4×C5#4111yescharacteristic
160C22×Dic5—21no—
161C22×Dic5—21no—
162C22×Dic5—21no—
163C22×Dic5—21no—
164C22×Dic5—22no—
165C22×Dic5—22no—
166C22×Dic5—22no—
167C22×Dic5—22no—
168C22×Dic5—41no—
169C22×Dic5—41no—
170C22×Dic5—41no—
171C22×Dic5—41no—
172C22×Dic5—41no—
173C22×Dic5—41no—
174C22×Dic5—41no—
175C22×Dic5—41no—
176C22×Dic5—41no—
177C22×Dic5—41no—
178C22×Dic5C22⋊C412yes—
179C22×Dic5C22⋊C412yes—
180C22×Dic5C4⋊C412yes—
181C2×C4×D5—22no—
182C2×C4×D5—22no—
183C2×C4×D5—22no—
184C2×C4×D5—22no—
185C2×C4×D5—22no—
186C2×C4×D5—22no—
187C2×C4×D5—22no—
188C2×C4×D5—22no—
189C2×C4×D5—22no—
190C2×C4×D5—22no—
191C2×C4×D5—22no—
192C2×C4×D5—22no—
193C2×C4×D5—22no—
194C2×C4×D5—22no—
195C2×C4×D5—22no—
196C2×C4×D5—22no—
197C2×C4×D5—22no—
198C2×C4×D5—22no—
199C2×C4×D5—22no—
200C2×C4×D5—22no—
201C2×C4×D5—22no—
202C2×C4×D5—22no—
203C2×C4×D5—22no—
204C2×C4×D5—22no—
205C2×C4×D5C4214yes—
206C2×C4×D5C22⋊C414yes—
207C2×C4×D5C4⋊C414yes—
208C2×C4×D5C4⋊C414yes—
209C2×C5×C8—22no—
210C2×C5×C8—22no—
211C2×C5×C8—22no—
212C2×C5×C8—41no—
213C2×C5×C8—41no—
214C2×C5×C8—41no—
215C2×C5×C8—41no—
216C5×C4⋊C4—22no—
217C5×C4⋊C4—22no—
218C5×C4⋊C4—22no—
219C5×C4⋊C4—22no—
220C5×C4⋊C4—22no—
221C5×C4⋊C4—41no—
222C5×C4⋊C4—41no—
223C5×C4⋊C4C22⋊C414yescomplemented
224#685—216no—
225#685—48no—
226C4⋊Dic5—22no—
227C4⋊Dic5—22no—
228C4⋊Dic5—22no—
229C4⋊Dic5—22no—
230C4⋊Dic5—22no—
231C4⋊Dic5—41no—
232C4⋊Dic5—41no—
233C4⋊Dic5C22⋊C414yescomplemented
234C4×Dic5—216no—
235C2×#168—22no—
236C2×#168—22no—
237C2×#168—22no—
238C2×#168—41no—
239C2×#168—41no—
240C2×#168—41no—
241C2×#168—41no—
242C24×C4—51no—
243C23×C8—51no—
244C23×C8C2×D511yescharacteristic
245C2×#117—54no—
246C2×#117—102no—
247C2×#117—102no—
248C2×#117—102no—
249C2×#117—102no—
250C2×#117—102no—
251C22×C4⋊C4—51no—
252C22×C4⋊C4—51no—
253C22×C4⋊C4C2×D511yescharacteristic
254C22×C4⋊C4C2×D511yescharacteristic
255C22×C22⋊C4—101no—
256C22×C22⋊C4—101no—
257C22×C42—101no—
258C2×C22⋊C8—54no—
259C2×C22⋊C8—102no—
260C2×C22⋊C8—102no—
261#380—54no—
262#380—102no—
263C2×#95—101no—
264#340—22no—
265#340—102no—
266#340—102no—
267#340—102no—
268C23×C5C2×C22⋊C411yescharacteristic
269C23×C5C2×C22⋊C411yescharacteristic
270C23×C5C2×C4⋊C411yescharacteristic
271C23×C5#12011yescharacteristic
272C23×C5#12011yescharacteristic
273C23×C5#12311yescharacteristic
274C23×C5#12311yescharacteristic
275C23×C5#13511yescharacteristic
276C23×C5#13511yescharacteristic
277C23×C5#13511yescharacteristic
278C23×C5#13511yescharacteristic
279C23×C5AGL(1,ℤ/8)11yescharacteristic
280C23×C5AGL(1,ℤ/8)11yescharacteristic
281C23×C5#13711yescharacteristic
282C23×C5#13711yescharacteristic
283C22×D5—22no—
284C22×D5—22no—
285C22×D5—22no—
286C22×D5—22no—
287C22×D5—22no—
288C22×D5—22no—
289C22×D5—22no—
290C22×D5—22no—
291C22×D5—22no—
292C22×D5—22no—
293C22×D5—22no—
294C22×D5—22no—
295C22×D5—22no—
296C22×D5—22no—
297C22×D5—22no—
298C22×D5—22no—
299C22×D5—22no—
300C22×D5—22no—
301C22×D5—41no—
302C22×D5—41no—
303C22×D5—41no—
304C22×D5—41no—
305C22×D5—41no—
306C22×D5—41no—
307C22×D5—41no—
308C22×D5—41no—
309C22×D5—41no—
310C22×D5—41no—
311C22×D5—41no—
312C22×D5—41no—
313C22×D5—41no—
314C22×D5—41no—
315C22×D5—41no—
316C22×D5—41no—
317C22×D5#9514yes—
318C2×C4×C5—24no—
319C2×C4×C5—42no—
320C2×C4×C5—42no—
321C2×C4×C5—42no—
322C2×C4×C5—42no—
323C2×C4×C5—42no—
324C2×C4×C5—42no—
325C2×C4×C5—42no—
326C2×C4×C5—42no—
327C2×C4×C5—42no—
328C2×C4×C5—81no—
329C2×C4×C5—81no—
330C2×C4×C5—81no—
331C2×C4×C5—81no—
332C2×C4×C5C2×C4211yescharacteristic
333C2×C4×C5C2×C22⋊C411yescharacteristic
334C2×C4×C5C2×C22⋊C411yescharacteristic
335C2×C4×C5C2×C22⋊C411yescharacteristic
336C2×C4×C5C2×C4⋊C411yescharacteristic
337C2×C4×C5C2×C4⋊C411yescharacteristic
338C2×C4×C5#11711yescharacteristic
339C2×C4×C5#11711yescharacteristic
340C2×C4×C5C4×D411yescharacteristic
341C2×C4×C5C4×D411yescharacteristic
342C2×C4×C5C4×D411yescharacteristic
343C2×C4×C5C4×D411yescharacteristic
344C2×C4×C5C4×D411yescharacteristic
345C2×C4×C5C4×D411yescharacteristic
346C2×C4×C5C4×D411yescharacteristic
347C2×C4×C5C4×D411yescharacteristic
348C2×C4×C5#12011yescharacteristic
349C2×C4×C5#12011yescharacteristic
350C2×C4×C5#12111yescharacteristic
351C2×C4×C5#12111yescharacteristic
352C2×C4×C5#12111yescharacteristic
353C2×C4×C5#12111yescharacteristic
354C2×C4×C5C22⋊Q811yescharacteristic
355C2×C4×C5C22⋊Q811yescharacteristic
356C2×C4×C5C22⋊Q811yescharacteristic
357C2×C4×C5C22⋊Q811yescharacteristic
358C2×C4×C5#12311yescharacteristic
359C2×C4×C5#12311yescharacteristic
360C2×Dic5—22no—
361C2×Dic5—22no—
362C2×Dic5—22no—
363C2×Dic5—22no—
364C2×Dic5—22no—
365C2×Dic5—22no—
366C2×Dic5—24no—
367C2×Dic5—42no—
368C2×Dic5—42no—
369C2×Dic5—42no—
370C2×Dic5—42no—
371C2×Dic5—42no—
372C2×Dic5—42no—
373C2×Dic5—42no—
374C2×Dic5—42no—
375C2×Dic5—42no—
376C2×Dic5—81no—
377C2×Dic5—81no—
378C2×Dic5—81no—
379C2×Dic5—81no—
380C2×Dic5#9514yes—
381C4×D5—24no—
382C4×D5—24no—
383C4×D5—24no—
384C4×D5—24no—
385C4×D5—24no—
386C4×D5—24no—
387C4×D5—24no—
388C4×D5—24no—
389C5×C8—42no—
390#168—42no—
391C25—51no—
392C23×C4—21no—
393C23×C4—21no—
394C23×C4—51no—
395C23×C4—52no—
396C23×C4—52no—
397C23×C4—52no—
398C23×C4—52no—
399C23×C4—52no—
400C23×C4—52no—
401C23×C4—101no—
402C23×C4—101no—
403C23×C4—101no—
404C23×C4—101no—
405C23×C4—101no—
406C23×C4—101no—
407C23×C4—101no—
408C23×C4—101no—
409C23×C4—101no—
410C23×C4—101no—
411C23×C4C22×D511yescharacteristic
412C22×C8—21no—
413C22×C8—21no—
414C22×C8—21no—
415C22×C8—21no—
416C22×C8—21no—
417C22×C8—21no—
418C22×C8—52no—
419C22×C8—101no—
420C22×C8—101no—
421C22×C8—101no—
422C22×C8—101no—
423C22×C8—101no—
424C22×C8—101no—
425C22×C8C4×D512yes—
426#117—108no—
427#117—108no—
428#117—108no—
429#117—108no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—21no—
433C2×C4⋊C4—21no—
434C2×C4⋊C4—21no—
435C2×C4⋊C4—21no—
436C2×C4⋊C4—21no—
437C2×C4⋊C4—21no—
438C2×C4⋊C4—52no—
439C2×C4⋊C4—52no—
440C2×C4⋊C4—52no—
441C2×C4⋊C4—52no—
442C2×C4⋊C4—101no—
443C2×C4⋊C4—101no—
444C2×C4⋊C4—101no—
445C2×C4⋊C4—101no—
446C2×C4⋊C4—101no—
447C2×C4⋊C4—101no—
448C2×C4⋊C4—101no—
449C2×C4⋊C4—101no—
450C2×C4⋊C4C4×D512yes—
451C2×C4⋊C4C4×D512yes—
452C2×C4⋊C4D2012yes—
453C2×C4⋊C4C22⋊D512yes—
454C2×C22⋊C4—104no—
455C2×C22⋊C4—104no—
456C2×C22⋊C4—104no—
457C2×C22⋊C4—104no—
458C2×C22⋊C4—202no—
459C2×C22⋊C4—202no—
460C2×C42—104no—
461C2×C42—104no—
462C2×C42—104no—
463C22⋊C8—108no—
464#95—104no—
465C22×C5C2×#9511yescharacteristic
466C22×C5#37911yescharacteristic
467C22×C5#38111yescharacteristic
468C22×C5#38511yescharacteristic
469C22×C5#38511yescharacteristic
470C22×C5#38611yescharacteristic
471C22×C5#38611yescharacteristic
472C22×C5#41611yescharacteristic
473C22×C5#41611yescharacteristic
474C22×C5#41611yescharacteristic
475C22×C5#41611yescharacteristic
476C22×C5#41711yescharacteristic
477C22×C5#41711yescharacteristic
478C22×C5#41811yescharacteristic
479C22×C5#41911yescharacteristic
480C22×C5#42711yescharacteristic
481C22×C5#42711yescharacteristic
482C22×C5#42811yescharacteristic
483C22×C5#42811yescharacteristic
484C22×C5#44911yescharacteristic
485C22×C5#44911yescharacteristic
486C22×C5#44911yescharacteristic
487C22×C5#44911yescharacteristic
488C22×C5#45211yescharacteristic
489C22×C5#45211yescharacteristic
490C22×C5#45211yescharacteristic
491C22×C5#45211yescharacteristic
492C22×C5#48211yescharacteristic
493C22×C5#48211yescharacteristic
494C22×C5#48211yescharacteristic
495C22×C5#48211yescharacteristic
496C22×C5#48511yescharacteristic
497C22×C5#48511yescharacteristic
498C22×C5#48511yescharacteristic
499C22×C5#48511yescharacteristic
500C2×D5—24no—
501C2×D5—24no—
502C2×D5—24no—
503C2×D5—42no—
504C2×D5—42no—
505C2×D5—42no—
506C2×D5—42no—
507C2×D5—42no—
508C2×D5—42no—
509C2×D5—42no—
510C2×D5—42no—
511C2×D5—42no—
512C2×D5—42no—
513C2×D5—42no—
514C2×D5—42no—
515C4×C5—44no—
516C4×C5—82no—
517C4×C5C4×C22⋊C411yescharacteristic
518C4×C5C4×C22⋊C411yescharacteristic
519C4×C5#38011yescharacteristic
520C4×C5#38011yescharacteristic
521C4×C5#38511yescharacteristic
522C4×C5#38511yescharacteristic
523C4×C5#38611yescharacteristic
524C4×C5#38611yescharacteristic
525Dic5—24no—
526Dic5—44no—
527Dic5—82no—
528C24—52no—
529C24—52no—
530C24—52no—
531C24—101no—
532C24—101no—
533C24—101no—
534C24—101no—
535C24—101no—
536C24—101no—
537C24—101no—
538C24—101no—
539C24—101no—
540C24—101no—
541C24—101no—
542C24—101no—
543C24D4×D511yescharacteristic
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—41no—
549C22×C4—41no—
550C22×C4—41no—
551C22×C4—41no—
552C22×C4—41no—
553C22×C4—41no—
554C22×C4—41no—
555C22×C4—41no—
556C22×C4—41no—
557C22×C4—41no—
558C22×C4—52no—
559C22×C4—52no—
560C22×C4—52no—
561C22×C4—54no—
562C22×C4—54no—
563C22×C4—54no—
564C22×C4—54no—
565C22×C4—101no—
566C22×C4—101no—
567C22×C4—101no—
568C22×C4—101no—
569C22×C4—102no—
570C22×C4—102no—
571C22×C4—102no—
572C22×C4—102no—
573C22×C4—102no—
574C22×C4—102no—
575C22×C4—102no—
576C22×C4—102no—
577C22×C4—102no—
578C22×C4—102no—
579C22×C4—102no—
580C22×C4—102no—
581C22×C4—102no—
582C22×C4—102no—
583C22×C4—102no—
584C22×C4—102no—
585C22×C4—102no—
586C22×C4—102no—
587C22×C4—102no—
588C22×C4—102no—
589C22×C4—102no—
590C22×C4—102no—
591C22×C4—102no—
592C22×C4—102no—
593C22×C4—102no—
594C22×C4—102no—
595C22×C4—102no—
596C22×C4—102no—
597C22×C4—201no—
598C22×C4—201no—
599C22×C4—201no—
600C22×C4—201no—
601C22×C4—201no—
602C22×C4—201no—
603C22×C4—201no—
604C22×C4—201no—
605C22×C4—201no—
606C22×C4—201no—
607C22×C4C2×C4×D511yescharacteristic
608C22×C4C2×C4×D511yescharacteristic
609C22×C4C2×C4×D511yescharacteristic
610C22×C4C2×D2011yescharacteristic
611C22×C4#70911yescharacteristic
612C22×C4#70911yescharacteristic
613C22×C4D4×D511yescharacteristic
614C22×C4D4×D511yescharacteristic
615C22×C4D4×D511yescharacteristic
616C22×C4D4×D511yescharacteristic
617C22×C4#71111yescharacteristic
618C22×C4Q8×D511yescharacteristic
619C22×C4#71311yescharacteristic
620C22×C4C2×C22⋊D511yescharacteristic
621C2×C8—22no—
622C2×C8—22no—
623C2×C8—22no—
624C2×C8—41no—
625C2×C8—41no—
626C2×C8—41no—
627C2×C8—41no—
628C2×C8—102no—
629C2×C8—102no—
630C2×C8—102no—
631C2×C8—201no—
632C2×C8—201no—
633C2×C8—201no—
634C2×C8—201no—
635C4⋊C4—22no—
636C4⋊C4—22no—
637C4⋊C4—22no—
638C4⋊C4—22no—
639C4⋊C4—22no—
640C4⋊C4—41no—
641C4⋊C4—41no—
642C4⋊C4—54no—
643C4⋊C4—102no—
644C4⋊C4—102no—
645C4⋊C4—102no—
646C4⋊C4—102no—
647C4⋊C4—102no—
648C4⋊C4—201no—
649C4⋊C4—201no—
650C4⋊C4#68514yescomplemented
651C22⋊C4—1016no—
652C22⋊C4—208no—
653C42—1016no—
654C2×C5C22⋊#9511yescharacteristic
655C2×C5#173511yescharacteristic
656C2×C5#173611yescharacteristic
657C2×C5#178811yescharacteristic
658C2×C5#178811yescharacteristic
659C2×C5#182511yescharacteristic
660C2×C5#182511yescharacteristic
661C2×C5#185411yescharacteristic
662C2×C5#185411yescharacteristic
663C2×C5#185411yescharacteristic
664C2×C5#185411yescharacteristic
665C2×C5#187311yescharacteristic
666C2×C5#187311yescharacteristic
667C2×C5#187511yescharacteristic
668C2×C5#187511yescharacteristic
669D5—44no—
670C23—54no—
671C23—102no—
672C23—102no—
673C23—102no—
674C23—102no—
675C23—102no—
676C23—102no—
677C23—102no—
678C23—102no—
679C23—102no—
680C23—102no—
681C23—102no—
682C23—102no—
683C23—102no—
684C23—102no—
685C23—102no—
686C23—102no—
687C23—102no—
688C23—102no—
689C23—201no—
690C23—201no—
691C23—201no—
692C23—201no—
693C23—201no—
694C23—201no—
695C23—201no—
696C23—201no—
697C23—201no—
698C23—201no—
699C23—201no—
700C23—201no—
701C23—201no—
702C23—201no—
703C23—201no—
704C23—201no—
705C23D5×C22⋊C411yescharacteristic
706C23D5×C22⋊C411yescharacteristic
707C23#402811yescharacteristic
708C23#402911yescharacteristic
709C23D5×C4⋊C411yescharacteristic
710C23#404011yescharacteristic
711C23#405711yescharacteristic
712C23#405811yescharacteristic
713C23#406011yescharacteristic
714C23#406111yescharacteristic
715C23#406211yescharacteristic
716C23#406211yescharacteristic
717C23#406411yescharacteristic
718C23#406511yescharacteristic
719C23#408311yescharacteristic
720C2×C4—24no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—54no—
731C2×C4—81no—
732C2×C4—81no—
733C2×C4—81no—
734C2×C4—81no—
735C2×C4—102no—
736C2×C4—102no—
737C2×C4—102no—
738C2×C4—102no—
739C2×C4—102no—
740C2×C4—102no—
741C2×C4—104no—
742C2×C4—104no—
743C2×C4—104no—
744C2×C4—104no—
745C2×C4—104no—
746C2×C4—104no—
747C2×C4—104no—
748C2×C4—104no—
749C2×C4—104no—
750C2×C4—202no—
751C2×C4—202no—
752C2×C4—202no—
753C2×C4—202no—
754C2×C4—202no—
755C2×C4—202no—
756C2×C4—202no—
757C2×C4—202no—
758C2×C4—202no—
759C2×C4—401no—
760C2×C4—401no—
761C2×C4—401no—
762C2×C4—401no—
763C2×C4C42×D511yescharacteristic
764C2×C4#401811yescharacteristic
765C2×C4C4×D2011yescharacteristic
766C2×C4C4×D2011yescharacteristic
767C2×C4D5×C22⋊C411yescharacteristic
768C2×C4D5×C22⋊C411yescharacteristic
769C2×C4#402711yescharacteristic
770C2×C4#402711yescharacteristic
771C2×C4#402811yescharacteristic
772C2×C4#402911yescharacteristic
773C2×C4#403011yescharacteristic
774C2×C4#403011yescharacteristic
775C2×C4D5×C4⋊C411yescharacteristic
776C2×C4D5×C4⋊C411yescharacteristic
777C2×C4#403811yescharacteristic
778C2×C4#403911yescharacteristic
779C2×C4#403911yescharacteristic
780C2×C4#404011yescharacteristic
781C2×C4#404111yescharacteristic
782C2×C4#404211yescharacteristic
783C2×C4#404211yescharacteristic
784C2×C4#404311yescharacteristic
785C2×C4C2×#68511yescharacteristic
786C2×C4C4×C22⋊D511yescharacteristic
787C2×C4C4×C22⋊D511yescharacteristic
788C2×C4#408311yescharacteristic
789C2×C4#408411yescharacteristic
790C2×C4#409211yescharacteristic
791C8—42no—
792C8—202no—
793C5#1073111yescharacteristic, complemented, Sylow
794C22—104no—
795C22—104no—
796C22—104no—
797C22—202no—
798C22—202no—
799C22—202no—
800C22—202no—
801C22—202no—
802C22—202no—
803C22—202no—
804C22—202no—
805C22—202no—
806C22—202no—
807C22—202no—
808C22—202no—
809C22D5×#9511yescharacteristic
810C22#6495311yescharacteristic
811C22#6495411yescharacteristic
812C22#6495711yescharacteristic
813C22#6505911yescharacteristic
814C22#6506011yescharacteristic
815C22#6506111yescharacteristic
816C22#6506111yescharacteristic
817C22#6506811yescharacteristic
818C22#6507011yescharacteristic
819C22#6507211yescharacteristic
820C22#6507311yescharacteristic
821C22#6509111yescharacteristic
822C22#6509211yescharacteristic
823C22#6509311yescharacteristic
824C22#6509311yescharacteristic
825C22#6509911yescharacteristic
826C22#6510011yescharacteristic
827C22#6510311yescharacteristic
828C22#6510411yescharacteristic
829C22#6514911yescharacteristic
830C22#6515011yescharacteristic
831C22#6515511yescharacteristic
832C22#6515611yescharacteristic
833C22#6516911yescharacteristic
834C22#6517011yescharacteristic
835C22#6517411yescharacteristic
836C22#6517711yescharacteristic
837C22#6524411yescharacteristic
838C22#6524511yescharacteristic
839C22#6527811yescharacteristic
840C22#6544711yescharacteristic
841C22#6546111yescharacteristic
842C22#6546211yescharacteristic
843C22#6547611yescharacteristic
844C4—44no—
845C4—82no—
846C4—104no—
847C4—204no—
848C4—402no—
849C4#6495411yescharacteristic
850C4#6495511yescharacteristic
851C4#6495611yescharacteristic
852C4#6495711yescharacteristic
853C4C4×#68511yescharacteristic
854C4#6524511yescharacteristic
855C4#6527611yescharacteristic
856C4#6527811yescharacteristic
857C2—204no—
858C2#1059960611yescharacteristic
859C2#1059965911yescharacteristic
860C2#1059966011yescharacteristic
861C2#1059966611yescharacteristic
862C2#1059966911yescharacteristic
863C2#1059967011yescharacteristic
864C2#1059967211yescharacteristic
865C2#1059967411yescharacteristic
866C2#1060021811yescharacteristic
867C2#1060099211yescharacteristic
868C2#1060099411yescharacteristic
869C2#1060106011yescharacteristic
870C2#1060106211yescharacteristic
871C2#1060137311yescharacteristic
872C2#1060142611yescharacteristic
subgroupG/H
centerC24D4×D5
commutatorC2×C4×C5C2×C42
FrattiniC23×C4C22×D5
FittingC2×C5×#340C2
socleC24×C5C2×D4
prime radicalC24×D5D4
cosocleC23×C4×C5C23
hypercenterC2×#340D5
hypocenterC5#10731
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C24 ◁ C23×C4 ◁ C2×#340

Complements

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

NH ≅ G/Ntype
4. C2×C5×#340C2semidirect
5. C2×#64771C2semidirect
6. C2×#64749C2semidirect
7. C2×#64749C2semidirect
23. C2×#4038C4semidirect
27. C2×#3952C4semidirect
29. #65276C4semidirect
115. C2×#340D5semidirect
223. C5×C4⋊C4C22⋊C4semidirect
233. C4⋊Dic5C22⋊C4semidirect
650. C4⋊C4#685semidirect
793. C5#10731semidirect

Maximal subgroups

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

subgroupindex
C22×#40382
C22×#39522
C2×#652762
C2×C5×#3402
C2×#647712
C2×#647492
#107315