Finite Group Databasebeta

← #12004576

Subgroups — #12004576

Order 1280.

1822 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D5×C4⋊C4C211yesmaximal, 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×D5—21no—
9C23×C4×D5C2211yescharacteristic
10C23×C5×C8C2211yescharacteristic
11C22×C5×C4⋊C4C2211yescharacteristic
12C22×C5×C4⋊C4C2211yescharacteristic
13C22×#685—21no—
14C22×C4⋊Dic5C2211yescharacteristic
15C22×C4⋊Dic5C2211yescharacteristic
16C22×#683—21no—
17C23×#168C2211yescharacteristic
18C2×D5×C4⋊C4—22no—
19C2×D5×C4⋊C4—22no—
20C2×D5×C4⋊C4—22no—
21C2×D5×C4⋊C4—22no—
22C2×D5×C4⋊C4—22no—
23C2×D5×C4⋊C4C414yescomplemented
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#10730—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×D5—24no—
51C22×C4×D5—24no—
52C22×C4×D5—24no—
53C22×C4×D5—42no—
54C22×C4×D5—42no—
55C22×C4×D5—42no—
56C22×C4×D5—42no—
57C22×C4×D5C2×C412yes—
58C22×C4×D5C2×C412yes—
59C22×C4×D5C2×C412yes—
60C22×C4×D5D412yes—
61C22×C4×D5D412yes—
62C22×C4×D5Q812yes—
63C22×C5×C8—21no—
64C22×C5×C8—21no—
65C22×C5×C8—21no—
66C22×C5×C8—21no—
67C22×C5×C8—21no—
68C22×C5×C8—21no—
69C22×C5×C8C2×C412yescomplemented
70C2×C5×C4⋊C4—21no—
71C2×C5×C4⋊C4—21no—
72C2×C5×C4⋊C4—21no—
73C2×C5×C4⋊C4—21no—
74C2×C5×C4⋊C4—21no—
75C2×C5×C4⋊C4—21no—
76C2×C5×C4⋊C4—21no—
77C2×C5×C4⋊C4—21no—
78C2×C5×C4⋊C4C2×C412yes—
79C2×C5×C4⋊C4C2×C412yescomplemented
80C2×C5×C4⋊C4D412yes—
81C2×C5×C4⋊C4D412yes—
82C2×#685—24no—
83C2×#685—42no—
84C2×#685—42no—
85C2×C4⋊Dic5—21no—
86C2×C4⋊Dic5—21no—
87C2×C4⋊Dic5—21no—
88C2×C4⋊Dic5—21no—
89C2×C4⋊Dic5—21no—
90C2×C4⋊Dic5—21no—
91C2×C4⋊Dic5—21no—
92C2×C4⋊Dic5—21no—
93C2×C4⋊Dic5C2×C412yes—
94C2×C4⋊Dic5C2×C412yescomplemented
95C2×C4⋊Dic5D412yes—
96C2×C4⋊Dic5D412yes—
97C2×#683—24no—
98C2×#683—24no—
99C2×#683—24no—
100C22×#168—21no—
101C22×#168—21no—
102C22×#168—21no—
103C22×#168—21no—
104C22×#168—21no—
105C22×#168—21no—
106C22×#168C2×C412yescomplemented
107D5×C4⋊C4—28no—
108D5×C4⋊C4—28no—
109D5×C4⋊C4—28no—
110D5×C4⋊C4—28no—
111#3963—24no—
112#3952—28no—
113C23×C4⋊C4—51no—
114C22×C22⋊C8—51no—
115C2×#380—51no—
116C2×#340—51no—
117C2×#340—51no—
118C2×#340—51no—
119C2×#340D511yescharacteristic, complemented
120C24×C5C2×D411yescharacteristic
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—
132C23×D5D812yes—
133C23×D5SD1612yes—
134C23×D5SD1612yes—
135C23×D5Q1612yes—
136C22×C4×C5—22no—
137C22×C4×C5—22no—
138C22×C4×C5—22no—
139C22×C4×C5—22no—
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×C5—41no—
147C22×C4×C5—41no—
148C22×C4×C5—41no—
149C22×C4×C5—41no—
150C22×C4×C5C22×C411yescharacteristic
151C22×C4×C5C22×C411yescharacteristic
152C22×C4×C5C22×C411yescharacteristic
153C22×C4×C5C2×D411yescharacteristic
154C22×C4×C5C2×D411yescharacteristic
155C22×C4×C5C2×D411yescharacteristic
156C22×C4×C5C2×D411yescharacteristic
157C22×C4×C5C2×D411yescharacteristic
158C22×C4×C5C2×D411yescharacteristic
159C22×C4×C5C2×Q811yescharacteristic
160C22×C4×C5#4111yescharacteristic
161C22×C4×C5#4111yescharacteristic
162C22×C4×C5#4111yescharacteristic
163C22×C4×C5#4111yescharacteristic
164C22×Dic5—21no—
165C22×Dic5—21no—
166C22×Dic5—21no—
167C22×Dic5—21no—
168C22×Dic5—22no—
169C22×Dic5—22no—
170C22×Dic5—22no—
171C22×Dic5—22no—
172C22×Dic5—41no—
173C22×Dic5—41no—
174C22×Dic5—41no—
175C22×Dic5—41no—
176C22×Dic5—41no—
177C22×Dic5—41no—
178C22×Dic5—41no—
179C22×Dic5—41no—
180C22×Dic5—41no—
181C22×Dic5—41no—
182C22×Dic5C22⋊C412yes—
183C22×Dic5C22⋊C412yes—
184C22×Dic5C4⋊C412yes—
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×D5—22no—
206C2×C4×D5—22no—
207C2×C4×D5—22no—
208C2×C4×D5—22no—
209C2×C4×D5—216no—
210C2×C4×D5—48no—
211C2×C4×D5—48no—
212C2×C4×D5—48no—
213C2×C4×D5—48no—
214C2×C4×D5—48no—
215C2×C4×D5—48no—
216C2×C4×D5C4214yes—
217C2×C4×D5C22⋊C414yes—
218C2×C4×D5C4⋊C414yes—
219C2×C4×D5C4⋊C414yes—
220C2×C5×C8—22no—
221C2×C5×C8—22no—
222C2×C5×C8—22no—
223C2×C5×C8—41no—
224C2×C5×C8—41no—
225C2×C5×C8—41no—
226C2×C5×C8—41no—
227C5×C4⋊C4—22no—
228C5×C4⋊C4—22no—
229C5×C4⋊C4—22no—
230C5×C4⋊C4—22no—
231C5×C4⋊C4—22no—
232C5×C4⋊C4—41no—
233C5×C4⋊C4—41no—
234C5×C4⋊C4C22⋊C414yescomplemented
235#685—48no—
236C4⋊Dic5—22no—
237C4⋊Dic5—22no—
238C4⋊Dic5—22no—
239C4⋊Dic5—22no—
240C4⋊Dic5—22no—
241C4⋊Dic5—41no—
242C4⋊Dic5—41no—
243C4⋊Dic5C22⋊C414yescomplemented
244#683—216no—
245C2×#168—22no—
246C2×#168—22no—
247C2×#168—22no—
248C2×#168—41no—
249C2×#168—41no—
250C2×#168—41no—
251C2×#168—41no—
252C24×C4—51no—
253C24×C4—101no—
254C23×C8—51no—
255C23×C8C2×D511yescharacteristic
256C22×C4⋊C4—51no—
257C22×C4⋊C4—51no—
258C22×C4⋊C4—54no—
259C22×C4⋊C4—102no—
260C22×C4⋊C4—102no—
261C22×C4⋊C4—102no—
262C22×C4⋊C4—101no—
263C22×C4⋊C4—102no—
264C22×C4⋊C4—102no—
265C22×C4⋊C4C2×D511yescharacteristic
266C22×C4⋊C4C2×D511yescharacteristic
267C22×C22⋊C4—101no—
268C2×C22⋊C8—54no—
269C2×C22⋊C8—102no—
270C2×C22⋊C8—102no—
271#380—54no—
272#380—102no—
273C2×#95—101no—
274#340—22no—
275#340—102no—
276#340—102no—
277#340—102no—
278C23×C5C2×C22⋊C411yescharacteristic
279C23×C5C2×C22⋊C411yescharacteristic
280C23×C5C2×C4⋊C411yescharacteristic
281C23×C5#12011yescharacteristic
282C23×C5#12011yescharacteristic
283C23×C5#12311yescharacteristic
284C23×C5#12311yescharacteristic
285C23×C5C2×D811yescharacteristic
286C23×C5C2×SD1611yescharacteristic
287C23×C5C2×SD1611yescharacteristic
288C23×C5C2×Q1611yescharacteristic
289C23×C5AGL(1,ℤ/8)11yescharacteristic
290C23×C5AGL(1,ℤ/8)11yescharacteristic
291C23×C5#13711yescharacteristic
292C23×C5#13711yescharacteristic
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—22no—
302C22×D5—22no—
303C22×D5—22no—
304C22×D5—22no—
305C22×D5—22no—
306C22×D5—22no—
307C22×D5—22no—
308C22×D5—22no—
309C22×D5—22no—
310C22×D5—22no—
311C22×D5—22no—
312C22×D5—22no—
313C22×D5—22no—
314C22×D5—22no—
315C22×D5—22no—
316C22×D5—22no—
317C22×D5—22no—
318C22×D5—22no—
319C22×D5—22no—
320C22×D5—22no—
321C22×D5#9514yes—
322C22×D5#10214yes—
323C22×D5#10214yes—
324C22×D5#10314yes—
325C22×D5#10314yes—
326C22×D5#10614yes—
327C22×D5#10714yes—
328C2×C4×C5—24no—
329C2×C4×C5—42no—
330C2×C4×C5—42no—
331C2×C4×C5—42no—
332C2×C4×C5—42no—
333C2×C4×C5—42no—
334C2×C4×C5—42no—
335C2×C4×C5—42no—
336C2×C4×C5—42no—
337C2×C4×C5—42no—
338C2×C4×C5—81no—
339C2×C4×C5—81no—
340C2×C4×C5—81no—
341C2×C4×C5—81no—
342C2×C4×C5C2×C4211yescharacteristic
343C2×C4×C5C2×C22⋊C411yescharacteristic
344C2×C4×C5C2×C22⋊C411yescharacteristic
345C2×C4×C5C2×C22⋊C411yescharacteristic
346C2×C4×C5C2×C4⋊C411yescharacteristic
347C2×C4×C5C2×C4⋊C411yescharacteristic
348C2×C4×C5#11711yescharacteristic
349C2×C4×C5#11711yescharacteristic
350C2×C4×C5C4×D411yescharacteristic
351C2×C4×C5C4×D411yescharacteristic
352C2×C4×C5C4×D411yescharacteristic
353C2×C4×C5C4×D411yescharacteristic
354C2×C4×C5C4×D411yescharacteristic
355C2×C4×C5C4×D411yescharacteristic
356C2×C4×C5C4×D411yescharacteristic
357C2×C4×C5C4×D411yescharacteristic
358C2×C4×C5#12011yescharacteristic
359C2×C4×C5#12011yescharacteristic
360C2×C4×C5#12111yescharacteristic
361C2×C4×C5#12111yescharacteristic
362C2×C4×C5#12111yescharacteristic
363C2×C4×C5#12111yescharacteristic
364C2×C4×C5C22⋊Q811yescharacteristic
365C2×C4×C5C22⋊Q811yescharacteristic
366C2×C4×C5C22⋊Q811yescharacteristic
367C2×C4×C5C22⋊Q811yescharacteristic
368C2×C4×C5#12311yescharacteristic
369C2×C4×C5#12311yescharacteristic
370C2×Dic5—22no—
371C2×Dic5—22no—
372C2×Dic5—22no—
373C2×Dic5—22no—
374C2×Dic5—22no—
375C2×Dic5—22no—
376C2×Dic5—24no—
377C2×Dic5—42no—
378C2×Dic5—42no—
379C2×Dic5—42no—
380C2×Dic5—42no—
381C2×Dic5—42no—
382C2×Dic5—42no—
383C2×Dic5—42no—
384C2×Dic5—42no—
385C2×Dic5—42no—
386C2×Dic5—81no—
387C2×Dic5—81no—
388C2×Dic5—81no—
389C2×Dic5—81no—
390C2×Dic5#9514yes—
391C4×D5—24no—
392C4×D5—24no—
393C4×D5—24no—
394C4×D5—24no—
395C4×D5—24no—
396C4×D5—24no—
397C4×D5—24no—
398C4×D5—24no—
399C4×D5—432no—
400C5×C8—42no—
401#168—42no—
402C25—51no—
403C23×C4—21no—
404C23×C4—21no—
405C23×C4—51no—
406C23×C4—52no—
407C23×C4—52no—
408C23×C4—52no—
409C23×C4—52no—
410C23×C4—52no—
411C23×C4—52no—
412C23×C4—104no—
413C23×C4—104no—
414C23×C4—104no—
415C23×C4—101no—
416C23×C4—101no—
417C23×C4—101no—
418C23×C4—101no—
419C23×C4—101no—
420C23×C4—101no—
421C23×C4—101no—
422C23×C4—101no—
423C23×C4—101no—
424C23×C4—101no—
425C23×C4—202no—
426C23×C4—202no—
427C23×C4—202no—
428C23×C4—202no—
429C23×C4C22×D511yescharacteristic
430C22×C8—21no—
431C22×C8—21no—
432C22×C8—21no—
433C22×C8—21no—
434C22×C8—21no—
435C22×C8—21no—
436C22×C8—52no—
437C22×C8—101no—
438C22×C8—101no—
439C22×C8—101no—
440C22×C8—101no—
441C22×C8—101no—
442C22×C8—101no—
443C22×C8C4×D512yescomplemented
444C2×C4⋊C4—21no—
445C2×C4⋊C4—21no—
446C2×C4⋊C4—21no—
447C2×C4⋊C4—21no—
448C2×C4⋊C4—21no—
449C2×C4⋊C4—21no—
450C2×C4⋊C4—21no—
451C2×C4⋊C4—21no—
452C2×C4⋊C4—52no—
453C2×C4⋊C4—52no—
454C2×C4⋊C4—52no—
455C2×C4⋊C4—52no—
456C2×C4⋊C4—108no—
457C2×C4⋊C4—108no—
458C2×C4⋊C4—108no—
459C2×C4⋊C4—104no—
460C2×C4⋊C4—104no—
461C2×C4⋊C4—104no—
462C2×C4⋊C4—101no—
463C2×C4⋊C4—101no—
464C2×C4⋊C4—101no—
465C2×C4⋊C4—108no—
466C2×C4⋊C4—101no—
467C2×C4⋊C4—101no—
468C2×C4⋊C4—101no—
469C2×C4⋊C4—101no—
470C2×C4⋊C4—101no—
471C2×C4⋊C4C4×D512yes—
472C2×C4⋊C4C4×D512yescomplemented
473C2×C4⋊C4D2012yes—
474C2×C4⋊C4C22⋊D512yes—
475C2×C22⋊C4—104no—
476C2×C22⋊C4—202no—
477C2×C22⋊C4—202no—
478C22⋊C8—108no—
479#95—104no—
480C22×C5C2×#9511yescharacteristic
481C22×C5#37911yescharacteristic
482C22×C5#38111yescharacteristic
483C22×C5#38511yescharacteristic
484C22×C5#38511yescharacteristic
485C22×C5#38611yescharacteristic
486C22×C5#38611yescharacteristic
487C22×C5C2×#10211yescharacteristic
488C22×C5C2×#10211yescharacteristic
489C22×C5C2×#10311yescharacteristic
490C22×C5C2×#10311yescharacteristic
491C22×C5#41711yescharacteristic
492C22×C5#41711yescharacteristic
493C22×C5#41811yescharacteristic
494C22×C5#41911yescharacteristic
495C22×C5C2×#10611yescharacteristic
496C22×C5C2×#10711yescharacteristic
497C22×C5#42811yescharacteristic
498C22×C5#42811yescharacteristic
499C22×C5#44711yescharacteristic
500C22×C5#44711yescharacteristic
501C22×C5#44811yescharacteristic
502C22×C5#44811yescharacteristic
503C22×C5#45011yescharacteristic
504C22×C5#45011yescharacteristic
505C22×C5#45111yescharacteristic
506C22×C5#45111yescharacteristic
507C22×C5#48011yescharacteristic
508C22×C5#48011yescharacteristic
509C22×C5#48111yescharacteristic
510C22×C5#48111yescharacteristic
511C22×C5#48311yescharacteristic
512C22×C5#48311yescharacteristic
513C22×C5#48411yescharacteristic
514C22×C5#48411yescharacteristic
515C2×D5—24no—
516C2×D5—24no—
517C2×D5—24no—
518C2×D5—24no—
519C2×D5—24no—
520C2×D5—24no—
521C2×D5—24no—
522C2×D5—24no—
523C2×D5—24no—
524C2×D5—24no—
525C2×D5—24no—
526C2×D5—24no—
527C2×D5—24no—
528C2×D5—24no—
529C2×D5#34018yescomplemented
530C4×C5—44no—
531C4×C5—82no—
532C4×C5C4×C22⋊C411yescharacteristic
533C4×C5C4×C22⋊C411yescharacteristic
534C4×C5#38011yescharacteristic
535C4×C5#38011yescharacteristic
536C4×C5#38511yescharacteristic
537C4×C5#38511yescharacteristic
538C4×C5#38611yescharacteristic
539C4×C5#38611yescharacteristic
540Dic5—24no—
541Dic5—44no—
542Dic5—82no—
543C24—52no—
544C24—52no—
545C24—52no—
546C24—52no—
547C24—52no—
548C24—52no—
549C24—52no—
550C24—101no—
551C24—101no—
552C24—101no—
553C24—101no—
554C24—101no—
555C24—101no—
556C24—101no—
557C24—101no—
558C24D4×D511yescharacteristic
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—41no—
564C22×C4—41no—
565C22×C4—41no—
566C22×C4—41no—
567C22×C4—41no—
568C22×C4—41no—
569C22×C4—41no—
570C22×C4—41no—
571C22×C4—41no—
572C22×C4—41no—
573C22×C4—52no—
574C22×C4—52no—
575C22×C4—52no—
576C22×C4—54no—
577C22×C4—54no—
578C22×C4—54no—
579C22×C4—54no—
580C22×C4—1016no—
581C22×C4—101no—
582C22×C4—101no—
583C22×C4—101no—
584C22×C4—101no—
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—102no—
598C22×C4—102no—
599C22×C4—102no—
600C22×C4—102no—
601C22×C4—102no—
602C22×C4—102no—
603C22×C4—102no—
604C22×C4—102no—
605C22×C4—102no—
606C22×C4—102no—
607C22×C4—102no—
608C22×C4—102no—
609C22×C4—102no—
610C22×C4—102no—
611C22×C4—102no—
612C22×C4—102no—
613C22×C4—208no—
614C22×C4—208no—
615C22×C4—208no—
616C22×C4—208no—
617C22×C4—208no—
618C22×C4—208no—
619C22×C4—201no—
620C22×C4—201no—
621C22×C4—201no—
622C22×C4—201no—
623C22×C4—201no—
624C22×C4—201no—
625C22×C4—201no—
626C22×C4—201no—
627C22×C4—201no—
628C22×C4—201no—
629C22×C4C2×C4×D511yescharacteristic
630C22×C4C2×C4×D511yescharacteristic
631C22×C4C2×C4×D511yescharacteristic
632C22×C4C2×D2011yescharacteristic
633C22×C4#70911yescharacteristic
634C22×C4#70911yescharacteristic
635C22×C4D4×D511yescharacteristic
636C22×C4D4×D511yescharacteristic
637C22×C4D4×D511yescharacteristic
638C22×C4D4×D511yescharacteristic
639C22×C4#71111yescharacteristic
640C22×C4Q8×D511yescharacteristic
641C22×C4#71311yescharacteristic
642C22×C4C2×C22⋊D511yescharacteristic
643C2×C8—22no—
644C2×C8—22no—
645C2×C8—22no—
646C2×C8—41no—
647C2×C8—41no—
648C2×C8—41no—
649C2×C8—41no—
650C2×C8—102no—
651C2×C8—102no—
652C2×C8—102no—
653C2×C8—201no—
654C2×C8—201no—
655C2×C8—201no—
656C2×C8—201no—
657C4⋊C4—22no—
658C4⋊C4—22no—
659C4⋊C4—22no—
660C4⋊C4—22no—
661C4⋊C4—22no—
662C4⋊C4—41no—
663C4⋊C4—41no—
664C4⋊C4—54no—
665C4⋊C4—1016no—
666C4⋊C4—102no—
667C4⋊C4—102no—
668C4⋊C4—102no—
669C4⋊C4—102no—
670C4⋊C4—102no—
671C4⋊C4—201no—
672C4⋊C4—201no—
673C4⋊C4#68514yescomplemented
674C22⋊C4—208no—
675C2×C5C22⋊#9511yescharacteristic
676C2×C5C2×#34011yescharacteristic
677C2×C5#173611yescharacteristic
678C2×C5#178611yescharacteristic
679C2×C5#178711yescharacteristic
680C2×C5#182311yescharacteristic
681C2×C5#182411yescharacteristic
682C2×C5#185211yescharacteristic
683C2×C5#185211yescharacteristic
684C2×C5#185311yescharacteristic
685C2×C5#185311yescharacteristic
686C2×C5#187211yescharacteristic
687C2×C5#187211yescharacteristic
688C2×C5#187411yescharacteristic
689C2×C5#187411yescharacteristic
690D5—28no—
691C23—54no—
692C23—54no—
693C23—54no—
694C23—54no—
695C23—54no—
696C23—54no—
697C23—54no—
698C23—102no—
699C23—102no—
700C23—102no—
701C23—102no—
702C23—102no—
703C23—102no—
704C23—102no—
705C23—102no—
706C23—102no—
707C23—102no—
708C23—102no—
709C23—102no—
710C23—102no—
711C23—102no—
712C23—102no—
713C23—102no—
714C23—102no—
715C23—102no—
716C23—102no—
717C23—102no—
718C23—102no—
719C23—102no—
720C23—102no—
721C23—102no—
722C23—102no—
723C23—102no—
724C23—102no—
725C23—102no—
726C23D5×C22⋊C411yescharacteristic
727C23D5×C22⋊C411yescharacteristic
728C23#402811yescharacteristic
729C23#402911yescharacteristic
730C23D5×C4⋊C411yescharacteristic
731C23#404011yescharacteristic
732C23D5×D811yescharacteristic
733C23#405711yescharacteristic
734C23D5×SD1611yescharacteristic
735C23D5×SD1611yescharacteristic
736C23#406011yescharacteristic
737C23#406111yescharacteristic
738C23D5×Q1611yescharacteristic
739C23#406411yescharacteristic
740C23#408311yescharacteristic
741C2×C4—24no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—54no—
752C2×C4—81no—
753C2×C4—81no—
754C2×C4—81no—
755C2×C4—81no—
756C2×C4—102no—
757C2×C4—102no—
758C2×C4—102no—
759C2×C4—102no—
760C2×C4—102no—
761C2×C4—102no—
762C2×C4—104no—
763C2×C4—104no—
764C2×C4—104no—
765C2×C4—104no—
766C2×C4—104no—
767C2×C4—104no—
768C2×C4—104no—
769C2×C4—104no—
770C2×C4—104no—
771C2×C4—2032no—
772C2×C4—202no—
773C2×C4—202no—
774C2×C4—202no—
775C2×C4—202no—
776C2×C4—202no—
777C2×C4—202no—
778C2×C4—202no—
779C2×C4—202no—
780C2×C4—202no—
781C2×C4—401no—
782C2×C4—401no—
783C2×C4—401no—
784C2×C4—401no—
785C2×C4C42×D511yescharacteristic
786C2×C4#401811yescharacteristic
787C2×C4C4×D2011yescharacteristic
788C2×C4C4×D2011yescharacteristic
789C2×C4D5×C22⋊C411yescharacteristic
790C2×C4D5×C22⋊C411yescharacteristic
791C2×C4#402711yescharacteristic
792C2×C4#402711yescharacteristic
793C2×C4#402811yescharacteristic
794C2×C4#402911yescharacteristic
795C2×C4#403011yescharacteristic
796C2×C4#403011yescharacteristic
797C2×C4D5×C4⋊C411yescharacteristic
798C2×C4D5×C4⋊C411yescharacteristic
799C2×C4#403811yescharacteristic
800C2×C4#403911yescharacteristic
801C2×C4#403911yescharacteristic
802C2×C4#404011yescharacteristic
803C2×C4#404111yescharacteristic
804C2×C4#404211yescharacteristic
805C2×C4#404211yescharacteristic
806C2×C4#404311yescharacteristic
807C2×C4C2×#68511yescharacteristic
808C2×C4C4×C22⋊D511yescharacteristic
809C2×C4C4×C22⋊D511yescharacteristic
810C2×C4#408311yescharacteristic
811C2×C4#408411yescharacteristic
812C2×C4#409211yescharacteristic
813C8—42no—
814C8—202no—
815C5#1073011yescharacteristic, complemented, Sylow
816C22—58no—
817C22—104no—
818C22—104no—
819C22—104no—
820C22—104no—
821C22—104no—
822C22—104no—
823C22—104no—
824C22—104no—
825C22—104no—
826C22—104no—
827C22—104no—
828C22—104no—
829C22—104no—
830C22—104no—
831C22D5×#9511yescharacteristic
832C22#6495311yescharacteristic
833C22#6495411yescharacteristic
834C22#6495711yescharacteristic
835C22D5×#10211yescharacteristic
836C22D5×#10211yescharacteristic
837C22#6505911yescharacteristic
838C22#6506011yescharacteristic
839C22#6506211yescharacteristic
840C22#6506311yescharacteristic
841C22#6506511yescharacteristic
842C22#6506611yescharacteristic
843C22D5×#10311yescharacteristic
844C22D5×#10311yescharacteristic
845C22#6509111yescharacteristic
846C22#6509211yescharacteristic
847C22#6509411yescharacteristic
848C22#6509511yescharacteristic
849C22#6509711yescharacteristic
850C22#6509811yescharacteristic
851C22D5×#10611yescharacteristic
852C22#6515011yescharacteristic
853C22#6515111yescharacteristic
854C22#6515211yescharacteristic
855C22D5×#10711yescharacteristic
856C22#6517011yescharacteristic
857C22#6517111yescharacteristic
858C22#6517311yescharacteristic
859C22#6524411yescharacteristic
860C22#6524511yescharacteristic
861C22#6527811yescharacteristic
862C22#6544511yescharacteristic
863C22#6545811yescharacteristic
864C22#6545911yescharacteristic
865C22#6547511yescharacteristic
866C4—44no—
867C4—82no—
868C4—104no—
869C4—204no—
870C4—402no—
871C4#6495411yescharacteristic
872C4#6495511yescharacteristic
873C4#6495611yescharacteristic
874C4#6495711yescharacteristic
875C4C4×#68511yescharacteristic
876C4#6524511yescharacteristic
877C4#6527611yescharacteristic
878C4#6527811yescharacteristic
879C2—108no—
880C2D5×#34011yescharacteristic
881C2#1059966011yescharacteristic
882C2#1059966411yescharacteristic
883C2#1059966511yescharacteristic
884C2#1059966711yescharacteristic
885C2#1059966811yescharacteristic
886C2#1059967111yescharacteristic
887C2#1059967311yescharacteristic
888C2#1060021811yescharacteristic
889C2#1060099111yescharacteristic
890C2#1060099311yescharacteristic
891C2#1060105911yescharacteristic
892C2#1060106111yescharacteristic
893C2#1060137211yescharacteristic
894C2#1060142511yescharacteristic
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#10730
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×D5×C4⋊C4C4semidirect
27. C2×#3952C4semidirect
29. #65276C4semidirect
69. C22×C5×C8C2×C4semidirect
79. C2×C5×C4⋊C4C2×C4semidirect
94. C2×C4⋊Dic5C2×C4semidirect
106. C22×#168C2×C4semidirect
119. C2×#340D5semidirect
234. C5×C4⋊C4C22⋊C4semidirect
243. C4⋊Dic5C22⋊C4semidirect
443. C22×C8C4×D5semidirect
472. C2×C4⋊C4C4×D5semidirect
529. C2×D5#340semidirect
673. C4⋊C4#685semidirect
815. C5#10730semidirect

Maximal subgroups

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

subgroupindex
C22×D5×C4⋊C42
C22×#39522
C2×#652762
C2×C5×#3402
C2×#647712
C2×#647492
#107305