Finite Group Databasebeta

← #12021551

Subgroups — #12021551

Order 1280.

2366 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D5×C4⋊C4C211yesmaximal, characteristic
2C2×#65276C211yesmaximal, characteristic
3C2×#65262C211yesmaximal, characteristic, complemented
4C2×#65217C211yesmaximal, characteristic, complemented
5C2×C4×#685C211yesmaximal, characteristic
6C2×#64956C212yesmaximal
7C5×C4⋊#95C211yesmaximal, characteristic, complemented
8#10602356C211yesmaximal, characteristic, complemented
9#10600218C212yesmaximal
10#10600202C212yesmaximal, complemented
11#10600202C212yesmaximal, complemented
12C23×C4×D5C2212yes—
13C23×C4×D5C2211yescharacteristic
14C22×C5×C4⋊C4C2211yescharacteristic
15C22×C5×C4⋊C4C2211yescharacteristic
16C22×C42×C5C2211yescharacteristic
17C22×#685C2212yes—
18C22×#685C2211yescharacteristic
19C22×#685C2211yescharacteristic
20C22×C4⋊Dic5C2211yescharacteristic
21C22×C4⋊Dic5C2211yescharacteristic
22C22×#683C2212yes—
23C22×#683C2212yes—
24C22×#683C2212yes—
25C22×C4×Dic5C2211yescharacteristic
26C2×D5×C4⋊C4—24no—
27C2×D5×C4⋊C4—24no—
28C2×D5×C4⋊C4C418yescomplemented
29C2×C5×#95C2212yes—
30C2×C5×#95C2212yes—
31C2×#3963C2211yescharacteristic
32C2×#3963C2211yescharacteristic
33C2×#3963C2212yes—
34C2×#3963C2212yes—
35C2×#3963C2212yes—
36C2×#3963C2212yes—
37C2×#3963C2212yes—
38#65276—24no—
39#65262—24no—
40C4×#685—24no—
41#65217—24no—
42#64956—28no—
43#13907—51nomaximal, Sylow
44C24×D5C2311yescharacteristic
45C23×C4×C5C2312yes—
46C23×C4×C5C2312yes—
47C23×C4×C5C2311yescharacteristic
48C23×C4×C5C2311yescharacteristic
49C23×C4×C5C2311yescharacteristic
50C23×Dic5C2312yes—
51C23×Dic5C2311yescharacteristic
52C23×Dic5C2311yescharacteristic
53C23×Dic5C2312yes—
54C23×Dic5C2311yescharacteristic
55C22×C4×D5—22no—
56C22×C4×D5—22no—
57C22×C4×D5—22no—
58C22×C4×D5—22no—
59C22×C4×D5—24no—
60C22×C4×D5—24no—
61C22×C4×D5—24no—
62C22×C4×D5—24no—
63C22×C4×D5—42no—
64C22×C4×D5—42no—
65C22×C4×D5C2×C418yes—
66C22×C4×D5C2×C414yes—
67C22×C4×D5D414yes—
68C22×C4×D5Q814yes—
69C2×C5×C4⋊C4—22no—
70C2×C5×C4⋊C4—22no—
71C2×C5×C4⋊C4—22no—
72C2×C5×C4⋊C4—22no—
73C2×C5×C4⋊C4—22no—
74C2×C5×C4⋊C4C2×C414yes—
75C2×C42×C5—22no—
76C2×C42×C5—22no—
77C2×C42×C5—22no—
78C2×#685—22no—
79C2×#685—22no—
80C2×#685—22no—
81C2×#685—22no—
82C2×#685—24no—
83C2×#685—24no—
84C2×#685—24no—
85C2×#685D414yes—
86C2×#685Q814yes—
87C2×C4⋊Dic5—22no—
88C2×C4⋊Dic5—22no—
89C2×C4⋊Dic5—22no—
90C2×C4⋊Dic5C2×C414yes—
91C2×C4⋊Dic5D414yes—
92C2×C4⋊Dic5D414yes—
93C2×#683—24no—
94C2×#683—24no—
95C2×#683—24no—
96C2×#683—24no—
97C2×#683—24no—
98C2×#683—24no—
99C2×#683—42no—
100C2×#683—42no—
101C2×#683C2×C418yes—
102C2×C4×Dic5—22no—
103C2×C4×Dic5—22no—
104C2×C4×Dic5—22no—
105D5×C4⋊C4—232no—
106C5×#95—24no—
107C5×#95—42no—
108#3963—24no—
109#3963—24no—
110#3963—22no—
111#3963—22no—
112#3963—24no—
113#3963—24no—
114#3963—42no—
115C23×C4⋊C4—51no—
116C2×#389—51no—
117C2×#389—51no—
118C2×#380—52no—
119C2×#380—51no—
120C2×C4×C22⋊C4—51no—
121#1441—52no—
122#1441—52no—
123C4⋊#95—51no—
124C4⋊#95D511yescharacteristic, complemented
125C22⋊#95—52no—
126C24×C5C2411yescharacteristic
127C23×D5—21no—
128C23×D5—21no—
129C23×D5—21no—
130C23×D5—21no—
131C23×D5—21no—
132C23×D5—21no—
133C23×D5—21no—
134C23×D5—21no—
135C23×D5C22×C412yes—
136C23×D5C2×D412yes—
137C23×D5C2×D412yes—
138C23×D5C2×Q812yes—
139C23×D5C2×Q812yes—
140C23×D5#4112yes—
141C23×D5#4112yes—
142C22×C4×C5—21no—
143C22×C4×C5—21no—
144C22×C4×C5—21no—
145C22×C4×C5—21no—
146C22×C4×C5—22no—
147C22×C4×C5—22no—
148C22×C4×C5—22no—
149C22×C4×C5—21no—
150C22×C4×C5—21no—
151C22×C4×C5—22no—
152C22×C4×C5—21no—
153C22×C4×C5—21no—
154C22×C4×C5—22no—
155C22×C4×C5—22no—
156C22×C4×C5—21no—
157C22×C4×C5—21no—
158C22×C4×C5—21no—
159C22×C4×C5—21no—
160C22×C4×C5—22no—
161C22×C4×C5—22no—
162C22×C4×C5—22no—
163C22×C4×C5—22no—
164C22×C4×C5—22no—
165C22×C4×C5—22no—
166C22×C4×C5—22no—
167C22×C4×C5C22×C414yes—
168C22×C4×C5C22×C412yes—
169C22×C4×C5C2×D412yes—
170C22×C4×C5C2×D412yes—
171C22×C4×C5C2×D412yes—
172C22×C4×C5C2×D412yes—
173C22×C4×C5C2×Q812yes—
174C22×C4×C5C2×Q812yes—
175C22×C4×C5#4112yes—
176C22×C4×C5#4112yes—
177C22×Dic5—21no—
178C22×Dic5—21no—
179C22×Dic5—22no—
180C22×Dic5—21no—
181C22×Dic5—21no—
182C22×Dic5—22no—
183C22×Dic5—22no—
184C22×Dic5—22no—
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—22no—
198C22×Dic5—22no—
199C22×Dic5—22no—
200C22×Dic5—22no—
201C22×Dic5—22no—
202C22×Dic5—22no—
203C22×Dic5—22no—
204C22×Dic5C22×C414yes—
205C22×Dic5C22×C412yes—
206C22×Dic5C2×D412yes—
207C22×Dic5C2×D414yes—
208C22×Dic5C2×D414yes—
209C22×Dic5C2×D412yes—
210C22×Dic5C2×Q812yes—
211C22×Dic5C2×Q812yes—
212C2×C4×D5—28no—
213C2×C4×D5—28no—
214C2×C4×D5—28no—
215C2×C4×D5—28no—
216C2×C4×D5—28no—
217C2×C4×D5—28no—
218C2×C4×D5—216no—
219C2×C4×D5—216no—
220C2×C4×D5—48no—
221C2×C4×D5—48no—
222C2×C4×D5—48no—
223C2×C4×D5—48no—
224C2×C4×D5—48no—
225C2×C4×D5C4⋊C4116yescomplemented
226C5×C4⋊C4—28no—
227C5×C4⋊C4—44no—
228C42×C5—44no—
229#685—28no—
230#685—28no—
231#685—48no—
232C4⋊Dic5—44no—
233C4⋊Dic5C22⋊C4116yescomplemented
234#683—216no—
235#683—48no—
236#683—48no—
237C4×Dic5—44no—
238C24×C4—51no—
239C24×C4—52no—
240C22×C4⋊C4—51no—
241C22×C4⋊C4—52no—
242C22×C4⋊C4—58no—
243C22×C4⋊C4—51no—
244C22×C4⋊C4—52no—
245C22×C4⋊C4—52no—
246C22×C4⋊C4—104no—
247C22×C4⋊C4—104no—
248C22×C4⋊C4C2×D511yescharacteristic
249C22×C4⋊C4C2×D511yescharacteristic
250C22×C22⋊C4—51no—
251C22×C22⋊C4—51no—
252C22×C22⋊C4—52no—
253C22×C42—51no—
254C22×C42C2×D511yescharacteristic
255#389—104no—
256#389—104no—
257#380—108no—
258#380—104no—
259C4×C22⋊C4—104no—
260C2×#95—52no—
261C2×#95—52no—
262C2×#95—52no—
263C2×#95—51no—
264C2×#95—51no—
265C2×#95—52no—
266C2×#95—52no—
267C2×#95C2×D512yes—
268C2×#95C2×D512yes—
269C23×C5C23×C411yescharacteristic
270C23×C5C22×D411yescharacteristic
271C23×C5C22×D411yescharacteristic
272C23×C5C22×D411yescharacteristic
273C23×C5C22×D411yescharacteristic
274C23×C5C22×Q811yescharacteristic
275C23×C5C22×Q811yescharacteristic
276C23×C5C2×#4111yescharacteristic
277C23×C5C2×#4111yescharacteristic
278C23×C5C2×#4111yescharacteristic
279C23×C5C2×#4111yescharacteristic
280C23×C5H(5,𝔽2)11yescharacteristic
281C23×C5H(5,𝔽2)11yescharacteristic
282C23×C52−1+411yescharacteristic
283C23×C52−1+411yescharacteristic
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—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×D5C2×C4⋊C414yes—
313C22×D5C4×D414yes—
314C22×D5C4×Q814yes—
315C22×D5#12114yes—
316C22×D5C22⋊Q814yes—
317C22×D5#12514yes—
318C22×D5C4⋊Q814yes—
319C2×C4×C5—24no—
320C2×C4×C5—24no—
321C2×C4×C5—24no—
322C2×C4×C5—22no—
323C2×C4×C5—22no—
324C2×C4×C5—22no—
325C2×C4×C5—22no—
326C2×C4×C5—22no—
327C2×C4×C5—22no—
328C2×C4×C5—41no—
329C2×C4×C5—41no—
330C2×C4×C5—41no—
331C2×C4×C5—41no—
332C2×C4×C5—42no—
333C2×C4×C5—42no—
334C2×C4×C5—42no—
335C2×C4×C5—42no—
336C2×C4×C5—41no—
337C2×C4×C5—41no—
338C2×C4×C5—41no—
339C2×C4×C5—41no—
340C2×C4×C5—42no—
341C2×C4×C5—42no—
342C2×C4×C5—42no—
343C2×C4×C5—42no—
344C2×C4×C5—42no—
345C2×C4×C5—42no—
346C2×C4×C5—42no—
347C2×C4×C5C2×C22⋊C414yes—
348C2×C4×C5C2×C4⋊C414yes—
349C2×C4×C5#11714yes—
350C2×C4×C5#12114yes—
351C2×C4×C5#12114yes—
352C2×C4×C5C22⋊Q814yes—
353C2×C4×C5C22⋊Q814yes—
354C2×Dic5—22no—
355C2×Dic5—22no—
356C2×Dic5—24no—
357C2×Dic5—24no—
358C2×Dic5—22no—
359C2×Dic5—22no—
360C2×Dic5—22no—
361C2×Dic5—22no—
362C2×Dic5—24no—
363C2×Dic5—24no—
364C2×Dic5—24no—
365C2×Dic5—24no—
366C2×Dic5—22no—
367C2×Dic5—22no—
368C2×Dic5—22no—
369C2×Dic5—22no—
370C2×Dic5—22no—
371C2×Dic5—22no—
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—42no—
381C2×Dic5—42no—
382C2×Dic5—42no—
383C2×Dic5—42no—
384C2×Dic5—42no—
385C2×Dic5—42no—
386C2×Dic5—42no—
387C2×Dic5C2×C22⋊C418yes—
388C2×Dic5C2×C4⋊C414yes—
389C4×D5—232no—
390C4×D5—432no—
391C25—51no—
392C23×C4—52no—
393C23×C4—51no—
394C23×C4—54no—
395C23×C4—54no—
396C23×C4—54no—
397C23×C4—51no—
398C23×C4—51no—
399C23×C4—58no—
400C23×C4—52no—
401C23×C4—104no—
402C23×C4—104no—
403C23×C4—104no—
404C23×C4—104no—
405C23×C4—102no—
406C23×C4—102no—
407C23×C4—102no—
408C23×C4—102no—
409C23×C4—202no—
410C23×C4—202no—
411C23×C4C22×D512yes—
412C23×C4C22×D512yes—
413C23×C4C22×D511yescharacteristic
414C23×C4C22×D511yescharacteristic
415C23×C4C22×D511yescharacteristic
416C2×C4⋊C4—22no—
417C2×C4⋊C4—22no—
418C2×C4⋊C4—22no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—22no—
421C2×C4⋊C4—54no—
422C2×C4⋊C4—54no—
423C2×C4⋊C4—54no—
424C2×C4⋊C4—58no—
425C2×C4⋊C4—1032no—
426C2×C4⋊C4—104no—
427C2×C4⋊C4—104no—
428C2×C4⋊C4—104no—
429C2×C4⋊C4—104no—
430C2×C4⋊C4—104no—
431C2×C4⋊C4—102no—
432C2×C4⋊C4—104no—
433C2×C4⋊C4—102no—
434C2×C4⋊C4—102no—
435C2×C4⋊C4—202no—
436C2×C4⋊C4—202no—
437C2×C4⋊C4C4×D514yes—
438C2×C22⋊C4—54no—
439C2×C22⋊C4—54no—
440C2×C22⋊C4—102no—
441C2×C22⋊C4—102no—
442C2×C22⋊C4—102no—
443C2×C22⋊C4—102no—
444C2×C22⋊C4—104no—
445C2×C22⋊C4—104no—
446C2×C22⋊C4—104no—
447C2×C42—22no—
448C2×C42—22no—
449C2×C42—22no—
450C2×C42—102no—
451C2×C42—102no—
452C2×C42—102no—
453#95—24no—
454#95—42no—
455#95—102no—
456#95—102no—
457#95—104no—
458#95—104no—
459#95—104no—
460#95—104no—
461#95—202no—
462C22×C5C22×C22⋊C411yescharacteristic
463C22×C5C22×C4⋊C411yescharacteristic
464C22×C5C2×#11711yescharacteristic
465C22×C5C2×C4×D411yescharacteristic
466C22×C5C2×C4×Q811yescharacteristic
467C22×C5#51811yescharacteristic
468C22×C5#51911yescharacteristic
469C22×C5C2×#12111yescharacteristic
470C22×C5C2×#12111yescharacteristic
471C22×C5C2×#12111yescharacteristic
472C22×C5C2×C22⋊Q811yescharacteristic
473C22×C5C2×C22⋊Q811yescharacteristic
474C22×C5C2×C22⋊Q811yescharacteristic
475C22×C5C2×#12511yescharacteristic
476C22×C5C2×C4⋊Q811yescharacteristic
477C22×C5#53711yescharacteristic
478C22×C5#53711yescharacteristic
479C22×C5#54411yescharacteristic
480C22×C5#54411yescharacteristic
481C22×C5D4211yescharacteristic
482C22×C5D4211yescharacteristic
483C22×C5#54611yescharacteristic
484C22×C5#54611yescharacteristic
485C22×C5#54711yescharacteristic
486C22×C5#54711yescharacteristic
487C22×C5#54811yescharacteristic
488C22×C5#54811yescharacteristic
489C22×C5D4×Q811yescharacteristic
490C22×C5D4×Q811yescharacteristic
491C22×C5#55211yescharacteristic
492C22×C5#55211yescharacteristic
493C22×C5#55311yescharacteristic
494C22×C5#55311yescharacteristic
495C22×C5#55411yescharacteristic
496C22×C5#55411yescharacteristic
497C2×D5—24no—
498C2×D5—24no—
499C2×D5—24no—
500C2×D5—24no—
501C2×D5—24no—
502C2×D5—24no—
503C2×D5—24no—
504C2×D5—24no—
505C2×D5—24no—
506C2×D5—24no—
507C2×D5—24no—
508C2×D5—24no—
509C2×D5—24no—
510C2×D5—24no—
511C2×D5#38918yescomplemented
512C4×C5—44no—
513C4×C5—42no—
514C4×C5—42no—
515C4×C5—82no—
516C4×C5#38018yescomplemented
517Dic5—28no—
518Dic5—24no—
519Dic5—42no—
520Dic5—42no—
521Dic5—82no—
522C24—52no—
523C24—52no—
524C24—52no—
525C24—52no—
526C24—52no—
527C24—52no—
528C24—52no—
529C24—101no—
530C24—101no—
531C24—101no—
532C24—101no—
533C24—101no—
534C24—101no—
535C24—101no—
536C24—101no—
537C24C23×D511yescharacteristic
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—22no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—21no—
548C22×C4—22no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—54no—
564C22×C4—52no—
565C22×C4—52no—
566C22×C4—54no—
567C22×C4—54no—
568C22×C4—52no—
569C22×C4—516no—
570C22×C4—52no—
571C22×C4—52no—
572C22×C4—1016no—
573C22×C4—1016no—
574C22×C4—101no—
575C22×C4—101no—
576C22×C4—102no—
577C22×C4—101no—
578C22×C4—101no—
579C22×C4—102no—
580C22×C4—102no—
581C22×C4—102no—
582C22×C4—108no—
583C22×C4—108no—
584C22×C4—108no—
585C22×C4—108no—
586C22×C4—108no—
587C22×C4—108no—
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—102no—
601C22×C4—102no—
602C22×C4—102no—
603C22×C4—102no—
604C22×C4—102no—
605C22×C4—102no—
606C22×C4—102no—
607C22×C4—208no—
608C22×C4—208no—
609C22×C4—208no—
610C22×C4—208no—
611C22×C4—208no—
612C22×C4C2×C4×D514yes—
613C22×C4C2×C4×D512yes—
614C22×C4#70912yes—
615C22×C4#70912yes—
616C22×C4D4×D512yes—
617C22×C4D4×D512yes—
618C22×C4D4×D512yes—
619C22×C4D4×D512yes—
620C22×C4Q8×D512yes—
621C22×C4Q8×D512yes—
622C4⋊C4—28no—
623C4⋊C4—44no—
624C4⋊C4—516no—
625C4⋊C4—1016no—
626C4⋊C4—208no—
627C4⋊C4—208no—
628C4⋊C4—204no—
629C22⋊C4—108no—
630C22⋊C4—108no—
631C22⋊C4—208no—
632C42—44no—
633C42—204no—
634C2×C5C2×#38011yescharacteristic
635C2×C5C2×#38911yescharacteristic
636C2×C5#231611yescharacteristic
637C2×C5D4×C22⋊C411yescharacteristic
638C2×C5Q8×C22⋊C411yescharacteristic
639C2×C5#234411yescharacteristic
640C2×C5#234511yescharacteristic
641C2×C5#241611yescharacteristic
642C2×C5#241611yescharacteristic
643C2×C5#241711yescharacteristic
644C2×C5#241711yescharacteristic
645C2×C5#244011yescharacteristic
646C2×C5#244011yescharacteristic
647C2×C5#244211yescharacteristic
648C2×C5#244211yescharacteristic
649D5—28no—
650C23—54no—
651C23—54no—
652C23—54no—
653C23—54no—
654C23—54no—
655C23—54no—
656C23—54no—
657C23—102no—
658C23—102no—
659C23—102no—
660C23—102no—
661C23—102no—
662C23—102no—
663C23—102no—
664C23—102no—
665C23—102no—
666C23—102no—
667C23—102no—
668C23—102no—
669C23—102no—
670C23—102no—
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—
685C23C22×C4×D511yescharacteristic
686C23C2×#70911yescharacteristic
687C23C2×#70911yescharacteristic
688C23C2×D4×D511yescharacteristic
689C23C2×D4×D511yescharacteristic
690C23C2×D4×D511yescharacteristic
691C23C2×D4×D511yescharacteristic
692C23#414411yescharacteristic
693C23C2×Q8×D511yescharacteristic
694C23C2×Q8×D511yescharacteristic
695C23#414711yescharacteristic
696C23D5×#4111yescharacteristic
697C23D5×#4111yescharacteristic
698C23#414911yescharacteristic
699C23#415011yescharacteristic
700C2×C4—24no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—24no—
704C2×C4—24no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—42no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—58no—
729C2×C4—54no—
730C2×C4—104no—
731C2×C4—102no—
732C2×C4—102no—
733C2×C4—102no—
734C2×C4—102no—
735C2×C4—102no—
736C2×C4—102no—
737C2×C4—104no—
738C2×C4—104no—
739C2×C4—104no—
740C2×C4—104no—
741C2×C4—104no—
742C2×C4—1032no—
743C2×C4—102no—
744C2×C4—102no—
745C2×C4—102no—
746C2×C4—102no—
747C2×C4—102no—
748C2×C4—102no—
749C2×C4—2032no—
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—202no—
759C2×C4—202no—
760C2×C4—202no—
761C2×C4—202no—
762C2×C4—202no—
763C2×C4—202no—
764C2×C4—202no—
765C2×C4#401814yes—
766C2×C4D5×C22⋊C414yes—
767C2×C4#403014yes—
768C2×C4#403014yes—
769C2×C4D5×C4⋊C414yes—
770C2×C4#404214yes—
771C2×C4#404214yes—
772C5#1390711yescharacteristic, complemented, Sylow
773C22—58no—
774C22—104no—
775C22—104no—
776C22—104no—
777C22—104no—
778C22—104no—
779C22—104no—
780C22—104no—
781C22—104no—
782C22—104no—
783C22—104no—
784C22—104no—
785C22—104no—
786C22—104no—
787C22—104no—
788C22C2×#401811yescharacteristic
789C22C2×D5×C22⋊C411yescharacteristic
790C22C2×#403011yescharacteristic
791C22C2×#403011yescharacteristic
792C22C2×D5×C4⋊C411yescharacteristic
793C22#6584111yescharacteristic
794C22C2×#404211yescharacteristic
795C22C2×#404211yescharacteristic
796C22#6584511yescharacteristic
797C22#6586311yescharacteristic
798C22#6586411yescharacteristic
799C22C4×D4×D511yescharacteristic
800C22#6587911yescharacteristic
801C22#6588511yescharacteristic
802C22#6589211yescharacteristic
803C22C4×Q8×D511yescharacteristic
804C22#6590611yescharacteristic
805C22#6591311yescharacteristic
806C22#6591511yescharacteristic
807C22D5×#12111yescharacteristic
808C22#6594211yescharacteristic
809C22#6594311yescharacteristic
810C22#6594611yescharacteristic
811C22D5×C22⋊Q811yescharacteristic
812C22#6596311yescharacteristic
813C22#6596611yescharacteristic
814C22#6596711yescharacteristic
815C22#6601011yescharacteristic
816C22#6601111yescharacteristic
817C22D5×#12511yescharacteristic
818C22#6602311yescharacteristic
819C22#6605111yescharacteristic
820C22D5×C4⋊Q811yescharacteristic
821C22#6606111yescharacteristic
822C22#6606311yescharacteristic
823C4—44no—
824C4—42no—
825C4—42no—
826C4—82no—
827C4—108no—
828C4—104no—
829C4—202no—
830C4—202no—
831C4—402no—
832C4#6495618yescomplemented
833C2—108no—
834C2C2×#6495611yescharacteristic
835C2#1060549811yescharacteristic
836C2#1060549911yescharacteristic
837C2#1060561811yescharacteristic
838C2#1060561911yescharacteristic
839C2#1060589411yescharacteristic
840C2#1060605711yescharacteristic
841C2#1060772911yescharacteristic
842C2#1060773311yescharacteristic
843C2D5×#38911yescharacteristic
844C2#1060792611yescharacteristic
845C2#1060816211yescharacteristic
846C2#1060817011yescharacteristic
847C2#1060834511yescharacteristic
848C2#1060835211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D5
commutatorC23×C5C23×C4
FittingC5×C4⋊#95C2
socle, cosocleC24×C5C24
prime radicalC24×D5C23
hypercenterC4⋊#95D5
hypocenterC5#13907
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
3. C2×#65262C2semidirect
4. C2×#65217C2semidirect
7. C5×C4⋊#95C2semidirect
8. #10602356C2semidirect
10. #10600202C2semidirect
11. #10600202C2semidirect
28. C2×D5×C4⋊C4C4semidirect
124. C4⋊#95D5semidirect
225. C2×C4×D5C4⋊C4semidirect
233. C4⋊Dic5C22⋊C4semidirect
511. C2×D5#389semidirect
516. C4×C5#380semidirect
772. C5#13907semidirect
832. C4#64956semidirect

Maximal subgroups

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

subgroupindex
C22×D5×C4⋊C42
C2×#652762
C2×#652622
C2×#652172
C2×C4×#6852
C2×#649562
C5×C4⋊#952
#106023562
#106002182
#106002022
#139075