Finite Group Databasebeta

← #12022428

Subgroups — #12022428

Order 1280.

2106 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#4043C211yesmaximal, characteristic
2C2×C4×C5×C4⋊C4C211yesmaximal, characteristic, complemented
3C2×#65276C211yesmaximal, characteristic
4C2×#65263C211yesmaximal, characteristic, complemented
5C2×#65274C211yesmaximal, characteristic, complemented
6C2×#65218C211yesmaximal, characteristic, complemented
7C2×C4×#685C211yesmaximal, characteristic
8#10602330C212yesmaximal
9#10602328C212yesmaximal, complemented
10#10600220C212yesmaximal
11#10600215C212yesmaximal, complemented
12C23×C4×D5C2211yescharacteristic
13C23×Dic10C2211yescharacteristic
14C22×C5×C4⋊C4C2211yescharacteristic
15C22×C5×C4⋊C4C2211yescharacteristic
16C22×C42×C5C2212yes—
17C22×C42×C5C2211yescharacteristic
18C22×#685C2211yescharacteristic
19C22×#685C2212yes—
20C22×#685C2212yes—
21C22×#685C2211yescharacteristic
22C22×C4⋊Dic5C2211yescharacteristic
23C22×C4⋊Dic5C2212yes—
24C22×C4⋊Dic5C2212yes—
25C22×C4×Dic5C2211yescharacteristic
26C2×#4043—24no—
27C2×#4043—24no—
28C2×#4043C418yescomplemented
29C4×C5×C4⋊C4—24no—
30C2×C5×#95C2212yes—
31C2×#3963C2211yescharacteristic
32C2×#3963C2212yes—
33C2×#3963C2212yes—
34C2×#3963C2212yes—
35C2×#3963C2212yes—
36C2×#3963C2211yescharacteristic
37C2×#3963C2212yes—
38C2×#3963C2212yes—
39#65276—24no—
40#65274—24no—
41#65263—24no—
42C4×#685—24no—
43#65218—24no—
44#13997—51nomaximal, Sylow
45C24×D5C2311yescharacteristic
46C23×C4×C5C2311yescharacteristic
47C23×C4×C5C2312yes—
48C23×C4×C5C2312yes—
49C23×C4×C5C2311yescharacteristic
50C23×C4×C5C2311yescharacteristic
51C23×Dic5C2312yes—
52C23×Dic5C2311yescharacteristic
53C23×Dic5C2312yes—
54C23×Dic5C2311yescharacteristic
55C23×Dic5C2311yescharacteristic
56C22×C4×D5—22no—
57C22×C4×D5—22no—
58C22×C4×D5—22no—
59C22×C4×D5—22no—
60C22×C4×D5—22no—
61C22×C4×D5—22no—
62C22×C4×D5C2×C414yes—
63C22×Dic10—22no—
64C22×Dic10—22no—
65C22×Dic10—22no—
66C22×Dic10—22no—
67C22×Dic10—22no—
68C22×Dic10—22no—
69C22×Dic10C2×C414yes—
70C2×C5×C4⋊C4—22no—
71C2×C5×C4⋊C4—22no—
72C2×C5×C4⋊C4C2×C414yes—
73C2×C5×C4⋊C4D414yes—
74C2×C5×C4⋊C4D414yes—
75C2×C5×C4⋊C4D414yes—
76C2×C42×C5—22no—
77C2×C42×C5—22no—
78C2×C42×C5—24no—
79C2×C42×C5—24no—
80C2×C42×C5—42no—
81C2×C42×C5D414yes—
82C2×#685—22no—
83C2×#685—24no—
84C2×#685—24no—
85C2×#685—22no—
86C2×#685—22no—
87C2×#685—22no—
88C2×#685—22no—
89C2×#685—24no—
90C2×#685—24no—
91C2×#685—42no—
92C2×#685C2×C418yes—
93C2×#685Q814yescomplemented
94C2×C4⋊Dic5—24no—
95C2×C4⋊Dic5—24no—
96C2×C4⋊Dic5—22no—
97C2×C4⋊Dic5—24no—
98C2×C4⋊Dic5—22no—
99C2×C4⋊Dic5—22no—
100C2×C4⋊Dic5—24no—
101C2×C4⋊Dic5—42no—
102C2×C4⋊Dic5C2×C418yes—
103C2×C4×Dic5—22no—
104C2×C4×Dic5—22no—
105C2×C4×Dic5—22no—
106#4043—232no—
107C5×#95—24no—
108#3963—24no—
109#3963—24no—
110#3963—22no—
111#3963—22no—
112#3963—24no—
113#3963—24no—
114#3963—24no—
115#3963—24no—
116C22×C22⋊Q8—51no—
117C2×#391—51no—
118C2×#391—51no—
119C2×#389—51no—
120C2×#380—51no—
121C2×C4×C4⋊C4D511yescharacteristic, complemented
122C2×C4×C22⋊C4—51no—
123#1445—52no—
124#1439—52no—
125#1437—52no—
126C4⋊#95—52no—
127C24×C5C2411yescharacteristic
128C23×D5—21no—
129C23×D5—21no—
130C23×D5—21no—
131C23×D5—21no—
132C23×D5—21no—
133C23×D5—21no—
134C23×D5—21no—
135C23×D5—21no—
136C23×D5—21no—
137C23×D5—21no—
138C23×D5—21no—
139C23×D5—21no—
140C23×D5C22×C412yes—
141C23×D5C2×Q812yes—
142C23×D5#4112yes—
143C22×C4×C5—21no—
144C22×C4×C5—21no—
145C22×C4×C5—22no—
146C22×C4×C5—22no—
147C22×C4×C5—21no—
148C22×C4×C5—22no—
149C22×C4×C5—21no—
150C22×C4×C5—22no—
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—22no—
159C22×C4×C5—22no—
160C22×C4×C5—21no—
161C22×C4×C5—21no—
162C22×C4×C5—22no—
163C22×C4×C5C22×C414yes—
164C22×C4×C5C22×C412yes—
165C22×C4×C5C2×D412yes—
166C22×C4×C5C2×D414yes—
167C22×C4×C5C2×D414yes—
168C22×C4×C5C2×D412yes—
169C22×C4×C5C2×D412yes—
170C22×C4×C5C2×D412yes—
171C22×C4×C5C2×D412yes—
172C22×C4×C5C2×D414yes—
173C22×C4×C5C2×D412yes—
174C22×C4×C5C2×Q812yes—
175C22×C4×C5#4112yes—
176C22×C4×C5#4112yes—
177C22×C4×C5#4112yes—
178C22×Dic5—22no—
179C22×Dic5—22no—
180C22×Dic5—22no—
181C22×Dic5—22no—
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—22no—
193C22×Dic5—22no—
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—22no—
203C22×Dic5—22no—
204C22×Dic5—22no—
205C22×Dic5—22no—
206C22×Dic5—22no—
207C22×Dic5—22no—
208C22×Dic5—22no—
209C22×Dic5C22×C414yes—
210C22×Dic5C22×C412yes—
211C22×Dic5C2×Q812yes—
212C22×Dic5#4112yes—
213C2×C4×D5—28no—
214C2×C4×D5—28no—
215C2×C4×D5—28no—
216C2×C4×D5—44no—
217C2×C4×D5—44no—
218C2×C4×D5—44no—
219C2×C4×D5—44no—
220C2×Dic10—28no—
221C2×Dic10—28no—
222C2×Dic10—28no—
223C2×Dic10—44no—
224C2×Dic10—44no—
225C2×Dic10—44no—
226C2×Dic10—44no—
227C5×C4⋊C4—28no—
228C5×C4⋊C4C22⋊C4116yescomplemented
229C42×C5—28no—
230C42×C5—48no—
231#685—28no—
232#685—216no—
233#685—28no—
234#685—48no—
235C4⋊Dic5—216no—
236C4⋊Dic5—48no—
237C4⋊Dic5—44no—
238C4×Dic5—44no—
239C23×Q8—51no—
240C24×C4—51no—
241C2×C22⋊Q8—58no—
242C2×C22⋊Q8—104no—
243C2×C22⋊Q8—104no—
244C22×C4⋊C4—52no—
245C22×C4⋊C4—51no—
246C22×C4⋊C4—52no—
247C22×C4⋊C4C2×D511yescharacteristic
248C22×C4⋊C4C2×D511yescharacteristic
249C22×C22⋊C4—52no—
250C22×C22⋊C4—51no—
251C22×C22⋊C4—51no—
252C22×C22⋊C4—52no—
253C22×C42—51no—
254C22×C42C2×D512yes—
255C22×C42C2×D511yescharacteristic
256#391—104no—
257#391—104no—
258#389—104no—
259#380—104no—
260C4×C4⋊C4—24no—
261C4×C22⋊C4—104no—
262C2×#95—51no—
263C2×#95—52no—
264C2×#95—52no—
265C2×#95—52no—
266C2×#95—52no—
267C2×#95—52no—
268C2×#95—52no—
269C2×#95—51no—
270C2×#95C2×D512yes—
271C23×C5C23×C411yescharacteristic
272C23×C5C22×D411yescharacteristic
273C23×C5C22×D411yescharacteristic
274C23×C5C22×D411yescharacteristic
275C23×C5C22×D411yescharacteristic
276C23×C5C22×Q811yescharacteristic
277C23×C5C2×#4111yescharacteristic
278C23×C5C2×#4111yescharacteristic
279C23×C5C2×#4111yescharacteristic
280C23×C5C2×#4111yescharacteristic
281C23×C5C2×#4111yescharacteristic
282C23×C5H(5,𝔽2)11yescharacteristic
283C23×C52−1+411yescharacteristic
284C23×C52−1+411yescharacteristic
285C23×C52−1+411yescharacteristic
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—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—41no—
318C22×D5—41no—
319C22×D5—41no—
320C22×D5C4×Q814yes—
321C2×C4×C5—24no—
322C2×C4×C5—24no—
323C2×C4×C5—22no—
324C2×C4×C5—22no—
325C2×C4×C5—24no—
326C2×C4×C5—22no—
327C2×C4×C5—24no—
328C2×C4×C5—24no—
329C2×C4×C5—24no—
330C2×C4×C5—22no—
331C2×C4×C5—22no—
332C2×C4×C5—22no—
333C2×C4×C5—22no—
334C2×C4×C5—24no—
335C2×C4×C5—22no—
336C2×C4×C5—22no—
337C2×C4×C5—24no—
338C2×C4×C5—24no—
339C2×C4×C5—42no—
340C2×C4×C5—42no—
341C2×C4×C5—42no—
342C2×C4×C5—41no—
343C2×C4×C5—41no—
344C2×C4×C5—42no—
345C2×C4×C5—41no—
346C2×C4×C5—41no—
347C2×C4×C5C2×C22⋊C418yes—
348C2×C4×C5C2×C22⋊C414yes—
349C2×C4×C5C4×D414yes—
350C2×C4×C5C4×D414yes—
351C2×C4×C5#12114yes—
352C2×C4×C5#12114yes—
353C2×C4×C5C22⋊Q814yescomplemented
354C2×C4×C5#12414yes—
355C2×C4×C5#12714yes—
356C2×Dic5—22no—
357C2×Dic5—24no—
358C2×Dic5—24no—
359C2×Dic5—24no—
360C2×Dic5—22no—
361C2×Dic5—22no—
362C2×Dic5—22no—
363C2×Dic5—22no—
364C2×Dic5—22no—
365C2×Dic5—22no—
366C2×Dic5—22no—
367C2×Dic5—22no—
368C2×Dic5—42no—
369C2×Dic5—42no—
370C2×Dic5—41no—
371C2×Dic5—41no—
372C2×Dic5—42no—
373C2×Dic5—41no—
374C2×Dic5—41no—
375C2×Dic5—41no—
376C2×Dic5—42no—
377C2×Dic5—41no—
378C2×Dic5—41no—
379C2×Dic5—41no—
380C2×Dic5—41no—
381C2×Dic5—41no—
382C2×Dic5—41no—
383C2×Dic5—41no—
384C2×Dic5—42no—
385C2×Dic5—42no—
386C2×Dic5—42no—
387C2×Dic5—42no—
388C2×Dic5—42no—
389C2×Dic5—42no—
390C2×Dic5—42no—
391C4×D5—416no—
392Dic10—416no—
393C25—51no—
394C22×Q8—54no—
395C22×Q8—102no—
396C22×Q8—102no—
397C22×Q8—102no—
398C22×Q8—102no—
399C22×Q8—102no—
400C22×Q8—102no—
401C23×C4—51no—
402C23×C4—52no—
403C23×C4—51no—
404C23×C4—51no—
405C23×C4—54no—
406C23×C4—52no—
407C23×C4—102no—
408C23×C4—102no—
409C23×C4—102no—
410C23×C4—102no—
411C23×C4—102no—
412C23×C4—102no—
413C23×C4C22×D512yes—
414C23×C4C22×D511yescharacteristic
415C23×C4C22×D512yes—
416C23×C4C22×D511yescharacteristic
417C23×C4C22×D511yescharacteristic
418C22⋊Q8—1032no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—22no—
421C2×C4⋊C4—58no—
422C2×C4⋊C4—104no—
423C2×C4⋊C4—104no—
424C2×C4⋊C4—104no—
425C2×C4⋊C4—102no—
426C2×C4⋊C4—104no—
427C2×C4⋊C4—102no—
428C2×C4⋊C4—102no—
429C2×C4⋊C4—202no—
430C2×C4⋊C4C4×D514yes—
431C2×C4⋊C4D2014yes—
432C2×C4⋊C4D2014yes—
433C2×C4⋊C4C22⋊D514yes—
434C2×C22⋊C4—58no—
435C2×C22⋊C4—54no—
436C2×C22⋊C4—102no—
437C2×C22⋊C4—102no—
438C2×C22⋊C4—104no—
439C2×C22⋊C4—102no—
440C2×C22⋊C4—102no—
441C2×C22⋊C4—102no—
442C2×C22⋊C4—104no—
443C2×C22⋊C4—104no—
444C2×C22⋊C4—104no—
445C2×C22⋊C4—202no—
446C2×C42—22no—
447C2×C42—22no—
448C2×C42—24no—
449C2×C42—24no—
450C2×C42—42no—
451C2×C42—102no—
452C2×C42—102no—
453C2×C42—102no—
454C2×C42D2014yes—
455#95—24no—
456#95—102no—
457#95—102no—
458#95—104no—
459#95—104no—
460#95—104no—
461#95—104no—
462#95—104no—
463#95—104no—
464C22×C5C22×C22⋊C411yescharacteristic
465C22×C5C2×C4×D411yescharacteristic
466C22×C5C2×C4×D411yescharacteristic
467C22×C5C2×C4×Q811yescharacteristic
468C22×C5C4×#4111yescharacteristic
469C22×C5#51911yescharacteristic
470C22×C5#52011yescharacteristic
471C22×C5C2×#12111yescharacteristic
472C22×C5C2×#12111yescharacteristic
473C22×C5C2×C22⋊Q811yescharacteristic
474C22×C5#52511yescharacteristic
475C22×C5C2×#12411yescharacteristic
476C22×C5#52911yescharacteristic
477C22×C5C2×#12711yescharacteristic
478C22×C5#53311yescharacteristic
479C22×C5#53611yescharacteristic
480C22×C5#53711yescharacteristic
481C22×C5#54111yescharacteristic
482C22×C5#54211yescharacteristic
483C22×C5#54611yescharacteristic
484C22×C5#54611yescharacteristic
485C22×C5#54611yescharacteristic
486C22×C5#54711yescharacteristic
487C22×C5#54711yescharacteristic
488C22×C5#54711yescharacteristic
489C22×C5#54811yescharacteristic
490C22×C5#54811yescharacteristic
491C22×C5#54811yescharacteristic
492C22×C5D4×Q811yescharacteristic
493C22×C5D4×Q811yescharacteristic
494C22×C5D4×Q811yescharacteristic
495C22×C5#55211yescharacteristic
496C22×C5#55211yescharacteristic
497C22×C5#55411yescharacteristic
498C22×C5#55611yescharacteristic
499C2×D5—24no—
500C2×D5—24no—
501C2×D5—24no—
502C2×D5—42no—
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—
514C4×C5—28no—
515C4×C5—24no—
516C4×C5—42no—
517C4×C5—44no—
518C4×C5#39018yes—
519Dic5—42no—
520Dic5—42no—
521Dic5—44no—
522Dic5—42no—
523Dic5—82no—
524C24—52no—
525C24—52no—
526C24—52no—
527C24—101no—
528C24—101no—
529C24—101no—
530C24—101no—
531C24—101no—
532C24—101no—
533C24—101no—
534C24—101no—
535C24—101no—
536C24—101no—
537C24—101no—
538C24—101no—
539C24C23×D511yescharacteristic
540C2×Q8—108no—
541C2×Q8—108no—
542C2×Q8—108no—
543C2×Q8—204no—
544C2×Q8—204no—
545C2×Q8—204no—
546C2×Q8—204no—
547C22×C4—21no—
548C22×C4—22no—
549C22×C4—21no—
550C22×C4—22no—
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—21no—
560C22×C4—21no—
561C22×C4—22no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—22no—
565C22×C4—21no—
566C22×C4—22no—
567C22×C4—54no—
568C22×C4—52no—
569C22×C4—52no—
570C22×C4—52no—
571C22×C4—101no—
572C22×C4—101no—
573C22×C4—101no—
574C22×C4—101no—
575C22×C4—101no—
576C22×C4—102no—
577C22×C4—102no—
578C22×C4—101no—
579C22×C4—101no—
580C22×C4—101no—
581C22×C4—102no—
582C22×C4—101no—
583C22×C4—101no—
584C22×C4—101no—
585C22×C4—102no—
586C22×C4—102no—
587C22×C4—101no—
588C22×C4—101no—
589C22×C4—101no—
590C22×C4—101no—
591C22×C4—101no—
592C22×C4—101no—
593C22×C4—102no—
594C22×C4—101no—
595C22×C4—108no—
596C22×C4—108no—
597C22×C4—108no—
598C22×C4—102no—
599C22×C4—102no—
600C22×C4—102no—
601C22×C4—102no—
602C22×C4—102no—
603C22×C4—102no—
604C22×C4—102no—
605C22×C4—204no—
606C22×C4—204no—
607C22×C4—204no—
608C22×C4—204no—
609C22×C4C2×C4×D514yes—
610C22×C4C2×C4×D512yes—
611C22×C4C2×D2012yes—
612C22×C4C2×D2014yes—
613C22×C4C2×D2012yes—
614C22×C4C2×D2014yes—
615C22×C4C2×D2012yes—
616C22×C4C2×D2012yes—
617C22×C4C2×D2012yes—
618C22×C4#70912yes—
619C22×C4#70912yes—
620C22×C4#71112yes—
621C22×C4Q8×D512yes—
622C22×C4C2×C22⋊D514yes—
623C22×C4C2×C22⋊D512yes—
624C4⋊C4—28no—
625C4⋊C4—1016no—
626C4⋊C4—208no—
627C4⋊C4—204no—
628C4⋊C4#685116yescomplemented
629C22⋊C4—108no—
630C22⋊C4—108no—
631C22⋊C4—1016no—
632C22⋊C4—208no—
633C42—28no—
634C42—48no—
635C42—204no—
636C2×C5C2×#39011yescharacteristic
637C2×C5C4×C22⋊Q811yescharacteristic
638C2×C5#232311yescharacteristic
639C2×C5#233911yescharacteristic
640C2×C5Q8×C22⋊C411yescharacteristic
641C2×C5#236011yescharacteristic
642C2×C5#236211yescharacteristic
643C2×C5#241511yescharacteristic
644C2×C5#241711yescharacteristic
645C2×C5#242711yescharacteristic
646C2×C5#242911yescharacteristic
647C2×C5#248911yescharacteristic
648C2×C5#249211yescharacteristic
649C2×C5#254011yescharacteristic
650C2×C5#254211yescharacteristic
651D5—44no—
652C23—54no—
653C23—102no—
654C23—102no—
655C23—102no—
656C23—102no—
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—201no—
672C23—201no—
673C23—201no—
674C23—201no—
675C23—201no—
676C23—201no—
677C23—201no—
678C23—201no—
679C23—201no—
680C23—201no—
681C23—201no—
682C23—201no—
683C23—201no—
684C23—201no—
685C23—201no—
686C23—201no—
687C23C22×C4×D511yescharacteristic
688C23C22×D2011yescharacteristic
689C23C22×D2011yescharacteristic
690C23C22×D2011yescharacteristic
691C23C2×#70911yescharacteristic
692C23C2×#70911yescharacteristic
693C23C2×#71111yescharacteristic
694C23#414411yescharacteristic
695C23C2×Q8×D511yescharacteristic
696C23#414711yescharacteristic
697C23D5×#4111yescharacteristic
698C23D5×#4111yescharacteristic
699C23#415011yescharacteristic
700C23#415011yescharacteristic
701C23C22×C22⋊D511yescharacteristic
702Q8—2016no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—22no—
710C2×C4—24no—
711C2×C4—24no—
712C2×C4—24no—
713C2×C4—22no—
714C2×C4—24no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—24no—
719C2×C4—24no—
720C2×C4—24no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—41no—
727C2×C4—42no—
728C2×C4—41no—
729C2×C4—102no—
730C2×C4—102no—
731C2×C4—104no—
732C2×C4—104no—
733C2×C4—102no—
734C2×C4—102no—
735C2×C4—104no—
736C2×C4—102no—
737C2×C4—102no—
738C2×C4—102no—
739C2×C4—102no—
740C2×C4—102no—
741C2×C4—201no—
742C2×C4—201no—
743C2×C4—201no—
744C2×C4—202no—
745C2×C4—201no—
746C2×C4—202no—
747C2×C4—201no—
748C2×C4—201no—
749C2×C4—201no—
750C2×C4—201no—
751C2×C4—202no—
752C2×C4—202no—
753C2×C4—201no—
754C2×C4—201no—
755C2×C4—201no—
756C2×C4—201no—
757C2×C4—2016no—
758C2×C4—202no—
759C2×C4—202no—
760C2×C4—202no—
761C2×C4—202no—
762C2×C4—202no—
763C2×C4—202no—
764C2×C4—202no—
765C2×C4C4×D2014yes—
766C2×C4C4×D2014yes—
767C2×C4#402014yes—
768C2×C4#402114yes—
769C2×C4#404314yescomplemented
770C2×C4C2×#68518yes—
771C2×C4C2×#68514yes—
772C2×C4#407614yes—
773C2×C4#407614yes—
774C5#1399711yescharacteristic, complemented, Sylow
775C22—104no—
776C22—104no—
777C22—104no—
778C22—202no—
779C22—202no—
780C22—202no—
781C22—202no—
782C22—202no—
783C22—202no—
784C22—202no—
785C22—202no—
786C22—202no—
787C22—202no—
788C22—202no—
789C22—202no—
790C22C2×C4×D2011yescharacteristic
791C22C2×C4×D2011yescharacteristic
792C22C2×#402011yescharacteristic
793C22C2×#402111yescharacteristic
794C22C2×#404311yescharacteristic
795C22#6584411yescharacteristic
796C22#6584511yescharacteristic
797C22#6584711yescharacteristic
798C22#6585811yescharacteristic
799C22#6586011yescharacteristic
800C22#6586311yescharacteristic
801C22#6586711yescharacteristic
802C22C4×#71111yescharacteristic
803C22#6588011yescharacteristic
804C22#6588811yescharacteristic
805C22#6588811yescharacteristic
806C22#6588911yescharacteristic
807C22#6588911yescharacteristic
808C22#6589111yescharacteristic
809C22#6589511yescharacteristic
810C22C4×Q8×D511yescharacteristic
811C22#6590611yescharacteristic
812C22Q8×D2011yescharacteristic
813C22Q8×D2011yescharacteristic
814C22#6591011yescharacteristic
815C22#6591011yescharacteristic
816C22#6591211yescharacteristic
817C22#6591711yescharacteristic
818C22C22×#68511yescharacteristic
819C22C2×#407611yescharacteristic
820C22C2×#407611yescharacteristic
821C22#6614011yescharacteristic
822C22Q8×C22⋊D511yescharacteristic
823C22#6615811yescharacteristic
824C22#6616511yescharacteristic
825C4—28no—
826C4—24no—
827C4—44no—
828C4—42no—
829C4—202no—
830C4—204no—
831C4—202no—
832C4—202no—
833C4—402no—
834C4#6522818yes—
835C2—204no—
836C2#1060537811yescharacteristic
837C2C4×#404311yescharacteristic
838C2#1060549311yescharacteristic
839C2#1060550411yescharacteristic
840C2#1060551711yescharacteristic
841C2#1060552011yescharacteristic
842C2#1060552911yescharacteristic
843C2#1060553111yescharacteristic
844C2C2×#6522811yescharacteristic
845C2#1061392511yescharacteristic
846C2#1061400811yescharacteristic
847C2#1061406111yescharacteristic
848C2#1061413911yescharacteristic
849C2Q8×#68511yescharacteristic
850C2#1061422711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D5
commutatorC23×C5C23×C4
FittingC2×C4×C5×C4⋊C4C2
socle, cosocleC24×C5C24
prime radicalC24×D5C23
hypercenterC2×C4×C4⋊C4D5
hypocenterC5#13997
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C4×C5×C4⋊C4C2semidirect
4. C2×#65263C2semidirect
5. C2×#65274C2semidirect
6. C2×#65218C2semidirect
9. #10602328C2semidirect
11. #10600215C2semidirect
28. C2×#4043C4semidirect
93. C2×#685Q8semidirect
121. C2×C4×C4⋊C4D5semidirect
228. C5×C4⋊C4C22⋊C4semidirect
353. C2×C4×C5C22⋊Q8semidirect
628. C4⋊C4#685semidirect
769. C2×C4#4043semidirect
774. C5#13997semidirect

Maximal subgroups

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

subgroupindex
C22×#40432
C2×C4×C5×C4⋊C42
C2×#652762
C2×#652632
C2×#652742
C2×#652182
C2×C4×#6852
#106023302
#106023282
#106002202
#106002152
#139975