Finite Group Databasebeta

← #12022697

Subgroups — #12022697

Order 1280.

2474 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D20C211yesmaximal, characteristic
2C2×C4×C5×C4⋊C4C211yesmaximal, characteristic, complemented
3C2×#65278C212yesmaximal, complemented
4C2×#65228C211yesmaximal, characteristic
5C2×#65228C211yesmaximal, characteristic
6C2×#65217C211yesmaximal, characteristic, complemented
7#10602363C212yesmaximal, complemented
8#10602328C211yesmaximal, characteristic, complemented
9#10602328C211yesmaximal, characteristic, complemented
10#10600221C212yesmaximal, complemented
11#10600218C212yesmaximal, complemented
12C23×D20C2211yescharacteristic
13C23×C4×D5C2212yes—
14C22×C5×C4⋊C4C2211yescharacteristic
15C22×C5×C4⋊C4C2211yescharacteristic
16C22×C42×C5C2211yescharacteristic
17C22×C42×C5C2211yescharacteristic
18C22×C42×C5C2211yescharacteristic
19C22×#685C2212yes—
20C22×#685C2212yes—
21C22×#685C2212yes—
22C22×#685C2212yes—
23C22×#685C2212yes—
24C22×C4⋊Dic5C2211yescharacteristic
25C22×C4⋊Dic5C2211yescharacteristic
26C22×C4⋊Dic5C2211yescharacteristic
27C22×#683C2212yes—
28C2×C4×D20—24no—
29C2×C4×D20—24no—
30C2×C4×D20—24no—
31C4×C5×C4⋊C4—24no—
32C2×C5×#95C2211yescharacteristic
33C2×C5×#95C2211yescharacteristic
34C2×#3963C2212yes—
35C2×#3963C2212yes—
36C2×#3963C2212yes—
37C2×#3963C2212yes—
38C2×#3963C2212yes—
39#65278—28no—
40#65228—24no—
41#65228C418yescomplemented
42#65217—24no—
43#14018—51nomaximal, Sylow
44C24×D5C2312yes—
45C23×C4×C5C2311yescharacteristic
46C23×C4×C5C2311yescharacteristic
47C23×C4×C5C2311yescharacteristic
48C23×C4×C5C2311yescharacteristic
49C23×C4×C5C2311yescharacteristic
50C23×C4×C5C2311yescharacteristic
51C23×C4×C5C2311yescharacteristic
52C23×Dic5C2312yes—
53C23×Dic5C2312yes—
54C23×Dic5C2312yes—
55C22×D20—22no—
56C22×D20—22no—
57C22×D20—22no—
58C22×D20—22no—
59C22×D20C2×C414yes—
60C22×D20D414yes—
61C22×D20Q814yes—
62C22×C4×D5—24no—
63C22×C4×D5—24no—
64C22×C4×D5—24no—
65C22×C4×D5—24no—
66C22×C4×D5—24no—
67C22×C4×D5—42no—
68C22×C4×D5—42no—
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⋊C4D414yescomplemented
75C2×C42×C5—22no—
76C2×C42×C5—22no—
77C2×C42×C5—22no—
78C2×C42×C5—22no—
79C2×C42×C5—22no—
80C2×C42×C5—22no—
81C2×C42×C5—22no—
82C2×C42×C5C2×C414yescomplemented
83C2×C42×C5D414yes—
84C2×#685—24no—
85C2×#685—24no—
86C2×#685—24no—
87C2×#685—24no—
88C2×#685—24no—
89C2×#685—24no—
90C2×#685—24no—
91C2×#685—24no—
92C2×#685—24no—
93C2×#685—42no—
94C2×#685—42no—
95C2×#685—42no—
96C2×#685—42no—
97C2×#685C2×C418yescomplemented
98C2×#685C2×C418yescomplemented
99C2×C4⋊Dic5—22no—
100C2×C4⋊Dic5—22no—
101C2×C4⋊Dic5—22no—
102C2×C4⋊Dic5—22no—
103C2×C4⋊Dic5—22no—
104C2×C4⋊Dic5—22no—
105C2×C4⋊Dic5—22no—
106C2×C4⋊Dic5C2×C414yescomplemented
107C2×C4⋊Dic5D414yes—
108C2×#683—24no—
109C2×#683—24no—
110C2×#683—42no—
111C4×D20—232no—
112C5×#95—22no—
113C5×#95—22no—
114#3963—24no—
115#3963—24no—
116#3963—24no—
117#3963—42no—
118#3963—42no—
119C22×C4×D4—51no—
120C2×#390—51no—
121C2×#390—51no—
122C2×#389—51no—
123C2×#385—52no—
124C2×C4×C4⋊C4D511yescharacteristic, complemented
125#1439—52no—
126#1439—52no—
127C4⋊#95—51no—
128C4⋊#95—51no—
129C22⋊#95—52no—
130C24×C5C2411yescharacteristic
131C23×D5—22no—
132C23×D5—22no—
133C23×D5—22no—
134C23×D5—22no—
135C23×D5—22no—
136C23×D5—22no—
137C23×D5—22no—
138C23×D5—22no—
139C23×D5—22no—
140C23×D5—22no—
141C23×D5—22no—
142C23×D5—22no—
143C23×D5C22×C414yes—
144C23×D5C2×D414yes—
145C23×D5C2×Q814yes—
146C22×C4×C5—21no—
147C22×C4×C5—21no—
148C22×C4×C5—21no—
149C22×C4×C5—21no—
150C22×C4×C5—21no—
151C22×C4×C5—21no—
152C22×C4×C5—21no—
153C22×C4×C5—21no—
154C22×C4×C5—21no—
155C22×C4×C5—21no—
156C22×C4×C5—21no—
157C22×C4×C5—21no—
158C22×C4×C5—21no—
159C22×C4×C5—21no—
160C22×C4×C5—21no—
161C22×C4×C5—21no—
162C22×C4×C5—21no—
163C22×C4×C5—21no—
164C22×C4×C5—21no—
165C22×C4×C5—21no—
166C22×C4×C5—21no—
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×C5C22×C412yes—
179C22×C4×C5C22×C412yes—
180C22×C4×C5C22×C412yes—
181C22×C4×C5C2×D412yes—
182C22×C4×C5C2×D412yes—
183C22×C4×C5C2×D412yes—
184C22×C4×C5C2×D412yes—
185C22×C4×C5C2×D412yes—
186C22×C4×C5C2×D412yes—
187C22×C4×C5C2×D412yes—
188C22×C4×C5C2×D412yes—
189C22×C4×C5C2×Q812yes—
190C22×C4×C5#4112yes—
191C22×C4×C5#4112yes—
192C22×C4×C5#4112yes—
193C22×C4×C5#4112yes—
194C22×C4×C5#4112yes—
195C22×Dic5—22no—
196C22×Dic5—22no—
197C22×Dic5—22no—
198C22×Dic5—22no—
199C22×Dic5—22no—
200C22×Dic5—22no—
201C22×Dic5—22no—
202C22×Dic5—22no—
203C22×Dic5—22no—
204C22×Dic5—22no—
205C22×Dic5—22no—
206C22×Dic5—22no—
207C22×Dic5—22no—
208C22×Dic5—22no—
209C22×Dic5—22no—
210C22×Dic5—22no—
211C22×Dic5—22no—
212C22×Dic5—22no—
213C22×Dic5—22no—
214C22×Dic5C22×C414yes—
215C22×Dic5C2×D414yes—
216C2×D20—28no—
217C2×D20—28no—
218C2×D20—28no—
219C2×D20—28no—
220C2×D20—28no—
221C2×D20—28no—
222C2×D20C4⋊C4116yescomplemented
223C2×C4×D5—216no—
224C2×C4×D5—48no—
225C2×C4×D5—48no—
226C2×C4×D5—48no—
227C2×C4×D5—48no—
228C2×C4×D5—48no—
229C2×C4×D5—48no—
230C5×C4⋊C4—28no—
231C5×C4⋊C4—28no—
232C42×C5—28no—
233C42×C5—28no—
234C42×C5—44no—
235#685—216no—
236#685—216no—
237#685—48no—
238#685—48no—
239#685—48no—
240C4⋊Dic5—28no—
241C4⋊Dic5—28no—
242C4⋊Dic5—44no—
243#683—48no—
244C23×D4—51no—
245C24×C4—52no—
246C2×C4×D4—104no—
247C2×C4×D4—104no—
248C2×C4×D4—104no—
249C22×C4⋊C4—51no—
250C22×C4⋊C4—51no—
251C22×C4⋊C4—51no—
252C22×C4⋊C4—52no—
253C22×C4⋊C4C2×D511yescharacteristic
254C22×C4⋊C4C2×D511yescharacteristic
255C22×C22⋊C4—52no—
256C22×C22⋊C4—52no—
257C22×C22⋊C4—52no—
258C22×C22⋊C4—52no—
259C22×C22⋊C4—52no—
260C22×C42C2×D511yescharacteristic
261C22×C42C2×D511yescharacteristic
262C22×C42C2×D511yescharacteristic
263#390—58no—
264#390—104no—
265#389—104no—
266#385—108no—
267C4×C4⋊C4—24no—
268C2×#95—52no—
269C2×#95—52no—
270C2×#95—52no—
271C2×#95—52no—
272C2×#95—52no—
273C2×#95C2×D511yescharacteristic
274C2×#95C2×D511yescharacteristic
275C23×C5C23×C411yescharacteristic
276C23×C5C22×D411yescharacteristic
277C23×C5C22×D411yescharacteristic
278C23×C5C22×D411yescharacteristic
279C23×C5C22×D411yescharacteristic
280C23×C5C22×Q811yescharacteristic
281C23×C5C2×#4111yescharacteristic
282C23×C5C2×#4111yescharacteristic
283C23×C5C2×#4111yescharacteristic
284C23×C5C2×#4111yescharacteristic
285C23×C5C2×#4111yescharacteristic
286C23×C5H(5,𝔽2)11yescharacteristic
287C23×C5H(5,𝔽2)11yescharacteristic
288C23×C5H(5,𝔽2)11yescharacteristic
289C23×C52−1+411yescharacteristic
290C22×D5—24no—
291C22×D5—24no—
292C22×D5—24no—
293C22×D5—24no—
294C22×D5—24no—
295C22×D5—24no—
296C22×D5—24no—
297C22×D5—24no—
298C22×D5—24no—
299C22×D5—24no—
300C22×D5—24no—
301C22×D5—24no—
302C22×D5—24no—
303C22×D5—24no—
304C22×D5—24no—
305C22×D5—24no—
306C22×D5—24no—
307C22×D5—24no—
308C22×D5—42no—
309C22×D5—42no—
310C22×D5—42no—
311C22×D5—42no—
312C22×D5—42no—
313C22×D5—42no—
314C22×D5—42no—
315C22×D5—42no—
316C22×D5—42no—
317C22×D5—42no—
318C22×D5—42no—
319C22×D5—42no—
320C22×D5—42no—
321C22×D5—42no—
322C22×D5—42no—
323C22×D5—42no—
324C22×D5C2×C4⋊C418yes—
325C2×C4×C5—22no—
326C2×C4×C5—22no—
327C2×C4×C5—22no—
328C2×C4×C5—22no—
329C2×C4×C5—22no—
330C2×C4×C5—22no—
331C2×C4×C5—22no—
332C2×C4×C5—22no—
333C2×C4×C5—22no—
334C2×C4×C5—22no—
335C2×C4×C5—22no—
336C2×C4×C5—22no—
337C2×C4×C5—22no—
338C2×C4×C5—22no—
339C2×C4×C5—22no—
340C2×C4×C5—22no—
341C2×C4×C5—22no—
342C2×C4×C5—22no—
343C2×C4×C5—22no—
344C2×C4×C5—22no—
345C2×C4×C5—22no—
346C2×C4×C5—22no—
347C2×C4×C5—22no—
348C2×C4×C5—22no—
349C2×C4×C5—41no—
350C2×C4×C5—41no—
351C2×C4×C5—41no—
352C2×C4×C5—41no—
353C2×C4×C5—41no—
354C2×C4×C5—41no—
355C2×C4×C5—41no—
356C2×C4×C5—41no—
357C2×C4×C5—41no—
358C2×C4×C5—41no—
359C2×C4×C5—41no—
360C2×C4×C5—41no—
361C2×C4×C5—41no—
362C2×C4×C5—41no—
363C2×C4×C5—41no—
364C2×C4×C5—41no—
365C2×C4×C5C2×C4⋊C414yes—
366C2×C4×C5C4×D414yes—
367C2×C4×C5C4×D414yes—
368C2×C4×C5C4×D414yescomplemented
369C2×C4×C5#12014yes—
370C2×C4×C5#12114yes—
371C2×C4×C5C22⋊Q814yes—
372C2×C4×C5C22⋊Q814yes—
373C2×C4×C5#12314yes—
374C2×Dic5—24no—
375C2×Dic5—24no—
376C2×Dic5—24no—
377C2×Dic5—24no—
378C2×Dic5—24no—
379C2×Dic5—24no—
380C2×Dic5—42no—
381C2×Dic5—42no—
382C2×Dic5—42no—
383C2×Dic5—42no—
384C2×Dic5—42no—
385C2×Dic5—42no—
386C2×Dic5—42no—
387C2×Dic5—42no—
388C2×Dic5—42no—
389C2×Dic5—42no—
390C2×Dic5—42no—
391C2×Dic5—42no—
392C2×Dic5—42no—
393C2×Dic5—42no—
394C2×Dic5—42no—
395D20—232no—
396C4×D5—432no—
397C25—52no—
398C22×D4—54no—
399C22×D4—54no—
400C22×D4—54no—
401C22×D4—102no—
402C22×D4—102no—
403C22×D4—102no—
404C22×D4—102no—
405C23×C4—52no—
406C23×C4—52no—
407C23×C4—52no—
408C23×C4—104no—
409C23×C4—104no—
410C23×C4—104no—
411C23×C4—104no—
412C23×C4—104no—
413C23×C4—202no—
414C23×C4—202no—
415C23×C4C22×D511yescharacteristic
416C23×C4C22×D511yescharacteristic
417C23×C4C22×D511yescharacteristic
418C23×C4C22×D511yescharacteristic
419C23×C4C22×D511yescharacteristic
420C23×C4C22×D511yescharacteristic
421C23×C4C22×D511yescharacteristic
422C4×D4—1032no—
423C2×C4⋊C4—22no—
424C2×C4⋊C4—22no—
425C2×C4⋊C4—22no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—22no—
428C2×C4⋊C4—54no—
429C2×C4⋊C4—54no—
430C2×C4⋊C4—102no—
431C2×C4⋊C4—102no—
432C2×C4⋊C4—102no—
433C2×C4⋊C4—102no—
434C2×C4⋊C4—104no—
435C2×C4⋊C4—104no—
436C2×C4⋊C4—102no—
437C2×C4⋊C4—102no—
438C2×C4⋊C4—102no—
439C2×C4⋊C4—202no—
440C2×C4⋊C4D2014yescomplemented
441C2×C22⋊C4—58no—
442C2×C22⋊C4—58no—
443C2×C22⋊C4—104no—
444C2×C22⋊C4—104no—
445C2×C22⋊C4—104no—
446C2×C22⋊C4—104no—
447C2×C22⋊C4—104no—
448C2×C22⋊C4—104no—
449C2×C22⋊C4—104no—
450C2×C22⋊C4—104no—
451C2×C22⋊C4—104no—
452C2×C22⋊C4—202no—
453C2×C22⋊C4—202no—
454C2×C22⋊C4—202no—
455C2×C22⋊C4—202no—
456C2×C42—22no—
457C2×C42—22no—
458C2×C42—22no—
459C2×C42—22no—
460C2×C42—22no—
461C2×C42—22no—
462C2×C42—22no—
463C2×C42C4×D514yescomplemented
464C2×C42C22⋊D514yes—
465#95—22no—
466#95—22no—
467#95—104no—
468#95—104no—
469#95—104no—
470#95—202no—
471#95—202no—
472C22×C5C22×C4⋊C411yescharacteristic
473C22×C5C2×C4×D411yescharacteristic
474C22×C5C2×C4×D411yescharacteristic
475C22×C5C2×C4×D411yescharacteristic
476C22×C5C4×#4111yescharacteristic
477C22×C5#51811yescharacteristic
478C22×C5#52011yescharacteristic
479C22×C5C2×#12011yescharacteristic
480C22×C5C2×#12111yescharacteristic
481C22×C5C2×C22⋊Q811yescharacteristic
482C22×C5C2×C22⋊Q811yescharacteristic
483C22×C5C2×#12311yescharacteristic
484C22×C5#52511yescharacteristic
485C22×C5#52911yescharacteristic
486C22×C5#53211yescharacteristic
487C22×C5#53511yescharacteristic
488C22×C5#53711yescharacteristic
489C22×C5#54011yescharacteristic
490C22×C5#54211yescharacteristic
491C22×C5D4211yescharacteristic
492C22×C5D4211yescharacteristic
493C22×C5#54611yescharacteristic
494C22×C5#54611yescharacteristic
495C22×C5#54611yescharacteristic
496C22×C5#54711yescharacteristic
497C22×C5#54811yescharacteristic
498C22×C5D4×Q811yescharacteristic
499C22×C5#55011yescharacteristic
500C22×C5#55011yescharacteristic
501C22×C5#55411yescharacteristic
502C22×C5#55411yescharacteristic
503C22×C5#55411yescharacteristic
504C22×C5#55611yescharacteristic
505C22×C5#55911yescharacteristic
506C22×C5#55911yescharacteristic
507C2×D5—28no—
508C2×D5—28no—
509C2×D5—28no—
510C2×D5—44no—
511C2×D5—44no—
512C2×D5—44no—
513C2×D5—44no—
514C2×D5—44no—
515C2×D5—44no—
516C2×D5—44no—
517C2×D5—44no—
518C2×D5—44no—
519C2×D5—44no—
520C2×D5—44no—
521C2×D5—44no—
522C4×C5—24no—
523C4×C5—24no—
524C4×C5—42no—
525C4×C5—42no—
526C4×C5—42no—
527C4×C5—42no—
528C4×C5#38518yescomplemented
529Dic5—44no—
530Dic5—44no—
531Dic5—82no—
532C24—54no—
533C24—54no—
534C24—54no—
535C24—102no—
536C24—102no—
537C24—102no—
538C24—102no—
539C24—102no—
540C24—102no—
541C24—102no—
542C24—102no—
543C24—102no—
544C24—102no—
545C24—102no—
546C24—102no—
547C24C23×D511yescharacteristic
548C2×D4—516no—
549C2×D4—108no—
550C2×D4—108no—
551C2×D4—108no—
552C2×D4—108no—
553C2×D4—108no—
554C2×D4—108no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—54no—
588C22×C4—54no—
589C22×C4—1016no—
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—208no—
610C22×C4—208no—
611C22×C4—208no—
612C22×C4—208no—
613C22×C4—208no—
614C22×C4—208no—
615C22×C4C2×C4×D512yes—
616C22×C4C2×C4×D512yes—
617C22×C4C2×C4×D512yes—
618C22×C4C2×D2012yes—
619C22×C4C2×D2012yes—
620C22×C4C2×D2012yes—
621C22×C4#70912yes—
622C22×C4#70912yes—
623C22×C4#70912yes—
624C22×C4#70912yes—
625C22×C4D4×D512yes—
626C22×C4D4×D512yes—
627C22×C4Q8×D512yes—
628C22×C4#71312yes—
629C22×C4C2×C22⋊D512yes—
630C22×C4C2×C22⋊D512yes—
631C22×C4C2×C22⋊D512yes—
632C4⋊C4—28no—
633C4⋊C4—28no—
634C4⋊C4—108no—
635C4⋊C4—108no—
636C4⋊C4—208no—
637C4⋊C4—204no—
638C22⋊C4—1016no—
639C22⋊C4—1016no—
640C22⋊C4—208no—
641C22⋊C4—208no—
642C22⋊C4—208no—
643C42—28no—
644C42—28no—
645C42—44no—
646C2×C5C2×#38511yescharacteristic
647C2×C5C4×#12111yescharacteristic
648C2×C5#232411yescharacteristic
649C2×C5D4×C4⋊C411yescharacteristic
650C2×C5#234911yescharacteristic
651C2×C5#236611yescharacteristic
652C2×C5#236711yescharacteristic
653C2×C5#240711yescharacteristic
654C2×C5#240811yescharacteristic
655C2×C5#244511yescharacteristic
656C2×C5#244711yescharacteristic
657C2×C5#245211yescharacteristic
658C2×C5#245411yescharacteristic
659C2×C5#253811yescharacteristic
660C2×C5#258011yescharacteristic
661D5—48no—
662C23—58no—
663C23—104no—
664C23—104no—
665C23—104no—
666C23—104no—
667C23—104no—
668C23—104no—
669C23—104no—
670C23—104no—
671C23—104no—
672C23—104no—
673C23—104no—
674C23—104no—
675C23—104no—
676C23—104no—
677C23—104no—
678C23—104no—
679C23—104no—
680C23—104no—
681C23—202no—
682C23—202no—
683C23—202no—
684C23—202no—
685C23—202no—
686C23—202no—
687C23—202no—
688C23—202no—
689C23—202no—
690C23—202no—
691C23—202no—
692C23—202no—
693C23—202no—
694C23—202no—
695C23—202no—
696C23—202no—
697C23C22×C4×D511yescharacteristic
698C23C22×D2011yescharacteristic
699C23C2×#70911yescharacteristic
700C23C2×#70911yescharacteristic
701C23C2×#70911yescharacteristic
702C23C2×#70911yescharacteristic
703C23C2×D4×D511yescharacteristic
704C23C2×D4×D511yescharacteristic
705C23C2×Q8×D511yescharacteristic
706C23C2×#71311yescharacteristic
707C23#414911yescharacteristic
708C23#414911yescharacteristic
709C23#414911yescharacteristic
710C23#415011yescharacteristic
711C23C22×C22⋊D511yescharacteristic
712D4—1032no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—104no—
754C2×C4—104no—
755C2×C4—104no—
756C2×C4—104no—
757C2×C4—104no—
758C2×C4—104no—
759C2×C4—2032no—
760C2×C4—202no—
761C2×C4—202no—
762C2×C4—202no—
763C2×C4—202no—
764C2×C4—202no—
765C2×C4—202no—
766C2×C4—202no—
767C2×C4—202no—
768C2×C4—202no—
769C2×C4—202no—
770C2×C4—202no—
771C2×C4—202no—
772C2×C4—202no—
773C2×C4—202no—
774C2×C4—202no—
775C2×C4C4×D2014yescomplemented
776C2×C4D5×C4⋊C414yes—
777C2×C4#403914yes—
778C2×C4#404014yes—
779C2×C4#404214yes—
780C2×C4C4×C22⋊D514yes—
781C2×C4#407614yes—
782C2×C4#408314yes—
783C2×C4#409214yes—
784C5#1401811yescharacteristic, complemented, Sylow
785C22—108no—
786C22—108no—
787C22—108no—
788C22—204no—
789C22—204no—
790C22—204no—
791C22—204no—
792C22—204no—
793C22—204no—
794C22—204no—
795C22—204no—
796C22—204no—
797C22—204no—
798C22—204no—
799C22—204no—
800C22C2×C4×D2011yescharacteristic
801C22C4×#70911yescharacteristic
802C22#6581111yescharacteristic
803C22#6581311yescharacteristic
804C22C2×D5×C4⋊C411yescharacteristic
805C22C2×#403911yescharacteristic
806C22C2×#404011yescharacteristic
807C22C2×#404211yescharacteristic
808C22#6585511yescharacteristic
809C22#6585711yescharacteristic
810C22#6586811yescharacteristic
811C22#6586911yescharacteristic
812C22D4×D2011yescharacteristic
813C22D4×D2011yescharacteristic
814C22#6588411yescharacteristic
815C22#6588411yescharacteristic
816C22#6588411yescharacteristic
817C22#6588511yescharacteristic
818C22#6588611yescharacteristic
819C22#6588711yescharacteristic
820C22Q8×D2011yescharacteristic
821C22#6591111yescharacteristic
822C22#6591311yescharacteristic
823C22#6591311yescharacteristic
824C22#6591311yescharacteristic
825C22#6591811yescharacteristic
826C22#6591911yescharacteristic
827C22#6591911yescharacteristic
828C22C2×C4×C22⋊D511yescharacteristic
829C22C2×#407611yescharacteristic
830C22#6612511yescharacteristic
831C22C2×#408311yescharacteristic
832C22C2×#409211yescharacteristic
833C22#6616411yescharacteristic
834C22#6616711yescharacteristic
835C4—24no—
836C4—24no—
837C4—42no—
838C4—42no—
839C4—42no—
840C4—42no—
841C4—204no—
842C4—204no—
843C4—402no—
844C4#6527818yescomplemented
845C2—208no—
846C2#1060538411yescharacteristic
847C2#1060538611yescharacteristic
848C2#1060540611yescharacteristic
849C2#1060540811yescharacteristic
850C2C4⋊C4×D2011yescharacteristic
851C2#1060550111yescharacteristic
852C2#1060551111yescharacteristic
853C2#1060551211yescharacteristic
854C2C4×#407611yescharacteristic
855C2C2×#6527811yescharacteristic
856C2#1061396711yescharacteristic
857C2#1061413311yescharacteristic
858C2#1061413411yescharacteristic
859C2#1061423111yescharacteristic
860C2#1061423211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D5
commutatorC23×C5C23×C4
FittingC2×C4×C5×C4⋊C4C2
socle, cosocleC24×C5C24
prime radicalC23×D20C22
hypercenterC2×C4×C4⋊C4D5
hypocenterC5#14018
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
3. C2×#65278C2semidirect
6. C2×#65217C2semidirect
7. #10602363C2semidirect
8. #10602328C2semidirect
9. #10602328C2semidirect
10. #10600221C2semidirect
11. #10600218C2semidirect
41. #65228C4semidirect
74. C2×C5×C4⋊C4D4semidirect
82. C2×C42×C5C2×C4semidirect
97. C2×#685C2×C4semidirect
98. C2×#685C2×C4semidirect
106. C2×C4⋊Dic5C2×C4semidirect
124. C2×C4×C4⋊C4D5semidirect
222. C2×D20C4⋊C4semidirect
368. C2×C4×C5C4×D4semidirect
440. C2×C4⋊C4D20semidirect
463. C2×C42C4×D5semidirect
528. C4×C5#385semidirect
775. C2×C4C4×D20semidirect
784. C5#14018semidirect
844. C4#65278semidirect

Maximal subgroups

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

subgroupindex
C22×C4×D202
C2×C4×C5×C4⋊C42
C2×#652782
C2×#652282
C2×#652172
#106023632
#106023282
#106002212
#106002182
#140185