Finite Group Databasebeta

← #12022695

Subgroups — #12022695

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×#4039C211yesmaximal, characteristic
2C2×C5×#389C211yesmaximal, characteristic, complemented
3C2×#65278C212yesmaximal, complemented
4C2×#65277C211yesmaximal, characteristic
5C2×#65228C211yesmaximal, characteristic
6C2×C4×#683C211yesmaximal, characteristic, complemented
7#10602363C212yesmaximal, complemented
8#10602356C211yesmaximal, characteristic, complemented
9#10602356C211yesmaximal, characteristic, complemented
10#10600221C212yesmaximal, complemented
11#10600218C212yesmaximal, complemented
12C23×D20C2211yescharacteristic
13C23×C4×D5C2212yes—
14C22×C5×C4⋊C4C2212yes—
15C22×C5×C4⋊C4C2211yescharacteristic
16C22×C5×C4⋊C4C2211yescharacteristic
17C22×C42×C5C2211yescharacteristic
18C22×#685C2212yes—
19C22×#685C2212yes—
20C22×#685C2212yes—
21C22×#685C2212yes—
22C22×#685C2212yes—
23C22×C4⋊Dic5C2211yescharacteristic
24C22×#683C2211yescharacteristic
25C22×#683C2211yescharacteristic
26C22×C4×Dic5C2211yescharacteristic
27C22×C4×Dic5C2211yescharacteristic
28C2×#4039—24no—
29C2×#4039—24no—
30C2×#4039—24no—
31C5×#389—24no—
32C2×C5×#95C2212yes—
33C2×#3963C2211yescharacteristic
34C2×#3963C2211yescharacteristic
35C2×#3963C2212yes—
36C2×#3963C2212yes—
37C2×#3963C2212yes—
38C2×#3963C2212yes—
39#65278—28no—
40#65277C418yescomplemented
41#65228—24no—
42C4×#683—24no—
43#14018—51nomaximal, Sylow
44C24×D5C2312yes—
45C23×C4×C5C2312yes—
46C23×C4×C5C2312yes—
47C23×C4×C5C2311yescharacteristic
48C23×C4×C5C2311yescharacteristic
49C23×C4×C5C2311yescharacteristic
50C23×Dic5C2312yes—
51C23×Dic5C2311yescharacteristic
52C23×Dic5C2311yescharacteristic
53C23×Dic5C2311yescharacteristic
54C23×Dic5C2311yescharacteristic
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—24no—
74C2×C5×C4⋊C4—24no—
75C2×C5×C4⋊C4—42no—
76C2×C5×C4⋊C4C2×C414yescomplemented
77C2×C5×C4⋊C4D414yes—
78C2×C42×C5—22no—
79C2×C42×C5—22no—
80C2×C42×C5—22no—
81C2×#685—24no—
82C2×#685—24no—
83C2×#685—24no—
84C2×#685—24no—
85C2×#685—24no—
86C2×#685—24no—
87C2×#685—24no—
88C2×#685—24no—
89C2×#685—24no—
90C2×#685—42no—
91C2×#685—42no—
92C2×#685—42no—
93C2×#685—42no—
94C2×#685C2×C418yescomplemented
95C2×#685C2×C418yescomplemented
96C2×C4⋊Dic5—22no—
97C2×C4⋊Dic5—22no—
98C2×C4⋊Dic5—22no—
99C2×#683—22no—
100C2×#683—22no—
101C2×#683—22no—
102C2×#683—22no—
103C2×#683—22no—
104C2×#683D414yescomplemented
105C2×C4×Dic5—22no—
106C2×C4×Dic5—22no—
107C2×C4×Dic5—22no—
108C2×C4×Dic5—22no—
109C2×C4×Dic5C2×C414yescomplemented
110C2×C4×Dic5D414yes—
111#4039—232no—
112C5×#95—24no—
113#3963—22no—
114#3963—22no—
115#3963—24no—
116#3963—24no—
117#3963—42no—
118#3963—42no—
119C22×C4×D4—51no—
120C2×#390—51no—
121C2×#390—51no—
122C2×#389D511yescharacteristic, complemented
123C2×#385—52no—
124C2×C4×C4⋊C4—51no—
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—22no—
153C22×C4×C5—22no—
154C22×C4×C5—22no—
155C22×C4×C5—22no—
156C22×C4×C5—22no—
157C22×C4×C5—22no—
158C22×C4×C5—22no—
159C22×C4×C5—21no—
160C22×C4×C5—21no—
161C22×C4×C5—22no—
162C22×C4×C5—21no—
163C22×C4×C5—22no—
164C22×C4×C5—22no—
165C22×C4×C5—22no—
166C22×C4×C5—22no—
167C22×C4×C5—21no—
168C22×C4×C5—21no—
169C22×C4×C5—21no—
170C22×C4×C5C22×C414yes—
171C22×C4×C5C22×C412yes—
172C22×C4×C5C2×D412yes—
173C22×C4×C5C2×D412yes—
174C22×C4×C5C2×D412yes—
175C22×C4×C5C2×D414yes—
176C22×C4×C5C2×D412yes—
177C22×C4×C5C2×Q812yes—
178C22×C4×C5#4112yes—
179C22×C4×C5#4112yes—
180C22×C4×C5#4112yes—
181C22×Dic5—21no—
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—21no—
193C22×Dic5—21no—
194C22×Dic5—21no—
195C22×Dic5—21no—
196C22×Dic5—21no—
197C22×Dic5—21no—
198C22×Dic5—21no—
199C22×Dic5—21no—
200C22×Dic5—21no—
201C22×Dic5—22no—
202C22×Dic5—22no—
203C22×Dic5—22no—
204C22×Dic5—22no—
205C22×Dic5—22no—
206C22×Dic5—22no—
207C22×Dic5—22no—
208C22×Dic5C22×C412yes—
209C22×Dic5C22×C412yes—
210C22×Dic5C2×D412yes—
211C22×Dic5C2×D412yes—
212C22×Dic5C2×D412yes—
213C22×Dic5C2×D412yes—
214C22×Dic5#4112yes—
215C22×Dic5#4112yes—
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—
232C5×C4⋊C4—48no—
233C42×C5—44no—
234#685—216no—
235#685—216no—
236#685—48no—
237#685—48no—
238#685—48no—
239C4⋊Dic5—44no—
240#683—28no—
241#683—28no—
242C4×Dic5—28no—
243C4×Dic5—28no—
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⋊C4C2×D512yes—
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×C42—51no—
261C22×C42—51no—
262C22×C42C2×D511yescharacteristic
263#390—58no—
264#390—104no—
265#389—24no—
266#385—108no—
267C4×C4⋊C4—104no—
268C2×#95—51no—
269C2×#95—52no—
270C2×#95—52no—
271C2×#95—51no—
272C2×#95—52no—
273C2×#95—52no—
274C2×#95C2×D512yes—
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—24no—
326C2×C4×C5—24no—
327C2×C4×C5—24no—
328C2×C4×C5—24no—
329C2×C4×C5—22no—
330C2×C4×C5—22no—
331C2×C4×C5—22no—
332C2×C4×C5—22no—
333C2×C4×C5—24no—
334C2×C4×C5—22no—
335C2×C4×C5—24no—
336C2×C4×C5—22no—
337C2×C4×C5—41no—
338C2×C4×C5—41no—
339C2×C4×C5—42no—
340C2×C4×C5—42no—
341C2×C4×C5—41no—
342C2×C4×C5—41no—
343C2×C4×C5—42no—
344C2×C4×C5—42no—
345C2×C4×C5—42no—
346C2×C4×C5—41no—
347C2×C4×C5—41no—
348C2×C4×C5—41no—
349C2×C4×C5—42no—
350C2×C4×C5—42no—
351C2×C4×C5—41no—
352C2×C4×C5—42no—
353C2×C4×C5C2×C4⋊C414yes—
354C2×C4×C5C4×D414yes—
355C2×C4×C5C4×D414yes—
356C2×C4×C5#12014yes—
357C2×C4×C5C22⋊Q814yes—
358C2×C4×C5C22⋊Q814yes—
359C2×C4×C5#12314yes—
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—22no—
369C2×Dic5—22no—
370C2×Dic5—22no—
371C2×Dic5—22no—
372C2×Dic5—22no—
373C2×Dic5—22no—
374C2×Dic5—22no—
375C2×Dic5—22no—
376C2×Dic5—22no—
377C2×Dic5—22no—
378C2×Dic5—41no—
379C2×Dic5—41no—
380C2×Dic5—41no—
381C2×Dic5—41no—
382C2×Dic5—41no—
383C2×Dic5—41no—
384C2×Dic5—41no—
385C2×Dic5—41no—
386C2×Dic5—42no—
387C2×Dic5—42no—
388C2×Dic5—42no—
389C2×Dic5—42no—
390C2×Dic5—42no—
391C2×Dic5—42no—
392C2×Dic5—42no—
393C2×Dic5C4×D414yescomplemented
394C2×Dic5#12114yes—
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—51no—
406C23×C4—51no—
407C23×C4—51no—
408C23×C4—51no—
409C23×C4—52no—
410C23×C4—104no—
411C23×C4—104no—
412C23×C4—104no—
413C23×C4—104no—
414C23×C4—104no—
415C23×C4—202no—
416C23×C4—202no—
417C23×C4C22×D512yes—
418C23×C4C22×D511yescharacteristic
419C23×C4C22×D511yescharacteristic
420C23×C4C22×D512yes—
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—24no—
428C2×C4⋊C4—24no—
429C2×C4⋊C4—42no—
430C2×C4⋊C4—54no—
431C2×C4⋊C4—102no—
432C2×C4⋊C4—102no—
433C2×C4⋊C4—102no—
434C2×C4⋊C4—102no—
435C2×C4⋊C4—102no—
436C2×C4⋊C4—102no—
437C2×C4⋊C4—102no—
438C2×C4⋊C4—102no—
439C2×C4⋊C4C4×D514yescomplemented
440C2×C4⋊C4C22⋊D514yes—
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—54no—
460C2×C42—54no—
461C2×C42—102no—
462C2×C42—102no—
463C2×C42—102no—
464C2×C42—102no—
465#95—24no—
466#95—102no—
467#95—102no—
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—44no—
523C4×C5—42no—
524C4×C5—44no—
525C4×C5—42no—
526C4×C5#38518yescomplemented
527Dic5—24no—
528Dic5—24no—
529Dic5—42no—
530Dic5—42no—
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—22no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—21no—
566C22×C4—22no—
567C22×C4—21no—
568C22×C4—22no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—22no—
578C22×C4—21no—
579C22×C4—52no—
580C22×C4—52no—
581C22×C4—52no—
582C22×C4—52no—
583C22×C4—52no—
584C22×C4—52no—
585C22×C4—52no—
586C22×C4—52no—
587C22×C4—1016no—
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—101no—
601C22×C4—101no—
602C22×C4—101no—
603C22×C4—101no—
604C22×C4—101no—
605C22×C4—101no—
606C22×C4—101no—
607C22×C4—101no—
608C22×C4—102no—
609C22×C4—102no—
610C22×C4—102no—
611C22×C4—102no—
612C22×C4—102no—
613C22×C4—102no—
614C22×C4—102no—
615C22×C4—208no—
616C22×C4—208no—
617C22×C4—208no—
618C22×C4—208no—
619C22×C4—208no—
620C22×C4—208no—
621C22×C4C2×C4×D514yes—
622C22×C4C2×C4×D512yes—
623C22×C4#70912yes—
624C22×C4D4×D512yes—
625C22×C4D4×D512yes—
626C22×C4D4×D512yes—
627C22×C4Q8×D512yes—
628C22×C4#71312yes—
629C22×C4#71312yes—
630C22×C4C2×C22⋊D514yes—
631C22×C4C2×C22⋊D512yes—
632C4⋊C4—28no—
633C4⋊C4—28no—
634C4⋊C4—48no—
635C4⋊C4—108no—
636C4⋊C4—108no—
637C4⋊C4—204no—
638C22⋊C4—1016no—
639C22⋊C4—1016no—
640C22⋊C4—208no—
641C22⋊C4—208no—
642C22⋊C4—208no—
643C42—44no—
644C42—108no—
645C42—108no—
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
698C23C2×#70911yescharacteristic
699C23C2×D4×D511yescharacteristic
700C23C2×D4×D511yescharacteristic
701C23C2×D4×D511yescharacteristic
702C23#414411yescharacteristic
703C23C2×Q8×D511yescharacteristic
704C23C2×#71311yescharacteristic
705C23C2×#71311yescharacteristic
706C23#414711yescharacteristic
707C23D5×#4111yescharacteristic
708C23D5×#4111yescharacteristic
709C23#414911yescharacteristic
710C23#414911yescharacteristic
711C23C22×C22⋊D511yescharacteristic
712D4—1032no—
713C2×C4—24no—
714C2×C4—24no—
715C2×C4—24no—
716C2×C4—24no—
717C2×C4—22no—
718C2×C4—24no—
719C2×C4—22no—
720C2×C4—24no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—41no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—54no—
742C2×C4—54no—
743C2×C4—102no—
744C2×C4—102no—
745C2×C4—102no—
746C2×C4—102no—
747C2×C4—102no—
748C2×C4—102no—
749C2×C4—102no—
750C2×C4—102no—
751C2×C4—102no—
752C2×C4—102no—
753C2×C4—102no—
754C2×C4—102no—
755C2×C4—102no—
756C2×C4—102no—
757C2×C4—102no—
758C2×C4—102no—
759C2×C4—102no—
760C2×C4—102no—
761C2×C4—2032no—
762C2×C4—201no—
763C2×C4—201no—
764C2×C4—201no—
765C2×C4—201no—
766C2×C4—201no—
767C2×C4—201no—
768C2×C4—201no—
769C2×C4—201no—
770C2×C4—202no—
771C2×C4—202no—
772C2×C4—202no—
773C2×C4—202no—
774C2×C4—202no—
775C2×C4—202no—
776C2×C4—202no—
777C2×C4D5×C4⋊C414yes—
778C2×C4#403914yes—
779C2×C4#404014yes—
780C2×C4#404214yes—
781C2×C4C4×C22⋊D514yes—
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×D5×C4⋊C411yescharacteristic
801C22C2×#403911yescharacteristic
802C22C2×#404011yescharacteristic
803C22C2×#404211yescharacteristic
804C22C4×D4×D511yescharacteristic
805C22#6587911yescharacteristic
806C22#6588711yescharacteristic
807C22#6589311yescharacteristic
808C22#6590211yescharacteristic
809C22C4×#71311yescharacteristic
810C22#6590811yescharacteristic
811C22#6591911yescharacteristic
812C22D5×#12111yescharacteristic
813C22#6594111yescharacteristic
814C22#6594311yescharacteristic
815C22#6594611yescharacteristic
816C22#6596111yescharacteristic
817C22#6596311yescharacteristic
818C22#6596411yescharacteristic
819C22#6596511yescharacteristic
820C22#6602411yescharacteristic
821C22#6602411yescharacteristic
822C22#6602511yescharacteristic
823C22#6603211yescharacteristic
824C22#6605911yescharacteristic
825C22#6606111yescharacteristic
826C22#6606411yescharacteristic
827C22#6606711yescharacteristic
828C22C2×C4×C22⋊D511yescharacteristic
829C22C2×#408311yescharacteristic
830C22D4×C22⋊D511yescharacteristic
831C22C2×#409211yescharacteristic
832C22#6615111yescharacteristic
833C22#6616311yescharacteristic
834C22#6616811yescharacteristic
835C4—42no—
836C4—44no—
837C4—44no—
838C4—42no—
839C4—104no—
840C4—104no—
841C4—202no—
842C4—202no—
843C4—402no—
844C4#6527818yescomplemented
845C2—208no—
846C2#1060769511yescharacteristic
847C2#1060773511yescharacteristic
848C2#1060773711yescharacteristic
849C2#1060779011yescharacteristic
850C2#1060780611yescharacteristic
851C2#1060792911yescharacteristic
852C2#1060793311yescharacteristic
853C2#1060793411yescharacteristic
854C2C2×#6527811yescharacteristic
855C2#1061407411yescharacteristic
856C2#1061419711yescharacteristic
857C2#1061437111yescharacteristic
858C2#1061454311yescharacteristic
859C2#1061476111yescharacteristic
860C2#1061496711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D5
commutatorC23×C5C23×C4
FittingC2×C5×#389C2
socle, cosocleC24×C5C24
prime radicalC23×D20C22
hypercenterC2×#389D5
hypocenterC5#14018
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
2. C2×C5×#389C2semidirect
3. C2×#65278C2semidirect
6. C2×C4×#683C2semidirect
7. #10602363C2semidirect
8. #10602356C2semidirect
9. #10602356C2semidirect
10. #10600221C2semidirect
11. #10600218C2semidirect
40. #65277C4semidirect
76. C2×C5×C4⋊C4C2×C4semidirect
94. C2×#685C2×C4semidirect
95. C2×#685C2×C4semidirect
104. C2×#683D4semidirect
109. C2×C4×Dic5C2×C4semidirect
122. C2×#389D5semidirect
222. C2×D20C4⋊C4semidirect
393. C2×Dic5C4×D4semidirect
439. C2×C4⋊C4C4×D5semidirect
526. C4×C5#385semidirect
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×#40392
C2×C5×#3892
C2×#652782
C2×#652772
C2×#652282
C2×C4×#6832
#106023632
#106023562
#106002212
#106002182
#140185