Finite Group Databasebeta

← #12022401

Subgroups — #12022401

Order 1280.

1802 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C5×C22⋊C4C211yesmaximal, characteristic
2C2×#65501C211yesmaximal, characteristic
3C2×#65501C211yesmaximal, characteristic
4C2×#65233C212yesmaximal
5C2×#65217C211yesmaximal, characteristic, complemented
6C2×C4×C4⋊Dic5C211yesmaximal, characteristic, complemented
7#10602342C212yesmaximal
8#10602328C211yesmaximal, characteristic, complemented
9#10602328C211yesmaximal, characteristic, complemented
10#10600206C212yesmaximal, complemented
11#10600195C212yesmaximal, complemented
12C24×C4×C5C2211yescharacteristic
13C22×C5×C22⋊C4C2211yescharacteristic
14C22×C5×C22⋊C4C2211yescharacteristic
15C22×C42×C5C2211yescharacteristic
16C22×C42×C5C2211yescharacteristic
17C22×C22⋊Dic5C2212yes—
18C22×C22⋊Dic5C2212yes—
19C22×C4⋊Dic5C2211yescharacteristic
20C22×C4⋊Dic5C2211yescharacteristic
21C22×C4⋊Dic5C2211yescharacteristic
22C22×C4⋊Dic5C2211yescharacteristic
23C22×#683C2212yes—
24C22×C4×Dic5C2212yes—
25C4×C5×C22⋊C4—24no—
26C2×C5×#95C2211yescharacteristic
27C2×C5×#95C2211yescharacteristic
28#65501—24no—
29#65501C418yescomplemented
30C2×#3963C2212yes—
31C2×#3963C2212yes—
32C2×#3963C2212yes—
33C2×#3963C2212yes—
34C2×#3963C2212yes—
35C2×#3963C2212yes—
36C2×#3963C2212yes—
37C2×#3963C2212yes—
38#65233—28no—
39C4×C4⋊Dic5—24no—
40#65217—24no—
41#13994—51nomaximal, Sylow
42C25×C5C2311yescharacteristic
43C23×C4×C5—22no—
44C23×C4×C5—22no—
45C23×C4×C5—22no—
46C23×C4×C5—22no—
47C23×C4×C5—22no—
48C23×C4×C5—22no—
49C23×C4×C5C2×C414yes—
50C23×C4×C5C2311yescharacteristic
51C23×C4×C5C2311yescharacteristic
52C23×C4×C5C2311yescharacteristic
53C23×C4×C5C2311yescharacteristic
54C23×C4×C5C2311yescharacteristic
55C23×C4×C5C2311yescharacteristic
56C23×Dic5C2312yes—
57C23×Dic5C2312yes—
58C23×Dic5C2312yes—
59C23×Dic5C2312yes—
60C2×C5×C22⋊C4—22no—
61C2×C5×C22⋊C4—22no—
62C2×C5×C22⋊C4—22no—
63C2×C5×C22⋊C4—22no—
64C2×C5×C22⋊C4—22no—
65C2×C5×C22⋊C4D414yes—
66C2×C42×C5—22no—
67C2×C42×C5—22no—
68C2×C42×C5—22no—
69C2×C42×C5—22no—
70C2×C42×C5—22no—
71C2×C42×C5D414yes—
72C2×C22⋊Dic5—24no—
73C2×C22⋊Dic5—24no—
74C2×C22⋊Dic5—24no—
75C2×C22⋊Dic5—24no—
76C2×C22⋊Dic5—42no—
77C2×C22⋊Dic5C2×C418yes—
78C2×C4⋊Dic5—22no—
79C2×C4⋊Dic5—22no—
80C2×C4⋊Dic5—22no—
81C2×C4⋊Dic5—22no—
82C2×C4⋊Dic5—22no—
83C2×C4⋊Dic5—22no—
84C2×C4⋊Dic5—22no—
85C2×C4⋊Dic5—22no—
86C2×C4⋊Dic5—22no—
87C2×C4⋊Dic5C2×C414yes—
88C2×C4⋊Dic5C2×C414yes—
89C2×C4⋊Dic5D414yes—
90C2×#683—24no—
91C2×#683—24no—
92C2×#683—42no—
93C2×C4×Dic5—24no—
94C2×C4×Dic5—24no—
95C2×C4×Dic5—24no—
96C5×#95—22no—
97C5×#95—22no—
98#3963—24no—
99#3963—24no—
100#3963—24no—
101#3963—24no—
102#3963—24no—
103#3963—24no—
104#3963—42no—
105#3963C2×C418yes—
106C2×#389—51no—
107C2×#388—52no—
108C2×#380—51no—
109C2×#380—51no—
110C2×C4×C4⋊C4—51no—
111C2×C4×C22⋊C4D511yescharacteristic
112#1442—52no—
113#1440—52no—
114C4⋊#95—51no—
115C4⋊#95—51no—
116#1434—52no—
117C24×C5—21no—
118C24×C5—21no—
119C24×C5—21no—
120C24×C5—21no—
121C24×C5—21no—
122C24×C5—21no—
123C24×C5—21no—
124C24×C5—21no—
125C24×C5—21no—
126C24×C5—21no—
127C24×C5—21no—
128C24×C5—21no—
129C24×C5C22×C412yes—
130C24×C5C2×D412yes—
131C24×C5#4112yes—
132C24×C5C2411yescharacteristic
133C22×C4×C5—21no—
134C22×C4×C5—21no—
135C22×C4×C5—21no—
136C22×C4×C5—21no—
137C22×C4×C5—21no—
138C22×C4×C5—21no—
139C22×C4×C5—21no—
140C22×C4×C5—21no—
141C22×C4×C5—21no—
142C22×C4×C5—21no—
143C22×C4×C5—21no—
144C22×C4×C5—21no—
145C22×C4×C5—21no—
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—28no—
162C22×C4×C5—28no—
163C22×C4×C5—28no—
164C22×C4×C5—44no—
165C22×C4×C5—44no—
166C22×C4×C5—44no—
167C22×C4×C5—44no—
168C22×C4×C5C22×C412yes—
169C22×C4×C5C22×C412yes—
170C22×C4×C5C2×D412yes—
171C22×C4×C5C2×D412yes—
172C22×C4×C5C2×D412yes—
173C22×C4×C5C2×D412yes—
174C22×C4×C5C2×D412yes—
175C22×C4×C5C2×D412yes—
176C22×C4×C5#4112yes—
177C22×C4×C5#4112yes—
178C22×C4×C5#4112yes—
179C22×C4×C5#4112yes—
180C22×C4×C5#4112yes—
181C22×C4×C5#4112yes—
182C22×Dic5—22no—
183C22×Dic5—22no—
184C22×Dic5—22no—
185C22×Dic5—22no—
186C22×Dic5—22no—
187C22×Dic5—22no—
188C22×Dic5—22no—
189C22×Dic5—22no—
190C22×Dic5—22no—
191C22×Dic5—22no—
192C22×Dic5—22no—
193C22×Dic5—22no—
194C22×Dic5—22no—
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×Dic5C22×C414yes—
208C22×Dic5C22×C414yes—
209C22×Dic5C2×D414yes—
210C5×C22⋊C4—28no—
211C5×C22⋊C4—28no—
212C42×C5—28no—
213C42×C5—44no—
214C22⋊Dic5—216no—
215C22⋊Dic5—48no—
216C4⋊Dic5—28no—
217C4⋊Dic5—28no—
218C4⋊Dic5—28no—
219C4⋊Dic5—44no—
220#683—48no—
221C4×Dic5—48no—
222C24×C4C2×D511yescharacteristic
223C22×C4⋊C4—51no—
224C22×C4⋊C4—51no—
225C22×C4⋊C4—51no—
226C22×C4⋊C4—51no—
227C22×C4⋊C4—52no—
228C22×C22⋊C4—52no—
229C22×C22⋊C4—52no—
230C22×C22⋊C4C2×D511yescharacteristic
231C22×C22⋊C4C2×D511yescharacteristic
232C22×C42—52no—
233C22×C42C2×D511yescharacteristic
234C22×C42C2×D511yescharacteristic
235#389—104no—
236#388—108no—
237#380—58no—
238#380—104no—
239C4×C4⋊C4—104no—
240C4×C22⋊C4—24no—
241C2×#95—52no—
242C2×#95—52no—
243C2×#95—52no—
244C2×#95—52no—
245C2×#95—52no—
246C2×#95—52no—
247C2×#95—52no—
248C2×#95—52no—
249C2×#95C2×D511yescharacteristic
250C2×#95C2×D511yescharacteristic
251C23×C5—22no—
252C23×C5—22no—
253C23×C5—22no—
254C23×C5—22no—
255C23×C5—22no—
256C23×C5—22no—
257C23×C5—22no—
258C23×C5—22no—
259C23×C5—22no—
260C23×C5—22no—
261C23×C5—22no—
262C23×C5—22no—
263C23×C5—22no—
264C23×C5—22no—
265C23×C5—22no—
266C23×C5—22no—
267C23×C5—22no—
268C23×C5—22no—
269C23×C5—41no—
270C23×C5—41no—
271C23×C5—41no—
272C23×C5—41no—
273C23×C5—41no—
274C23×C5—41no—
275C23×C5—41no—
276C23×C5—41no—
277C23×C5—41no—
278C23×C5—41no—
279C23×C5—41no—
280C23×C5—41no—
281C23×C5—41no—
282C23×C5—41no—
283C23×C5—41no—
284C23×C5—41no—
285C23×C5C4×D414yes—
286C23×C5C23×C411yescharacteristic
287C23×C5C22×D411yescharacteristic
288C23×C5C22×D411yescharacteristic
289C23×C5C22×D411yescharacteristic
290C23×C5C2×#4111yescharacteristic
291C23×C5C2×#4111yescharacteristic
292C23×C5C2×#4111yescharacteristic
293C23×C5C2×#4111yescharacteristic
294C23×C5C2×#4111yescharacteristic
295C23×C5C2×#4111yescharacteristic
296C23×C5C2×#4111yescharacteristic
297C23×C5H(5,𝔽2)11yescharacteristic
298C23×C52−1+411yescharacteristic
299C23×C52−1+411yescharacteristic
300C23×C52−1+411yescharacteristic
301C2×C4×C5—22no—
302C2×C4×C5—22no—
303C2×C4×C5—22no—
304C2×C4×C5—22no—
305C2×C4×C5—22no—
306C2×C4×C5—22no—
307C2×C4×C5—22no—
308C2×C4×C5—22no—
309C2×C4×C5—22no—
310C2×C4×C5—22no—
311C2×C4×C5—22no—
312C2×C4×C5—22no—
313C2×C4×C5—22no—
314C2×C4×C5—22no—
315C2×C4×C5—22no—
316C2×C4×C5—22no—
317C2×C4×C5—22no—
318C2×C4×C5—22no—
319C2×C4×C5—41no—
320C2×C4×C5—41no—
321C2×C4×C5—41no—
322C2×C4×C5—41no—
323C2×C4×C5—41no—
324C2×C4×C5—41no—
325C2×C4×C5—41no—
326C2×C4×C5—41no—
327C2×C4×C5—41no—
328C2×C4×C5—41no—
329C2×C4×C5—41no—
330C2×C4×C5—41no—
331C2×C4×C5—41no—
332C2×C4×C5—41no—
333C2×C4×C5—41no—
334C2×C4×C5—41no—
335C2×C4×C5—416no—
336C2×C4×C5#11714yes—
337C2×C4×C5C4×D414yes—
338C2×C4×C5C4×D414yes—
339C2×C4×C5#12114yes—
340C2×C4×C5#12114yes—
341C2×C4×C5#12314yes—
342C2×C4×C5#12414yes—
343C2×C4×C5#12614yes—
344C2×Dic5—24no—
345C2×Dic5—24no—
346C2×Dic5—24no—
347C2×Dic5—24no—
348C2×Dic5—24no—
349C2×Dic5—24no—
350C2×Dic5—24no—
351C2×Dic5—24no—
352C2×Dic5—24no—
353C2×Dic5—42no—
354C2×Dic5—42no—
355C2×Dic5—42no—
356C2×Dic5—42no—
357C2×Dic5—42no—
358C2×Dic5—42no—
359C2×Dic5—42no—
360C2×Dic5—42no—
361C2×Dic5—42no—
362C2×Dic5—42no—
363C2×Dic5—42no—
364C2×Dic5—42no—
365C2×Dic5—42no—
366C2×Dic5—42no—
367C2×Dic5—42no—
368C2×Dic5—42no—
369C2×Dic5—42no—
370C2×Dic5—42no—
371C2×Dic5—42no—
372C25C22×D511yescharacteristic
373C23×C4—22no—
374C23×C4—22no—
375C23×C4—22no—
376C23×C4—22no—
377C23×C4—22no—
378C23×C4—22no—
379C23×C4—52no—
380C23×C4—52no—
381C23×C4—52no—
382C23×C4—52no—
383C23×C4C4×D514yes—
384C23×C4C22×D511yescharacteristic
385C23×C4C22×D511yescharacteristic
386C23×C4C22×D511yescharacteristic
387C23×C4C22×D511yescharacteristic
388C23×C4C22×D511yescharacteristic
389C23×C4C22×D511yescharacteristic
390C2×C4⋊C4—54no—
391C2×C4⋊C4—54no—
392C2×C4⋊C4—54no—
393C2×C4⋊C4—102no—
394C2×C4⋊C4—102no—
395C2×C4⋊C4—102no—
396C2×C4⋊C4—102no—
397C2×C4⋊C4—102no—
398C2×C4⋊C4—102no—
399C2×C4⋊C4—104no—
400C2×C4⋊C4—104no—
401C2×C4⋊C4—102no—
402C2×C4⋊C4—102no—
403C2×C4⋊C4—102no—
404C2×C4⋊C4—202no—
405C2×C22⋊C4—22no—
406C2×C22⋊C4—22no—
407C2×C22⋊C4—22no—
408C2×C22⋊C4—22no—
409C2×C22⋊C4—22no—
410C2×C22⋊C4—58no—
411C2×C22⋊C4—104no—
412C2×C22⋊C4—104no—
413C2×C22⋊C4—104no—
414C2×C22⋊C4—104no—
415C2×C22⋊C4—202no—
416C2×C22⋊C4D2014yes—
417C2×C42—22no—
418C2×C42—22no—
419C2×C42—22no—
420C2×C42—22no—
421C2×C42—22no—
422C2×C42—104no—
423C2×C42—104no—
424C2×C42—104no—
425C2×C42C22⋊D514yes—
426#95—22no—
427#95—22no—
428#95—58no—
429#95—104no—
430#95—104no—
431#95—104no—
432#95—104no—
433#95—104no—
434#95—104no—
435#95—202no—
436C22×C5—24no—
437C22×C5—24no—
438C22×C5—24no—
439C22×C5—42no—
440C22×C5—42no—
441C22×C5—42no—
442C22×C5—42no—
443C22×C5—42no—
444C22×C5—42no—
445C22×C5—42no—
446C22×C5—42no—
447C22×C5—42no—
448C22×C5—42no—
449C22×C5—42no—
450C22×C5—42no—
451C22×C5C2×#11711yescharacteristic
452C22×C5C2×C4×D411yescharacteristic
453C22×C5C2×C4×D411yescharacteristic
454C22×C5C2×C4×D411yescharacteristic
455C22×C5C4×#4111yescharacteristic
456C22×C5#51911yescharacteristic
457C22×C5#52011yescharacteristic
458C22×C5C2×#12111yescharacteristic
459C22×C5C2×#12111yescharacteristic
460C22×C5C2×#12311yescharacteristic
461C22×C5#52511yescharacteristic
462C22×C5C2×#12411yescharacteristic
463C22×C5C2×#12611yescharacteristic
464C22×C5#52911yescharacteristic
465C22×C5#53211yescharacteristic
466C22×C5#53611yescharacteristic
467C22×C5#53711yescharacteristic
468C22×C5#54111yescharacteristic
469C22×C5#54211yescharacteristic
470C22×C5D4211yescharacteristic
471C22×C5#54711yescharacteristic
472C22×C5#54711yescharacteristic
473C22×C5#54711yescharacteristic
474C22×C5#54711yescharacteristic
475C22×C5#54811yescharacteristic
476C22×C5#54811yescharacteristic
477C22×C5#55211yescharacteristic
478C22×C5#55211yescharacteristic
479C22×C5#55211yescharacteristic
480C22×C5#55211yescharacteristic
481C22×C5#55211yescharacteristic
482C22×C5#55311yescharacteristic
483C22×C5#55511yescharacteristic
484C22×C5#55511yescharacteristic
485C22×C5#55611yescharacteristic
486C4×C5—24no—
487C4×C5—42no—
488C4×C5—42no—
489C4×C5—42no—
490C4×C5—42no—
491C4×C5#38818yescomplemented
492Dic5—44no—
493Dic5—44no—
494Dic5—44no—
495Dic5—82no—
496C24—21no—
497C24—21no—
498C24—21no—
499C24—21no—
500C24—21no—
501C24—21no—
502C24—21no—
503C24—21no—
504C24—21no—
505C24—21no—
506C24—21no—
507C24—21no—
508C24C2×C4×D512yes—
509C24C2×D2012yes—
510C24#70912yes—
511C24C23×D511yescharacteristic
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—28no—
541C22×C4—28no—
542C22×C4—28no—
543C22×C4—44no—
544C22×C4—44no—
545C22×C4—44no—
546C22×C4—44no—
547C22×C4—54no—
548C22×C4—54no—
549C22×C4—54no—
550C22×C4—102no—
551C22×C4—102no—
552C22×C4—102no—
553C22×C4—102no—
554C22×C4—102no—
555C22×C4—102no—
556C22×C4—102no—
557C22×C4—102no—
558C22×C4—102no—
559C22×C4—102no—
560C22×C4—102no—
561C22×C4—102no—
562C22×C4—102no—
563C22×C4—102no—
564C22×C4—102no—
565C22×C4—102no—
566C22×C4—102no—
567C22×C4—102no—
568C22×C4—102no—
569C22×C4—102no—
570C22×C4—102no—
571C22×C4—102no—
572C22×C4—102no—
573C22×C4—102no—
574C22×C4—102no—
575C22×C4C2×C4×D512yes—
576C22×C4C2×C4×D512yes—
577C22×C4C2×D2012yes—
578C22×C4C2×D2012yes—
579C22×C4#70912yes—
580C22×C4#70912yes—
581C22×C4#70912yes—
582C22×C4D4×D512yes—
583C22×C4#71112yes—
584C22×C4#71112yes—
585C22×C4#71112yes—
586C22×C4C2×C22⋊D512yes—
587C22×C4C2×C22⋊D512yes—
588C22×C4C2×C22⋊D512yes—
589C4⋊C4—108no—
590C4⋊C4—108no—
591C4⋊C4—108no—
592C4⋊C4—208no—
593C4⋊C4—204no—
594C22⋊C4—28no—
595C22⋊C4—28no—
596C22⋊C4—1016no—
597C22⋊C4—208no—
598C42—28no—
599C42—44no—
600C42—208no—
601C2×C5—44no—
602C2×C5C2×#38811yescharacteristic
603C2×C5C4×#12111yescharacteristic
604C2×C5#232311yescharacteristic
605C2×C5#234411yescharacteristic
606C2×C5#234611yescharacteristic
607C2×C5#236111yescharacteristic
608C2×C5#236211yescharacteristic
609C2×C5#248511yescharacteristic
610C2×C5#248611yescharacteristic
611C2×C5#248911yescharacteristic
612C2×C5#249111yescharacteristic
613C2×C5#249511yescharacteristic
614C2×C5#249611yescharacteristic
615C2×C5#253611yescharacteristic
616C2×C5#253711yescharacteristic
617C23—22no—
618C23—22no—
619C23—22no—
620C23—22no—
621C23—22no—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23C4×D2014yes—
652C23C22×C4×D511yescharacteristic
653C23C22×D2011yescharacteristic
654C23C2×#70911yescharacteristic
655C23C2×#70911yescharacteristic
656C23C2×#70911yescharacteristic
657C23C2×#70911yescharacteristic
658C23C2×D4×D511yescharacteristic
659C23C2×#71111yescharacteristic
660C23C2×#71111yescharacteristic
661C23C2×#71111yescharacteristic
662C23#414911yescharacteristic
663C23#415011yescharacteristic
664C23#415011yescharacteristic
665C23#415011yescharacteristic
666C23C22×C22⋊D511yescharacteristic
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—416no—
702C2×C4—104no—
703C2×C4—104no—
704C2×C4—104no—
705C2×C4—104no—
706C2×C4—104no—
707C2×C4—104no—
708C2×C4—104no—
709C2×C4—104no—
710C2×C4—104no—
711C2×C4—202no—
712C2×C4—202no—
713C2×C4—202no—
714C2×C4—202no—
715C2×C4—202no—
716C2×C4—202no—
717C2×C4—202no—
718C2×C4—202no—
719C2×C4—202no—
720C2×C4—202no—
721C2×C4—202no—
722C2×C4—202no—
723C2×C4—202no—
724C2×C4—202no—
725C2×C4—202no—
726C2×C4—202no—
727C2×C4—202no—
728C2×C4—202no—
729C2×C4—202no—
730C2×C4#402314yes—
731C2×C4#402514yes—
732C2×C4#402714yes—
733C2×C4#403114yes—
734C2×C4C4×C22⋊D514yes—
735C2×C4#407614yes—
736C2×C4#408114yes—
737C2×C4#408414yes—
738C5#1399411yescharacteristic, complemented, Sylow
739C22—24no—
740C22—24no—
741C22—24no—
742C22—42no—
743C22—42no—
744C22—42no—
745C22—42no—
746C22—42no—
747C22—42no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—42no—
754C22C2×C4×D2011yescharacteristic
755C22C4×#70911yescharacteristic
756C22#6581111yescharacteristic
757C22#6581311yescharacteristic
758C22C2×#402311yescharacteristic
759C22C2×#402511yescharacteristic
760C22C2×#402711yescharacteristic
761C22C2×#403111yescharacteristic
762C22#6585011yescharacteristic
763C22#6585211yescharacteristic
764C22#6585711yescharacteristic
765C22#6586811yescharacteristic
766C22#6587511yescharacteristic
767C22#6587511yescharacteristic
768C22#6587511yescharacteristic
769C22#6587511yescharacteristic
770C22#6587511yescharacteristic
771C22#6587611yescharacteristic
772C22D4×D2011yescharacteristic
773C22#6588511yescharacteristic
774C22#6588611yescharacteristic
775C22#6588611yescharacteristic
776C22#6588911yescharacteristic
777C22#6588911yescharacteristic
778C22#6588911yescharacteristic
779C22#6589711yescharacteristic
780C22#6589711yescharacteristic
781C22#6589911yescharacteristic
782C22C2×C4×C22⋊D511yescharacteristic
783C22C2×#407611yescharacteristic
784C22#6612511yescharacteristic
785C22C2×#408111yescharacteristic
786C22C2×#408411yescharacteristic
787C22#6615911yescharacteristic
788C22#6616711yescharacteristic
789C4—24no—
790C4—42no—
791C4—42no—
792C4—42no—
793C4—42no—
794C4—204no—
795C4—204no—
796C4—204no—
797C4—402no—
798C4#6523318yescomplemented
799C2—44no—
800C2#1060518711yescharacteristic
801C2#1060519011yescharacteristic
802C2#1060519811yescharacteristic
803C2#1060519911yescharacteristic
804C2#1060523611yescharacteristic
805C2#1060523811yescharacteristic
806C2#1060524211yescharacteristic
807C2#1060524311yescharacteristic
808C2C4×#407611yescharacteristic
809C2C2×#6523311yescharacteristic
810C2#1061396611yescharacteristic
811C2#1061410311yescharacteristic
812C2#1061410411yescharacteristic
813C2#1061410611yescharacteristic
814C2#1061414811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D5
commutatorC23×C5C23×C4
FittingC2×C4×C5×C22⋊C4C2
socle, cosocleC24×C5C24
prime radicalC25×C5C23
hypercenterC2×C4×C22⋊C4D5
hypocenterC5#13994
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
5. C2×#65217C2semidirect
6. C2×C4×C4⋊Dic5C2semidirect
8. #10602328C2semidirect
9. #10602328C2semidirect
10. #10600206C2semidirect
11. #10600195C2semidirect
29. #65501C4semidirect
491. C4×C5#388semidirect
738. C5#13994semidirect
798. C4#65233semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C5×C22⋊C42
C2×#655012
C2×#652332
C2×#652172
C2×C4×C4⋊Dic52
#106023422
#106023282
#106002062
#106001952
#139945