Finite Group Databasebeta

← #12022737

Subgroups — #12022737

Order 1280.

1954 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65277C211yesmaximal, characteristic
2C2×#65277C211yesmaximal, characteristic
3C2×C4⋊C4×Dic5C211yesmaximal, characteristic, complemented
4C2×#65228C211yesmaximal, characteristic
5C2×C4×C4⋊Dic5C211yesmaximal, characteristic, complemented
6C2×#64959C212yesmaximal, complemented
7C5×C4⋊#95C211yesmaximal, characteristic, complemented
8#10602356C211yesmaximal, characteristic, complemented
9#10600222C212yesmaximal, complemented
10#10600220C212yesmaximal, complemented
11#10600201C212yesmaximal, complemented
12C23×D20C2211yescharacteristic
13C22×C5×C4⋊C4C2211yescharacteristic
14C22×C5×C4⋊C4C2211yescharacteristic
15C22×C42×C5C2211yescharacteristic
16C22×#685C2212yes—
17C22×#685C2212yes—
18C22×#685C2212yes—
19C22×#685C2212yes—
20C22×#685C2212yes—
21C22×#685C2212yes—
22C22×C4⋊Dic5C2211yescharacteristic
23C22×C4⋊Dic5C2211yescharacteristic
24C22×C4⋊Dic5C2211yescharacteristic
25C22×C4×Dic5C2211yescharacteristic
26C22×C4×Dic5C2212yes—
27C22×C4×Dic5C2211yescharacteristic
28C2×C5×#95C2212yes—
29C2×C5×#95C2212yes—
30C2×#3963C2212yes—
31C2×#3963C2211yescharacteristic
32C2×#3963C2211yescharacteristic
33C2×#3963C2212yes—
34C2×#3963C2212yes—
35#65277—24no—
36#65277—24no—
37C4⋊C4×Dic5—24no—
38#65228C418yescomplemented
39C4×C4⋊Dic5—24no—
40#64959—28no—
41#14022—51nomaximal, Sylow
42C24×D5C2312yes—
43C23×C4×C5C2312yes—
44C23×C4×C5C2311yescharacteristic
45C23×C4×C5C2312yes—
46C23×C4×C5C2311yescharacteristic
47C23×C4×C5C2311yescharacteristic
48C23×Dic5C2312yes—
49C23×Dic5C2311yescharacteristic
50C23×Dic5C2311yescharacteristic
51C23×Dic5C2311yescharacteristic
52C23×Dic5C2311yescharacteristic
53C22×D20—22no—
54C22×D20—22no—
55C22×D20—22no—
56C22×D20—22no—
57C22×D20—22no—
58C22×D20—22no—
59C22×D20C2×C414yes—
60C2×C5×C4⋊C4—22no—
61C2×C5×C4⋊C4—22no—
62C2×C5×C4⋊C4—22no—
63C2×C5×C4⋊C4—22no—
64C2×C5×C4⋊C4—22no—
65C2×C5×C4⋊C4D414yes—
66C2×C42×C5—22no—
67C2×C42×C5—22no—
68C2×C42×C5C2×C414yes—
69C2×#685—24no—
70C2×#685—24no—
71C2×#685—24no—
72C2×#685—24no—
73C2×#685—24no—
74C2×#685—24no—
75C2×#685—24no—
76C2×#685—24no—
77C2×#685—24no—
78C2×#685—24no—
79C2×#685—42no—
80C2×#685—42no—
81C2×#685—42no—
82C2×#685—42no—
83C2×#685—42no—
84C2×#685—42no—
85C2×#685C2×C418yes—
86C2×#685C2×C418yes—
87C2×C4⋊Dic5—22no—
88C2×C4⋊Dic5—22no—
89C2×C4⋊Dic5—22no—
90C2×C4⋊Dic5—22no—
91C2×C4⋊Dic5—22no—
92C2×C4⋊Dic5—22no—
93C2×C4⋊Dic5—22no—
94C2×C4⋊Dic5C2×C414yes—
95C2×C4⋊Dic5D414yescomplemented
96C2×C4×Dic5—22no—
97C2×C4×Dic5—22no—
98C2×C4×Dic5—22no—
99C2×C4×Dic5—24no—
100C2×C4×Dic5—22no—
101C2×C4×Dic5—22no—
102C2×C4×Dic5—24no—
103C2×C4×Dic5—42no—
104C2×C4×Dic5D414yes—
105C5×#95—24no—
106C5×#95—42no—
107#3963—24no—
108#3963—24no—
109#3963—22no—
110#3963—22no—
111#3963—42no—
112C2×#390—51no—
113C2×#390—51no—
114C2×#390—51no—
115C2×#388—52no—
116C2×C4×C4⋊C4—51no—
117C2×C4×C4⋊C4—51no—
118#1440—52no—
119#1439—52no—
120#1437—52no—
121C4⋊#95—51no—
122C4⋊#95D511yescharacteristic, complemented
123C24×C5C2411yescharacteristic
124C23×D5—22no—
125C23×D5—22no—
126C23×D5—22no—
127C23×D5—22no—
128C23×D5—22no—
129C23×D5—22no—
130C23×D5—22no—
131C23×D5—22no—
132C23×D5—22no—
133C23×D5—22no—
134C23×D5—22no—
135C23×D5—22no—
136C23×D5—22no—
137C23×D5—22no—
138C23×D5C22×C414yes—
139C22×C4×C5—21no—
140C22×C4×C5—21no—
141C22×C4×C5—21no—
142C22×C4×C5—21no—
143C22×C4×C5—21no—
144C22×C4×C5—22no—
145C22×C4×C5—21no—
146C22×C4×C5—22no—
147C22×C4×C5—22no—
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—21no—
155C22×C4×C5—22no—
156C22×C4×C5—22no—
157C22×C4×C5—22no—
158C22×C4×C5—22no—
159C22×C4×C5—22no—
160C22×C4×C5—22no—
161C22×C4×C5—22no—
162C22×C4×C5C22×C412yes—
163C22×C4×C5C22×C412yes—
164C22×C4×C5C22×C412yes—
165C22×C4×C5C2×D414yes—
166C22×C4×C5C2×D412yes—
167C22×C4×C5C2×D412yes—
168C22×C4×C5C2×D412yes—
169C22×C4×C5#4112yes—
170C22×C4×C5#4112yes—
171C22×C4×C5#4112yes—
172C22×C4×C5#4112yes—
173C22×C4×C5#4112yes—
174C22×Dic5—21no—
175C22×Dic5—21no—
176C22×Dic5—21no—
177C22×Dic5—21no—
178C22×Dic5—21no—
179C22×Dic5—22no—
180C22×Dic5—21no—
181C22×Dic5—21no—
182C22×Dic5—22no—
183C22×Dic5—21no—
184C22×Dic5—21no—
185C22×Dic5—21no—
186C22×Dic5—21no—
187C22×Dic5—21no—
188C22×Dic5—22no—
189C22×Dic5—21no—
190C22×Dic5—21no—
191C22×Dic5—21no—
192C22×Dic5—21no—
193C22×Dic5—22no—
194C22×Dic5—21no—
195C22×Dic5—22no—
196C22×Dic5—22no—
197C22×Dic5—21no—
198C22×Dic5—21no—
199C22×Dic5—21no—
200C22×Dic5—21no—
201C22×Dic5—21no—
202C22×Dic5C22×C414yes—
203C22×Dic5C2×D412yes—
204C22×Dic5C2×D412yes—
205C22×Dic5C2×D412yes—
206C22×Dic5C2×D412yes—
207C22×Dic5#4112yes—
208C22×Dic5#4112yes—
209C2×D20—28no—
210C2×D20—28no—
211C2×D20—28no—
212C2×D20—44no—
213C2×D20—44no—
214C2×D20—44no—
215C2×D20—44no—
216C5×C4⋊C4—28no—
217C5×C4⋊C4—44no—
218C42×C5—28no—
219#685—216no—
220#685—48no—
221#685—48no—
222#685—48no—
223#685—48no—
224#685—48no—
225C4⋊Dic5—28no—
226C4⋊Dic5—28no—
227C4⋊Dic5—28no—
228C4×Dic5—28no—
229C4×Dic5—48no—
230C4×Dic5—44no—
231C23×D4—51no—
232C22×C4⋊C4—51no—
233C22×C4⋊C4—51no—
234C22×C4⋊C4—51no—
235C22×C4⋊C4C2×D511yescharacteristic
236C22×C4⋊C4C2×D511yescharacteristic
237C22×C22⋊C4—52no—
238C22×C22⋊C4—52no—
239C22×C22⋊C4—52no—
240C22×C22⋊C4—52no—
241C22×C22⋊C4—52no—
242C22×C22⋊C4—52no—
243C22×C42—51no—
244C22×C42—51no—
245C22×C42—52no—
246C22×C42C2×D511yescharacteristic
247#390—58no—
248#390—104no—
249#390—104no—
250#388—108no—
251C4×C4⋊C4—104no—
252C4×C4⋊C4—104no—
253C2×#95—52no—
254C2×#95—51no—
255C2×#95—52no—
256C2×#95—51no—
257C2×#95—52no—
258C2×#95C2×D512yes—
259C2×#95C2×D512yes—
260C23×C5C23×C411yescharacteristic
261C23×C5C22×D411yescharacteristic
262C23×C5C22×D411yescharacteristic
263C23×C5C22×D411yescharacteristic
264C23×C5C2×#4111yescharacteristic
265C23×C5C2×#4111yescharacteristic
266C23×C5C2×#4111yescharacteristic
267C23×C5C2×#4111yescharacteristic
268C23×C5C2×#4111yescharacteristic
269C23×C5C2×#4111yescharacteristic
270C23×C5C2×#4111yescharacteristic
271C23×C5H(5,𝔽2)11yescharacteristic
272C23×C5H(5,𝔽2)11yescharacteristic
273C23×C5H(5,𝔽2)11yescharacteristic
274C23×C52−1+411yescharacteristic
275C22×D5—24no—
276C22×D5—24no—
277C22×D5—24no—
278C22×D5—24no—
279C22×D5—24no—
280C22×D5—24no—
281C22×D5—24no—
282C22×D5—42no—
283C22×D5—42no—
284C22×D5—42no—
285C22×D5—42no—
286C22×D5—42no—
287C22×D5—42no—
288C22×D5—42no—
289C22×D5—42no—
290C22×D5—42no—
291C22×D5—42no—
292C22×D5—42no—
293C22×D5—42no—
294C22×D5—42no—
295C22×D5—42no—
296C22×D5—42no—
297C22×D5—42no—
298C22×D5—42no—
299C22×D5—42no—
300C22×D5—42no—
301C22×D5—42no—
302C22×D5—42no—
303C22×D5—42no—
304C22×D5—42no—
305C22×D5—42no—
306C22×D5—42no—
307C22×D5—42no—
308C22×D5—42no—
309C22×D5—42no—
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—24no—
320C2×C4×C5—24no—
321C2×C4×C5—24no—
322C2×C4×C5—42no—
323C2×C4×C5—41no—
324C2×C4×C5—41no—
325C2×C4×C5—41no—
326C2×C4×C5—42no—
327C2×C4×C5—41no—
328C2×C4×C5—42no—
329C2×C4×C5—42no—
330C2×C4×C5—42no—
331C2×C4×C5—42no—
332C2×C4×C5—42no—
333C2×C4×C5—42no—
334C2×C4×C5—42no—
335C2×C4×C5—42no—
336C2×C4×C5—42no—
337C2×C4×C5#11714yes—
338C2×C4×C5C4×D414yes—
339C2×C4×C5C4×D414yes—
340C2×C4×C5C4×D414yes—
341C2×C4×C5#12114yes—
342C2×C4×C5#12314yes—
343C2×C4×C5#12414yes—
344C2×C4×C5#12614yes—
345C2×Dic5—22no—
346C2×Dic5—22no—
347C2×Dic5—22no—
348C2×Dic5—22no—
349C2×Dic5—22no—
350C2×Dic5—22no—
351C2×Dic5—24no—
352C2×Dic5—24no—
353C2×Dic5—24no—
354C2×Dic5—22no—
355C2×Dic5—22no—
356C2×Dic5—22no—
357C2×Dic5—22no—
358C2×Dic5—22no—
359C2×Dic5—22no—
360C2×Dic5—22no—
361C2×Dic5—22no—
362C2×Dic5—22no—
363C2×Dic5—41no—
364C2×Dic5—41no—
365C2×Dic5—41no—
366C2×Dic5—41no—
367C2×Dic5—42no—
368C2×Dic5—41no—
369C2×Dic5—41no—
370C2×Dic5—42no—
371C2×Dic5—42no—
372C2×Dic5—41no—
373C2×Dic5—41no—
374C2×Dic5—41no—
375C2×Dic5—41no—
376C2×Dic5—41no—
377C2×Dic5—41no—
378C2×Dic5—42no—
379C2×Dic5#12114yes—
380D20—416no—
381C25—52no—
382C22×D4—54no—
383C22×D4—102no—
384C22×D4—102no—
385C22×D4—102no—
386C22×D4—102no—
387C22×D4—102no—
388C22×D4—102no—
389C23×C4—51no—
390C23×C4—52no—
391C23×C4—51no—
392C23×C4—51no—
393C23×C4—51no—
394C23×C4C22×D512yes—
395C23×C4C22×D511yescharacteristic
396C23×C4C22×D512yes—
397C23×C4C22×D511yescharacteristic
398C23×C4C22×D511yescharacteristic
399C2×C4⋊C4—22no—
400C2×C4⋊C4—22no—
401C2×C4⋊C4—22no—
402C2×C4⋊C4—22no—
403C2×C4⋊C4—22no—
404C2×C4⋊C4—54no—
405C2×C4⋊C4—54no—
406C2×C4⋊C4—102no—
407C2×C4⋊C4—102no—
408C2×C4⋊C4—102no—
409C2×C4⋊C4—102no—
410C2×C4⋊C4—102no—
411C2×C4⋊C4—102no—
412C2×C4⋊C4—102no—
413C2×C4⋊C4D2014yes—
414C2×C22⋊C4—58no—
415C2×C22⋊C4—58no—
416C2×C22⋊C4—104no—
417C2×C22⋊C4—104no—
418C2×C22⋊C4—104no—
419C2×C22⋊C4—104no—
420C2×C22⋊C4—104no—
421C2×C22⋊C4—104no—
422C2×C22⋊C4—104no—
423C2×C22⋊C4—104no—
424C2×C22⋊C4—104no—
425C2×C22⋊C4—104no—
426C2×C22⋊C4—202no—
427C2×C22⋊C4—202no—
428C2×C22⋊C4—202no—
429C2×C22⋊C4—202no—
430C2×C22⋊C4—202no—
431C2×C22⋊C4—202no—
432C2×C42—22no—
433C2×C42—22no—
434C2×C42—54no—
435C2×C42—102no—
436C2×C42—102no—
437C2×C42—104no—
438C2×C42—104no—
439C2×C42—102no—
440C2×C42—102no—
441C2×C42—102no—
442C2×C42—202no—
443C2×C42C4×D514yes—
444#95—24no—
445#95—42no—
446#95—102no—
447#95—102no—
448#95—104no—
449#95—104no—
450#95—202no—
451C22×C5C2×#11711yescharacteristic
452C22×C5C2×C4×D411yescharacteristic
453C22×C5C2×C4×D411yescharacteristic
454C22×C5C2×C4×D411yescharacteristic
455C22×C5C4×#4111yescharacteristic
456C22×C5#51811yescharacteristic
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#53511yescharacteristic
467C22×C5#53711yescharacteristic
468C22×C5#54011yescharacteristic
469C22×C5#54211yescharacteristic
470C22×C5D4211yescharacteristic
471C22×C5#54611yescharacteristic
472C22×C5#54711yescharacteristic
473C22×C5#54811yescharacteristic
474C22×C5#55011yescharacteristic
475C22×C5#55011yescharacteristic
476C22×C5#55011yescharacteristic
477C22×C5#55311yescharacteristic
478C22×C5#55311yescharacteristic
479C22×C5#55511yescharacteristic
480C22×C5#55611yescharacteristic
481C22×C5#55611yescharacteristic
482C22×C5#55911yescharacteristic
483C22×C5#55911yescharacteristic
484C22×C5#55911yescharacteristic
485C22×C5#55911yescharacteristic
486C2×D5—44no—
487C2×D5—44no—
488C2×D5—44no—
489C2×D5—44no—
490C2×D5—44no—
491C2×D5—44no—
492C2×D5—44no—
493C2×D5—82no—
494C2×D5—82no—
495C2×D5—82no—
496C2×D5—82no—
497C2×D5—82no—
498C2×D5—82no—
499C2×D5—82no—
500C2×D5—82no—
501C4×C5—24no—
502C4×C5—42no—
503C4×C5—44no—
504C4×C5—82no—
505C4×C5#38818yescomplemented
506Dic5—24no—
507Dic5—44no—
508Dic5—42no—
509Dic5—42no—
510Dic5—42no—
511C24—54no—
512C24—102no—
513C24—102no—
514C24—102no—
515C24—102no—
516C24—102no—
517C24—102no—
518C24—102no—
519C24—102no—
520C24—102no—
521C24—102no—
522C24—102no—
523C24—102no—
524C24—102no—
525C24—102no—
526C24C23×D511yescharacteristic
527C2×D4—108no—
528C2×D4—108no—
529C2×D4—108no—
530C2×D4—204no—
531C2×D4—204no—
532C2×D4—204no—
533C2×D4—204no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—22no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—21no—
544C22×C4—22no—
545C22×C4—21no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—52no—
558C22×C4—52no—
559C22×C4—52no—
560C22×C4—54no—
561C22×C4—52no—
562C22×C4—52no—
563C22×C4—52no—
564C22×C4—101no—
565C22×C4—101no—
566C22×C4—101no—
567C22×C4—101no—
568C22×C4—101no—
569C22×C4—102no—
570C22×C4—101no—
571C22×C4—101no—
572C22×C4—102no—
573C22×C4—102no—
574C22×C4—101no—
575C22×C4—101no—
576C22×C4—101no—
577C22×C4—101no—
578C22×C4—101no—
579C22×C4—101no—
580C22×C4—101no—
581C22×C4—102no—
582C22×C4—101no—
583C22×C4—101no—
584C22×C4—101no—
585C22×C4—101no—
586C22×C4—101no—
587C22×C4—101no—
588C22×C4—102no—
589C22×C4—102no—
590C22×C4—101no—
591C22×C4—101no—
592C22×C4C2×C4×D512yes—
593C22×C4C2×C4×D512yes—
594C22×C4C2×C4×D512yes—
595C22×C4C2×D2014yes—
596C22×C4C2×D2012yes—
597C22×C4#70912yes—
598C22×C4D4×D512yes—
599C22×C4D4×D512yes—
600C22×C4#71112yes—
601C22×C4#71112yes—
602C22×C4#71312yes—
603C22×C4#71312yes—
604C4⋊C4—28no—
605C4⋊C4—44no—
606C4⋊C4—108no—
607C4⋊C4—108no—
608C4⋊C4—108no—
609C22⋊C4—1016no—
610C22⋊C4—208no—
611C22⋊C4—208no—
612C22⋊C4—208no—
613C22⋊C4—208no—
614C22⋊C4—208no—
615C42—28no—
616C42—108no—
617C42—208no—
618C42—204no—
619C2×C5C2×#38811yescharacteristic
620C2×C5C4×#12111yescharacteristic
621C2×C5#232411yescharacteristic
622C2×C5#235411yescharacteristic
623C2×C5#235711yescharacteristic
624C2×C5#236611yescharacteristic
625C2×C5#236711yescharacteristic
626C2×C5#241411yescharacteristic
627C2×C5#241611yescharacteristic
628C2×C5#244511yescharacteristic
629C2×C5#244811yescharacteristic
630C2×C5#251211yescharacteristic
631C2×C5#251311yescharacteristic
632C2×C5#254811yescharacteristic
633C2×C5#259211yescharacteristic
634D5—84no—
635C23—104no—
636C23—104no—
637C23—104no—
638C23—104no—
639C23—104no—
640C23—104no—
641C23—104no—
642C23—202no—
643C23—202no—
644C23—202no—
645C23—202no—
646C23—202no—
647C23—202no—
648C23—202no—
649C23—202no—
650C23—202no—
651C23—202no—
652C23—202no—
653C23—202no—
654C23—202no—
655C23—202no—
656C23—202no—
657C23—202no—
658C23—202no—
659C23—202no—
660C23—202no—
661C23—202no—
662C23—202no—
663C23—202no—
664C23—202no—
665C23—202no—
666C23—202no—
667C23—202no—
668C23—202no—
669C23—202no—
670C23C22×C4×D511yescharacteristic
671C23C22×D2011yescharacteristic
672C23C2×#70911yescharacteristic
673C23C2×D4×D511yescharacteristic
674C23C2×D4×D511yescharacteristic
675C23C2×#71111yescharacteristic
676C23C2×#71111yescharacteristic
677C23#414411yescharacteristic
678C23C2×#71311yescharacteristic
679C23C2×#71311yescharacteristic
680C23#414711yescharacteristic
681C23D5×#4111yescharacteristic
682C23D5×#4111yescharacteristic
683C23#414911yescharacteristic
684C23#414911yescharacteristic
685D4—2016no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—24no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—24no—
697C2×C4—24no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—42no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—54no—
714C2×C4—102no—
715C2×C4—102no—
716C2×C4—102no—
717C2×C4—102no—
718C2×C4—102no—
719C2×C4—102no—
720C2×C4—102no—
721C2×C4—104no—
722C2×C4—104no—
723C2×C4—102no—
724C2×C4—104no—
725C2×C4—102no—
726C2×C4—102no—
727C2×C4—102no—
728C2×C4—102no—
729C2×C4—102no—
730C2×C4—102no—
731C2×C4—102no—
732C2×C4—201no—
733C2×C4—201no—
734C2×C4—201no—
735C2×C4—201no—
736C2×C4—202no—
737C2×C4—202no—
738C2×C4—201no—
739C2×C4—201no—
740C2×C4—201no—
741C2×C4—201no—
742C2×C4—202no—
743C2×C4—202no—
744C2×C4—201no—
745C2×C4—201no—
746C2×C4—201no—
747C2×C4—201no—
748C2×C4C4×D2014yes—
749C2×C4#402714yes—
750C2×C4#403114yes—
751C2×C4#403214yes—
752C2×C4#403814yes—
753C2×C4#403914yes—
754C2×C4#404114yes—
755C2×C4#404414yes—
756C5#1402211yescharacteristic, complemented, Sylow
757C22—204no—
758C22—204no—
759C22—204no—
760C22—204no—
761C22—204no—
762C22—204no—
763C22—204no—
764C22—402no—
765C22—402no—
766C22—402no—
767C22—402no—
768C22—402no—
769C22—402no—
770C22—402no—
771C22—402no—
772C22C2×C4×D2011yescharacteristic
773C22C2×#402711yescharacteristic
774C22C2×#403111yescharacteristic
775C22C2×#403211yescharacteristic
776C22C2×#403811yescharacteristic
777C22C2×#403911yescharacteristic
778C22#6583811yescharacteristic
779C22C2×#404111yescharacteristic
780C22C2×#404411yescharacteristic
781C22#6585511yescharacteristic
782C22#6585611yescharacteristic
783C22D4×D2011yescharacteristic
784C22#6588711yescharacteristic
785C22#6588811yescharacteristic
786C22#6589311yescharacteristic
787C22#6590211yescharacteristic
788C22#6591011yescharacteristic
789C22#6591111yescharacteristic
790C22#6591911yescharacteristic
791C22#6593011yescharacteristic
792C22D5×#12111yescharacteristic
793C22#6594111yescharacteristic
794C22#6595311yescharacteristic
795C22#6595811yescharacteristic
796C22#6596111yescharacteristic
797C22#6596311yescharacteristic
798C22#6597711yescharacteristic
799C22#6601511yescharacteristic
800C22#6601511yescharacteristic
801C22#6602911yescharacteristic
802C22#6602911yescharacteristic
803C22#6605211yescharacteristic
804C22#6606011yescharacteristic
805C22#6606611yescharacteristic
806C22#6606811yescharacteristic
807C4—24no—
808C4—42no—
809C4—44no—
810C4—82no—
811C4—104no—
812C4—202no—
813C4—202no—
814C4—202no—
815C4—204no—
816C4#6495918yescomplemented
817C2—404no—
818C2C2×#6495911yescharacteristic
819C2#1060538411yescharacteristic
820C2#1060538511yescharacteristic
821C2#1060559611yescharacteristic
822C2#1060560311yescharacteristic
823C2#1060589111yescharacteristic
824C2#1060605511yescharacteristic
825C2#1060777811yescharacteristic
826C2#1060777911yescharacteristic
827C2#1060794011yescharacteristic
828C2#1060794211yescharacteristic
829C2#1060804811yescharacteristic
830C2#1060808411yescharacteristic
831C2#1060823811yescharacteristic
832C2#1060828611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D5
commutatorC23×C5C23×C4
FittingC5×C4⋊#95C2
socle, cosocleC24×C5C24
prime radicalC23×D20C22
hypercenterC4⋊#95D5
hypocenterC5#14022
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
3. C2×C4⋊C4×Dic5C2semidirect
5. C2×C4×C4⋊Dic5C2semidirect
6. C2×#64959C2semidirect
7. C5×C4⋊#95C2semidirect
8. #10602356C2semidirect
9. #10600222C2semidirect
10. #10600220C2semidirect
11. #10600201C2semidirect
38. #65228C4semidirect
95. C2×C4⋊Dic5D4semidirect
122. C4⋊#95D5semidirect
505. C4×C5#388semidirect
756. C5#14022semidirect
816. C4#64959semidirect

Maximal subgroups

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

subgroupindex
C2×#652772
C2×C4⋊C4×Dic52
C2×#652282
C2×C4×C4⋊Dic52
C2×#649592
C5×C4⋊#952
#106023562
#106002222
#106002202
#106002012
#140225