Finite Group Databasebeta

← #12022150

Subgroups — #12022150

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×C5×#389C211yesmaximal, characteristic, complemented
2C2×#65276C211yesmaximal, characteristic
3C2×#65276C211yesmaximal, characteristic
4C2×#65279C212yesmaximal
5C2×C4×C4⋊Dic5C211yesmaximal, characteristic, complemented
6C2×C4×#685C211yesmaximal, characteristic
7#10602357C212yesmaximal, complemented
8#10602356C211yesmaximal, characteristic, complemented
9#10602356C211yesmaximal, characteristic, complemented
10#10600222C212yesmaximal
11#10600210C212yesmaximal, complemented
12C23×C4×D5C2211yescharacteristic
13C22×C5×C4⋊C4C2211yescharacteristic
14C22×C5×C4⋊C4C2212yes—
15C22×C5×C4⋊C4C2211yescharacteristic
16C22×C42×C5C2211yescharacteristic
17C22×#685C2211yescharacteristic
18C22×#685C2212yes—
19C22×#685C2212yes—
20C22×#685C2211yescharacteristic
21C22×C4⋊Dic5C2211yescharacteristic
22C22×C4⋊Dic5C2211yescharacteristic
23C22×C4×Dic5C2211yescharacteristic
24C22×C4×Dic5C2212yes—
25C5×#389—24no—
26C2×C5×#95C2212yes—
27C2×#3963C2211yescharacteristic
28C2×#3963C2212yes—
29C2×#3963C2212yes—
30C2×#3963C2212yes—
31C2×#3963C2212yes—
32C2×#3963C2211yescharacteristic
33C2×#3963C2212yes—
34C2×#3963C2212yes—
35C2×#3963C2212yes—
36#65279—28no—
37#65276—24no—
38#65276C418yescomplemented
39C4×#685—24no—
40C4×C4⋊Dic5—24no—
41#13974—51nomaximal, Sylow
42C24×D5C2311yescharacteristic
43C23×C4×C5C2312yes—
44C23×C4×C5C2312yes—
45C23×C4×C5C2311yescharacteristic
46C23×C4×C5C2311yescharacteristic
47C23×C4×C5C2311yescharacteristic
48C23×Dic5C2312yes—
49C23×Dic5C2311yescharacteristic
50C23×Dic5C2312yes—
51C23×Dic5C2311yescharacteristic
52C23×Dic5C2311yescharacteristic
53C22×C4×D5—22no—
54C22×C4×D5—22no—
55C22×C4×D5—22no—
56C22×C4×D5—22no—
57C22×C4×D5—22no—
58C22×C4×D5—22no—
59C22×C4×D5C2×C414yes—
60C2×C5×C4⋊C4—22no—
61C2×C5×C4⋊C4—22no—
62C2×C5×C4⋊C4—24no—
63C2×C5×C4⋊C4—22no—
64C2×C5×C4⋊C4—22no—
65C2×C5×C4⋊C4—24no—
66C2×C5×C4⋊C4—24no—
67C2×C5×C4⋊C4—22no—
68C2×C5×C4⋊C4C2×C414yes—
69C2×C42×C5—22no—
70C2×C42×C5—22no—
71C2×C42×C5D414yes—
72C2×#685—24no—
73C2×#685—22no—
74C2×#685—24no—
75C2×#685—22no—
76C2×#685—22no—
77C2×#685—22no—
78C2×#685—22no—
79C2×#685—24no—
80C2×#685—24no—
81C2×#685—42no—
82C2×#685C2×C418yes—
83C2×#685D414yes—
84C2×C4⋊Dic5—22no—
85C2×C4⋊Dic5—22no—
86C2×C4⋊Dic5—22no—
87C2×C4⋊Dic5—22no—
88C2×C4⋊Dic5C2×C414yes—
89C2×C4⋊Dic5D414yes—
90C2×C4×Dic5—22no—
91C2×C4×Dic5—24no—
92C2×C4×Dic5—22no—
93C2×C4×Dic5—22no—
94C2×C4×Dic5—24no—
95C2×C4×Dic5—42no—
96C5×#95—24no—
97#3963—22no—
98#3963—22no—
99#3963—24no—
100#3963—24no—
101#3963—24no—
102#3963—24no—
103#3963—24no—
104#3963—42no—
105#3963C2×C418yes—
106C2×#389D511yescharacteristic, complemented
107C2×#388—52no—
108C2×#380—51no—
109C2×#380—51no—
110C2×C4×C4⋊C4—51no—
111C2×C4×C22⋊C4—51no—
112#1443—52no—
113#1440—52no—
114#1436—52no—
115C4⋊#95—51no—
116C4⋊#95—51no—
117C24×C5C2411yescharacteristic
118C23×D5—21no—
119C23×D5—21no—
120C23×D5—21no—
121C23×D5—21no—
122C23×D5—21no—
123C23×D5—21no—
124C23×D5—21no—
125C23×D5—21no—
126C23×D5—21no—
127C23×D5—21no—
128C23×D5—21no—
129C23×D5—21no—
130C23×D5C22×C412yes—
131C23×D5C2×D412yes—
132C23×D5#4112yes—
133C22×C4×C5—21no—
134C22×C4×C5—21no—
135C22×C4×C5—21no—
136C22×C4×C5—21no—
137C22×C4×C5—21no—
138C22×C4×C5—22no—
139C22×C4×C5—22no—
140C22×C4×C5—21no—
141C22×C4×C5—22no—
142C22×C4×C5—22no—
143C22×C4×C5—22no—
144C22×C4×C5—22no—
145C22×C4×C5—21no—
146C22×C4×C5—21no—
147C22×C4×C5—21no—
148C22×C4×C5—21no—
149C22×C4×C5—22no—
150C22×C4×C5—22no—
151C22×C4×C5—22no—
152C22×C4×C5—22no—
153C22×C4×C5—22no—
154C22×C4×C5—22no—
155C22×C4×C5—22no—
156C22×C4×C5C22×C414yes—
157C22×C4×C5C22×C412yes—
158C22×C4×C5C2×D412yes—
159C22×C4×C5C2×D412yes—
160C22×C4×C5C2×D412yes—
161C22×C4×C5C2×D412yes—
162C22×C4×C5C2×D412yes—
163C22×C4×C5#4112yes—
164C22×C4×C5#4112yes—
165C22×C4×C5#4112yes—
166C22×C4×C5#4112yes—
167C22×C4×C5#4112yes—
168C22×Dic5—21no—
169C22×Dic5—21no—
170C22×Dic5—22no—
171C22×Dic5—22no—
172C22×Dic5—22no—
173C22×Dic5—21no—
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—21no—
183C22×Dic5—21no—
184C22×Dic5—22no—
185C22×Dic5—22no—
186C22×Dic5—22no—
187C22×Dic5—21no—
188C22×Dic5—22no—
189C22×Dic5—21no—
190C22×Dic5—21no—
191C22×Dic5—22no—
192C22×Dic5—22no—
193C22×Dic5—22no—
194C22×Dic5—21no—
195C22×Dic5—21no—
196C22×Dic5—22no—
197C22×Dic5—21no—
198C22×Dic5C22×C412yes—
199C22×Dic5C22×C414yes—
200C22×Dic5C2×D412yes—
201C22×Dic5C2×D414yes—
202C22×Dic5#4112yes—
203C2×C4×D5—28no—
204C2×C4×D5—28no—
205C2×C4×D5—28no—
206C2×C4×D5—44no—
207C2×C4×D5—44no—
208C2×C4×D5—44no—
209C2×C4×D5—44no—
210C5×C4⋊C4—28no—
211C5×C4⋊C4—48no—
212C5×C4⋊C4—44no—
213C42×C5—28no—
214#685—28no—
215#685—216no—
216#685—28no—
217#685—48no—
218C4⋊Dic5—28no—
219C4⋊Dic5—28no—
220C4×Dic5—48no—
221C4×Dic5—44no—
222C24×C4—51no—
223C22×C4⋊C4—51no—
224C22×C4⋊C4—51no—
225C22×C4⋊C4C2×D511yescharacteristic
226C22×C4⋊C4C2×D512yes—
227C22×C4⋊C4C2×D511yescharacteristic
228C22×C22⋊C4—52no—
229C22×C22⋊C4—51no—
230C22×C22⋊C4—51no—
231C22×C22⋊C4—52no—
232C22×C42—51no—
233C22×C42—52no—
234C22×C42C2×D511yescharacteristic
235#389—24no—
236#388—108no—
237#380—58no—
238#380—104no—
239C4×C4⋊C4—104no—
240C4×C22⋊C4—104no—
241C2×#95—52no—
242C2×#95—52no—
243C2×#95—52no—
244C2×#95—52no—
245C2×#95—51no—
246C2×#95—52no—
247C2×#95—52no—
248C2×#95—51no—
249C2×#95—52no—
250C2×#95C2×D512yes—
251C23×C5C23×C411yescharacteristic
252C23×C5C22×D411yescharacteristic
253C23×C5C22×D411yescharacteristic
254C23×C5C22×D411yescharacteristic
255C23×C5C2×#4111yescharacteristic
256C23×C5C2×#4111yescharacteristic
257C23×C5C2×#4111yescharacteristic
258C23×C5C2×#4111yescharacteristic
259C23×C5C2×#4111yescharacteristic
260C23×C5C2×#4111yescharacteristic
261C23×C5C2×#4111yescharacteristic
262C23×C5H(5,𝔽2)11yescharacteristic
263C23×C52−1+411yescharacteristic
264C23×C52−1+411yescharacteristic
265C23×C52−1+411yescharacteristic
266C22×D5—22no—
267C22×D5—22no—
268C22×D5—22no—
269C22×D5—22no—
270C22×D5—22no—
271C22×D5—22no—
272C22×D5—22no—
273C22×D5—22no—
274C22×D5—22no—
275C22×D5—22no—
276C22×D5—22no—
277C22×D5—22no—
278C22×D5—22no—
279C22×D5—22no—
280C22×D5—22no—
281C22×D5—22no—
282C22×D5—22no—
283C22×D5—22no—
284C22×D5—41no—
285C22×D5—41no—
286C22×D5—41no—
287C22×D5—41no—
288C22×D5—41no—
289C22×D5—41no—
290C22×D5—41no—
291C22×D5—41no—
292C22×D5—41no—
293C22×D5—41no—
294C22×D5—41no—
295C22×D5—41no—
296C22×D5—41no—
297C22×D5—41no—
298C22×D5—41no—
299C22×D5—41no—
300C22×D5C4×D414yes—
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—24no—
308C2×C4×C5—24no—
309C2×C4×C5—24no—
310C2×C4×C5—22no—
311C2×C4×C5—22no—
312C2×C4×C5—22no—
313C2×C4×C5—42no—
314C2×C4×C5—42no—
315C2×C4×C5—42no—
316C2×C4×C5—42no—
317C2×C4×C5—41no—
318C2×C4×C5—41no—
319C2×C4×C5—41no—
320C2×C4×C5—41no—
321C2×C4×C5—42no—
322C2×C4×C5—42no—
323C2×C4×C5—42no—
324C2×C4×C5—42no—
325C2×C4×C5—42no—
326C2×C4×C5—42no—
327C2×C4×C5—42no—
328C2×C4×C5#11714yes—
329C2×C4×C5C4×D414yes—
330C2×C4×C5C4×D414yes—
331C2×C4×C5#12114yes—
332C2×C4×C5#12114yes—
333C2×C4×C5#12314yes—
334C2×C4×C5#12414yes—
335C2×C4×C5#12614yes—
336C2×Dic5—22no—
337C2×Dic5—24no—
338C2×Dic5—24no—
339C2×Dic5—22no—
340C2×Dic5—22no—
341C2×Dic5—24no—
342C2×Dic5—22no—
343C2×Dic5—24no—
344C2×Dic5—22no—
345C2×Dic5—24no—
346C2×Dic5—22no—
347C2×Dic5—22no—
348C2×Dic5—24no—
349C2×Dic5—22no—
350C2×Dic5—22no—
351C2×Dic5—41no—
352C2×Dic5—41no—
353C2×Dic5—41no—
354C2×Dic5—41no—
355C2×Dic5—41no—
356C2×Dic5—41no—
357C2×Dic5—42no—
358C2×Dic5—41no—
359C2×Dic5—41no—
360C2×Dic5—42no—
361C2×Dic5—42no—
362C2×Dic5—42no—
363C2×Dic5—42no—
364C2×Dic5—42no—
365C2×Dic5—41no—
366C2×Dic5—41no—
367C2×Dic5—42no—
368C2×Dic5—42no—
369C2×Dic5—41no—
370C2×Dic5—41no—
371C4×D5—416no—
372C25—51no—
373C23×C4—52no—
374C23×C4—52no—
375C23×C4—51no—
376C23×C4—51no—
377C23×C4—51no—
378C23×C4—54no—
379C23×C4—102no—
380C23×C4—102no—
381C23×C4—102no—
382C23×C4—102no—
383C23×C4—102no—
384C23×C4—102no—
385C23×C4C22×D512yes—
386C23×C4C22×D512yes—
387C23×C4C22×D511yescharacteristic
388C23×C4C22×D511yescharacteristic
389C23×C4C22×D511yescharacteristic
390C2×C4⋊C4—22no—
391C2×C4⋊C4—22no—
392C2×C4⋊C4—22no—
393C2×C4⋊C4—24no—
394C2×C4⋊C4—24no—
395C2×C4⋊C4—22no—
396C2×C4⋊C4—24no—
397C2×C4⋊C4—22no—
398C2×C4⋊C4—54no—
399C2×C4⋊C4—54no—
400C2×C4⋊C4—102no—
401C2×C4⋊C4—102no—
402C2×C4⋊C4—102no—
403C2×C4⋊C4—102no—
404C2×C4⋊C4C4×D514yes—
405C2×C22⋊C4—58no—
406C2×C22⋊C4—54no—
407C2×C22⋊C4—102no—
408C2×C22⋊C4—104no—
409C2×C22⋊C4—104no—
410C2×C22⋊C4—102no—
411C2×C22⋊C4—102no—
412C2×C22⋊C4—102no—
413C2×C22⋊C4—102no—
414C2×C22⋊C4—104no—
415C2×C22⋊C4—104no—
416C2×C22⋊C4—202no—
417C2×C42—22no—
418C2×C42—22no—
419C2×C42—104no—
420C2×C42—104no—
421C2×C42—102no—
422C2×C42—102no—
423C2×C42—102no—
424C2×C42—202no—
425C2×C42C22⋊D514yes—
426#95—24no—
427#95—58no—
428#95—104no—
429#95—104no—
430#95—104no—
431#95—104no—
432#95—104no—
433#95—102no—
434#95—102no—
435#95—202no—
436C22×C5C2×#11711yescharacteristic
437C22×C5C2×C4×D411yescharacteristic
438C22×C5C2×C4×D411yescharacteristic
439C22×C5C2×C4×D411yescharacteristic
440C22×C5C4×#4111yescharacteristic
441C22×C5#51911yescharacteristic
442C22×C5#52011yescharacteristic
443C22×C5C2×#12111yescharacteristic
444C22×C5C2×#12111yescharacteristic
445C22×C5C2×#12311yescharacteristic
446C22×C5#52511yescharacteristic
447C22×C5C2×#12411yescharacteristic
448C22×C5C2×#12611yescharacteristic
449C22×C5#52911yescharacteristic
450C22×C5#53211yescharacteristic
451C22×C5#53611yescharacteristic
452C22×C5#53711yescharacteristic
453C22×C5#54111yescharacteristic
454C22×C5#54211yescharacteristic
455C22×C5D4211yescharacteristic
456C22×C5#54711yescharacteristic
457C22×C5#54711yescharacteristic
458C22×C5#54711yescharacteristic
459C22×C5#54711yescharacteristic
460C22×C5#54811yescharacteristic
461C22×C5#54811yescharacteristic
462C22×C5#55211yescharacteristic
463C22×C5#55211yescharacteristic
464C22×C5#55211yescharacteristic
465C22×C5#55311yescharacteristic
466C22×C5#55311yescharacteristic
467C22×C5#55311yescharacteristic
468C22×C5#55611yescharacteristic
469C22×C5#55611yescharacteristic
470C22×C5#55611yescharacteristic
471C2×D5—24no—
472C2×D5—24no—
473C2×D5—24no—
474C2×D5—42no—
475C2×D5—42no—
476C2×D5—42no—
477C2×D5—42no—
478C2×D5—42no—
479C2×D5—42no—
480C2×D5—42no—
481C2×D5—42no—
482C2×D5—42no—
483C2×D5—42no—
484C2×D5—42no—
485C2×D5—42no—
486C4×C5—24no—
487C4×C5—42no—
488C4×C5—44no—
489C4×C5—82no—
490C4×C5#38818yescomplemented
491Dic5—42no—
492Dic5—44no—
493Dic5—44no—
494Dic5—42no—
495Dic5—42no—
496C24—52no—
497C24—52no—
498C24—52no—
499C24—101no—
500C24—101no—
501C24—101no—
502C24—101no—
503C24—101no—
504C24—101no—
505C24—101no—
506C24—101no—
507C24—101no—
508C24—101no—
509C24—101no—
510C24—101no—
511C24C23×D511yescharacteristic
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—22no—
517C22×C4—21no—
518C22×C4—22no—
519C22×C4—21no—
520C22×C4—22no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—52no—
536C22×C4—54no—
537C22×C4—52no—
538C22×C4—54no—
539C22×C4—52no—
540C22×C4—102no—
541C22×C4—101no—
542C22×C4—101no—
543C22×C4—102no—
544C22×C4—102no—
545C22×C4—102no—
546C22×C4—101no—
547C22×C4—101no—
548C22×C4—101no—
549C22×C4—101no—
550C22×C4—101no—
551C22×C4—101no—
552C22×C4—102no—
553C22×C4—102no—
554C22×C4—101no—
555C22×C4—101no—
556C22×C4—101no—
557C22×C4—101no—
558C22×C4—102no—
559C22×C4—102no—
560C22×C4—102no—
561C22×C4—102no—
562C22×C4—101no—
563C22×C4—101no—
564C22×C4—102no—
565C22×C4—102no—
566C22×C4—101no—
567C22×C4—101no—
568C22×C4—101no—
569C22×C4—101no—
570C22×C4—108no—
571C22×C4—108no—
572C22×C4—108no—
573C22×C4—204no—
574C22×C4—204no—
575C22×C4—204no—
576C22×C4—204no—
577C22×C4C2×C4×D514yes—
578C22×C4C2×C4×D512yes—
579C22×C4#70912yes—
580C22×C4D4×D512yes—
581C22×C4D4×D512yes—
582C22×C4#71112yes—
583C22×C4#71112yes—
584C22×C4#71312yes—
585C22×C4#71312yes—
586C22×C4C2×C22⋊D512yes—
587C22×C4C2×C22⋊D512yes—
588C22×C4C2×C22⋊D512yes—
589C4⋊C4—28no—
590C4⋊C4—48no—
591C4⋊C4—44no—
592C4⋊C4—108no—
593C4⋊C4—108no—
594C22⋊C4—1016no—
595C22⋊C4—108no—
596C22⋊C4—108no—
597C22⋊C4—208no—
598C42—28no—
599C42—208no—
600C42—204no—
601C2×C5C2×#38811yescharacteristic
602C2×C5C4×#12111yescharacteristic
603C2×C5#232311yescharacteristic
604C2×C5#234411yescharacteristic
605C2×C5#234711yescharacteristic
606C2×C5#236111yescharacteristic
607C2×C5#236211yescharacteristic
608C2×C5#241511yescharacteristic
609C2×C5#241611yescharacteristic
610C2×C5#242111yescharacteristic
611C2×C5#242211yescharacteristic
612C2×C5#249411yescharacteristic
613C2×C5#249611yescharacteristic
614C2×C5#254711yescharacteristic
615C2×C5#256211yescharacteristic
616D5—44no—
617C23—54no—
618C23—102no—
619C23—102no—
620C23—102no—
621C23—102no—
622C23—102no—
623C23—102no—
624C23—102no—
625C23—102no—
626C23—102no—
627C23—102no—
628C23—102no—
629C23—102no—
630C23—102no—
631C23—102no—
632C23—102no—
633C23—102no—
634C23—102no—
635C23—102no—
636C23—201no—
637C23—201no—
638C23—201no—
639C23—201no—
640C23—201no—
641C23—201no—
642C23—201no—
643C23—201no—
644C23—201no—
645C23—201no—
646C23—201no—
647C23—201no—
648C23—201no—
649C23—201no—
650C23—201no—
651C23—201no—
652C23C22×C4×D511yescharacteristic
653C23C2×#70911yescharacteristic
654C23C2×D4×D511yescharacteristic
655C23C2×D4×D511yescharacteristic
656C23C2×#71111yescharacteristic
657C23C2×#71111yescharacteristic
658C23C2×#71311yescharacteristic
659C23C2×#71311yescharacteristic
660C23#414711yescharacteristic
661C23#414711yescharacteristic
662C23D5×#4111yescharacteristic
663C23D5×#4111yescharacteristic
664C23#414911yescharacteristic
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—24no—
674C2×C4—24no—
675C2×C4—24no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—102no—
695C2×C4—102no—
696C2×C4—102no—
697C2×C4—104no—
698C2×C4—102no—
699C2×C4—104no—
700C2×C4—102no—
701C2×C4—104no—
702C2×C4—102no—
703C2×C4—102no—
704C2×C4—104no—
705C2×C4—104no—
706C2×C4—104no—
707C2×C4—102no—
708C2×C4—102no—
709C2×C4—202no—
710C2×C4—202no—
711C2×C4—201no—
712C2×C4—201no—
713C2×C4—201no—
714C2×C4—201no—
715C2×C4—201no—
716C2×C4—202no—
717C2×C4—201no—
718C2×C4—201no—
719C2×C4—201no—
720C2×C4—201no—
721C2×C4—201no—
722C2×C4—202no—
723C2×C4—202no—
724C2×C4—202no—
725C2×C4—201no—
726C2×C4—201no—
727C2×C4—202no—
728C2×C4—202no—
729C2×C4—2016no—
730C2×C4#403814yes—
731C2×C4#403914yes—
732C2×C4#404014yes—
733C2×C4#404414yes—
734C2×C4C4×C22⋊D514yes—
735C2×C4#408414yes—
736C2×C4#408514yes—
737C2×C4#409314yes—
738C5#1397411yescharacteristic, complemented, Sylow
739C22—104no—
740C22—104no—
741C22—104no—
742C22—202no—
743C22—202no—
744C22—202no—
745C22—202no—
746C22—202no—
747C22—202no—
748C22—202no—
749C22—202no—
750C22—202no—
751C22—202no—
752C22—202no—
753C22—202no—
754C22C2×#403811yescharacteristic
755C22C2×#403911yescharacteristic
756C22C2×#404011yescharacteristic
757C22C2×#404411yescharacteristic
758C22C4×#71111yescharacteristic
759C22C4×D4×D511yescharacteristic
760C22#6588211yescharacteristic
761C22#6589111yescharacteristic
762C22#6590611yescharacteristic
763C22#6590811yescharacteristic
764C22#6591611yescharacteristic
765C22#6591711yescharacteristic
766C22#6593211yescharacteristic
767C22#6594311yescharacteristic
768C22#6594511yescharacteristic
769C22#6595211yescharacteristic
770C22#6596511yescharacteristic
771C22#6596711yescharacteristic
772C22#6597311yescharacteristic
773C22#6597511yescharacteristic
774C22#6602811yescharacteristic
775C22#6602811yescharacteristic
776C22#6602911yescharacteristic
777C22#6602911yescharacteristic
778C22#6606011yescharacteristic
779C22#6606011yescharacteristic
780C22#6606611yescharacteristic
781C22#6606611yescharacteristic
782C22C2×C4×C22⋊D511yescharacteristic
783C22C2×#408411yescharacteristic
784C22C2×#408511yescharacteristic
785C22C2×#409311yescharacteristic
786C22#6615011yescharacteristic
787C22#6616211yescharacteristic
788C22#6616711yescharacteristic
789C4—24no—
790C4—42no—
791C4—44no—
792C4—82no—
793C4—202no—
794C4—204no—
795C4—204no—
796C4—202no—
797C4—202no—
798C4#6527918yescomplemented
799C2—204no—
800C2#1060771111yescharacteristic
801C2#1060771511yescharacteristic
802C2#1060793111yescharacteristic
803C2#1060793711yescharacteristic
804C2#1060794511yescharacteristic
805C2#1060794611yescharacteristic
806C2#1060796411yescharacteristic
807C2#1060796811yescharacteristic
808C2C2×#6527911yescharacteristic
809C2C4×#408411yescharacteristic
810C2#1061421911yescharacteristic
811C2#1061443611yescharacteristic
812C2#1061454511yescharacteristic
813C2#1061479411yescharacteristic
814C2#1061497111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D5
commutatorC23×C5C23×C4
FittingC2×C5×#389C2
socle, cosocleC24×C5C24
prime radicalC24×D5C23
hypercenterC2×#389D5
hypocenterC5#13974
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
1. C2×C5×#389C2semidirect
5. C2×C4×C4⋊Dic5C2semidirect
7. #10602357C2semidirect
8. #10602356C2semidirect
9. #10602356C2semidirect
11. #10600210C2semidirect
38. #65276C4semidirect
106. C2×#389D5semidirect
490. C4×C5#388semidirect
738. C5#13974semidirect
798. C4#65279semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#3892
C2×#652762
C2×#652792
C2×C4×C4⋊Dic52
C2×C4×#6852
#106023572
#106023562
#106002222
#106002102
#139745