Finite Group Databasebeta

← #12022403

Subgroups — #12022403

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×#380C211yesmaximal, characteristic
2C2×#65501C211yesmaximal, characteristic
3C2×C4×C22⋊Dic5C211yesmaximal, characteristic
4C2×#65274C211yesmaximal, characteristic, complemented
5C2×C4⋊C4×Dic5C211yesmaximal, characteristic, complemented
6C2×#65240C212yesmaximal
7#10602356C211yesmaximal, characteristic, complemented
8#10602356C211yesmaximal, characteristic, complemented
9#10602341C212yesmaximal
10#10600205C212yesmaximal, complemented
11#10600194C212yesmaximal, complemented
12C24×C4×C5C2211yescharacteristic
13C22×C5×C4⋊C4C2211yescharacteristic
14C22×C5×C4⋊C4C2211yescharacteristic
15C22×C5×C22⋊C4C2212yes—
16C22×C22⋊Dic5C2211yescharacteristic
17C22×C22⋊Dic5C2212yes—
18C22×C22⋊Dic5C2211yescharacteristic
19C22×C4⋊Dic5C2211yescharacteristic
20C22×C4⋊Dic5C2212yes—
21C22×C4⋊Dic5C2211yescharacteristic
22C22×C4×Dic5C2212yes—
23C22×C4×Dic5C2211yescharacteristic
24C22×C4×Dic5C2211yescharacteristic
25C5×#380C418yescomplemented
26C2×C5×#95C2212yes—
27#65501—24no—
28C4×C22⋊Dic5—24no—
29C2×#3963C2211yescharacteristic
30C2×#3963C2212yes—
31C2×#3963C2212yes—
32C2×#3963C2212yes—
33C2×#3963C2212yes—
34C2×#3963C2211yescharacteristic
35C2×#3963C2212yes—
36C2×#3963C2212yes—
37C2×#3963C2212yes—
38#65274—24no—
39C4⋊C4×Dic5—24no—
40#65240—28no—
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×C5C2312yes—
52C23×C4×C5C2312yes—
53C23×C4×C5C2311yescharacteristic
54C23×Dic5C2312yes—
55C23×Dic5C2311yescharacteristic
56C23×Dic5C2312yes—
57C23×Dic5C2311yescharacteristic
58C23×Dic5C2311yescharacteristic
59C23×Dic5C2311yescharacteristic
60C2×C5×C4⋊C4—22no—
61C2×C5×C4⋊C4—22no—
62C2×C5×C4⋊C4—22no—
63C2×C5×C4⋊C4—22no—
64C2×C5×C4⋊C4C2×C414yes—
65C2×C5×C4⋊C4C2×C414yes—
66C2×C5×C22⋊C4—24no—
67C2×C5×C22⋊C4—24no—
68C2×C5×C22⋊C4C2×C418yes—
69C2×C22⋊Dic5—22no—
70C2×C22⋊Dic5—22no—
71C2×C22⋊Dic5—22no—
72C2×C22⋊Dic5—22no—
73C2×C22⋊Dic5—22no—
74C2×C22⋊Dic5—24no—
75C2×C22⋊Dic5—24no—
76C2×C22⋊Dic5—42no—
77C2×C22⋊Dic5D414yes—
78C2×C4⋊Dic5—22no—
79C2×C4⋊Dic5—22no—
80C2×C4⋊Dic5—22no—
81C2×C4⋊Dic5—22no—
82C2×C4⋊Dic5—22no—
83C2×C4⋊Dic5—24no—
84C2×C4⋊Dic5—24no—
85C2×C4⋊Dic5—42no—
86C2×C4⋊Dic5D414yes—
87C2×C4×Dic5—22no—
88C2×C4×Dic5—22no—
89C2×C4×Dic5—22no—
90C2×C4×Dic5—22no—
91C2×C4×Dic5—22no—
92C2×C4×Dic5—24no—
93C2×C4×Dic5—24no—
94C2×C4×Dic5—24no—
95C2×C4×Dic5D414yes—
96C5×#95C2×C418yes—
97#3963—24no—
98#3963—24no—
99#3963—22no—
100#3963—22no—
101#3963—24no—
102#3963—24no—
103#3963—24no—
104#3963—24no—
105#3963—42no—
106C2×#389—51no—
107C2×#388—52no—
108C2×#380—51no—
109C2×#380D511yescharacteristic
110C2×C4×C4⋊C4—51no—
111C2×C4×C22⋊C4—51no—
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—22no—
134C22×C4×C5—22no—
135C22×C4×C5—22no—
136C22×C4×C5—22no—
137C22×C4×C5—21no—
138C22×C4×C5—21no—
139C22×C4×C5—22no—
140C22×C4×C5—22no—
141C22×C4×C5—22no—
142C22×C4×C5—22no—
143C22×C4×C5—21no—
144C22×C4×C5—21no—
145C22×C4×C5—21no—
146C22×C4×C5—21no—
147C22×C4×C5—22no—
148C22×C4×C5—22no—
149C22×C4×C5—22no—
150C22×C4×C5—22no—
151C22×C4×C5—28no—
152C22×C4×C5—28no—
153C22×C4×C5—28no—
154C22×C4×C5—44no—
155C22×C4×C5—44no—
156C22×C4×C5—44no—
157C22×C4×C5—44no—
158C22×C4×C5C22×C414yes—
159C22×C4×C5C22×C414yes—
160C22×C4×C5C22×C412yes—
161C22×C4×C5C22×C412yes—
162C22×C4×C5C2×D412yes—
163C22×C4×C5C2×D412yes—
164C22×C4×C5#4112yes—
165C22×C4×C5#4112yes—
166C22×C4×C5#4112yes—
167C22×C4×C5#4112yes—
168C22×Dic5—21no—
169C22×Dic5—21no—
170C22×Dic5—21no—
171C22×Dic5—21no—
172C22×Dic5—21no—
173C22×Dic5—21no—
174C22×Dic5—22no—
175C22×Dic5—21no—
176C22×Dic5—22no—
177C22×Dic5—21no—
178C22×Dic5—21no—
179C22×Dic5—21no—
180C22×Dic5—21no—
181C22×Dic5—21no—
182C22×Dic5—21no—
183C22×Dic5—21no—
184C22×Dic5—21no—
185C22×Dic5—21no—
186C22×Dic5—22no—
187C22×Dic5—22no—
188C22×Dic5—22no—
189C22×Dic5—21no—
190C22×Dic5—21no—
191C22×Dic5—21no—
192C22×Dic5—21no—
193C22×Dic5—22no—
194C22×Dic5—21no—
195C22×Dic5—21no—
196C22×Dic5—22no—
197C22×Dic5—22no—
198C22×Dic5—22no—
199C22×Dic5—22no—
200C22×Dic5—22no—
201C22×Dic5—22no—
202C22×Dic5—22no—
203C22×Dic5C2×D412yes—
204C22×Dic5C2×D414yes—
205C22×Dic5C2×D412yes—
206C22×Dic5C2×D412yes—
207C22×Dic5C2×D412yes—
208C22×Dic5#4112yes—
209C22×Dic5#4112yes—
210C5×C4⋊C4—28no—
211C5×C4⋊C4—28no—
212C5×C22⋊C4—216no—
213C22⋊Dic5—28no—
214C22⋊Dic5—28no—
215C22⋊Dic5—48no—
216C4⋊Dic5—28no—
217C4⋊Dic5—48no—
218C4⋊Dic5—44no—
219C4×Dic5—28no—
220C4×Dic5—44no—
221C4×Dic5—48no—
222C24×C4C2×D511yescharacteristic
223C22×C4⋊C4—51no—
224C22×C4⋊C4—51no—
225C22×C4⋊C4—52no—
226C22×C4⋊C4C2×D511yescharacteristic
227C22×C4⋊C4C2×D511yescharacteristic
228C22×C22⋊C4—51no—
229C22×C22⋊C4—51no—
230C22×C22⋊C4—52no—
231C22×C22⋊C4C2×D512yes—
232C22×C42—51no—
233C22×C42—52no—
234C22×C42—51no—
235#389—104no—
236#388—108no—
237#380—104no—
238#380Dic518yescomplemented
239C4×C4⋊C4—104no—
240C4×C22⋊C4—104no—
241C2×#95—51no—
242C2×#95—52no—
243C2×#95—52no—
244C2×#95—52no—
245C2×#95—52no—
246C2×#95—52no—
247C2×#95—52no—
248C2×#95—51no—
249C2×#95—52no—
250C2×#95C2×D512yes—
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—24no—
303C2×C4×C5—24no—
304C2×C4×C5—24no—
305C2×C4×C5—24no—
306C2×C4×C5—22no—
307C2×C4×C5—22no—
308C2×C4×C5—24no—
309C2×C4×C5—24no—
310C2×C4×C5—42no—
311C2×C4×C5—41no—
312C2×C4×C5—41no—
313C2×C4×C5—42no—
314C2×C4×C5—41no—
315C2×C4×C5—41no—
316C2×C4×C5—42no—
317C2×C4×C5—42no—
318C2×C4×C5—42no—
319C2×C4×C5—42no—
320C2×C4×C5—42no—
321C2×C4×C5—42no—
322C2×C4×C5—416no—
323C2×C4×C5#11714yes—
324C2×C4×C5C4×D414yes—
325C2×C4×C5C4×D414yes—
326C2×C4×C5#12114yes—
327C2×C4×C5#12314yes—
328C2×C4×C5#12414yes—
329C2×C4×C5#12614yes—
330C2×Dic5—22no—
331C2×Dic5—22no—
332C2×Dic5—22no—
333C2×Dic5—22no—
334C2×Dic5—22no—
335C2×Dic5—22no—
336C2×Dic5—24no—
337C2×Dic5—22no—
338C2×Dic5—22no—
339C2×Dic5—22no—
340C2×Dic5—22no—
341C2×Dic5—22no—
342C2×Dic5—22no—
343C2×Dic5—24no—
344C2×Dic5—22no—
345C2×Dic5—24no—
346C2×Dic5—22no—
347C2×Dic5—22no—
348C2×Dic5—41no—
349C2×Dic5—41no—
350C2×Dic5—42no—
351C2×Dic5—41no—
352C2×Dic5—41no—
353C2×Dic5—42no—
354C2×Dic5—42no—
355C2×Dic5—41no—
356C2×Dic5—41no—
357C2×Dic5—41no—
358C2×Dic5—41no—
359C2×Dic5—41no—
360C2×Dic5—41no—
361C2×Dic5—41no—
362C2×Dic5—42no—
363C2×Dic5—41no—
364C2×Dic5—42no—
365C2×Dic5—42no—
366C2×Dic5—42no—
367C2×Dic5—42no—
368C2×Dic5—42no—
369C2×Dic5—42no—
370C2×Dic5—42no—
371C2×Dic5#12114yes—
372C25C22×D511yescharacteristic
373C23×C4—22no—
374C23×C4—22no—
375C23×C4—22no—
376C23×C4—22no—
377C23×C4—22no—
378C23×C4—22no—
379C23×C4—51no—
380C23×C4—51no—
381C23×C4—52no—
382C23×C4—51no—
383C23×C4—51no—
384C23×C4—52no—
385C23×C4C2×Dic514yes—
386C23×C4C22×D512yes—
387C23×C4C22×D512yes—
388C23×C4C22×D511yescharacteristic
389C23×C4C22×D511yescharacteristic
390C2×C4⋊C4—22no—
391C2×C4⋊C4—22no—
392C2×C4⋊C4—22no—
393C2×C4⋊C4—22no—
394C2×C4⋊C4—54no—
395C2×C4⋊C4—102no—
396C2×C4⋊C4—102no—
397C2×C4⋊C4—104no—
398C2×C4⋊C4—104no—
399C2×C4⋊C4—102no—
400C2×C4⋊C4—102no—
401C2×C4⋊C4—102no—
402C2×C4⋊C4—202no—
403C2×C4⋊C4C2×Dic514yes—
404C2×C4⋊C4C2×Dic514yes—
405C2×C22⋊C4—24no—
406C2×C22⋊C4—24no—
407C2×C22⋊C4—54no—
408C2×C22⋊C4—102no—
409C2×C22⋊C4—102no—
410C2×C22⋊C4—102no—
411C2×C22⋊C4—102no—
412C2×C22⋊C4—102no—
413C2×C22⋊C4—104no—
414C2×C22⋊C4—104no—
415C2×C22⋊C4—202no—
416C2×C22⋊C4C2×Dic518yes—
417C2×C42—54no—
418C2×C42—102no—
419C2×C42—102no—
420C2×C42—104no—
421C2×C42—104no—
422C2×C42—104no—
423C2×C42—102no—
424C2×C42—102no—
425C2×C42—102no—
426#95—102no—
427#95—102no—
428#95—104no—
429#95—104no—
430#95—104no—
431#95—104no—
432#95—104no—
433#95—104no—
434#95—202no—
435#95C2×Dic518yes—
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—44no—
487C4×C5—42no—
488C4×C5—44no—
489C4×C5#38818yescomplemented
490Dic5—24no—
491Dic5—42no—
492Dic5—42no—
493Dic5—44no—
494Dic5—42no—
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—
508C24D4×D512yes—
509C24#71112yes—
510C24C22×Dic512yes—
511C24C23×D511yescharacteristic
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—28no—
531C22×C4—28no—
532C22×C4—28no—
533C22×C4—44no—
534C22×C4—44no—
535C22×C4—44no—
536C22×C4—44no—
537C22×C4—52no—
538C22×C4—52no—
539C22×C4—52no—
540C22×C4—52no—
541C22×C4—52no—
542C22×C4—54no—
543C22×C4—52no—
544C22×C4—101no—
545C22×C4—101no—
546C22×C4—101no—
547C22×C4—101no—
548C22×C4—101no—
549C22×C4—101no—
550C22×C4—101no—
551C22×C4—102no—
552C22×C4—101no—
553C22×C4—101no—
554C22×C4—101no—
555C22×C4—102no—
556C22×C4—102no—
557C22×C4—101no—
558C22×C4—101no—
559C22×C4—101no—
560C22×C4—101no—
561C22×C4—101no—
562C22×C4—101no—
563C22×C4—102no—
564C22×C4—101no—
565C22×C4—102no—
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—102no—
575C22×C4—102no—
576C22×C4—102no—
577C22×C4—102no—
578C22×C4—102no—
579C22×C4#70912yes—
580C22×C4#70912yes—
581C22×C4D4×D512yes—
582C22×C4D4×D512yes—
583C22×C4#71112yes—
584C22×C4#71112yes—
585C22×C4C22×Dic512yes—
586C22×C4C22×Dic514yes—
587C22×C4C22×Dic514yes—
588C22×C4C22×Dic512yes—
589C4⋊C4—28no—
590C4⋊C4—28no—
591C4⋊C4—108no—
592C4⋊C4—208no—
593C4⋊C4—204no—
594C22⋊C4—216no—
595C22⋊C4—108no—
596C22⋊C4—108no—
597C22⋊C4—208no—
598C42—108no—
599C42—208no—
600C42—204no—
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—
651C23D4×Dic514yes—
652C23C2×#70911yescharacteristic
653C23C2×#70911yescharacteristic
654C23C2×D4×D511yescharacteristic
655C23C2×D4×D511yescharacteristic
656C23C2×D4×D511yescharacteristic
657C23C2×#71111yescharacteristic
658C23C2×#71111yescharacteristic
659C23C2×#71111yescharacteristic
660C23#414711yescharacteristic
661C23#414711yescharacteristic
662C23D5×#4111yescharacteristic
663C23D5×#4111yescharacteristic
664C23#414911yescharacteristic
665C23#415011yescharacteristic
666C23C23×Dic511yescharacteristic
667C2×C4—22no—
668C2×C4—24no—
669C2×C4—24no—
670C2×C4—24no—
671C2×C4—24no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—24no—
675C2×C4—24no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—416no—
689C2×C4—54no—
690C2×C4—102no—
691C2×C4—102no—
692C2×C4—102no—
693C2×C4—102no—
694C2×C4—102no—
695C2×C4—102no—
696C2×C4—102no—
697C2×C4—104no—
698C2×C4—102no—
699C2×C4—102no—
700C2×C4—102no—
701C2×C4—102no—
702C2×C4—102no—
703C2×C4—104no—
704C2×C4—102no—
705C2×C4—102no—
706C2×C4—104no—
707C2×C4—102no—
708C2×C4—201no—
709C2×C4—201no—
710C2×C4—202no—
711C2×C4—201no—
712C2×C4—201no—
713C2×C4—201no—
714C2×C4—202no—
715C2×C4—201no—
716C2×C4—201no—
717C2×C4—202no—
718C2×C4—201no—
719C2×C4—201no—
720C2×C4—201no—
721C2×C4—202no—
722C2×C4—201no—
723C2×C4—201no—
724C2×C4—202no—
725C2×C4—202no—
726C2×C4—202no—
727C2×C4—202no—
728C2×C4—202no—
729C2×C4—202no—
730C2×C4—202no—
731C2×C4#402514yes—
732C2×C4#402914yes—
733C2×C4#403014yes—
734C2×C4#403114yes—
735C2×C4#407214yes—
736C2×C4D4×Dic514yes—
737C2×C4D4×Dic514yes—
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×#402511yescharacteristic
755C22C2×#402911yescharacteristic
756C22C2×#403011yescharacteristic
757C22C2×#403111yescharacteristic
758C22#6584111yescharacteristic
759C22#6584111yescharacteristic
760C22#6584711yescharacteristic
761C22#6584711yescharacteristic
762C22#6586311yescharacteristic
763C22#6586311yescharacteristic
764C22#6586611yescharacteristic
765C22#6586611yescharacteristic
766C22#6593011yescharacteristic
767C22#6593211yescharacteristic
768C22#6593411yescharacteristic
769C22D5×#12111yescharacteristic
770C22#6594011yescharacteristic
771C22#6594311yescharacteristic
772C22#6594511yescharacteristic
773C22#6595211yescharacteristic
774C22#6595911yescharacteristic
775C22#6596211yescharacteristic
776C22#6596311yescharacteristic
777C22#6596511yescharacteristic
778C22#6596711yescharacteristic
779C22#6597311yescharacteristic
780C22#6597511yescharacteristic
781C22#6597711yescharacteristic
782C22C2×#407211yescharacteristic
783C22C2×D4×Dic511yescharacteristic
784C22C2×D4×Dic511yescharacteristic
785C22C2×D4×Dic511yescharacteristic
786C22#6614611yescharacteristic
787C22#41×Dic511yescharacteristic
788C22#6616111yescharacteristic
789C4—42no—
790C4—44no—
791C4—44no—
792C4—104no—
793C4—202no—
794C4—204no—
795C4—202no—
796C4—202no—
797C4—402no—
798C4#6524018yescomplemented
799C2—44no—
800C2#1060564211yescharacteristic
801C2#1060564411yescharacteristic
802C2#1060564611yescharacteristic
803C2#1060565211yescharacteristic
804C2#1060565411yescharacteristic
805C2#1060566511yescharacteristic
806C2#1060566611yescharacteristic
807C2#1060575511yescharacteristic
808C2C2×#6524011yescharacteristic
809C2#1061389011yescharacteristic
810C2#1061397011yescharacteristic
811C2Dic5×#12111yescharacteristic
812C2#1061436711yescharacteristic
813C2#1061447511yescharacteristic
814C2#1061447911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D5
commutatorC23×C5C23×C4
FittingC2×C5×#380C2
socle, cosocleC24×C5C24
prime radicalC25×C5C23
hypercenterC2×#380D5
hypocenterC5#13994
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
4. C2×#65274C2semidirect
5. C2×C4⋊C4×Dic5C2semidirect
7. #10602356C2semidirect
8. #10602356C2semidirect
10. #10600205C2semidirect
11. #10600194C2semidirect
25. C5×#380C4semidirect
238. #380Dic5semidirect
489. C4×C5#388semidirect
738. C5#13994semidirect
798. C4#65240semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#3802
C2×#655012
C2×C4×C22⋊Dic52
C2×#652742
C2×C4⋊C4×Dic52
C2×#652402
#106023562
#106023412
#106002052
#106001942
#139945