Finite Group Databasebeta

← #12021247

Subgroups — #12021247

Order 1280.

1846 conjugacy classes of subgroups.

The subgroup lattice has 822 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×#65265C211yesmaximal, characteristic, complemented
5C2×C4⋊C4×Dic5C211yesmaximal, characteristic, complemented
6C2×#65233C212yesmaximal
7#10602356C211yesmaximal, characteristic, complemented
8#10602356C211yesmaximal, characteristic, complemented
9#10602340C212yesmaximal
10#10600206C212yesmaximal, complemented
11#10600199C212yesmaximal, complemented
12C24×C4×C5C2211yescharacteristic
13C22×C5×C4⋊C4C2211yescharacteristic
14C22×C5×C4⋊C4C2211yescharacteristic
15C22×C5×C22⋊C4C2212yes—
16C22×C22⋊Dic5C2212yes—
17C22×C22⋊Dic5C2211yescharacteristic
18C22×C22⋊Dic5C2211yescharacteristic
19C22×C4⋊Dic5C2211yescharacteristic
20C22×C4⋊Dic5C2211yescharacteristic
21C22×#683C2212yes—
22C22×#683C2212yes—
23C22×C4×Dic5C2212yes—
24C22×C4×Dic5C2211yescharacteristic
25C22×C4×Dic5C2211yescharacteristic
26C5×#380—24no—
27C2×C5×#95C2212yes—
28#65501—24no—
29C4×C22⋊Dic5C418yescomplemented
30C2×#3963C2212yes—
31C2×#3963C2212yes—
32C2×#3963C2212yes—
33C2×#3963C2212yes—
34C2×#3963C2212yes—
35C2×#3963C2212yes—
36C2×#3963C2211yescharacteristic
37C2×#3963C2211yescharacteristic
38#65265—24no—
39C4⋊C4×Dic5—24no—
40#65233—28no—
41#13876—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×C5C2312yes—
51C23×C4×C5C2311yescharacteristic
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⋊C4—22no—
65C2×C5×C4⋊C4D414yes—
66C2×C5×C22⋊C4—24no—
67C2×C5×C22⋊C4—24no—
68C2×C5×C22⋊C4—42no—
69C2×C22⋊Dic5—22no—
70C2×C22⋊Dic5—22no—
71C2×C22⋊Dic5—24no—
72C2×C22⋊Dic5—24no—
73C2×C22⋊Dic5—42no—
74C2×C22⋊Dic5C2×C414yes—
75C2×C22⋊Dic5C2×C414yes—
76C2×C22⋊Dic5D414yes—
77C2×C22⋊Dic5Q814yes—
78C2×C4⋊Dic5—22no—
79C2×C4⋊Dic5—22no—
80C2×C4⋊Dic5—22no—
81C2×C4⋊Dic5—22no—
82C2×C4⋊Dic5—22no—
83C2×C4⋊Dic5D414yes—
84C2×#683—24no—
85C2×#683—24no—
86C2×#683—24no—
87C2×#683—24no—
88C2×#683—42no—
89C2×#683—42no—
90C2×C4×Dic5—22no—
91C2×C4×Dic5—22no—
92C2×C4×Dic5—22no—
93C2×C4×Dic5—22no—
94C2×C4×Dic5—24no—
95C2×C4×Dic5—24no—
96C2×C4×Dic5—42no—
97C2×C4×Dic5C2×C414yes—
98C2×C4×Dic5C2×C414yes—
99C5×#95—24no—
100#3963—24no—
101#3963—24no—
102#3963—24no—
103#3963—24no—
104#3963—24no—
105#3963—42no—
106#3963C2×C414yes—
107#3963C2×C414yes—
108C2×#388—52no—
109C2×#384—51no—
110C2×#380—51no—
111C2×#380D511yescharacteristic
112C2×C4×C4⋊C4—51no—
113C2×C4×C22⋊C4—51no—
114#1442—52no—
115#1439—52no—
116#1436—52no—
117C4⋊#95—51no—
118C4⋊#95—51no—
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×C5—21no—
130C24×C5—21no—
131C24×C5C22×C412yes—
132C24×C5C2×D412yes—
133C24×C5C2×Q812yes—
134C24×C5C2411yescharacteristic
135C22×C4×C5—22no—
136C22×C4×C5—21no—
137C22×C4×C5—21no—
138C22×C4×C5—22no—
139C22×C4×C5—22no—
140C22×C4×C5—21no—
141C22×C4×C5—21no—
142C22×C4×C5—21no—
143C22×C4×C5—21no—
144C22×C4×C5—22no—
145C22×C4×C5—22no—
146C22×C4×C5—22no—
147C22×C4×C5—28no—
148C22×C4×C5—28no—
149C22×C4×C5—28no—
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×C5—22no—
157C22×C4×C5—44no—
158C22×C4×C5—44no—
159C22×C4×C5—44no—
160C22×C4×C5—44no—
161C22×C4×C5C22×C412yes—
162C22×C4×C5C22×C412yes—
163C22×C4×C5C2×D412yes—
164C22×C4×C5C2×D414yes—
165C22×C4×C5C2×D412yes—
166C22×C4×C5#4112yes—
167C22×C4×C5#4112yes—
168C22×C4×C5#4112yes—
169C22×C4×C5#4112yes—
170C22×Dic5—21no—
171C22×Dic5—21no—
172C22×Dic5—21no—
173C22×Dic5—21no—
174C22×Dic5—21no—
175C22×Dic5—21no—
176C22×Dic5—21no—
177C22×Dic5—21no—
178C22×Dic5—21no—
179C22×Dic5—21no—
180C22×Dic5—21no—
181C22×Dic5—21no—
182C22×Dic5—22no—
183C22×Dic5—21no—
184C22×Dic5—22no—
185C22×Dic5—21no—
186C22×Dic5—21no—
187C22×Dic5—21no—
188C22×Dic5—22no—
189C22×Dic5—22no—
190C22×Dic5—22no—
191C22×Dic5—21no—
192C22×Dic5—22no—
193C22×Dic5—21no—
194C22×Dic5—22no—
195C22×Dic5—22no—
196C22×Dic5—22no—
197C22×Dic5—22no—
198C22×Dic5—22no—
199C22×Dic5—22no—
200C22×Dic5—22no—
201C22×Dic5C22×C412yes—
202C22×Dic5C22×C412yes—
203C22×Dic5C22×C412yes—
204C22×Dic5C22×C412yes—
205C22×Dic5C2×D414yes—
206C22×Dic5C2×D412yes—
207C22×Dic5C2×D412yes—
208C22×Dic5C2×Q812yes—
209C22×Dic5C2×Q812yes—
210C22×Dic5#4112yes—
211C22×Dic5#4112yes—
212C5×C4⋊C4—28no—
213C5×C4⋊C4—44no—
214C5×C22⋊C4—48no—
215C22⋊Dic5—28no—
216C22⋊Dic5—48no—
217C22⋊Dic5C4⋊C4116yescomplemented
218C4⋊Dic5—28no—
219C4⋊Dic5—44no—
220#683—48no—
221#683—48no—
222C4×Dic5—28no—
223C4×Dic5—28no—
224C4×Dic5—48no—
225C24×C4C2×D511yescharacteristic
226C22×C4⋊C4—51no—
227C22×C4⋊C4—51no—
228C22×C4⋊C4—52no—
229C22×C4⋊C4—52no—
230C22×C4⋊C4C2×D511yescharacteristic
231C22×C4⋊C4C2×D511yescharacteristic
232C22×C22⋊C4—51no—
233C22×C22⋊C4—51no—
234C22×C22⋊C4—52no—
235C22×C22⋊C4C2×D512yes—
236C22×C42—51no—
237C22×C42—51no—
238C22×C42—52no—
239#388—108no—
240#384—104no—
241#380—24no—
242#380—104no—
243C4×C4⋊C4—104no—
244C4×C22⋊C4—58no—
245C2×#95—51no—
246C2×#95—51no—
247C2×#95—52no—
248C2×#95—52no—
249C2×#95—52no—
250C2×#95—52no—
251C2×#95—52no—
252C2×#95—52no—
253C2×#95C2×D512yes—
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—22no—
270C23×C5—22no—
271C23×C5—22no—
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×C5—41no—
286C23×C5—41no—
287C23×C5—41no—
288C23×C5C2×C4⋊C414yes—
289C23×C5C23×C411yescharacteristic
290C23×C5C22×D411yescharacteristic
291C23×C5C22×D411yescharacteristic
292C23×C5C22×D411yescharacteristic
293C23×C5C22×Q811yescharacteristic
294C23×C5C2×#4111yescharacteristic
295C23×C5C2×#4111yescharacteristic
296C23×C5C2×#4111yescharacteristic
297C23×C5C2×#4111yescharacteristic
298C23×C5C2×#4111yescharacteristic
299C23×C5C2×#4111yescharacteristic
300C23×C5H(5,𝔽2)11yescharacteristic
301C23×C5H(5,𝔽2)11yescharacteristic
302C23×C52−1+411yescharacteristic
303C23×C52−1+411yescharacteristic
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—41no—
311C2×C4×C5—41no—
312C2×C4×C5—41no—
313C2×C4×C5—41no—
314C2×C4×C5—42no—
315C2×C4×C5—42no—
316C2×C4×C5—42no—
317C2×C4×C5—42no—
318C2×C4×C5—416no—
319C2×C4×C5—42no—
320C2×C4×C5—42no—
321C2×C4×C5—42no—
322C2×C4×C5—42no—
323C2×C4×C5—42no—
324C2×C4×C5—42no—
325C2×C4×C5—42no—
326C2×C4×C5#11714yes—
327C2×C4×C5C4×D414yes—
328C2×C4×C5C4×D414yes—
329C2×C4×C5#12114yes—
330C2×C4×C5#12314yes—
331C2×C4×C5#12414yes—
332C2×C4×C5#12614yes—
333C2×Dic5—22no—
334C2×Dic5—22no—
335C2×Dic5—22no—
336C2×Dic5—22no—
337C2×Dic5—22no—
338C2×Dic5—22no—
339C2×Dic5—22no—
340C2×Dic5—22no—
341C2×Dic5—22no—
342C2×Dic5—22no—
343C2×Dic5—22no—
344C2×Dic5—22no—
345C2×Dic5—22no—
346C2×Dic5—22no—
347C2×Dic5—22no—
348C2×Dic5—22no—
349C2×Dic5—22no—
350C2×Dic5—22no—
351C2×Dic5—22no—
352C2×Dic5—22no—
353C2×Dic5—22no—
354C2×Dic5—24no—
355C2×Dic5—24no—
356C2×Dic5—24no—
357C2×Dic5—42no—
358C2×Dic5—42no—
359C2×Dic5—42no—
360C2×Dic5—41no—
361C2×Dic5—41no—
362C2×Dic5—42no—
363C2×Dic5—41no—
364C2×Dic5—41no—
365C2×Dic5—42no—
366C2×Dic5—42no—
367C2×Dic5—42no—
368C2×Dic5—42no—
369C2×Dic5—42no—
370C2×Dic5—42no—
371C2×Dic5—42no—
372C2×Dic5C2×C4⋊C414yes—
373C2×Dic5C2×C4⋊C414yes—
374C2×Dic5#11714yes—
375C25C22×D511yescharacteristic
376C23×C4—22no—
377C23×C4—22no—
378C23×C4—22no—
379C23×C4—22no—
380C23×C4—22no—
381C23×C4—22no—
382C23×C4—51no—
383C23×C4—51no—
384C23×C4—51no—
385C23×C4—52no—
386C23×C4—51no—
387C23×C4—52no—
388C23×C4C4×D514yes—
389C23×C4C22×D512yes—
390C23×C4C22×D511yescharacteristic
391C23×C4C22×D512yes—
392C23×C4C22×D511yescharacteristic
393C2×C4⋊C4—22no—
394C2×C4⋊C4—22no—
395C2×C4⋊C4—22no—
396C2×C4⋊C4—22no—
397C2×C4⋊C4—22no—
398C2×C4⋊C4—54no—
399C2×C4⋊C4—102no—
400C2×C4⋊C4—102no—
401C2×C4⋊C4—104no—
402C2×C4⋊C4—104no—
403C2×C4⋊C4—104no—
404C2×C4⋊C4—104no—
405C2×C4⋊C4—102no—
406C2×C4⋊C4—102no—
407C2×C4⋊C4—102no—
408C2×C4⋊C4—202no—
409C2×C4⋊C4—202no—
410C2×C4⋊C4C22⋊D514yes—
411C2×C22⋊C4—24no—
412C2×C22⋊C4—24no—
413C2×C22⋊C4—42no—
414C2×C22⋊C4—54no—
415C2×C22⋊C4—54no—
416C2×C22⋊C4—54no—
417C2×C22⋊C4—54no—
418C2×C22⋊C4—102no—
419C2×C22⋊C4—102no—
420C2×C22⋊C4—104no—
421C2×C22⋊C4—104no—
422C2×C22⋊C4—202no—
423C2×C42—54no—
424C2×C42—54no—
425C2×C42—102no—
426C2×C42—102no—
427C2×C42—102no—
428C2×C42—102no—
429C2×C42—104no—
430C2×C42—104no—
431C2×C42—202no—
432#95—24no—
433#95—54no—
434#95—54no—
435#95—104no—
436#95—104no—
437#95—104no—
438#95—104no—
439#95—104no—
440#95—202no—
441C22×C5—24no—
442C22×C5—24no—
443C22×C5—24no—
444C22×C5—42no—
445C22×C5—42no—
446C22×C5—42no—
447C22×C5—42no—
448C22×C5—42no—
449C22×C5—42no—
450C22×C5—42no—
451C22×C5—42no—
452C22×C5—42no—
453C22×C5—42no—
454C22×C5—42no—
455C22×C5—42no—
456C22×C5C22×C4⋊C411yescharacteristic
457C22×C5C2×#11711yescharacteristic
458C22×C5C2×#11711yescharacteristic
459C22×C5C2×C4×D411yescharacteristic
460C22×C5C2×C4×D411yescharacteristic
461C22×C5#52011yescharacteristic
462C22×C5#52011yescharacteristic
463C22×C5C2×#12111yescharacteristic
464C22×C5C2×#12311yescharacteristic
465C22×C5C2×#12411yescharacteristic
466C22×C5C2×#12611yescharacteristic
467C22×C5#53211yescharacteristic
468C22×C5#53211yescharacteristic
469C22×C5#53311yescharacteristic
470C22×C5#53311yescharacteristic
471C22×C5#54011yescharacteristic
472C22×C5#54111yescharacteristic
473C22×C5#54211yescharacteristic
474C22×C5#54211yescharacteristic
475C22×C5D4211yescharacteristic
476C22×C5D4211yescharacteristic
477C22×C5#54611yescharacteristic
478C22×C5#54711yescharacteristic
479C22×C5#54711yescharacteristic
480C22×C5#54711yescharacteristic
481C22×C5#54811yescharacteristic
482C22×C5D4×Q811yescharacteristic
483C22×C5D4×Q811yescharacteristic
484C22×C5#55011yescharacteristic
485C22×C5#55211yescharacteristic
486C22×C5#55311yescharacteristic
487C22×C5#55411yescharacteristic
488C22×C5#55411yescharacteristic
489C22×C5#55511yescharacteristic
490C22×C5#55611yescharacteristic
491C4×C5—44no—
492C4×C5—42no—
493C4×C5—82no—
494C4×C5#38818yescomplemented
495Dic5—24no—
496Dic5—24no—
497Dic5—24no—
498Dic5—42no—
499Dic5—44no—
500Dic5—82no—
501C24—21no—
502C24—21no—
503C24—21no—
504C24—21no—
505C24—21no—
506C24—21no—
507C24—21no—
508C24—21no—
509C24—21no—
510C24—21no—
511C24—21no—
512C24—21no—
513C24C2×C4×D512yes—
514C24D4×D512yes—
515C24Q8×D512yes—
516C24C23×D511yescharacteristic
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—21no—
529C22×C4—28no—
530C22×C4—28no—
531C22×C4—28no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—44no—
540C22×C4—44no—
541C22×C4—44no—
542C22×C4—44no—
543C22×C4—52no—
544C22×C4—52no—
545C22×C4—52no—
546C22×C4—52no—
547C22×C4—52no—
548C22×C4—52no—
549C22×C4—52no—
550C22×C4—52no—
551C22×C4—52no—
552C22×C4—52no—
553C22×C4—54no—
554C22×C4—101no—
555C22×C4—101no—
556C22×C4—101no—
557C22×C4—101no—
558C22×C4—101no—
559C22×C4—101no—
560C22×C4—101no—
561C22×C4—101no—
562C22×C4—101no—
563C22×C4—101no—
564C22×C4—101no—
565C22×C4—101no—
566C22×C4—101no—
567C22×C4—102no—
568C22×C4—102no—
569C22×C4—102no—
570C22×C4—101no—
571C22×C4—101no—
572C22×C4—102no—
573C22×C4—101no—
574C22×C4—102no—
575C22×C4—101no—
576C22×C4—101no—
577C22×C4—102no—
578C22×C4—102no—
579C22×C4—102no—
580C22×C4—102no—
581C22×C4—102no—
582C22×C4—102no—
583C22×C4—102no—
584C22×C4—102no—
585C22×C4C2×C4×D512yes—
586C22×C4C2×C4×D512yes—
587C22×C4#70912yes—
588C22×C4D4×D512yes—
589C22×C4#71112yes—
590C22×C4#71112yes—
591C22×C4#71112yes—
592C22×C4C2×C22⋊D514yes—
593C22×C4C2×C22⋊D512yes—
594C4⋊C4—28no—
595C4⋊C4—44no—
596C4⋊C4—108no—
597C4⋊C4—208no—
598C4⋊C4—208no—
599C4⋊C4—204no—
600C22⋊C4—48no—
601C22⋊C4—516no—
602C22⋊C4—108no—
603C22⋊C4—208no—
604C42—108no—
605C42—108no—
606C42—208no—
607C2×C5—44no—
608C2×C5#228511yescharacteristic
609C2×C5C2×#38811yescharacteristic
610C2×C5#231411yescharacteristic
611C2×C5D4×C4⋊C411yescharacteristic
612C2×C5D4×C4⋊C411yescharacteristic
613C2×C5#235211yescharacteristic
614C2×C5#235411yescharacteristic
615C2×C5#242211yescharacteristic
616C2×C5#242311yescharacteristic
617C2×C5#242811yescharacteristic
618C2×C5#242911yescharacteristic
619C2×C5#249111yescharacteristic
620C2×C5#249211yescharacteristic
621C2×C5#249611yescharacteristic
622C2×C5#249711yescharacteristic
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—22no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23D5×C4⋊C414yes—
658C23C22×C4×D511yescharacteristic
659C23C2×#70911yescharacteristic
660C23C2×D4×D511yescharacteristic
661C23C2×D4×D511yescharacteristic
662C23C2×#71111yescharacteristic
663C23C2×#71111yescharacteristic
664C23C2×#71111yescharacteristic
665C23#414411yescharacteristic
666C23C2×Q8×D511yescharacteristic
667C23#414711yescharacteristic
668C23D5×#4111yescharacteristic
669C23D5×#4111yescharacteristic
670C23#414911yescharacteristic
671C23#415011yescharacteristic
672C23C22×C22⋊D511yescharacteristic
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—24no—
677C2×C4—24no—
678C2×C4—24no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—416no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—54no—
696C2×C4—54no—
697C2×C4—54no—
698C2×C4—102no—
699C2×C4—102no—
700C2×C4—102no—
701C2×C4—102no—
702C2×C4—102no—
703C2×C4—102no—
704C2×C4—102no—
705C2×C4—102no—
706C2×C4—102no—
707C2×C4—102no—
708C2×C4—102no—
709C2×C4—102no—
710C2×C4—102no—
711C2×C4—102no—
712C2×C4—102no—
713C2×C4—102no—
714C2×C4—102no—
715C2×C4—102no—
716C2×C4—102no—
717C2×C4—102no—
718C2×C4—102no—
719C2×C4—104no—
720C2×C4—104no—
721C2×C4—104no—
722C2×C4—201no—
723C2×C4—201no—
724C2×C4—202no—
725C2×C4—201no—
726C2×C4—202no—
727C2×C4—201no—
728C2×C4—202no—
729C2×C4—202no—
730C2×C4—202no—
731C2×C4—202no—
732C2×C4—202no—
733C2×C4—202no—
734C2×C4—202no—
735C2×C4—202no—
736C2×C4—202no—
737C2×C4#402314yes—
738C2×C4#402514yes—
739C2×C4#402714yes—
740C2×C4#403114yes—
741C2×C4C4×C22⋊D514yes—
742C2×C4#408114yes—
743C2×C4#408414yes—
744C5#1387611yescharacteristic, complemented, Sylow
745C22—24no—
746C22—24no—
747C22—24no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—42no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—42no—
758C22—42no—
759C22—42no—
760C22C2×#402311yescharacteristic
761C22C2×#402511yescharacteristic
762C22C2×#402711yescharacteristic
763C22C2×#403111yescharacteristic
764C22C2×D5×C4⋊C411yescharacteristic
765C22#6583811yescharacteristic
766C22#6584111yescharacteristic
767C22#6584511yescharacteristic
768C22D5×#11711yescharacteristic
769C22#6585711yescharacteristic
770C22#6586611yescharacteristic
771C22#6586711yescharacteristic
772C22#6593011yescharacteristic
773C22#6593011yescharacteristic
774C22#6593711yescharacteristic
775C22#6594311yescharacteristic
776C22#6594511yescharacteristic
777C22#6594611yescharacteristic
778C22#6594811yescharacteristic
779C22#6595311yescharacteristic
780C22#6595611yescharacteristic
781C22#6595611yescharacteristic
782C22#6595911yescharacteristic
783C22#6596611yescharacteristic
784C22#6596711yescharacteristic
785C22#6596911yescharacteristic
786C22#6597311yescharacteristic
787C22#6597711yescharacteristic
788C22C2×C4×C22⋊D511yescharacteristic
789C22C2×#408111yescharacteristic
790C22C2×#408411yescharacteristic
791C22D4×C22⋊D511yescharacteristic
792C22Q8×C22⋊D511yescharacteristic
793C22#6615811yescharacteristic
794C22#6616811yescharacteristic
795C4—42no—
796C4—44no—
797C4—82no—
798C4—104no—
799C4—104no—
800C4—104no—
801C4—204no—
802C4—202no—
803C4—402no—
804C4#6523318yescomplemented
805C2—44no—
806C2#1060559511yescharacteristic
807C2#1060559911yescharacteristic
808C2#1060564611yescharacteristic
809C2#1060564711yescharacteristic
810C2#1060565311yescharacteristic
811C2#1060565511yescharacteristic
812C2#1060574111yescharacteristic
813C2#1060574311yescharacteristic
814C2C2×#6523311yescharacteristic
815C2C4⋊C4×C22⋊D511yescharacteristic
816C2#1061397211yescharacteristic
817C2#1061437511yescharacteristic
818C2#1061437911yescharacteristic
819C2#1061448511yescharacteristic
820C2#1061448811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D5
commutatorC23×C5C23×C4
FittingC2×C5×#380C2
socle, cosocleC24×C5C24
prime radicalC25×C5C23
hypercenterC2×#380D5
hypocenterC5#13876
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
4. C2×#65265C2semidirect
5. C2×C4⋊C4×Dic5C2semidirect
7. #10602356C2semidirect
8. #10602356C2semidirect
10. #10600206C2semidirect
11. #10600199C2semidirect
29. C4×C22⋊Dic5C4semidirect
217. C22⋊Dic5C4⋊C4semidirect
494. C4×C5#388semidirect
744. C5#13876semidirect
804. C4#65233semidirect

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×#652652
C2×C4⋊C4×Dic52
C2×#652332
#106023562
#106023402
#106002062
#106001992
#138765