Finite Group Databasebeta

← #12022699

Subgroups — #12022699

Order 1280.

2474 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D4×Dic5C211yesmaximal, characteristic
2C2×C5×#390C211yesmaximal, characteristic
3C2×#65510C211yesmaximal, characteristic
4C2×#65274C211yesmaximal, characteristic, complemented
5C2×#65239C212yesmaximal, complemented
6C2×C4×C4⋊Dic5C211yesmaximal, characteristic, complemented
7#10602356C211yesmaximal, characteristic, complemented
8#10602339C212yesmaximal, complemented
9#10602339C212yesmaximal, complemented
10#10602337C212yesmaximal, complemented
11#10602328C211yesmaximal, characteristic, complemented
12C23×C5×D4C2211yescharacteristic
13C24×Dic5C2212yes—
14C22×C5×C4⋊C4C2211yescharacteristic
15C22×C5×C22⋊C4C2212yes—
16C22×C5×C22⋊C4C2212yes—
17C22×C42×C5C2211yescharacteristic
18C22×C22⋊Dic5C2212yes—
19C22×C22⋊Dic5C2212yes—
20C22×C22⋊Dic5C2212yes—
21C2×D4×Dic5—24no—
22C2×D4×Dic5—24no—
23C2×D4×Dic5—24no—
24C22×C4⋊Dic5C2211yescharacteristic
25C22×C4⋊Dic5C2211yescharacteristic
26C22×C4⋊Dic5C2212yes—
27C22×C4⋊Dic5C2211yescharacteristic
28C22×C4⋊Dic5C2211yescharacteristic
29C22×C4×Dic5C2211yescharacteristic
30C22×C4×Dic5C2211yescharacteristic
31C5×#390C418yescomplemented
32#65510—24no—
33C2×#3963C2211yescharacteristic
34C2×#3963C2211yescharacteristic
35C2×#3963C2212yes—
36C2×#3963C2212yes—
37C2×#3963C2212yes—
38C2×#3963C2212yes—
39C2×#3963C2212yes—
40#65274—24no—
41#65239—28no—
42C4×C4⋊Dic5—24no—
43#14018—51nomaximal, Sylow
44C25×C5C2312yes—
45C22×C5×D4—22no—
46C22×C5×D4—22no—
47C22×C5×D4—22no—
48C22×C5×D4—22no—
49C22×C5×D4C2×C414yes—
50C22×C5×D4D414yes—
51C22×C5×D4Q814yes—
52C23×C4×C5C2312yes—
53C23×C4×C5C2311yescharacteristic
54C23×C4×C5C2311yescharacteristic
55C23×C4×C5C2311yescharacteristic
56C23×Dic5—24no—
57C23×Dic5—24no—
58C23×Dic5—24no—
59C23×Dic5—24no—
60C23×Dic5—24no—
61C23×Dic5—42no—
62C23×Dic5—42no—
63C23×Dic5C2312yes—
64C23×Dic5C2311yescharacteristic
65C23×Dic5C2311yescharacteristic
66C23×Dic5C2312yes—
67C23×Dic5C2311yescharacteristic
68C23×Dic5C2311yescharacteristic
69C2×C5×C4⋊C4—22no—
70C2×C5×C4⋊C4—22no—
71C2×C5×C4⋊C4C2×C414yescomplemented
72C2×C5×C22⋊C4—24no—
73C2×C5×C22⋊C4—24no—
74C2×C5×C22⋊C4—42no—
75C2×C5×C22⋊C4—42no—
76C2×C5×C22⋊C4C2×C418yescomplemented
77C2×C5×C22⋊C4C2×C418yescomplemented
78C2×C42×C5—22no—
79C2×C42×C5—22no—
80C2×C42×C5C2×C414yescomplemented
81C2×C22⋊Dic5—24no—
82C2×C22⋊Dic5—24no—
83C2×C22⋊Dic5—24no—
84C2×C22⋊Dic5—24no—
85C2×C22⋊Dic5—24no—
86C2×C22⋊Dic5—24no—
87C2×C22⋊Dic5—24no—
88C2×C22⋊Dic5—42no—
89C2×C22⋊Dic5—42no—
90D4×Dic5—232no—
91C2×C4⋊Dic5—22no—
92C2×C4⋊Dic5—22no—
93C2×C4⋊Dic5—22no—
94C2×C4⋊Dic5—22no—
95C2×C4⋊Dic5—22no—
96C2×C4⋊Dic5—22no—
97C2×C4⋊Dic5—22no—
98C2×C4⋊Dic5—22no—
99C2×C4⋊Dic5—22no—
100C2×C4⋊Dic5—22no—
101C2×C4⋊Dic5—24no—
102C2×C4⋊Dic5—24no—
103C2×C4⋊Dic5—42no—
104C2×C4⋊Dic5D414yes—
105C2×C4⋊Dic5D414yescomplemented
106C2×C4×Dic5—22no—
107C2×C4×Dic5—22no—
108C2×C4×Dic5—22no—
109C2×C4×Dic5—22no—
110C2×C4×Dic5—22no—
111C2×C4×Dic5D414yes—
112#3963—24no—
113#3963—22no—
114#3963—22no—
115#3963—24no—
116#3963—24no—
117#3963—42no—
118#3963—42no—
119C22×C4×D4—51no—
120C2×#390—51no—
121C2×#390D511yescharacteristic
122C2×#389—51no—
123C2×#385—52no—
124C2×C4×C4⋊C4—51no—
125#1439—52no—
126#1439—52no—
127C4⋊#95—51no—
128C4⋊#95—51no—
129C22⋊#95—52no—
130C24×C5—22no—
131C24×C5—22no—
132C24×C5—22no—
133C24×C5—22no—
134C24×C5—22no—
135C24×C5—22no—
136C24×C5—22no—
137C24×C5—22no—
138C24×C5—22no—
139C24×C5—22no—
140C24×C5—22no—
141C24×C5—22no—
142C24×C5C22×C414yes—
143C24×C5C2×D414yes—
144C24×C5C2×Q814yes—
145C24×C5C2411yescharacteristic
146C2×C5×D4—28no—
147C2×C5×D4—28no—
148C2×C5×D4—28no—
149C2×C5×D4—28no—
150C2×C5×D4—28no—
151C2×C5×D4—28no—
152C2×C5×D4C4⋊C4116yescomplemented
153C22×C4×C5—21no—
154C22×C4×C5—21no—
155C22×C4×C5—21no—
156C22×C4×C5—21no—
157C22×C4×C5—21no—
158C22×C4×C5—22no—
159C22×C4×C5—22no—
160C22×C4×C5—21no—
161C22×C4×C5—22no—
162C22×C4×C5—22no—
163C22×C4×C5—21no—
164C22×C4×C5—21no—
165C22×C4×C5—22no—
166C22×C4×C5—22no—
167C22×C4×C5—21no—
168C22×C4×C5—21no—
169C22×C4×C5C22×C412yes—
170C22×C4×C5C22×C414yes—
171C22×C4×C5C22×C412yes—
172C22×C4×C5C22×C412yes—
173C22×C4×C5C2×D412yes—
174C22×C4×C5C2×D412yes—
175C22×C4×C5C2×D412yes—
176C22×C4×C5C2×D412yes—
177C22×C4×C5C2×Q812yes—
178C22×C4×C5#4112yes—
179C22×C4×C5#4112yes—
180C22×C4×C5#4112yes—
181C22×Dic5—21no—
182C22×Dic5—21no—
183C22×Dic5—21no—
184C22×Dic5—21no—
185C22×Dic5—216no—
186C22×Dic5—21no—
187C22×Dic5—21no—
188C22×Dic5—21no—
189C22×Dic5—21no—
190C22×Dic5—22no—
191C22×Dic5—22no—
192C22×Dic5—22no—
193C22×Dic5—21no—
194C22×Dic5—21no—
195C22×Dic5—21no—
196C22×Dic5—21no—
197C22×Dic5—22no—
198C22×Dic5—21no—
199C22×Dic5—21no—
200C22×Dic5—21no—
201C22×Dic5—21no—
202C22×Dic5—21no—
203C22×Dic5—21no—
204C22×Dic5—22no—
205C22×Dic5—22no—
206C22×Dic5—21no—
207C22×Dic5—21no—
208C22×Dic5—21no—
209C22×Dic5—21no—
210C22×Dic5—22no—
211C22×Dic5—22no—
212C22×Dic5—22no—
213C22×Dic5—22no—
214C22×Dic5—22no—
215C22×Dic5—22no—
216C22×Dic5—22no—
217C22×Dic5—48no—
218C22×Dic5—48no—
219C22×Dic5—48no—
220C22×Dic5—48no—
221C22×Dic5—48no—
222C22×Dic5—48no—
223C22×Dic5C2×D412yes—
224C22×Dic5C2×D412yes—
225C22×Dic5C2×D414yes—
226C22×Dic5C2×D412yes—
227C22×Dic5C2×D412yes—
228C22×Dic5#4112yes—
229C22×Dic5#4112yes—
230C5×C4⋊C4—28no—
231C5×C22⋊C4—216no—
232C5×C22⋊C4—48no—
233C42×C5—28no—
234C22⋊Dic5—216no—
235C22⋊Dic5—48no—
236C22⋊Dic5—48no—
237C4⋊Dic5—28no—
238C4⋊Dic5—28no—
239C4⋊Dic5—28no—
240C4⋊Dic5—48no—
241C4⋊Dic5—44no—
242C4×Dic5—28no—
243C4×Dic5—44no—
244C23×D4C2×D511yescharacteristic
245C24×C4—52no—
246C2×C4×D4—104no—
247C2×C4×D4—104no—
248C2×C4×D4—104no—
249C22×C4⋊C4—51no—
250C22×C4⋊C4—51no—
251C22×C4⋊C4—51no—
252C22×C4⋊C4—51no—
253C22×C4⋊C4—52no—
254C22×C4⋊C4C2×D511yescharacteristic
255C22×C22⋊C4—52no—
256C22×C22⋊C4—52no—
257C22×C22⋊C4—52no—
258C22×C22⋊C4C2×D512yes—
259C22×C22⋊C4C2×D512yes—
260C22×C42—51no—
261C22×C42—51no—
262C22×C42C2×D511yescharacteristic
263#390—104no—
264#390Dic518yescomplemented
265#389—104no—
266#385—108no—
267C4×C4⋊C4—104no—
268C2×#95—51no—
269C2×#95—52no—
270C2×#95—52no—
271C2×#95—52no—
272C2×#95—51no—
273C2×#95—52no—
274C2×#95—52no—
275C23×C5—24no—
276C23×C5—24no—
277C23×C5—24no—
278C23×C5—24no—
279C23×C5—24no—
280C23×C5—24no—
281C23×C5—24no—
282C23×C5—24no—
283C23×C5—24no—
284C23×C5—24no—
285C23×C5—24no—
286C23×C5—24no—
287C23×C5—24no—
288C23×C5—24no—
289C23×C5—24no—
290C23×C5—24no—
291C23×C5—24no—
292C23×C5—24no—
293C23×C5—42no—
294C23×C5—42no—
295C23×C5—42no—
296C23×C5—42no—
297C23×C5—42no—
298C23×C5—42no—
299C23×C5—42no—
300C23×C5—42no—
301C23×C5—42no—
302C23×C5—42no—
303C23×C5—42no—
304C23×C5—42no—
305C23×C5—42no—
306C23×C5—42no—
307C23×C5—42no—
308C23×C5—42no—
309C23×C5C2×C4⋊C418yes—
310C23×C5C23×C411yescharacteristic
311C23×C5C22×D411yescharacteristic
312C23×C5C22×D411yescharacteristic
313C23×C5C22×D411yescharacteristic
314C23×C5C22×D411yescharacteristic
315C23×C5C22×Q811yescharacteristic
316C23×C5C2×#4111yescharacteristic
317C23×C5C2×#4111yescharacteristic
318C23×C5C2×#4111yescharacteristic
319C23×C5C2×#4111yescharacteristic
320C23×C5C2×#4111yescharacteristic
321C23×C5H(5,𝔽2)11yescharacteristic
322C23×C5H(5,𝔽2)11yescharacteristic
323C23×C5H(5,𝔽2)11yescharacteristic
324C23×C52−1+411yescharacteristic
325C5×D4—232no—
326C2×C4×C5—22no—
327C2×C4×C5—22no—
328C2×C4×C5—22no—
329C2×C4×C5—22no—
330C2×C4×C5—22no—
331C2×C4×C5—22no—
332C2×C4×C5—22no—
333C2×C4×C5—24no—
334C2×C4×C5—24no—
335C2×C4×C5—22no—
336C2×C4×C5—24no—
337C2×C4×C5—22no—
338C2×C4×C5—41no—
339C2×C4×C5—41no—
340C2×C4×C5—41no—
341C2×C4×C5—41no—
342C2×C4×C5—42no—
343C2×C4×C5—42no—
344C2×C4×C5—42no—
345C2×C4×C5—42no—
346C2×C4×C5C2×C4⋊C414yes—
347C2×C4×C5C4×D414yes—
348C2×C4×C5C4×D414yes—
349C2×C4×C5C4×D414yescomplemented
350C2×C4×C5#12014yes—
351C2×C4×C5C22⋊Q814yes—
352C2×C4×C5C22⋊Q814yes—
353C2×C4×C5#12314yes—
354C2×Dic5—22no—
355C2×Dic5—22no—
356C2×Dic5—22no—
357C2×Dic5—22no—
358C2×Dic5—22no—
359C2×Dic5—22no—
360C2×Dic5—22no—
361C2×Dic5—24no—
362C2×Dic5—22no—
363C2×Dic5—22no—
364C2×Dic5—22no—
365C2×Dic5—22no—
366C2×Dic5—22no—
367C2×Dic5—24no—
368C2×Dic5—22no—
369C2×Dic5—22no—
370C2×Dic5—24no—
371C2×Dic5—22no—
372C2×Dic5—432no—
373C2×Dic5—41no—
374C2×Dic5—41no—
375C2×Dic5—42no—
376C2×Dic5—41no—
377C2×Dic5—42no—
378C2×Dic5—41no—
379C2×Dic5—42no—
380C2×Dic5—41no—
381C2×Dic5—41no—
382C2×Dic5—41no—
383C2×Dic5—42no—
384C2×Dic5—41no—
385C2×Dic5—41no—
386C2×Dic5—41no—
387C2×Dic5—41no—
388C2×Dic5—41no—
389C2×Dic5—42no—
390C2×Dic5—42no—
391C2×Dic5—42no—
392C2×Dic5—42no—
393C2×Dic5—42no—
394C2×Dic5—42no—
395C2×Dic5—42no—
396C2×Dic5#12114yes—
397C25C22×D512yes—
398C22×D4—22no—
399C22×D4—22no—
400C22×D4—22no—
401C22×D4—22no—
402C22×D4Dic1014yes—
403C22×D4D2014yes—
404C22×D4C2×Dic514yes—
405C23×C4—51no—
406C23×C4—51no—
407C23×C4—51no—
408C23×C4—51no—
409C23×C4—52no—
410C23×C4—52no—
411C23×C4—104no—
412C23×C4—104no—
413C23×C4—104no—
414C23×C4—104no—
415C23×C4—104no—
416C23×C4—202no—
417C23×C4—202no—
418C23×C4C22×D512yes—
419C23×C4C22×D511yescharacteristic
420C23×C4C22×D511yescharacteristic
421C23×C4C22×D511yescharacteristic
422C4×D4—1032no—
423C2×C4⋊C4—22no—
424C2×C4⋊C4—22no—
425C2×C4⋊C4—54no—
426C2×C4⋊C4—54no—
427C2×C4⋊C4—102no—
428C2×C4⋊C4—102no—
429C2×C4⋊C4—102no—
430C2×C4⋊C4—102no—
431C2×C4⋊C4—102no—
432C2×C4⋊C4—102no—
433C2×C4⋊C4—102no—
434C2×C4⋊C4—104no—
435C2×C4⋊C4—104no—
436C2×C4⋊C4—102no—
437C2×C4⋊C4—102no—
438C2×C4⋊C4—102no—
439C2×C4⋊C4—202no—
440C2×C4⋊C4C2×Dic514yescomplemented
441C2×C22⋊C4—24no—
442C2×C22⋊C4—24no—
443C2×C22⋊C4—42no—
444C2×C22⋊C4—42no—
445C2×C22⋊C4—104no—
446C2×C22⋊C4—104no—
447C2×C22⋊C4—104no—
448C2×C22⋊C4—104no—
449C2×C22⋊C4—104no—
450C2×C22⋊C4—104no—
451C2×C22⋊C4—104no—
452C2×C22⋊C4—202no—
453C2×C22⋊C4—202no—
454C2×C22⋊C4C2×Dic518yescomplemented
455C2×C22⋊C4C2×Dic518yescomplemented
456C2×C42—22no—
457C2×C42—22no—
458C2×C42—54no—
459C2×C42—102no—
460C2×C42—102no—
461C2×C42—102no—
462C2×C42—102no—
463C2×C42—102no—
464C2×C42C2×Dic514yescomplemented
465#95—102no—
466#95—102no—
467#95—104no—
468#95—104no—
469#95—104no—
470#95—202no—
471#95—202no—
472C22×C5—28no—
473C22×C5—28no—
474C22×C5—28no—
475C22×C5—44no—
476C22×C5—44no—
477C22×C5—44no—
478C22×C5—44no—
479C22×C5—44no—
480C22×C5—44no—
481C22×C5—44no—
482C22×C5—44no—
483C22×C5—44no—
484C22×C5—44no—
485C22×C5—44no—
486C22×C5—44no—
487C22×C5C22×C4⋊C411yescharacteristic
488C22×C5C2×C4×D411yescharacteristic
489C22×C5C2×C4×D411yescharacteristic
490C22×C5C2×C4×D411yescharacteristic
491C22×C5C4×#4111yescharacteristic
492C22×C5#51811yescharacteristic
493C22×C5#52011yescharacteristic
494C22×C5C2×#12011yescharacteristic
495C22×C5C2×#12111yescharacteristic
496C22×C5C2×C22⋊Q811yescharacteristic
497C22×C5C2×C22⋊Q811yescharacteristic
498C22×C5C2×#12311yescharacteristic
499C22×C5#52511yescharacteristic
500C22×C5#52911yescharacteristic
501C22×C5#53211yescharacteristic
502C22×C5#53511yescharacteristic
503C22×C5#53711yescharacteristic
504C22×C5#54011yescharacteristic
505C22×C5#54211yescharacteristic
506C22×C5D4211yescharacteristic
507C22×C5D4211yescharacteristic
508C22×C5#54611yescharacteristic
509C22×C5#54611yescharacteristic
510C22×C5#54611yescharacteristic
511C22×C5#54711yescharacteristic
512C22×C5#54811yescharacteristic
513C22×C5D4×Q811yescharacteristic
514C22×C5#55011yescharacteristic
515C22×C5#55011yescharacteristic
516C22×C5#55411yescharacteristic
517C22×C5#55411yescharacteristic
518C22×C5#55411yescharacteristic
519C22×C5#55611yescharacteristic
520C22×C5#55911yescharacteristic
521C22×C5#55911yescharacteristic
522C4×C5—24no—
523C4×C5—42no—
524C4×C5—44no—
525C4×C5#38518yescomplemented
526Dic5—24no—
527Dic5—42no—
528Dic5—42no—
529Dic5—42no—
530Dic5—44no—
531Dic5—82no—
532C24—22no—
533C24—22no—
534C24—22no—
535C24—22no—
536C24—22no—
537C24—22no—
538C24—22no—
539C24—22no—
540C24—22no—
541C24—22no—
542C24—22no—
543C24—22no—
544C24C2×Dic1014yes—
545C24C2×D2014yes—
546C24C22×Dic514yes—
547C24C23×D511yescharacteristic
548C2×D4—28no—
549C2×D4—28no—
550C2×D4—28no—
551C2×D4—28no—
552C2×D4—28no—
553C2×D4—28no—
554C2×D4C4⋊Dic5116yescomplemented
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—21no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—22no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—52no—
572C22×C4—52no—
573C22×C4—52no—
574C22×C4—52no—
575C22×C4—54no—
576C22×C4—52no—
577C22×C4—52no—
578C22×C4—101no—
579C22×C4—101no—
580C22×C4—101no—
581C22×C4—101no—
582C22×C4—1016no—
583C22×C4—101no—
584C22×C4—101no—
585C22×C4—101no—
586C22×C4—102no—
587C22×C4—101no—
588C22×C4—101no—
589C22×C4—101no—
590C22×C4—102no—
591C22×C4—101no—
592C22×C4—101no—
593C22×C4—102no—
594C22×C4—101no—
595C22×C4—101no—
596C22×C4—101no—
597C22×C4—101no—
598C22×C4—101no—
599C22×C4—102no—
600C22×C4—101no—
601C22×C4—101no—
602C22×C4—102no—
603C22×C4—102no—
604C22×C4—101no—
605C22×C4—101no—
606C22×C4—101no—
607C22×C4—102no—
608C22×C4—102no—
609C22×C4—102no—
610C22×C4—102no—
611C22×C4—102no—
612C22×C4—102no—
613C22×C4—102no—
614C22×C4—208no—
615C22×C4—208no—
616C22×C4—208no—
617C22×C4—208no—
618C22×C4—208no—
619C22×C4—208no—
620C22×C4C2×Dic1012yes—
621C22×C4C2×D2012yes—
622C22×C4D4×D512yes—
623C22×C4D4×D512yes—
624C22×C4D4×D512yes—
625C22×C4#71112yes—
626C22×C4#71112yes—
627C22×C4#71112yes—
628C22×C4C22×Dic512yes—
629C22×C4C22×Dic514yes—
630C22×C4C22×Dic512yes—
631C22×C4C22×Dic512yes—
632C4⋊C4—28no—
633C4⋊C4—108no—
634C4⋊C4—108no—
635C4⋊C4—108no—
636C4⋊C4—208no—
637C4⋊C4—204no—
638C22⋊C4—216no—
639C22⋊C4—48no—
640C22⋊C4—1016no—
641C22⋊C4—208no—
642C22⋊C4—208no—
643C42—28no—
644C42—108no—
645C42—204no—
646C2×C5—48no—
647C2×C5C2×#38511yescharacteristic
648C2×C5C4×#12111yescharacteristic
649C2×C5#232411yescharacteristic
650C2×C5D4×C4⋊C411yescharacteristic
651C2×C5#234911yescharacteristic
652C2×C5#236611yescharacteristic
653C2×C5#236711yescharacteristic
654C2×C5#240711yescharacteristic
655C2×C5#240811yescharacteristic
656C2×C5#244511yescharacteristic
657C2×C5#244711yescharacteristic
658C2×C5#245211yescharacteristic
659C2×C5#245411yescharacteristic
660C2×C5#253811yescharacteristic
661C2×C5#258011yescharacteristic
662C23—24no—
663C23—24no—
664C23—24no—
665C23—24no—
666C23—24no—
667C23—24no—
668C23—24no—
669C23—24no—
670C23—24no—
671C23—24no—
672C23—24no—
673C23—24no—
674C23—24no—
675C23—24no—
676C23—24no—
677C23—24no—
678C23—24no—
679C23—24no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23C2×C4⋊Dic518yes—
697C23C22×Dic1011yescharacteristic
698C23C22×D2011yescharacteristic
699C23C2×D4×D511yescharacteristic
700C23C2×D4×D511yescharacteristic
701C23C2×D4×D511yescharacteristic
702C23C2×#71111yescharacteristic
703C23C2×#71111yescharacteristic
704C23C2×#71111yescharacteristic
705C23#414411yescharacteristic
706C23#414411yescharacteristic
707C23D5×#4111yescharacteristic
708C23D5×#4111yescharacteristic
709C23#414911yescharacteristic
710C23#415011yescharacteristic
711C23C23×Dic511yescharacteristic
712D4—232no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—24no—
721C2×C4—24no—
722C2×C4—22no—
723C2×C4—24no—
724C2×C4—22no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—42no—
733C2×C4—54no—
734C2×C4—102no—
735C2×C4—102no—
736C2×C4—102no—
737C2×C4—102no—
738C2×C4—102no—
739C2×C4—102no—
740C2×C4—102no—
741C2×C4—104no—
742C2×C4—102no—
743C2×C4—104no—
744C2×C4—102no—
745C2×C4—102no—
746C2×C4—102no—
747C2×C4—102no—
748C2×C4—102no—
749C2×C4—102no—
750C2×C4—104no—
751C2×C4—102no—
752C2×C4—2032no—
753C2×C4—201no—
754C2×C4—201no—
755C2×C4—201no—
756C2×C4—201no—
757C2×C4—202no—
758C2×C4—202no—
759C2×C4—201no—
760C2×C4—201no—
761C2×C4—201no—
762C2×C4—201no—
763C2×C4—202no—
764C2×C4—202no—
765C2×C4—201no—
766C2×C4—201no—
767C2×C4—201no—
768C2×C4—201no—
769C2×C4—202no—
770C2×C4—202no—
771C2×C4—202no—
772C2×C4—202no—
773C2×C4—202no—
774C2×C4—202no—
775C2×C4—202no—
776C2×C4#402414yes—
777C2×C4#402414yes—
778C2×C4#402814yes—
779C2×C4#403214yes—
780C2×C4C2×C4⋊Dic514yes—
781C2×C4D4×Dic514yes—
782C2×C4D4×Dic514yes—
783C2×C4D4×Dic514yescomplemented
784C5#1401811yescharacteristic, complemented, Sylow
785C22—28no—
786C22—28no—
787C22—28no—
788C22—44no—
789C22—44no—
790C22—44no—
791C22—44no—
792C22—44no—
793C22—44no—
794C22—44no—
795C22—44no—
796C22—44no—
797C22—44no—
798C22—44no—
799C22—44no—
800C22C2×#402411yescharacteristic
801C22C2×#402411yescharacteristic
802C22C2×#402811yescharacteristic
803C22C2×#403211yescharacteristic
804C22D4×Dic1011yescharacteristic
805C22#6587311yescharacteristic
806C22#6587311yescharacteristic
807C22#6587711yescharacteristic
808C22D4×D2011yescharacteristic
809C22#6588811yescharacteristic
810C22#6588811yescharacteristic
811C22#6588911yescharacteristic
812C22#6593011yescharacteristic
813C22#6593411yescharacteristic
814C22#6593711yescharacteristic
815C22D5×#12111yescharacteristic
816C22#6594011yescharacteristic
817C22#6594111yescharacteristic
818C22#6594211yescharacteristic
819C22#6595311yescharacteristic
820C22#6600511yescharacteristic
821C22#6601011yescharacteristic
822C22#6601111yescharacteristic
823C22#6601511yescharacteristic
824C22#6604711yescharacteristic
825C22#6605111yescharacteristic
826C22#6605211yescharacteristic
827C22#6605211yescharacteristic
828C22C22×C4⋊Dic511yescharacteristic
829C22C2×D4×Dic511yescharacteristic
830C22C2×D4×Dic511yescharacteristic
831C22C2×D4×Dic511yescharacteristic
832C22#6613211yescharacteristic
833C22#41×Dic511yescharacteristic
834C22#6616111yescharacteristic
835C4—24no—
836C4—42no—
837C4—44no—
838C4—104no—
839C4—202no—
840C4—202no—
841C4—204no—
842C4—202no—
843C4—402no—
844C4#6523918yescomplemented
845C2—48no—
846C2#1060804811yescharacteristic
847C2#1060805011yescharacteristic
848C2#1060805411yescharacteristic
849C2#1060805611yescharacteristic
850C2#1060807711yescharacteristic
851C2#1060809511yescharacteristic
852C2#1060816611yescharacteristic
853C2#1060816711yescharacteristic
854C2C2×#6523911yescharacteristic
855C2D4×C4⋊Dic511yescharacteristic
856C2#1061406411yescharacteristic
857C2Dic5×#12111yescharacteristic
858C2#1061436411yescharacteristic
859C2#1061468611yescharacteristic
860C2#1061490411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D5
commutatorC23×C5C23×C4
FittingC2×C5×#390C2
socle, cosocleC24×C5C24
prime radicalC23×C5×D4C22
hypercenterC2×#390D5
hypocenterC5#14018
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#390

Complements

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

NH ≅ G/Ntype
4. C2×#65274C2semidirect
5. C2×#65239C2semidirect
6. C2×C4×C4⋊Dic5C2semidirect
7. #10602356C2semidirect
8. #10602339C2semidirect
9. #10602339C2semidirect
10. #10602337C2semidirect
11. #10602328C2semidirect
31. C5×#390C4semidirect
71. C2×C5×C4⋊C4C2×C4semidirect
76. C2×C5×C22⋊C4C2×C4semidirect
77. C2×C5×C22⋊C4C2×C4semidirect
80. C2×C42×C5C2×C4semidirect
105. C2×C4⋊Dic5D4semidirect
152. C2×C5×D4C4⋊C4semidirect
264. #390Dic5semidirect
349. C2×C4×C5C4×D4semidirect
440. C2×C4⋊C4C2×Dic5semidirect
454. C2×C22⋊C4C2×Dic5semidirect
455. C2×C22⋊C4C2×Dic5semidirect
464. C2×C42C2×Dic5semidirect
525. C4×C5#385semidirect
554. C2×D4C4⋊Dic5semidirect
783. C2×C4D4×Dic5semidirect
784. C5#14018semidirect
844. C4#65239semidirect

Maximal subgroups

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

subgroupindex
C22×D4×Dic52
C2×C5×#3902
C2×#655102
C2×#652742
C2×#652392
C2×C4×C4⋊Dic52
#106023562
#106023392
#106023372
#106023282
#140185