Finite Group Databasebeta

← #12022691

Subgroups — #12022691

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×C4×C5×D4C211yesmaximal, characteristic
2C2×#65510C211yesmaximal, characteristic
3C2×#65510C211yesmaximal, characteristic
4C2×#65499C212yesmaximal, complemented
5C2×#65262C211yesmaximal, characteristic, complemented
6C2×C4×#683C211yesmaximal, characteristic, complemented
7#10602920C212yesmaximal, complemented
8#10602356C211yesmaximal, characteristic, complemented
9#10602340C212yesmaximal, complemented
10#10602340C212yesmaximal, complemented
11#10602328C211yesmaximal, characteristic, complemented
12C23×C5×D4C2211yescharacteristic
13C24×C4×C5C2212yes—
14C2×C4×C5×D4—24no—
15C2×C4×C5×D4—24no—
16C2×C4×C5×D4—24no—
17C22×C5×C4⋊C4C2211yescharacteristic
18C22×C5×C22⋊C4C2212yes—
19C22×C42×C5C2211yescharacteristic
20C22×C22⋊Dic5C2212yes—
21C22×C22⋊Dic5C2212yes—
22C22×C22⋊Dic5C2212yes—
23C22×C22⋊Dic5C2212yes—
24C22×C4⋊Dic5C2211yescharacteristic
25C22×C4⋊Dic5C2211yescharacteristic
26C22×#683C2211yescharacteristic
27C22×#683C2212yes—
28C22×#683C2211yescharacteristic
29C22×C4×Dic5C2211yescharacteristic
30C22×C4×Dic5C2211yescharacteristic
31#65510—24no—
32#65510C418yescomplemented
33#65499—28no—
34C2×#3963C2211yescharacteristic
35C2×#3963C2211yescharacteristic
36C2×#3963C2212yes—
37C2×#3963C2212yes—
38C2×#3963C2212yes—
39C2×#3963C2212yes—
40C2×#3963C2212yes—
41#65262—24no—
42C4×#683—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×C5—24no—
53C23×C4×C5—24no—
54C23×C4×C5—24no—
55C23×C4×C5—24no—
56C23×C4×C5—24no—
57C23×C4×C5—42no—
58C23×C4×C5—42no—
59C23×C4×C5C2311yescharacteristic
60C23×C4×C5C2312yes—
61C23×C4×C5C2311yescharacteristic
62C23×C4×C5C2311yescharacteristic
63C23×Dic5C2312yes—
64C23×Dic5C2311yescharacteristic
65C23×Dic5C2312yes—
66C23×Dic5C2311yescharacteristic
67C23×Dic5C2311yescharacteristic
68C23×Dic5C2311yescharacteristic
69C4×C5×D4—232no—
70C2×C5×C4⋊C4—22no—
71C2×C5×C4⋊C4—22no—
72C2×C5×C4⋊C4D414yes—
73C2×C5×C22⋊C4—24no—
74C2×C5×C22⋊C4—24no—
75C2×C5×C22⋊C4—24no—
76C2×C42×C5—22no—
77C2×C42×C5—22no—
78C2×C42×C5D414yes—
79C2×C22⋊Dic5—24no—
80C2×C22⋊Dic5—24no—
81C2×C22⋊Dic5—24no—
82C2×C22⋊Dic5—24no—
83C2×C22⋊Dic5—24no—
84C2×C22⋊Dic5—24no—
85C2×C22⋊Dic5—42no—
86C2×C22⋊Dic5—42no—
87C2×C22⋊Dic5—42no—
88C2×C22⋊Dic5—42no—
89C2×C22⋊Dic5C2×C418yescomplemented
90C2×C22⋊Dic5C2×C418yescomplemented
91C2×C4⋊Dic5—22no—
92C2×C4⋊Dic5—22no—
93C2×C4⋊Dic5—22no—
94C2×C4⋊Dic5—22no—
95C2×C4⋊Dic5—22no—
96C2×C4⋊Dic5C2×C414yescomplemented
97C2×#683—22no—
98C2×#683—22no—
99C2×#683—22no—
100C2×#683—22no—
101C2×#683—22no—
102C2×#683—24no—
103C2×#683—24no—
104C2×#683—42no—
105C2×#683D414yescomplemented
106C2×C4×Dic5—22no—
107C2×C4×Dic5—22no—
108C2×C4×Dic5—22no—
109C2×C4×Dic5—22no—
110C2×C4×Dic5—22no—
111C2×C4×Dic5C2×C414yescomplemented
112#3963—22no—
113#3963—22no—
114#3963—24no—
115#3963—24no—
116#3963—24no—
117#3963—42no—
118#3963—42no—
119C22×C4×D4D511yescharacteristic
120C2×#390—51no—
121C2×#390—51no—
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—216no—
158C22×C4×C5—21no—
159C22×C4×C5—21no—
160C22×C4×C5—22no—
161C22×C4×C5—22no—
162C22×C4×C5—22no—
163C22×C4×C5—22no—
164C22×C4×C5—21no—
165C22×C4×C5—21no—
166C22×C4×C5—22no—
167C22×C4×C5—22no—
168C22×C4×C5—21no—
169C22×C4×C5—21no—
170C22×C4×C5—48no—
171C22×C4×C5—48no—
172C22×C4×C5—48no—
173C22×C4×C5—48no—
174C22×C4×C5—48no—
175C22×C4×C5—48no—
176C22×C4×C5C22×C412yes—
177C22×C4×C5C2×D412yes—
178C22×C4×C5C2×D412yes—
179C22×C4×C5C2×D414yes—
180C22×C4×C5C2×D412yes—
181C22×C4×C5C2×D412yes—
182C22×C4×C5C2×D412yes—
183C22×C4×C5C2×D412yes—
184C22×C4×C5C2×Q812yes—
185C22×C4×C5#4112yes—
186C22×C4×C5#4112yes—
187C22×C4×C5#4112yes—
188C22×Dic5—21no—
189C22×Dic5—21no—
190C22×Dic5—21no—
191C22×Dic5—21no—
192C22×Dic5—21no—
193C22×Dic5—21no—
194C22×Dic5—22no—
195C22×Dic5—21no—
196C22×Dic5—21no—
197C22×Dic5—21no—
198C22×Dic5—21no—
199C22×Dic5—22no—
200C22×Dic5—21no—
201C22×Dic5—22no—
202C22×Dic5—21no—
203C22×Dic5—21no—
204C22×Dic5—21no—
205C22×Dic5—22no—
206C22×Dic5—21no—
207C22×Dic5—21no—
208C22×Dic5—21no—
209C22×Dic5—21no—
210C22×Dic5—22no—
211C22×Dic5—22no—
212C22×Dic5—21no—
213C22×Dic5—21no—
214C22×Dic5—21no—
215C22×Dic5—21no—
216C22×Dic5—22no—
217C22×Dic5—22no—
218C22×Dic5—22no—
219C22×Dic5—22no—
220C22×Dic5—22no—
221C22×Dic5—22no—
222C22×Dic5—22no—
223C22×Dic5C22×C412yes—
224C22×Dic5C22×C414yes—
225C22×Dic5C22×C412yes—
226C22×Dic5C2×D412yes—
227C22×Dic5C2×D412yes—
228C22×Dic5#4112yes—
229C22×Dic5#4112yes—
230C5×C4⋊C4—28no—
231C5×C22⋊C4—216no—
232C42×C5—28no—
233C22⋊Dic5—216no—
234C22⋊Dic5—48no—
235C22⋊Dic5—48no—
236C22⋊Dic5—48no—
237C4⋊Dic5—28no—
238C4⋊Dic5—44no—
239#683—28no—
240#683—28no—
241#683—48no—
242C4×Dic5—28no—
243C4×Dic5—44no—
244C23×D4C2×D511yescharacteristic
245C24×C4C2×D512yes—
246C2×C4×D4—24no—
247C2×C4×D4—24no—
248C2×C4×D4—24no—
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⋊C4—52no—
259C22×C22⋊C4C2×D512yes—
260C22×C42—51no—
261C22×C42—51no—
262C22×C42C2×D511yescharacteristic
263#390—58no—
264#390—104no—
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—22no—
335C2×C4×C5—22no—
336C2×C4×C5—24no—
337C2×C4×C5—24no—
338C2×C4×C5—432no—
339C2×C4×C5—42no—
340C2×C4×C5—42no—
341C2×C4×C5—42no—
342C2×C4×C5—41no—
343C2×C4×C5—42no—
344C2×C4×C5—41no—
345C2×C4×C5—41no—
346C2×C4×C5—41no—
347C2×C4×C5C2×C4⋊C414yes—
348C2×C4×C5C4×D414yes—
349C2×C4×C5C4×D414yes—
350C2×C4×C5#12014yes—
351C2×C4×C5#12114yes—
352C2×C4×C5C22⋊Q814yes—
353C2×C4×C5C22⋊Q814yes—
354C2×C4×C5#12314yes—
355C2×Dic5—22no—
356C2×Dic5—22no—
357C2×Dic5—22no—
358C2×Dic5—22no—
359C2×Dic5—22no—
360C2×Dic5—22no—
361C2×Dic5—22no—
362C2×Dic5—24no—
363C2×Dic5—24no—
364C2×Dic5—22no—
365C2×Dic5—24no—
366C2×Dic5—22no—
367C2×Dic5—22no—
368C2×Dic5—22no—
369C2×Dic5—22no—
370C2×Dic5—22no—
371C2×Dic5—22no—
372C2×Dic5—22no—
373C2×Dic5—41no—
374C2×Dic5—41no—
375C2×Dic5—41no—
376C2×Dic5—41no—
377C2×Dic5—41no—
378C2×Dic5—41no—
379C2×Dic5—41no—
380C2×Dic5—41no—
381C2×Dic5—42no—
382C2×Dic5—41no—
383C2×Dic5—41no—
384C2×Dic5—41no—
385C2×Dic5—42no—
386C2×Dic5—42no—
387C2×Dic5—41no—
388C2×Dic5—42no—
389C2×Dic5—42no—
390C2×Dic5—42no—
391C2×Dic5—42no—
392C2×Dic5—42no—
393C2×Dic5—42no—
394C2×Dic5—42no—
395C2×Dic5—42no—
396C2×Dic5C4×D414yescomplemented
397C25C22×D512yes—
398C22×D4—22no—
399C22×D4—22no—
400C22×D4—22no—
401C22×D4—22no—
402C22×D4Dic1014yes—
403C22×D4C4×D514yes—
404C22×D4C22⋊D514yes—
405C23×C4—24no—
406C23×C4—24no—
407C23×C4—24no—
408C23×C4—24no—
409C23×C4—24no—
410C23×C4—42no—
411C23×C4—42no—
412C23×C4—51no—
413C23×C4—51no—
414C23×C4—52no—
415C23×C4—51no—
416C23×C4—51no—
417C23×C4—52no—
418C23×C4C22×D511yescharacteristic
419C23×C4C22×D512yes—
420C23×C4C22×D511yescharacteristic
421C23×C4C22×D511yescharacteristic
422C4×D4—232no—
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—102no—
436C2×C4⋊C4—102no—
437C2×C4⋊C4—104no—
438C2×C4⋊C4—102no—
439C2×C4⋊C4—202no—
440C2×C4⋊C4C22⋊D514yes—
441C2×C22⋊C4—24no—
442C2×C22⋊C4—24no—
443C2×C22⋊C4—24no—
444C2×C22⋊C4—58no—
445C2×C22⋊C4—58no—
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⋊C4—202no—
455C2×C22⋊C4—202no—
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×C42C22⋊D514yes—
465#95—104no—
466#95—104no—
467#95—102no—
468#95—102no—
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—44no—
529Dic5—42no—
530Dic5—42no—
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×C4×D514yes—
546C24C2×C22⋊D514yes—
547C24C23×D511yescharacteristic
548C2×D4—28no—
549C2×D4—28no—
550C2×D4—28no—
551C2×D4—28no—
552C2×D4—28no—
553C2×D4—28no—
554C2×D4#683116yescomplemented
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—216no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—48no—
573C22×C4—48no—
574C22×C4—48no—
575C22×C4—48no—
576C22×C4—48no—
577C22×C4—48no—
578C22×C4—52no—
579C22×C4—52no—
580C22×C4—52no—
581C22×C4—52no—
582C22×C4—54no—
583C22×C4—52no—
584C22×C4—52no—
585C22×C4—101no—
586C22×C4—101no—
587C22×C4—101no—
588C22×C4—101no—
589C22×C4—101no—
590C22×C4—102no—
591C22×C4—102no—
592C22×C4—101no—
593C22×C4—101no—
594C22×C4—101no—
595C22×C4—101no—
596C22×C4—102no—
597C22×C4—101no—
598C22×C4—102no—
599C22×C4—101no—
600C22×C4—102no—
601C22×C4—101no—
602C22×C4—101no—
603C22×C4—101no—
604C22×C4—101no—
605C22×C4—101no—
606C22×C4—101no—
607C22×C4—101no—
608C22×C4—101no—
609C22×C4—102no—
610C22×C4—101no—
611C22×C4—101no—
612C22×C4—101no—
613C22×C4—102no—
614C22×C4—102no—
615C22×C4—102no—
616C22×C4—102no—
617C22×C4—102no—
618C22×C4—102no—
619C22×C4—102no—
620C22×C4C2×Dic1012yes—
621C22×C4C2×C4×D512yes—
622C22×C4#70912yes—
623C22×C4#70912yes—
624C22×C4D4×D512yes—
625C22×C4#71112yes—
626C22×C4C2×C22⋊D512yes—
627C22×C4C2×C22⋊D514yes—
628C22×C4C2×C22⋊D512yes—
629C22×C4C2×C22⋊D512yes—
630C22×C4C2×C22⋊D512yes—
631C22×C4C2×C22⋊D512yes—
632C4⋊C4—28no—
633C4⋊C4—108no—
634C4⋊C4—108no—
635C4⋊C4—108no—
636C4⋊C4—208no—
637C4⋊C4—204no—
638C22⋊C4—216no—
639C22⋊C4—1016no—
640C22⋊C4—208no—
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×#68318yes—
697C23C22×Dic1011yescharacteristic
698C23C22×C4×D511yescharacteristic
699C23C2×#70911yescharacteristic
700C23C2×#70911yescharacteristic
701C23C2×D4×D511yescharacteristic
702C23C2×#71111yescharacteristic
703C23#414411yescharacteristic
704C23#414411yescharacteristic
705C23D5×#4111yescharacteristic
706C23D5×#4111yescharacteristic
707C23#414911yescharacteristic
708C23#415011yescharacteristic
709C23C22×C22⋊D511yescharacteristic
710C23C22×C22⋊D511yescharacteristic
711C23C22×C22⋊D511yescharacteristic
712D4—232no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—24no—
720C2×C4—24no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—24no—
725C2×C4—432no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—54no—
735C2×C4—102no—
736C2×C4—102no—
737C2×C4—102no—
738C2×C4—102no—
739C2×C4—102no—
740C2×C4—102no—
741C2×C4—102no—
742C2×C4—104no—
743C2×C4—104no—
744C2×C4—102no—
745C2×C4—102no—
746C2×C4—104no—
747C2×C4—102no—
748C2×C4—102no—
749C2×C4—102no—
750C2×C4—102no—
751C2×C4—102no—
752C2×C4—102no—
753C2×C4—202no—
754C2×C4—201no—
755C2×C4—201no—
756C2×C4—201no—
757C2×C4—201no—
758C2×C4—202no—
759C2×C4—202no—
760C2×C4—201no—
761C2×C4—201no—
762C2×C4—201no—
763C2×C4—201no—
764C2×C4—201no—
765C2×C4—201no—
766C2×C4—202no—
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×C4C2×#68314yes—
777C2×C4#407014yes—
778C2×C4#407014yes—
779C2×C4C4×C22⋊D514yes—
780C2×C4C4×C22⋊D514yes—
781C2×C4#407514yes—
782C2×C4#408414yes—
783C2×C4#409914yes—
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—
800C22C4×#71111yescharacteristic
801C22D4×Dic1011yescharacteristic
802C22#6587311yescharacteristic
803C22#6587311yescharacteristic
804C22#6587611yescharacteristic
805C22#6587711yescharacteristic
806C22C4×D4×D511yescharacteristic
807C22#6587911yescharacteristic
808C22#6588011yescharacteristic
809C22#6588211yescharacteristic
810C22#6588711yescharacteristic
811C22#6589111yescharacteristic
812C22#6589311yescharacteristic
813C22#6589311yescharacteristic
814C22#6589511yescharacteristic
815C22#6589611yescharacteristic
816C22C22×#68311yescharacteristic
817C22C2×#407011yescharacteristic
818C22C2×#407011yescharacteristic
819C22C2×C4×C22⋊D511yescharacteristic
820C22C2×C4×C22⋊D511yescharacteristic
821C22C2×#407511yescharacteristic
822C22C2×#408411yescharacteristic
823C22D4×C22⋊D511yescharacteristic
824C22D4×C22⋊D511yescharacteristic
825C22#6613911yescharacteristic
826C22#6614011yescharacteristic
827C22#6614011yescharacteristic
828C22#6615811yescharacteristic
829C22#6616211yescharacteristic
830C22#6616311yescharacteristic
831C22#6616511yescharacteristic
832C22#6616711yescharacteristic
833C22#6616811yescharacteristic
834C22C2×#409911yescharacteristic
835C4—24no—
836C4—42no—
837C4—44no—
838C4—104no—
839C4—202no—
840C4—204no—
841C4—202no—
842C4—202no—
843C4—402no—
844C4#6549918yescomplemented
845C2—48no—
846C2D4×#68311yescharacteristic
847C2#1061406511yescharacteristic
848C2#1061407411yescharacteristic
849C2#1061407511yescharacteristic
850C2#1061408911yescharacteristic
851C2#1061409011yescharacteristic
852C2#1061409311yescharacteristic
853C2#1061409411yescharacteristic
854C2#1061410711yescharacteristic
855C2#1061411911yescharacteristic
856C2C4×#408411yescharacteristic
857C2#1061412711yescharacteristic
858C2C2×#6549911yescharacteristic
859C2#1061578411yescharacteristic
860C2#1061582811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D5
commutatorC23×C5C23×C4
FittingC22×C4×C5×D4C2
socle, cosocleC24×C5C24
prime radicalC23×C5×D4C22
hypercenterC22×C4×D4D5
hypocenterC5#14018
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
4. C2×#65499C2semidirect
5. C2×#65262C2semidirect
6. C2×C4×#683C2semidirect
7. #10602920C2semidirect
8. #10602356C2semidirect
9. #10602340C2semidirect
10. #10602340C2semidirect
11. #10602328C2semidirect
32. #65510C4semidirect
89. C2×C22⋊Dic5C2×C4semidirect
90. C2×C22⋊Dic5C2×C4semidirect
96. C2×C4⋊Dic5C2×C4semidirect
105. C2×#683D4semidirect
111. C2×C4×Dic5C2×C4semidirect
152. C2×C5×D4C4⋊C4semidirect
396. C2×Dic5C4×D4semidirect
525. C4×C5#385semidirect
554. C2×D4#683semidirect
784. C5#14018semidirect
844. C4#65499semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C5×D42
C2×#655102
C2×#654992
C2×#652622
C2×C4×#6832
#106029202
#106023562
#106023402
#106023282
#140185