Finite Group Databasebeta

← #12030523

Subgroups — #12030523

Order 1280.

2430 conjugacy classes of subgroups.

The subgroup lattice has 1060 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C42×D5C211yesmaximal, characteristic
2C2×#65222C211yesmaximal, characteristic, complemented
3C2×#64957C211yesmaximal, characteristic
4C2×#64957C211yesmaximal, characteristic
5C2×#64942C211yesmaximal, characteristic, complemented
6C5×#1434C211yesmaximal, characteristic, complemented
7#10600218C211yesmaximal, characteristic
8#10600218C211yesmaximal, characteristic
9#10600218C211yesmaximal, characteristic
10#10600218C211yesmaximal, characteristic
11#10600200C211yesmaximal, characteristic, complemented
12#10600200C211yesmaximal, characteristic, complemented
13#10600200C211yesmaximal, characteristic, complemented
14#10600198C211yesmaximal, characteristic, complemented
15#10600195C211yesmaximal, characteristic, complemented
16C23×C4×D5C2211yescharacteristic
17C23×C4×D5C2211yescharacteristic
18C23×C4×D5C2211yescharacteristic
19C22×C42×C5C2211yescharacteristic
20C22×#685C2211yescharacteristic
21C22×#685C2211yescharacteristic
22C22×#685C2211yescharacteristic
23C22×#685C2211yescharacteristic
24C22×C4⋊Dic5C2211yescharacteristic
25C22×C4⋊Dic5C2211yescharacteristic
26C22×#683C2211yescharacteristic
27C22×#683C2211yescharacteristic
28C22×C4×Dic5C2211yescharacteristic
29C22×C4×Dic5C2211yescharacteristic
30C22×C4×Dic5C2211yescharacteristic
31C2×C42×D5—24no—
32C2×C42×D5—24no—
33C2×C42×D5—24no—
34C2×C5×#95C2211yescharacteristic
35C2×C5×#95C2211yescharacteristic
36C2×C5×#95C2211yescharacteristic
37C2×C5×#95C2211yescharacteristic
38C2×C5×#95C2211yescharacteristic
39C2×C5×#95C2211yescharacteristic
40C2×#3963C2211yescharacteristic
41C2×#3963C2211yescharacteristic
42C2×#3963C2211yescharacteristic
43C2×#3963C2211yescharacteristic
44C2×#3963C2211yescharacteristic
45C2×#3963C2211yescharacteristic
46C2×#3963C2211yescharacteristic
47C2×#3963C2211yescharacteristic
48C2×#3963C2211yescharacteristic
49C2×#3963C2211yescharacteristic
50C2×#3963C2211yescharacteristic
51C2×#3963C2211yescharacteristic
52C2×#3963C2211yescharacteristic
53C2×#3963C2211yescharacteristic
54#65222—24no—
55#64957—24no—
56#64957C418yescomplemented
57#64942—24no—
58#14695—51nomaximal, Sylow
59C24×D5C2311yescharacteristic
60C23×C4×C5C2311yescharacteristic
61C23×C4×C5C2311yescharacteristic
62C23×C4×C5C2311yescharacteristic
63C23×C4×C5C2311yescharacteristic
64C23×C4×C5C2311yescharacteristic
65C23×C4×C5C2311yescharacteristic
66C23×C4×C5C2311yescharacteristic
67C23×Dic5C2311yescharacteristic
68C23×Dic5C2311yescharacteristic
69C23×Dic5C2311yescharacteristic
70C23×Dic5C2311yescharacteristic
71C23×Dic5C2311yescharacteristic
72C23×Dic5C2311yescharacteristic
73C23×Dic5C2311yescharacteristic
74C22×C4×D5—22no—
75C22×C4×D5—22no—
76C22×C4×D5—22no—
77C22×C4×D5—22no—
78C22×C4×D5—22no—
79C22×C4×D5—22no—
80C22×C4×D5—22no—
81C22×C4×D5—22no—
82C22×C4×D5—22no—
83C22×C4×D5—22no—
84C22×C4×D5—22no—
85C22×C4×D5—22no—
86C22×C4×D5—22no—
87C22×C4×D5—22no—
88C22×C4×D5—22no—
89C22×C4×D5—22no—
90C22×C4×D5—22no—
91C22×C4×D5—22no—
92C22×C4×D5C2×C414yes—
93C22×C4×D5D414yes—
94C22×C4×D5Q814yes—
95C2×C42×C5—22no—
96C2×C42×C5—22no—
97C2×C42×C5D414yes—
98C2×#685—22no—
99C2×#685—22no—
100C2×#685—22no—
101C2×#685—22no—
102C2×#685—22no—
103C2×#685—22no—
104C2×#685—22no—
105C2×#685—22no—
106C2×#685—22no—
107C2×#685—22no—
108C2×#685C2×C414yes—
109C2×#685C2×C414yes—
110C2×C4⋊Dic5—22no—
111C2×C4⋊Dic5—22no—
112C2×C4⋊Dic5—22no—
113C2×C4⋊Dic5—22no—
114C2×C4⋊Dic5—22no—
115C2×C4⋊Dic5C2×C414yescomplemented
116C2×#683—22no—
117C2×#683—22no—
118C2×#683—22no—
119C2×#683—22no—
120C2×#683—22no—
121C2×#683C2×C414yescomplemented
122C2×C4×Dic5—22no—
123C2×C4×Dic5—22no—
124C2×C4×Dic5—22no—
125C2×C4×Dic5—22no—
126C2×C4×Dic5—22no—
127C2×C4×Dic5—22no—
128C2×C4×Dic5—22no—
129C2×C4×Dic5—22no—
130C2×C4×Dic5D414yes—
131C42×D5—232no—
132C5×#95—22no—
133C5×#95—22no—
134C5×#95—22no—
135C5×#95—22no—
136C5×#95—22no—
137C5×#95C2×C414yescomplemented
138#3963—22no—
139#3963—22no—
140#3963—22no—
141#3963—22no—
142#3963—22no—
143#3963—22no—
144#3963—22no—
145#3963—22no—
146#3963—22no—
147#3963—22no—
148#3963—22no—
149#3963—22no—
150#3963—22no—
151#3963C2×C414yescomplemented
152C23×C42—51no—
153C2×#387—51no—
154C2×#387—51no—
155C2×#385—51no—
156C2×#385—51no—
157#1436—51no—
158#1436—51no—
159#1436—51no—
160#1436—51no—
161#1434—51no—
162#1434D511yescharacteristic, complemented
163C22⋊#95—51no—
164C22⋊#95—51no—
165C22⋊#95—51no—
166C22⋊#95—51no—
167C24×C5C2411yescharacteristic
168C23×D5—21no—
169C23×D5—21no—
170C23×D5—21no—
171C23×D5—21no—
172C23×D5—21no—
173C23×D5—21no—
174C23×D5—21no—
175C23×D5—21no—
176C23×D5C22×C412yes—
177C23×D5C2×D412yes—
178C23×D5C2×Q812yes—
179C23×D5#4112yes—
180C23×D5#4112yes—
181C23×D5#4112yes—
182C23×D5#4112yes—
183C22×C4×C5—21no—
184C22×C4×C5—21no—
185C22×C4×C5—21no—
186C22×C4×C5—21no—
187C22×C4×C5—21no—
188C22×C4×C5—21no—
189C22×C4×C5—21no—
190C22×C4×C5—21no—
191C22×C4×C5—21no—
192C22×C4×C5—21no—
193C22×C4×C5—21no—
194C22×C4×C5—21no—
195C22×C4×C5—21no—
196C22×C4×C5—21no—
197C22×C4×C5—21no—
198C22×C4×C5—21no—
199C22×C4×C5—21no—
200C22×C4×C5—21no—
201C22×C4×C5—21no—
202C22×C4×C5—21no—
203C22×C4×C5—21no—
204C22×C4×C5—21no—
205C22×C4×C5—21no—
206C22×C4×C5—21no—
207C22×C4×C5—21no—
208C22×C4×C5—21no—
209C22×C4×C5—21no—
210C22×C4×C5—21no—
211C22×C4×C5—21no—
212C22×C4×C5—21no—
213C22×C4×C5—21no—
214C22×C4×C5—21no—
215C22×C4×C5—21no—
216C22×C4×C5—21no—
217C22×C4×C5—21no—
218C22×C4×C5—21no—
219C22×C4×C5—21no—
220C22×C4×C5—21no—
221C22×C4×C5C22×C412yes—
222C22×C4×C5C22×C412yes—
223C22×C4×C5C22×C412yes—
224C22×C4×C5C2×D412yes—
225C22×C4×C5C2×D412yes—
226C22×C4×C5C2×D412yes—
227C22×C4×C5C2×D412yes—
228C22×C4×C5C2×D412yes—
229C22×C4×C5C2×Q812yes—
230C22×C4×C5#4112yes—
231C22×C4×C5#4112yes—
232C22×Dic5—21no—
233C22×Dic5—21no—
234C22×Dic5—21no—
235C22×Dic5—21no—
236C22×Dic5—21no—
237C22×Dic5—21no—
238C22×Dic5—21no—
239C22×Dic5—21no—
240C22×Dic5—21no—
241C22×Dic5—21no—
242C22×Dic5—21no—
243C22×Dic5—21no—
244C22×Dic5—21no—
245C22×Dic5—21no—
246C22×Dic5—21no—
247C22×Dic5—21no—
248C22×Dic5—21no—
249C22×Dic5—21no—
250C22×Dic5—21no—
251C22×Dic5—21no—
252C22×Dic5—21no—
253C22×Dic5—21no—
254C22×Dic5—21no—
255C22×Dic5—21no—
256C22×Dic5—21no—
257C22×Dic5—21no—
258C22×Dic5—21no—
259C22×Dic5—21no—
260C22×Dic5—21no—
261C22×Dic5—21no—
262C22×Dic5—21no—
263C22×Dic5—21no—
264C22×Dic5—21no—
265C22×Dic5—21no—
266C22×Dic5—21no—
267C22×Dic5—21no—
268C22×Dic5—21no—
269C22×Dic5—21no—
270C22×Dic5C22×C412yes—
271C22×Dic5C22×C412yes—
272C22×Dic5C22×C412yes—
273C22×Dic5C2×D412yes—
274C22×Dic5C2×D412yes—
275C22×Dic5C2×D412yes—
276C22×Dic5C2×Q812yes—
277C22×Dic5#4112yes—
278C22×Dic5#4112yes—
279C22×Dic5#4112yes—
280C22×Dic5#4112yes—
281C2×C4×D5—28no—
282C2×C4×D5—28no—
283C2×C4×D5—28no—
284C2×C4×D5—28no—
285C2×C4×D5—28no—
286C2×C4×D5—28no—
287C2×C4×D5—28no—
288C2×C4×D5—28no—
289C2×C4×D5—28no—
290C2×C4×D5—28no—
291C2×C4×D5—28no—
292C2×C4×D5—28no—
293C2×C4×D5—28no—
294C2×C4×D5—28no—
295C2×C4×D5—28no—
296C2×C4×D5—28no—
297C2×C4×D5—28no—
298C2×C4×D5—28no—
299C2×C4×D5—28no—
300C2×C4×D5—28no—
301C2×C4×D5—28no—
302C42×C5—28no—
303#685—28no—
304#685—28no—
305#685—44no—
306#685—44no—
307C4⋊Dic5—28no—
308C4⋊Dic5—44no—
309#683—28no—
310#683—44no—
311C4×Dic5—28no—
312C4×Dic5—28no—
313C4×Dic5—28no—
314C24×C4—51no—
315C24×C4—51no—
316C24×C4—51no—
317C22×C4⋊C4—51no—
318C22×C4⋊C4—51no—
319C22×C4⋊C4—51no—
320C22×C4⋊C4—51no—
321C22×C22⋊C4—51no—
322C22×C22⋊C4—51no—
323C22×C22⋊C4—51no—
324C22×C22⋊C4—51no—
325C22×C42—51no—
326C22×C42—51no—
327C22×C42—51no—
328C22×C42—104no—
329C22×C42—104no—
330C22×C42—104no—
331C22×C42C2×D511yescharacteristic
332#387—104no—
333#387—104no—
334#385—58no—
335#385—104no—
336C2×#95—51no—
337C2×#95—51no—
338C2×#95—51no—
339C2×#95—51no—
340C2×#95—51no—
341C2×#95—51no—
342C2×#95—51no—
343C2×#95—51no—
344C2×#95—51no—
345C2×#95—51no—
346C2×#95—51no—
347C2×#95—51no—
348C2×#95—51no—
349C2×#95—51no—
350C2×#95C2×D511yescharacteristic
351C2×#95C2×D511yescharacteristic
352C2×#95C2×D511yescharacteristic
353C2×#95C2×D511yescharacteristic
354C2×#95C2×D511yescharacteristic
355C2×#95C2×D511yescharacteristic
356C23×C5C23×C411yescharacteristic
357C23×C5C22×D411yescharacteristic
358C23×C5C22×D411yescharacteristic
359C23×C5C22×D411yescharacteristic
360C23×C5C22×Q811yescharacteristic
361C23×C5C2×#4111yescharacteristic
362C23×C5C2×#4111yescharacteristic
363C23×C5C2×#4111yescharacteristic
364C23×C5C2×#4111yescharacteristic
365C23×C5C2×#4111yescharacteristic
366C23×C5C2×#4111yescharacteristic
367C23×C5C2×#4111yescharacteristic
368C23×C5C2×#4111yescharacteristic
369C23×C5C2×#4111yescharacteristic
370C23×C5C2×#4111yescharacteristic
371C22×D5—22no—
372C22×D5—22no—
373C22×D5—22no—
374C22×D5—22no—
375C22×D5—22no—
376C22×D5—22no—
377C22×D5—22no—
378C22×D5—22no—
379C22×D5—22no—
380C22×D5—22no—
381C22×D5—22no—
382C22×D5—22no—
383C22×D5—22no—
384C22×D5—22no—
385C22×D5—22no—
386C22×D5—22no—
387C22×D5—22no—
388C22×D5—22no—
389C22×D5—22no—
390C22×D5—22no—
391C22×D5—22no—
392C22×D5—22no—
393C22×D5—22no—
394C22×D5—22no—
395C22×D5—22no—
396C22×D5—22no—
397C22×D5—22no—
398C22×D5—22no—
399C22×D5#11714yes—
400C22×D5C4×D414yes—
401C22×D5C4×Q814yes—
402C22×D5C22⋊Q814yes—
403C22×D5#12314yes—
404C22×D5#12514yes—
405C22×D5#12614yes—
406C2×C4×C5—22no—
407C2×C4×C5—22no—
408C2×C4×C5—22no—
409C2×C4×C5—22no—
410C2×C4×C5—22no—
411C2×C4×C5—22no—
412C2×C4×C5—22no—
413C2×C4×C5—22no—
414C2×C4×C5—22no—
415C2×C4×C5—22no—
416C2×C4×C5—22no—
417C2×C4×C5—22no—
418C2×C4×C5—22no—
419C2×C4×C5—22no—
420C2×C4×C5—22no—
421C2×C4×C5—22no—
422C2×C4×C5—22no—
423C2×C4×C5—22no—
424C2×C4×C5—22no—
425C2×C4×C5—22no—
426C2×C4×C5—22no—
427C2×C4×C5—22no—
428C2×C4×C5—22no—
429C2×C4×C5—22no—
430C2×C4×C5—41no—
431C2×C4×C5—41no—
432C2×C4×C5—41no—
433C2×C4×C5—41no—
434C2×C4×C5—41no—
435C2×C4×C5—41no—
436C2×C4×C5—41no—
437C2×C4×C5—41no—
438C2×C4×C5—41no—
439C2×C4×C5—41no—
440C2×C4×C5—41no—
441C2×C4×C5—41no—
442C2×C4×C5—41no—
443C2×C4×C5—41no—
444C2×C4×C5—41no—
445C2×C4×C5—41no—
446C2×C4×C5—41no—
447C2×C4×C5—41no—
448C2×C4×C5—41no—
449C2×C4×C5—41no—
450C2×C4×C5—41no—
451C2×C4×C5—41no—
452C2×C4×C5C4×D414yes—
453C2×C4×C5#12014yes—
454C2×C4×C5C22⋊Q814yes—
455C2×Dic5—22no—
456C2×Dic5—22no—
457C2×Dic5—22no—
458C2×Dic5—22no—
459C2×Dic5—22no—
460C2×Dic5—22no—
461C2×Dic5—22no—
462C2×Dic5—22no—
463C2×Dic5—22no—
464C2×Dic5—22no—
465C2×Dic5—22no—
466C2×Dic5—22no—
467C2×Dic5—22no—
468C2×Dic5—22no—
469C2×Dic5—22no—
470C2×Dic5—22no—
471C2×Dic5—22no—
472C2×Dic5—22no—
473C2×Dic5—22no—
474C2×Dic5—22no—
475C2×Dic5—22no—
476C2×Dic5—22no—
477C2×Dic5—22no—
478C2×Dic5—22no—
479C2×Dic5—41no—
480C2×Dic5—41no—
481C2×Dic5—41no—
482C2×Dic5—41no—
483C2×Dic5—41no—
484C2×Dic5—41no—
485C2×Dic5—41no—
486C2×Dic5—41no—
487C2×Dic5—41no—
488C2×Dic5—41no—
489C2×Dic5—41no—
490C2×Dic5—41no—
491C2×Dic5—41no—
492C2×Dic5—41no—
493C2×Dic5—41no—
494C2×Dic5—41no—
495C2×Dic5—41no—
496C2×Dic5—41no—
497C2×Dic5—41no—
498C2×Dic5—41no—
499C2×Dic5—41no—
500C2×Dic5—41no—
501C2×Dic5C4×D414yes—
502C2×Dic5C22⋊Q814yes—
503C2×Dic5#12314yes—
504C4×D5—232no—
505C4×D5—232no—
506C4×D5—232no—
507C25—51no—
508C23×C4—51no—
509C23×C4—51no—
510C23×C4—51no—
511C23×C4—51no—
512C23×C4—51no—
513C23×C4—54no—
514C23×C4—54no—
515C23×C4—54no—
516C23×C4—51no—
517C23×C4—51no—
518C23×C4—102no—
519C23×C4—102no—
520C23×C4—102no—
521C23×C4—102no—
522C23×C4—102no—
523C23×C4—102no—
524C23×C4—102no—
525C23×C4—102no—
526C23×C4—102no—
527C23×C4—102no—
528C23×C4—102no—
529C23×C4—102no—
530C23×C4—102no—
531C23×C4—102no—
532C23×C4—102no—
533C23×C4—102no—
534C23×C4—102no—
535C23×C4—102no—
536C23×C4C22×D511yescharacteristic
537C23×C4C22×D511yescharacteristic
538C23×C4C22×D511yescharacteristic
539C23×C4C22×D511yescharacteristic
540C23×C4C22×D511yescharacteristic
541C23×C4C22×D511yescharacteristic
542C23×C4C22×D511yescharacteristic
543C2×C4⋊C4—54no—
544C2×C4⋊C4—54no—
545C2×C4⋊C4—102no—
546C2×C4⋊C4—102no—
547C2×C4⋊C4—102no—
548C2×C4⋊C4—102no—
549C2×C4⋊C4—102no—
550C2×C4⋊C4—102no—
551C2×C4⋊C4—102no—
552C2×C4⋊C4—102no—
553C2×C4⋊C4—102no—
554C2×C4⋊C4—102no—
555C2×C22⋊C4—54no—
556C2×C22⋊C4—54no—
557C2×C22⋊C4—102no—
558C2×C22⋊C4—102no—
559C2×C22⋊C4—102no—
560C2×C22⋊C4—102no—
561C2×C22⋊C4—102no—
562C2×C22⋊C4—102no—
563C2×C22⋊C4—102no—
564C2×C22⋊C4—102no—
565C2×C22⋊C4—102no—
566C2×C22⋊C4—102no—
567C2×C42—22no—
568C2×C42—22no—
569C2×C42—54no—
570C2×C42—1032no—
571C2×C42—102no—
572C2×C42—102no—
573C2×C42—102no—
574C2×C42—102no—
575C2×C42—102no—
576C2×C42—102no—
577C2×C42—102no—
578C2×C42—102no—
579C2×C42D2014yes—
580#95—22no—
581#95—22no—
582#95—22no—
583#95—22no—
584#95—22no—
585#95—54no—
586#95—102no—
587#95—102no—
588#95—102no—
589#95—102no—
590#95—102no—
591#95—102no—
592#95—102no—
593#95—102no—
594#95—102no—
595#95—102no—
596#95—102no—
597#95—102no—
598#95—102no—
599#95C4×D514yescomplemented
600C22×C5C2×#11711yescharacteristic
601C22×C5C2×C4×D411yescharacteristic
602C22×C5C2×C4×D411yescharacteristic
603C22×C5C2×C4×D411yescharacteristic
604C22×C5C2×C4×Q811yescharacteristic
605C22×C5C4×#4111yescharacteristic
606C22×C5C4×#4111yescharacteristic
607C22×C5C2×#12011yescharacteristic
608C22×C5C2×C22⋊Q811yescharacteristic
609C22×C5C2×C22⋊Q811yescharacteristic
610C22×C5C2×C22⋊Q811yescharacteristic
611C22×C5C2×#12311yescharacteristic
612C22×C5C2×#12311yescharacteristic
613C22×C5#52511yescharacteristic
614C22×C5#52511yescharacteristic
615C22×C5#52511yescharacteristic
616C22×C5#52511yescharacteristic
617C22×C5#52511yescharacteristic
618C22×C5#52511yescharacteristic
619C22×C5#52511yescharacteristic
620C22×C5#52511yescharacteristic
621C22×C5#52511yescharacteristic
622C22×C5#52511yescharacteristic
623C22×C5C2×#12511yescharacteristic
624C22×C5C2×#12611yescharacteristic
625C22×C5#52911yescharacteristic
626C22×C5#52911yescharacteristic
627C22×C5#52911yescharacteristic
628C22×C5#52911yescharacteristic
629C22×C5#52911yescharacteristic
630C22×C5#52911yescharacteristic
631C22×C5#52911yescharacteristic
632C22×C5#52911yescharacteristic
633C22×C5#53311yescharacteristic
634C22×C5#53311yescharacteristic
635C2×D5—24no—
636C2×D5—24no—
637C2×D5—24no—
638C2×D5—24no—
639C2×D5—24no—
640C2×D5—24no—
641C2×D5—24no—
642C2×D5—24no—
643C2×D5—24no—
644C2×D5—24no—
645C2×D5—24no—
646C2×D5—24no—
647C2×D5—24no—
648C2×D5—24no—
649C2×D5#38718yescomplemented
650C4×C5—24no—
651C4×C5—24no—
652C4×C5—24no—
653C4×C5—42no—
654C4×C5—42no—
655C4×C5—81no—
656C4×C5—81no—
657Dic5—24no—
658Dic5—24no—
659Dic5—24no—
660Dic5—42no—
661Dic5—42no—
662Dic5—81no—
663Dic5—81no—
664C24—52no—
665C24—52no—
666C24—52no—
667C24—52no—
668C24—52no—
669C24—52no—
670C24—52no—
671C24—101no—
672C24—101no—
673C24—101no—
674C24—101no—
675C24—101no—
676C24—101no—
677C24—101no—
678C24—101no—
679C24C23×D511yescharacteristic
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—52no—
719C22×C4—52no—
720C22×C4—52no—
721C22×C4—52no—
722C22×C4—52no—
723C22×C4—52no—
724C22×C4—52no—
725C22×C4—52no—
726C22×C4—52no—
727C22×C4—52no—
728C22×C4—52no—
729C22×C4—108no—
730C22×C4—108no—
731C22×C4—108no—
732C22×C4—108no—
733C22×C4—108no—
734C22×C4—108no—
735C22×C4—108no—
736C22×C4—108no—
737C22×C4—108no—
738C22×C4—108no—
739C22×C4—108no—
740C22×C4—108no—
741C22×C4—108no—
742C22×C4—108no—
743C22×C4—108no—
744C22×C4—108no—
745C22×C4—108no—
746C22×C4—108no—
747C22×C4—101no—
748C22×C4—101no—
749C22×C4—101no—
750C22×C4—101no—
751C22×C4—101no—
752C22×C4—101no—
753C22×C4—101no—
754C22×C4—101no—
755C22×C4—101no—
756C22×C4—101no—
757C22×C4—101no—
758C22×C4—101no—
759C22×C4—108no—
760C22×C4—108no—
761C22×C4—108no—
762C22×C4—101no—
763C22×C4—101no—
764C22×C4—101no—
765C22×C4—101no—
766C22×C4—101no—
767C22×C4—101no—
768C22×C4—101no—
769C22×C4—101no—
770C22×C4—101no—
771C22×C4—101no—
772C22×C4—101no—
773C22×C4—101no—
774C22×C4—101no—
775C22×C4—101no—
776C22×C4—101no—
777C22×C4—101no—
778C22×C4—101no—
779C22×C4—101no—
780C22×C4—101no—
781C22×C4—101no—
782C22×C4—101no—
783C22×C4—101no—
784C22×C4—101no—
785C22×C4—101no—
786C22×C4—101no—
787C22×C4—101no—
788C22×C4C2×C4×D512yes—
789C22×C4C2×C4×D512yes—
790C22×C4C2×C4×D512yes—
791C22×C4C2×D2012yes—
792C22×C4C2×D2012yes—
793C22×C4C2×D2012yes—
794C22×C4#70912yes—
795C22×C4D4×D512yes—
796C22×C4D4×D512yes—
797C22×C4#71112yes—
798C22×C4Q8×D512yes—
799C4⋊C4—108no—
800C4⋊C4—108no—
801C4⋊C4—204no—
802C4⋊C4—204no—
803C22⋊C4—108no—
804C22⋊C4—108no—
805C22⋊C4—204no—
806C22⋊C4—204no—
807C42—28no—
808C42—108no—
809C42—108no—
810C42—108no—
811C2×C5C2×#38711yescharacteristic
812C2×C5#229011yescharacteristic
813C2×C5#229011yescharacteristic
814C2×C5C4×#12011yescharacteristic
815C2×C5C4×#12311yescharacteristic
816C2×C5C4×C22⋊Q811yescharacteristic
817C2×C5C4×C22⋊Q811yescharacteristic
818C2×C5#284811yescharacteristic
819C2×C5#284911yescharacteristic
820C2×C5#285111yescharacteristic
821C2×C5#285111yescharacteristic
822C2×C5#285211yescharacteristic
823C2×C5#285211yescharacteristic
824C2×C5#285311yescharacteristic
825C2×C5#285511yescharacteristic
826D5—28no—
827C23—54no—
828C23—54no—
829C23—54no—
830C23—54no—
831C23—54no—
832C23—54no—
833C23—54no—
834C23—102no—
835C23—102no—
836C23—102no—
837C23—102no—
838C23—102no—
839C23—102no—
840C23—102no—
841C23—102no—
842C23—102no—
843C23—102no—
844C23—102no—
845C23—102no—
846C23—102no—
847C23—102no—
848C23—102no—
849C23—102no—
850C23—102no—
851C23—102no—
852C23—102no—
853C23—102no—
854C23—102no—
855C23—102no—
856C23—102no—
857C23—102no—
858C23—102no—
859C23—102no—
860C23—102no—
861C23—102no—
862C23C22×C4×D511yescharacteristic
863C23C22×D2011yescharacteristic
864C23C2×#70911yescharacteristic
865C23C2×D4×D511yescharacteristic
866C23C2×D4×D511yescharacteristic
867C23C2×#71111yescharacteristic
868C23C2×Q8×D511yescharacteristic
869C23D5×#4111yescharacteristic
870C23D5×#4111yescharacteristic
871C23D5×#4111yescharacteristic
872C23D5×#4111yescharacteristic
873C23D5×#4111yescharacteristic
874C23D5×#4111yescharacteristic
875C23D5×#4111yescharacteristic
876C23D5×#4111yescharacteristic
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—22no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—22no—
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—22no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—54no—
924C2×C4—54no—
925C2×C4—54no—
926C2×C4—1032no—
927C2×C4—1032no—
928C2×C4—1032no—
929C2×C4—102no—
930C2×C4—102no—
931C2×C4—102no—
932C2×C4—102no—
933C2×C4—102no—
934C2×C4—102no—
935C2×C4—102no—
936C2×C4—102no—
937C2×C4—102no—
938C2×C4—102no—
939C2×C4—102no—
940C2×C4—102no—
941C2×C4—102no—
942C2×C4—102no—
943C2×C4—102no—
944C2×C4—102no—
945C2×C4—102no—
946C2×C4—102no—
947C2×C4—102no—
948C2×C4—102no—
949C2×C4—102no—
950C2×C4—102no—
951C2×C4—102no—
952C2×C4—102no—
953C2×C4—201no—
954C2×C4—201no—
955C2×C4—201no—
956C2×C4—201no—
957C2×C4—201no—
958C2×C4—201no—
959C2×C4—201no—
960C2×C4—201no—
961C2×C4—201no—
962C2×C4—201no—
963C2×C4—201no—
964C2×C4—201no—
965C2×C4—201no—
966C2×C4—201no—
967C2×C4—201no—
968C2×C4—201no—
969C2×C4—201no—
970C2×C4—201no—
971C2×C4—201no—
972C2×C4—201no—
973C2×C4—201no—
974C2×C4—201no—
975C2×C4C4×D2014yes—
976C2×C4#402814yes—
977C2×C4#404314yes—
978C5#1469511yescharacteristic, complemented, Sylow
979C22—58no—
980C22—104no—
981C22—104no—
982C22—104no—
983C22—104no—
984C22—104no—
985C22—104no—
986C22—104no—
987C22—104no—
988C22—104no—
989C22—104no—
990C22—104no—
991C22—104no—
992C22—104no—
993C22—104no—
994C22C2×C4×D2011yescharacteristic
995C22C2×#402811yescharacteristic
996C22C2×#404311yescharacteristic
997C22D5×#11711yescharacteristic
998C22#6585611yescharacteristic
999C22#6585811yescharacteristic
1000C22#6585811yescharacteristic
1001C22#6585811yescharacteristic
1002C22#6585811yescharacteristic
1003C22#6586211yescharacteristic
1004C22#6586211yescharacteristic
1005C22C4×#71111yescharacteristic
1006C22C4×D4×D511yescharacteristic
1007C22C4×D4×D511yescharacteristic
1008C22#6588111yescharacteristic
1009C22#6588111yescharacteristic
1010C22#6589111yescharacteristic
1011C22C4×Q8×D511yescharacteristic
1012C22#6591211yescharacteristic
1013C22#6594011yescharacteristic
1014C22#6594011yescharacteristic
1015C22D5×C22⋊Q811yescharacteristic
1016C22D5×C22⋊Q811yescharacteristic
1017C22D5×#12311yescharacteristic
1018C22D5×#12311yescharacteristic
1019C22#6599011yescharacteristic
1020C22#6599011yescharacteristic
1021C22#6601411yescharacteristic
1022C22#6601411yescharacteristic
1023C22D5×#12511yescharacteristic
1024C22#6602211yescharacteristic
1025C22D5×#12611yescharacteristic
1026C22#6604011yescharacteristic
1027C22#6604011yescharacteristic
1028C22#6604011yescharacteristic
1029C4—24no—
1030C4—24no—
1031C4—24no—
1032C4—42no—
1033C4—42no—
1034C4—81no—
1035C4—81no—
1036C4—104no—
1037C4—104no—
1038C4—104no—
1039C4—202no—
1040C4—202no—
1041C4—401no—
1042C4—401no—
1043C2—108no—
1044C2#1060514511yescharacteristic
1045C2C4×#402811yescharacteristic
1046C2C4×#404311yescharacteristic
1047C2#1060578011yescharacteristic
1048C2#1060587711yescharacteristic
1049C2#1060598811yescharacteristic
1050C2#1060604811yescharacteristic
1051C2#1060667211yescharacteristic
1052C2D5×#38711yescharacteristic
1053C2#1060717611yescharacteristic
1054C2#1060717911yescharacteristic
1055C2#1060718011yescharacteristic
1056C2#1060718411yescharacteristic
1057C2#1060768911yescharacteristic
1058C2#1060769011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D5
commutatorC23×C5C23×C4
FittingC5×#1434C2
socle, cosocleC24×C5C24
prime radicalC24×D5C23
hypercenter#1434D5
hypocenterC5#14695
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ #1434

Complements

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

NH ≅ G/Ntype
2. C2×#65222C2semidirect
5. C2×#64942C2semidirect
6. C5×#1434C2semidirect
11. #10600200C2semidirect
12. #10600200C2semidirect
13. #10600200C2semidirect
14. #10600198C2semidirect
15. #10600195C2semidirect
56. #64957C4semidirect
115. C2×C4⋊Dic5C2×C4semidirect
121. C2×#683C2×C4semidirect
137. C5×#95C2×C4semidirect
151. #3963C2×C4semidirect
162. #1434D5semidirect
599. #95C4×D5semidirect
649. C2×D5#387semidirect
978. C5#14695semidirect

Maximal subgroups

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

subgroupindex
C22×C42×D52
C2×#652222
C2×#649572
C2×#649422
C5×#14342
#106002182
#106002002
#106001982
#106001952
#146955