Finite Group Databasebeta

← #12022685

Subgroups — #12022685

Order 1280.

1810 conjugacy classes of subgroups.

The subgroup lattice has 914 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×Dic10C211yesmaximal, characteristic
2C2×#65261C211yesmaximal, characteristic
3C2×#64935C211yesmaximal, characteristic
4C2×#64935C211yesmaximal, characteristic
5C2×#64938C211yesmaximal, characteristic
6C5×#1436C211yesmaximal, characteristic
7#10602361C211yesmaximal, characteristic
8#10602329C211yesmaximal, characteristic
9#10600213C211yesmaximal, characteristic
10#10600206C211yesmaximal, characteristic
11#10600205C211yesmaximal, characteristic
12#10600199C211yesmaximal, characteristic
13#10600198C211yesmaximal, characteristic
14#10600197C211yesmaximal, characteristic
15#10600197C211yesmaximal, characteristic
16C23×Dic10C2211yescharacteristic
17C22×C5×C4⋊C4C2211yescharacteristic
18C22×C42×C5C2211yescharacteristic
19C22×C4⋊Dic5C2211yescharacteristic
20C22×#683C2211yescharacteristic
21C22×#683C2211yescharacteristic
22C22×#683C2211yescharacteristic
23C22×#683C2211yescharacteristic
24C22×#683C2211yescharacteristic
25C22×#683C2211yescharacteristic
26C22×#683C2211yescharacteristic
27C22×C4×Dic5C2211yescharacteristic
28C22×C4×Dic5C2211yescharacteristic
29C22×C4×Dic5C2211yescharacteristic
30C22×C4×Dic5C2211yescharacteristic
31C2×C4×Dic10—24no—
32C2×C4×Dic10—24no—
33C2×C4×Dic10—24no—
34C2×C5×#95C2211yescharacteristic
35C2×C5×#95C2211yescharacteristic
36C2×C5×#95C2211yescharacteristic
37C2×C5×#95C2211yescharacteristic
38C2×C5×#95C2211yescharacteristic
39C2×#3963C2211yescharacteristic
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#65261—24no—
55#64938—24no—
56#64935—24no—
57#64935C418yescomplemented
58#14017—51nomaximal, Sylow
59C23×C4×C5C2311yescharacteristic
60C23×C4×C5C2311yescharacteristic
61C23×C4×C5C2311yescharacteristic
62C23×C4×C5C2311yescharacteristic
63C23×C4×C5C2311yescharacteristic
64C23×C4×C5C2311yescharacteristic
65C23×C4×C5C2311yescharacteristic
66C23×Dic5C2311yescharacteristic
67C23×Dic5C2311yescharacteristic
68C23×Dic5C2311yescharacteristic
69C23×Dic5C2311yescharacteristic
70C23×Dic5C2311yescharacteristic
71C23×Dic5C2311yescharacteristic
72C23×Dic5C2311yescharacteristic
73C23×Dic5C2311yescharacteristic
74C22×Dic10—22no—
75C22×Dic10—22no—
76C22×Dic10—22no—
77C22×Dic10—22no—
78C22×Dic10C2×C414yes—
79C22×Dic10D414yes—
80C22×Dic10Q814yes—
81C2×C5×C4⋊C4—22no—
82C2×C5×C4⋊C4—22no—
83C2×C5×C4⋊C4—41no—
84C2×C42×C5—22no—
85C2×C42×C5—22no—
86C2×C42×C5—22no—
87C2×C4⋊Dic5—22no—
88C2×C4⋊Dic5—22no—
89C2×C4⋊Dic5—22no—
90C2×#683—22no—
91C2×#683—22no—
92C2×#683—22no—
93C2×#683—22no—
94C2×#683—22no—
95C2×#683—22no—
96C2×#683—22no—
97C2×#683—22no—
98C2×#683—22no—
99C2×#683—22no—
100C2×#683—22no—
101C2×#683—22no—
102C2×#683—22no—
103C2×#683—22no—
104C2×#683—22no—
105C2×#683—22no—
106C2×#683—22no—
107C2×#683—41no—
108C2×#683C2×C414yes—
109C2×#683D414yes—
110C2×#683Q814yescomplemented
111C2×C4×Dic5—22no—
112C2×C4×Dic5—22no—
113C2×C4×Dic5—22no—
114C2×C4×Dic5—22no—
115C2×C4×Dic5—22no—
116C2×C4×Dic5—22no—
117C2×C4×Dic5—22no—
118C2×C4×Dic5—22no—
119C2×C4×Dic5—22no—
120C2×C4×Dic5—22no—
121C2×C4×Dic5C2×C414yes—
122C2×C4×Dic5D414yes—
123C4×Dic10—232no—
124C5×#95—22no—
125C5×#95—22no—
126C5×#95—22no—
127C5×#95—41no—
128C5×#95C2×C414yes—
129#3963—22no—
130#3963—22no—
131#3963—22no—
132#3963—22no—
133#3963—22no—
134#3963—22no—
135#3963—22no—
136#3963—22no—
137#3963—22no—
138#3963—41no—
139#3963—41no—
140#3963—41no—
141#3963C2×C414yes—
142#3963C2×C414yes—
143#3963C2×C414yes—
144C22×C4×Q8—51no—
145C2×#391—51no—
146C2×#391—51no—
147C2×#389—51no—
148C2×C4×C4⋊C4—51no—
149#1444—51no—
150#1444—51no—
151#1442—51no—
152#1442—51no—
153#1436—51no—
154#1436—51no—
155#1436—51no—
156#1436D511yescharacteristic
157C4⋊#95—51no—
158C4⋊#95—51no—
159C24×C5C2411yescharacteristic
160C22×C4×C5—21no—
161C22×C4×C5—21no—
162C22×C4×C5—21no—
163C22×C4×C5—21no—
164C22×C4×C5—21no—
165C22×C4×C5—21no—
166C22×C4×C5—21no—
167C22×C4×C5—21no—
168C22×C4×C5—21no—
169C22×C4×C5—21no—
170C22×C4×C5—21no—
171C22×C4×C5—21no—
172C22×C4×C5—21no—
173C22×C4×C5—21no—
174C22×C4×C5—21no—
175C22×C4×C5—21no—
176C22×C4×C5—21no—
177C22×C4×C5—21no—
178C22×C4×C5—21no—
179C22×C4×C5—21no—
180C22×C4×C5—21no—
181C22×C4×C5—21no—
182C22×C4×C5—21no—
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×C5C22×C412yes—
200C22×C4×C5C22×C412yes—
201C22×C4×C5C22×C412yes—
202C22×C4×C5C2×D412yes—
203C22×C4×C5C2×D412yes—
204C22×C4×C5C2×D412yes—
205C22×C4×C5C2×Q812yes—
206C22×C4×C5C2×Q812yes—
207C22×C4×C5#4112yes—
208C22×C4×C5#4112yes—
209C22×Dic5—21no—
210C22×Dic5—21no—
211C22×Dic5—21no—
212C22×Dic5—21no—
213C22×Dic5—21no—
214C22×Dic5—21no—
215C22×Dic5—21no—
216C22×Dic5—21no—
217C22×Dic5—21no—
218C22×Dic5—21no—
219C22×Dic5—21no—
220C22×Dic5—21no—
221C22×Dic5—21no—
222C22×Dic5—21no—
223C22×Dic5—21no—
224C22×Dic5—21no—
225C22×Dic5—21no—
226C22×Dic5—21no—
227C22×Dic5—21no—
228C22×Dic5—21no—
229C22×Dic5—21no—
230C22×Dic5—21no—
231C22×Dic5—21no—
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×Dic5C22×C412yes—
249C22×Dic5C22×C412yes—
250C22×Dic5C22×C412yes—
251C22×Dic5C22×C412yes—
252C22×Dic5C2×D412yes—
253C22×Dic5C2×D412yes—
254C22×Dic5C2×D412yes—
255C22×Dic5C2×D412yes—
256C22×Dic5C2×D412yes—
257C22×Dic5C2×D412yes—
258C22×Dic5C2×Q812yes—
259C22×Dic5C2×Q812yes—
260C22×Dic5C2×Q812yes—
261C22×Dic5C2×Q812yes—
262C22×Dic5#4112yes—
263C22×Dic5#4112yes—
264C22×Dic5#4112yes—
265C2×Dic10—28no—
266C2×Dic10—28no—
267C2×Dic10—28no—
268C2×Dic10—28no—
269C2×Dic10—28no—
270C2×Dic10—28no—
271C2×Dic10C4⋊C4116yescomplemented
272C5×C4⋊C4—44no—
273C42×C5—28no—
274C4⋊Dic5—28no—
275#683—28no—
276#683—28no—
277#683—28no—
278#683—28no—
279#683—28no—
280#683—44no—
281#683—44no—
282C4×Dic5—28no—
283C4×Dic5—28no—
284C4×Dic5—28no—
285C4×Dic5—44no—
286C23×Q8—51no—
287C2×C4×Q8—104no—
288C2×C4×Q8—104no—
289C2×C4×Q8—104no—
290C22×C4⋊C4—51no—
291C22×C4⋊C4—51no—
292C22×C4⋊C4—51no—
293C22×C4⋊C4—51no—
294C22×C4⋊C4—51no—
295C22×C4⋊C4—51no—
296C22×C4⋊C4—51no—
297C22×C4⋊C4—51no—
298C22×C4⋊C4C2×D511yescharacteristic
299C22×C42—51no—
300C22×C42—51no—
301C22×C42—51no—
302C22×C42—51no—
303C22×C42C2×D511yescharacteristic
304#391—58no—
305#391—104no—
306#389—104no—
307C4×C4⋊C4—104no—
308C2×#95—51no—
309C2×#95—51no—
310C2×#95—51no—
311C2×#95—51no—
312C2×#95—51no—
313C2×#95—51no—
314C2×#95—51no—
315C2×#95—51no—
316C2×#95—51no—
317C2×#95—51no—
318C2×#95—51no—
319C2×#95—51no—
320C2×#95—51no—
321C2×#95—51no—
322C2×#95—51no—
323C2×#95C2×D511yescharacteristic
324C2×#95C2×D511yescharacteristic
325C2×#95C2×D511yescharacteristic
326C2×#95C2×D511yescharacteristic
327C2×#95C2×D511yescharacteristic
328C23×C5C23×C411yescharacteristic
329C23×C5C22×D411yescharacteristic
330C23×C5C22×D411yescharacteristic
331C23×C5C22×D411yescharacteristic
332C23×C5C22×Q811yescharacteristic
333C23×C5C22×Q811yescharacteristic
334C23×C5C2×#4111yescharacteristic
335C23×C5C2×#4111yescharacteristic
336C23×C5C2×#4111yescharacteristic
337C23×C5C2×#4111yescharacteristic
338C23×C5C2×#4111yescharacteristic
339C23×C5H(5,𝔽2)11yescharacteristic
340C23×C52−1+411yescharacteristic
341C23×C52−1+411yescharacteristic
342C23×C52−1+411yescharacteristic
343C2×C4×C5—22no—
344C2×C4×C5—22no—
345C2×C4×C5—22no—
346C2×C4×C5—22no—
347C2×C4×C5—22no—
348C2×C4×C5—22no—
349C2×C4×C5—22no—
350C2×C4×C5—22no—
351C2×C4×C5—22no—
352C2×C4×C5—22no—
353C2×C4×C5—22no—
354C2×C4×C5—22no—
355C2×C4×C5—22no—
356C2×C4×C5—22no—
357C2×C4×C5—22no—
358C2×C4×C5—22no—
359C2×C4×C5—22no—
360C2×C4×C5—22no—
361C2×C4×C5—22no—
362C2×C4×C5—22no—
363C2×C4×C5—22no—
364C2×C4×C5—22no—
365C2×C4×C5—22no—
366C2×C4×C5—22no—
367C2×C4×C5—41no—
368C2×C4×C5—41no—
369C2×C4×C5—41no—
370C2×C4×C5—41no—
371C2×C4×C5—41no—
372C2×C4×C5—41no—
373C2×C4×C5—41no—
374C2×C4×C5—41no—
375C2×C4×C5—41no—
376C2×C4×C5—41no—
377C2×C4×C5—41no—
378C2×C4×C5—41no—
379C2×C4×C5—41no—
380C2×C4×C5—41no—
381C2×C4×C5—41no—
382C2×C4×C5—41no—
383C2×C4×C5—41no—
384C2×C4×C5—41no—
385C2×C4×C5—41no—
386C2×C4×C5—41no—
387C2×C4×C5—41no—
388C2×C4×C5—41no—
389C2×C4×C5—41no—
390C2×C4×C5C2×C4⋊C414yes—
391C2×C4×C5C22⋊Q814yes—
392C2×Dic5—22no—
393C2×Dic5—22no—
394C2×Dic5—22no—
395C2×Dic5—22no—
396C2×Dic5—22no—
397C2×Dic5—22no—
398C2×Dic5—22no—
399C2×Dic5—22no—
400C2×Dic5—22no—
401C2×Dic5—22no—
402C2×Dic5—22no—
403C2×Dic5—22no—
404C2×Dic5—22no—
405C2×Dic5—22no—
406C2×Dic5—22no—
407C2×Dic5—22no—
408C2×Dic5—22no—
409C2×Dic5—22no—
410C2×Dic5—22no—
411C2×Dic5—22no—
412C2×Dic5—22no—
413C2×Dic5—22no—
414C2×Dic5—22no—
415C2×Dic5—22no—
416C2×Dic5—41no—
417C2×Dic5—41no—
418C2×Dic5—41no—
419C2×Dic5—41no—
420C2×Dic5—41no—
421C2×Dic5—41no—
422C2×Dic5—41no—
423C2×Dic5—41no—
424C2×Dic5—41no—
425C2×Dic5—41no—
426C2×Dic5—41no—
427C2×Dic5—41no—
428C2×Dic5—41no—
429C2×Dic5—41no—
430C2×Dic5—41no—
431C2×Dic5—41no—
432C2×Dic5—41no—
433C2×Dic5—41no—
434C2×Dic5—41no—
435C2×Dic5—41no—
436C2×Dic5—41no—
437C2×Dic5—41no—
438C2×Dic5—41no—
439C2×Dic5C2×C4⋊C414yes—
440C2×Dic5C2×C4⋊C414yes—
441C2×Dic5C4×D414yes—
442C2×Dic5C4×D414yes—
443C2×Dic5C4×Q814yescomplemented
444C2×Dic5#12014yes—
445C2×Dic5C22⋊Q814yes—
446C2×Dic5C22⋊Q814yes—
447C2×Dic5#12314yes—
448Dic10—232no—
449C22×Q8—54no—
450C22×Q8—54no—
451C22×Q8—54no—
452C22×Q8—102no—
453C22×Q8—102no—
454C22×Q8—102no—
455C22×Q8—102no—
456C23×C4—51no—
457C23×C4—51no—
458C23×C4—51no—
459C23×C4—51no—
460C23×C4—51no—
461C23×C4—51no—
462C23×C4—51no—
463C23×C4—51no—
464C23×C4C22×D511yescharacteristic
465C23×C4C22×D511yescharacteristic
466C23×C4C22×D511yescharacteristic
467C23×C4C22×D511yescharacteristic
468C23×C4C22×D511yescharacteristic
469C23×C4C22×D511yescharacteristic
470C23×C4C22×D511yescharacteristic
471C4×Q8—1032no—
472C2×C4⋊C4—22no—
473C2×C4⋊C4—22no—
474C2×C4⋊C4—41no—
475C2×C4⋊C4—54no—
476C2×C4⋊C4—54no—
477C2×C4⋊C4—54no—
478C2×C4⋊C4—102no—
479C2×C4⋊C4—102no—
480C2×C4⋊C4—102no—
481C2×C4⋊C4—102no—
482C2×C4⋊C4—102no—
483C2×C4⋊C4—102no—
484C2×C4⋊C4—102no—
485C2×C4⋊C4—102no—
486C2×C4⋊C4—102no—
487C2×C4⋊C4—102no—
488C2×C4⋊C4—102no—
489C2×C4⋊C4—102no—
490C2×C4⋊C4—102no—
491C2×C4⋊C4—102no—
492C2×C4⋊C4—102no—
493C2×C4⋊C4—102no—
494C2×C4⋊C4—102no—
495C2×C4⋊C4—102no—
496C2×C4⋊C4—102no—
497C2×C4⋊C4—102no—
498C2×C4⋊C4—201no—
499C2×C42—22no—
500C2×C42—22no—
501C2×C42—22no—
502C2×C42—54no—
503C2×C42—54no—
504C2×C42—102no—
505C2×C42—102no—
506C2×C42—102no—
507C2×C42—102no—
508C2×C42—102no—
509C2×C42—102no—
510C2×C42—102no—
511C2×C42—102no—
512C2×C42—102no—
513C2×C42—102no—
514#95—22no—
515#95—22no—
516#95—22no—
517#95—41no—
518#95—54no—
519#95—54no—
520#95—54no—
521#95—102no—
522#95—102no—
523#95—102no—
524#95—102no—
525#95—102no—
526#95—102no—
527#95—102no—
528#95—102no—
529#95—102no—
530#95—201no—
531#95—201no—
532#95—201no—
533#95C4×D514yes—
534C22×C5C22×C4⋊C411yescharacteristic
535C22×C5C2×C4×D411yescharacteristic
536C22×C5C2×C4×D411yescharacteristic
537C22×C5C2×C4×Q811yescharacteristic
538C22×C5C4×#4111yescharacteristic
539C22×C5#51911yescharacteristic
540C22×C5#52011yescharacteristic
541C22×C5C2×#12011yescharacteristic
542C22×C5C2×C22⋊Q811yescharacteristic
543C22×C5C2×C22⋊Q811yescharacteristic
544C22×C5C2×C22⋊Q811yescharacteristic
545C22×C5C2×#12311yescharacteristic
546C22×C5#52511yescharacteristic
547C22×C5#52911yescharacteristic
548C22×C5#53311yescharacteristic
549C22×C5#53611yescharacteristic
550C22×C5#53711yescharacteristic
551C22×C5#54111yescharacteristic
552C22×C5#54211yescharacteristic
553C22×C5#54611yescharacteristic
554C22×C5#54711yescharacteristic
555C22×C5#54811yescharacteristic
556C22×C5#54811yescharacteristic
557C22×C5#54811yescharacteristic
558C22×C5D4×Q811yescharacteristic
559C22×C5D4×Q811yescharacteristic
560C22×C5#55011yescharacteristic
561C22×C5#55611yescharacteristic
562C22×C5#55611yescharacteristic
563C22×C5#55711yescharacteristic
564C22×C5#55711yescharacteristic
565C22×C5#55711yescharacteristic
566C22×C5#55711yescharacteristic
567C22×C5Q8211yescharacteristic
568C22×C5#55911yescharacteristic
569C4×C5—24no—
570C4×C5—24no—
571C4×C5—42no—
572C4×C5—42no—
573C4×C5—42no—
574C4×C5—42no—
575C4×C5—81no—
576Dic5—24no—
577Dic5—24no—
578Dic5—42no—
579Dic5—42no—
580Dic5—42no—
581Dic5—42no—
582Dic5—81no—
583Dic5#38518yes—
584C24C23×D511yescharacteristic
585C2×Q8—516no—
586C2×Q8—108no—
587C2×Q8—108no—
588C2×Q8—108no—
589C2×Q8—108no—
590C2×Q8—108no—
591C2×Q8—108no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—52no—
632C22×C4—52no—
633C22×C4—52no—
634C22×C4—52no—
635C22×C4—52no—
636C22×C4—52no—
637C22×C4—52no—
638C22×C4—52no—
639C22×C4—52no—
640C22×C4—52no—
641C22×C4—52no—
642C22×C4—52no—
643C22×C4—52no—
644C22×C4—52no—
645C22×C4—52no—
646C22×C4—52no—
647C22×C4—52no—
648C22×C4—101no—
649C22×C4—101no—
650C22×C4—101no—
651C22×C4—101no—
652C22×C4—101no—
653C22×C4—101no—
654C22×C4—101no—
655C22×C4—101no—
656C22×C4—101no—
657C22×C4—101no—
658C22×C4—101no—
659C22×C4—101no—
660C22×C4—101no—
661C22×C4—101no—
662C22×C4—101no—
663C22×C4—101no—
664C22×C4—101no—
665C22×C4—101no—
666C22×C4—101no—
667C22×C4—101no—
668C22×C4—101no—
669C22×C4—101no—
670C22×C4—101no—
671C22×C4—101no—
672C22×C4—101no—
673C22×C4—101no—
674C22×C4—101no—
675C22×C4—101no—
676C22×C4—101no—
677C22×C4—101no—
678C22×C4—101no—
679C22×C4—101no—
680C22×C4—101no—
681C22×C4—101no—
682C22×C4—101no—
683C22×C4—101no—
684C22×C4—101no—
685C22×C4—101no—
686C22×C4—101no—
687C22×C4C2×C4×D512yes—
688C22×C4C2×C4×D512yes—
689C22×C4C2×C4×D512yes—
690C22×C4#70912yes—
691C22×C4#70912yes—
692C22×C4D4×D512yes—
693C22×C4D4×D512yes—
694C22×C4D4×D512yes—
695C22×C4Q8×D512yes—
696C22×C4Q8×D512yes—
697C4⋊C4—44no—
698C4⋊C4—108no—
699C4⋊C4—108no—
700C4⋊C4—108no—
701C4⋊C4—108no—
702C4⋊C4—108no—
703C4⋊C4—108no—
704C4⋊C4—204no—
705C4⋊C4—204no—
706C42—28no—
707C42—108no—
708C42—108no—
709C42—108no—
710C42—204no—
711C2×C5C2×#38511yescharacteristic
712C2×C5C4×C22⋊Q811yescharacteristic
713C2×C5#232311yescharacteristic
714C2×C5Q8×C4⋊C411yescharacteristic
715C2×C5#235111yescharacteristic
716C2×C5#236511yescharacteristic
717C2×C5#236711yescharacteristic
718C2×C5#240711yescharacteristic
719C2×C5#240911yescharacteristic
720C2×C5#244611yescharacteristic
721C2×C5#244811yescharacteristic
722C2×C5#245111yescharacteristic
723C2×C5#245311yescharacteristic
724C2×C5#258111yescharacteristic
725C2×C5#258211yescharacteristic
726C23C22×C4×D511yescharacteristic
727C23C2×#70911yescharacteristic
728C23C2×#70911yescharacteristic
729C23C2×D4×D511yescharacteristic
730C23C2×D4×D511yescharacteristic
731C23C2×D4×D511yescharacteristic
732C23#414411yescharacteristic
733C23C2×Q8×D511yescharacteristic
734C23C2×Q8×D511yescharacteristic
735C23D5×#4111yescharacteristic
736C23D5×#4111yescharacteristic
737C23D5×#4111yescharacteristic
738C23#415011yescharacteristic
739C23#415011yescharacteristic
740C23#415011yescharacteristic
741Q8—1032no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—54no—
790C2×C4—54no—
791C2×C4—54no—
792C2×C4—54no—
793C2×C4—54no—
794C2×C4—54no—
795C2×C4—54no—
796C2×C4—54no—
797C2×C4—54no—
798C2×C4—102no—
799C2×C4—102no—
800C2×C4—102no—
801C2×C4—102no—
802C2×C4—102no—
803C2×C4—102no—
804C2×C4—102no—
805C2×C4—102no—
806C2×C4—102no—
807C2×C4—102no—
808C2×C4—102no—
809C2×C4—102no—
810C2×C4—102no—
811C2×C4—102no—
812C2×C4—102no—
813C2×C4—102no—
814C2×C4—102no—
815C2×C4—102no—
816C2×C4—102no—
817C2×C4—102no—
818C2×C4—102no—
819C2×C4—102no—
820C2×C4—102no—
821C2×C4—102no—
822C2×C4—201no—
823C2×C4—201no—
824C2×C4—201no—
825C2×C4—201no—
826C2×C4—201no—
827C2×C4—201no—
828C2×C4—201no—
829C2×C4—201no—
830C2×C4—201no—
831C2×C4—201no—
832C2×C4—201no—
833C2×C4—201no—
834C2×C4—201no—
835C2×C4—201no—
836C2×C4—201no—
837C2×C4—201no—
838C2×C4—201no—
839C2×C4—201no—
840C2×C4—201no—
841C2×C4—201no—
842C2×C4—201no—
843C2×C4—201no—
844C2×C4—201no—
845C2×C4D5×C4⋊C414yes—
846C2×C4#404214yes—
847C5#1401711yescharacteristic, complemented, Sylow
848C22C4×#70911yescharacteristic
849C22#6582411yescharacteristic
850C22C2×D5×C4⋊C411yescharacteristic
851C22C2×#404211yescharacteristic
852C22#6585011yescharacteristic
853C22#6586211yescharacteristic
854C22#6586711yescharacteristic
855C22C4×D4×D511yescharacteristic
856C22C4×D4×D511yescharacteristic
857C22#6588011yescharacteristic
858C22#6588111yescharacteristic
859C22#6588611yescharacteristic
860C22#6588611yescharacteristic
861C22#6588611yescharacteristic
862C22#6589311yescharacteristic
863C22#6590111yescharacteristic
864C22#6590111yescharacteristic
865C22C4×Q8×D511yescharacteristic
866C22#6591211yescharacteristic
867C22D5×#12011yescharacteristic
868C22#6593311yescharacteristic
869C22#6594211yescharacteristic
870C22D5×C22⋊Q811yescharacteristic
871C22D5×C22⋊Q811yescharacteristic
872C22#6596611yescharacteristic
873C22#6596611yescharacteristic
874C22#6598211yescharacteristic
875C22D5×#12311yescharacteristic
876C22#6598911yescharacteristic
877C22#6600311yescharacteristic
878C22#6601911yescharacteristic
879C22#6601911yescharacteristic
880C22#6603511yescharacteristic
881C22#6603611yescharacteristic
882C22#6605611yescharacteristic
883C4—24no—
884C4—24no—
885C4—42no—
886C4—42no—
887C4—42no—
888C4—42no—
889C4—58no—
890C4—81no—
891C4—104no—
892C4—104no—
893C4—202no—
894C4—202no—
895C4—202no—
896C4—202no—
897C4—401no—
898C2#1060520311yescharacteristic
899C2#1060536811yescharacteristic
900C2C4×#404211yescharacteristic
901C2#1060613611yescharacteristic
902C2D5×#38511yescharacteristic
903C2#1060641911yescharacteristic
904C2#1060669811yescharacteristic
905C2#1060671611yescharacteristic
906C2#1060671911yescharacteristic
907C2#1060682111yescharacteristic
908C2#1060719111yescharacteristic
909C2#1060723311yescharacteristic
910C2#1060771211yescharacteristic
911C2#1060780811yescharacteristic
912C2#1060824111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D5
commutatorC23×C5C23×C4
FittingC5×#1436C2
socle, prime radical, cosocleC24×C5C24
hypercenter#1436D5
hypocenterC5#14017
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
57. #64935C4semidirect
110. C2×#683Q8semidirect
271. C2×Dic10C4⋊C4semidirect
443. C2×Dic5C4×Q8semidirect
847. C5#14017semidirect

Maximal subgroups

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

subgroupindex
C22×C4×Dic102
C2×#652612
C2×#649352
C2×#649382
C5×#14362
#106023612
#106023292
#106002132
#106002062
#106002052
#106001992
#106001982
#106001972
#140175