Finite Group Databasebeta

← #12023107

Subgroups — #12023107

Order 1280.

1838 conjugacy classes of subgroups.

The subgroup lattice has 936 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#4034C211yesmaximal, characteristic
2C2×#65263C211yesmaximal, characteristic
3C2×#65261C211yesmaximal, characteristic
4C2×#64935C211yesmaximal, characteristic
5C2×#64938C211yesmaximal, characteristic
6C5×#1441C211yesmaximal, characteristic
7#10602357C211yesmaximal, characteristic
8#10600217C211yesmaximal, characteristic
9#10600217C211yesmaximal, characteristic
10#10600204C211yesmaximal, characteristic
11#10600200C211yesmaximal, characteristic
12#10600197C211yesmaximal, characteristic
13#10600197C211yesmaximal, characteristic
14#10600197C211yesmaximal, characteristic
15Dic5×#95C211yesmaximal, characteristic
16C23×Dic10C2211yescharacteristic
17C23×Dic10C2211yescharacteristic
18C22×C5×C4⋊C4C2211yescharacteristic
19C22×C5×C4⋊C4C2211yescharacteristic
20C22×C4⋊Dic5C2211yescharacteristic
21C22×#683C2211yescharacteristic
22C22×#683C2211yescharacteristic
23C22×#683C2211yescharacteristic
24C22×#683C2211yescharacteristic
25C22×#683C2211yescharacteristic
26C22×C4×Dic5C2211yescharacteristic
27C22×C4×Dic5C2211yescharacteristic
28C22×C4×Dic5C2211yescharacteristic
29C22×C4×Dic5C2211yescharacteristic
30C22×C4×Dic5C2211yescharacteristic
31C2×#4034—24no—
32C2×#4034—24no—
33C2×#4034C418yescomplemented
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#65263—24no—
55#65261—24no—
56#64938—24no—
57#64935—24no—
58#14053—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×Dic10—22no—
79C22×Dic10—22no—
80C22×Dic10—22no—
81C22×Dic10—22no—
82C22×Dic10—41no—
83C22×Dic10—41no—
84C22×Dic10—41no—
85C22×Dic10—41no—
86C22×Dic10C2×C414yes—
87C22×Dic10C2×C414yes—
88C2×C5×C4⋊C4—22no—
89C2×C5×C4⋊C4—22no—
90C2×C5×C4⋊C4—22no—
91C2×C5×C4⋊C4—22no—
92C2×C5×C4⋊C4—41no—
93C2×C5×C4⋊C4C2×C414yes—
94C2×C4⋊Dic5—22no—
95C2×C4⋊Dic5—22no—
96C2×C4⋊Dic5C2×C414yes—
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—41no—
107C2×#683C2×C414yes—
108C2×#683C2×C414yes—
109C2×#683D414yes—
110C2×#683D414yes—
111C2×#683Q814yescomplemented
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×Dic5—22no—
122C2×C4×Dic5—22no—
123C2×C4×Dic5—41no—
124C2×C4×Dic5—41no—
125C2×C4×Dic5C2×C414yes—
126C2×C4×Dic5Q814yescomplemented
127#4034—232no—
128C5×#95—22no—
129C5×#95—22no—
130C5×#95—22no—
131C5×#95—22no—
132C5×#95—41no—
133#3963—22no—
134#3963—22no—
135#3963—22no—
136#3963—22no—
137#3963—22no—
138#3963—22no—
139#3963—22no—
140#3963—22no—
141#3963—22no—
142#3963—22no—
143#3963—41no—
144#3963—41no—
145#3963—41no—
146#3963D414yes—
147#3963Q814yescomplemented
148C22×C4⋊Q8—51no—
149C2×#391—51no—
150C2×#391—51no—
151C2×#389—51no—
152C2×C4×C4⋊C4—51no—
153#1446—51no—
154#1446—51no—
155#1441—51no—
156#1441D511yescharacteristic
157#1436—51no—
158#1436—51no—
159C4⋊#95—51no—
160C4⋊#95—51no—
161C4⋊#95—51no—
162C4×#95—51no—
163C24×C5C2411yescharacteristic
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×C5—21no—
200C22×C4×C5—21no—
201C22×C4×C5—21no—
202C22×C4×C5—21no—
203C22×C4×C5C22×C412yes—
204C22×C4×C5C22×C412yes—
205C22×C4×C5C22×C412yes—
206C22×C4×C5C2×D412yes—
207C22×C4×C5C2×D412yes—
208C22×C4×C5C2×D412yes—
209C22×C4×C5C2×Q812yes—
210C22×C4×C5C2×Q812yes—
211C22×C4×C5C2×Q812yes—
212C22×C4×C5#4112yes—
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×Dic5—21no—
249C22×Dic5—21no—
250C22×Dic5C22×C412yes—
251C22×Dic5C22×C412yes—
252C22×Dic5C22×C412yes—
253C22×Dic5C22×C412yes—
254C22×Dic5C2×D412yes—
255C22×Dic5C2×D412yes—
256C22×Dic5C2×D412yes—
257C22×Dic5C2×D412yes—
258C22×Dic5C2×D412yes—
259C22×Dic5C2×D412yes—
260C22×Dic5C2×Q812yes—
261C22×Dic5C2×Q812yes—
262C22×Dic5C2×Q812yes—
263C22×Dic5C2×Q812yes—
264C22×Dic5C2×Q812yes—
265C22×Dic5C2×Q812yes—
266C22×Dic5#4112yes—
267C22×Dic5#4112yes—
268C22×Dic5#4112yes—
269C2×Dic10—28no—
270C2×Dic10—28no—
271C2×Dic10—28no—
272C2×Dic10—28no—
273C2×Dic10—44no—
274C2×Dic10—44no—
275C2×Dic10—44no—
276C2×Dic10—44no—
277C2×Dic10—44no—
278C2×Dic10—44no—
279C2×Dic10—44no—
280C2×Dic10—44no—
281C2×Dic10—44no—
282C2×Dic10—44no—
283C5×C4⋊C4—28no—
284C5×C4⋊C4—44no—
285C4⋊Dic5—28no—
286#683—28no—
287#683—28no—
288#683—44no—
289#683—44no—
290#683C22⋊C4116yes—
291C4×Dic5—28no—
292C4×Dic5—28no—
293C4×Dic5—44no—
294C4×Dic5—44no—
295C4×Dic5—44no—
296C23×Q8—51no—
297C23×Q8—51no—
298C2×C4⋊Q8—58no—
299C2×C4⋊Q8—104no—
300C2×C4⋊Q8—104no—
301C22×C4⋊C4—51no—
302C22×C4⋊C4—51no—
303C22×C4⋊C4—51no—
304C22×C4⋊C4—51no—
305C22×C4⋊C4—51no—
306C22×C4⋊C4—51no—
307C22×C4⋊C4C2×D511yescharacteristic
308C22×C4⋊C4C2×D511yescharacteristic
309C22×C42—51no—
310C22×C42—51no—
311C22×C42—51no—
312C22×C42—51no—
313C22×C42—51no—
314#391—104no—
315#391—104no—
316#389—104no—
317C4×C4⋊C4—104no—
318C2×#95—51no—
319C2×#95—51no—
320C2×#95—51no—
321C2×#95—51no—
322C2×#95—51no—
323C2×#95—51no—
324C2×#95—51no—
325C2×#95—51no—
326C2×#95—51no—
327C2×#95—51no—
328C2×#95—51no—
329C2×#95—51no—
330C2×#95—51no—
331C2×#95—51no—
332C2×#95—51no—
333C2×#95C2×D511yescharacteristic
334C2×#95C2×D511yescharacteristic
335C2×#95C2×D511yescharacteristic
336C2×#95C2×D511yescharacteristic
337C2×#95C2×D511yescharacteristic
338C23×C5C23×C411yescharacteristic
339C23×C5C22×D411yescharacteristic
340C23×C5C22×D411yescharacteristic
341C23×C5C22×D411yescharacteristic
342C23×C5C22×Q811yescharacteristic
343C23×C5C22×Q811yescharacteristic
344C23×C5C22×Q811yescharacteristic
345C23×C5C2×#4111yescharacteristic
346C23×C5C2×#4111yescharacteristic
347C23×C5C2×#4111yescharacteristic
348C23×C5C2×#4111yescharacteristic
349C23×C5H(5,𝔽2)11yescharacteristic
350C23×C5H(5,𝔽2)11yescharacteristic
351C23×C52−1+411yescharacteristic
352C23×C52−1+411yescharacteristic
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—22no—
368C2×C4×C5—22no—
369C2×C4×C5—22no—
370C2×C4×C5—22no—
371C2×C4×C5—22no—
372C2×C4×C5—22no—
373C2×C4×C5—22no—
374C2×C4×C5—22no—
375C2×C4×C5—22no—
376C2×C4×C5—22no—
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×C5—41no—
391C2×C4×C5—41no—
392C2×C4×C5—41no—
393C2×C4×C5—41no—
394C2×C4×C5—41no—
395C2×C4×C5—41no—
396C2×C4×C5—41no—
397C2×C4×C5—41no—
398C2×C4×C5—41no—
399C2×C4×C5—41no—
400C2×C4×C5C2×C22⋊C414yes—
401C2×C4×C5C4×Q814yes—
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—22no—
417C2×Dic5—22no—
418C2×Dic5—22no—
419C2×Dic5—22no—
420C2×Dic5—22no—
421C2×Dic5—22no—
422C2×Dic5—22no—
423C2×Dic5—22no—
424C2×Dic5—22no—
425C2×Dic5—22no—
426C2×Dic5—22no—
427C2×Dic5—22no—
428C2×Dic5—22no—
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×Dic5—41no—
440C2×Dic5—41no—
441C2×Dic5—41no—
442C2×Dic5—41no—
443C2×Dic5—41no—
444C2×Dic5—41no—
445C2×Dic5—41no—
446C2×Dic5—41no—
447C2×Dic5—41no—
448C2×Dic5C2×C22⋊C414yes—
449C2×Dic5C2×C22⋊C414yes—
450C2×Dic5C4×D414yes—
451C2×Dic5C4×Q814yes—
452C2×Dic5C4×Q814yes—
453C2×Dic5C22⋊Q814yes—
454C2×Dic5C22⋊Q814yes—
455C2×Dic5#12414yes—
456C2×Dic5C4⋊Q814yes—
457C2×Dic5C4⋊Q814yescomplemented
458Dic10—416no—
459Dic10—416no—
460C22×Q8—54no—
461C22×Q8—54no—
462C22×Q8—102no—
463C22×Q8—102no—
464C22×Q8—102no—
465C22×Q8—102no—
466C22×Q8—102no—
467C22×Q8—102no—
468C22×Q8—102no—
469C22×Q8—102no—
470C22×Q8—201no—
471C22×Q8—201no—
472C22×Q8—201no—
473C22×Q8—201no—
474C23×C4—51no—
475C23×C4—51no—
476C23×C4—51no—
477C23×C4—51no—
478C23×C4—51no—
479C23×C4—51no—
480C23×C4—51no—
481C23×C4—51no—
482C23×C4C22×D511yescharacteristic
483C23×C4C22×D511yescharacteristic
484C23×C4C22×D511yescharacteristic
485C23×C4C22×D511yescharacteristic
486C23×C4C22×D511yescharacteristic
487C23×C4C22×D511yescharacteristic
488C23×C4C22×D511yescharacteristic
489C4⋊Q8—1032no—
490C2×C4⋊C4—22no—
491C2×C4⋊C4—22no—
492C2×C4⋊C4—22no—
493C2×C4⋊C4—22no—
494C2×C4⋊C4—41no—
495C2×C4⋊C4—54no—
496C2×C4⋊C4—54no—
497C2×C4⋊C4—54no—
498C2×C4⋊C4—54no—
499C2×C4⋊C4—54no—
500C2×C4⋊C4—54no—
501C2×C4⋊C4—102no—
502C2×C4⋊C4—102no—
503C2×C4⋊C4—102no—
504C2×C4⋊C4—102no—
505C2×C4⋊C4—102no—
506C2×C4⋊C4—102no—
507C2×C4⋊C4—102no—
508C2×C4⋊C4—102no—
509C2×C4⋊C4—102no—
510C2×C4⋊C4—102no—
511C2×C4⋊C4—102no—
512C2×C4⋊C4—201no—
513C2×C4⋊C4C4×D514yes—
514C2×C42—54no—
515C2×C42—54no—
516C2×C42—102no—
517C2×C42—102no—
518C2×C42—102no—
519C2×C42—102no—
520C2×C42—102no—
521C2×C42—102no—
522C2×C42—102no—
523C2×C42—102no—
524C2×C42—102no—
525C2×C42—102no—
526C2×C42—102no—
527C2×C42—201no—
528C2×C42—201no—
529#95—22no—
530#95—22no—
531#95—22no—
532#95—22no—
533#95—41no—
534#95—54no—
535#95—54no—
536#95—102no—
537#95—102no—
538#95—102no—
539#95—102no—
540#95—102no—
541#95—102no—
542#95—102no—
543#95—102no—
544#95—102no—
545#95—102no—
546#95—201no—
547#95—201no—
548#95—201no—
549C22×C5C22×C22⋊C411yescharacteristic
550C22×C5C2×C4×D411yescharacteristic
551C22×C5C2×C4×Q811yescharacteristic
552C22×C5C2×C4×Q811yescharacteristic
553C22×C5C2×C4×Q811yescharacteristic
554C22×C5#51811yescharacteristic
555C22×C5#51911yescharacteristic
556C22×C5C2×C22⋊Q811yescharacteristic
557C22×C5C2×C22⋊Q811yescharacteristic
558C22×C5C2×#12411yescharacteristic
559C22×C5C2×C4⋊Q811yescharacteristic
560C22×C5C2×C4⋊Q811yescharacteristic
561C22×C5#53211yescharacteristic
562C22×C5#53311yescharacteristic
563C22×C5#53311yescharacteristic
564C22×C5#54211yescharacteristic
565C22×C5#54211yescharacteristic
566C22×C5#54411yescharacteristic
567C22×C5#54411yescharacteristic
568C22×C5D4211yescharacteristic
569C22×C5D4211yescharacteristic
570C22×C5#54611yescharacteristic
571C22×C5#54611yescharacteristic
572C22×C5#54711yescharacteristic
573C22×C5#54811yescharacteristic
574C22×C5#54811yescharacteristic
575C22×C5D4×Q811yescharacteristic
576C22×C5D4×Q811yescharacteristic
577C22×C5D4×Q811yescharacteristic
578C22×C5#55411yescharacteristic
579C22×C5#55411yescharacteristic
580C22×C5#55511yescharacteristic
581C22×C5#55611yescharacteristic
582C22×C5#55711yescharacteristic
583C22×C5Q8211yescharacteristic
584C4×C5—24no—
585C4×C5—24no—
586C4×C5—42no—
587C4×C5—42no—
588C4×C5—42no—
589C4×C5—42no—
590C4×C5—81no—
591Dic5—24no—
592Dic5—24no—
593Dic5—24no—
594Dic5—42no—
595Dic5—42no—
596Dic5—42no—
597Dic5—81no—
598Dic5#39118yescomplemented
599C24C23×D511yescharacteristic
600C2×Q8—108no—
601C2×Q8—108no—
602C2×Q8—108no—
603C2×Q8—108no—
604C2×Q8—204no—
605C2×Q8—204no—
606C2×Q8—204no—
607C2×Q8—204no—
608C2×Q8—204no—
609C2×Q8—204no—
610C2×Q8—204no—
611C2×Q8—204no—
612C2×Q8—204no—
613C2×Q8—204no—
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—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—52no—
654C22×C4—52no—
655C22×C4—52no—
656C22×C4—52no—
657C22×C4—52no—
658C22×C4—52no—
659C22×C4—52no—
660C22×C4—52no—
661C22×C4—52no—
662C22×C4—52no—
663C22×C4—52no—
664C22×C4—52no—
665C22×C4—52no—
666C22×C4—52no—
667C22×C4—52no—
668C22×C4—52no—
669C22×C4—52no—
670C22×C4—52no—
671C22×C4—52no—
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×C4—101no—
688C22×C4—101no—
689C22×C4—101no—
690C22×C4—101no—
691C22×C4—101no—
692C22×C4—101no—
693C22×C4—101no—
694C22×C4—101no—
695C22×C4—101no—
696C22×C4—101no—
697C22×C4—101no—
698C22×C4—101no—
699C22×C4—101no—
700C22×C4—101no—
701C22×C4—101no—
702C22×C4—101no—
703C22×C4—101no—
704C22×C4—101no—
705C22×C4—101no—
706C22×C4—101no—
707C22×C4—101no—
708C22×C4—101no—
709C22×C4C2×C4×D512yes—
710C22×C4C2×C4×D512yes—
711C22×C4C2×C4×D512yes—
712C22×C4D4×D512yes—
713C22×C4D4×D512yes—
714C22×C4D4×D512yes—
715C22×C4#71112yes—
716C22×C4Q8×D512yes—
717C22×C4Q8×D512yes—
718C22×C4Q8×D512yes—
719C4⋊C4—28no—
720C4⋊C4—44no—
721C4⋊C4—516no—
722C4⋊C4—108no—
723C4⋊C4—108no—
724C4⋊C4—108no—
725C4⋊C4—204no—
726C4⋊C4—204no—
727C42—108no—
728C42—108no—
729C42—204no—
730C42—204no—
731C42—204no—
732C2×C5C2×#39111yescharacteristic
733C2×C5C4×C4⋊Q811yescharacteristic
734C2×C5#233111yescharacteristic
735C2×C5D4×C22⋊C411yescharacteristic
736C2×C5Q8×C22⋊C411yescharacteristic
737C2×C5#236511yescharacteristic
738C2×C5#236911yescharacteristic
739C2×C5#243911yescharacteristic
740C2×C5#244011yescharacteristic
741C2×C5#245111yescharacteristic
742C2×C5#245211yescharacteristic
743C2×C5#249111yescharacteristic
744C2×C5#249211yescharacteristic
745C2×C5#255011yescharacteristic
746C2×C5#255111yescharacteristic
747C23C22×C4×D511yescharacteristic
748C23C2×D4×D511yescharacteristic
749C23C2×D4×D511yescharacteristic
750C23C2×D4×D511yescharacteristic
751C23C2×#71111yescharacteristic
752C23#414411yescharacteristic
753C23C2×Q8×D511yescharacteristic
754C23C2×Q8×D511yescharacteristic
755C23C2×Q8×D511yescharacteristic
756C23D5×#4111yescharacteristic
757C23D5×#4111yescharacteristic
758C23D5×#4111yescharacteristic
759C23#414911yescharacteristic
760C23#415011yescharacteristic
761C23#415011yescharacteristic
762Q8—2016no—
763Q8—2016no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—54no—
812C2×C4—54no—
813C2×C4—54no—
814C2×C4—54no—
815C2×C4—54no—
816C2×C4—54no—
817C2×C4—54no—
818C2×C4—54no—
819C2×C4—54no—
820C2×C4—54no—
821C2×C4—102no—
822C2×C4—102no—
823C2×C4—102no—
824C2×C4—102no—
825C2×C4—102no—
826C2×C4—102no—
827C2×C4—102no—
828C2×C4—102no—
829C2×C4—102no—
830C2×C4—102no—
831C2×C4—102no—
832C2×C4—102no—
833C2×C4—102no—
834C2×C4—102no—
835C2×C4—102no—
836C2×C4—102no—
837C2×C4—102no—
838C2×C4—102no—
839C2×C4—102no—
840C2×C4—102no—
841C2×C4—102no—
842C2×C4—102no—
843C2×C4—102no—
844C2×C4—102no—
845C2×C4—102no—
846C2×C4—102no—
847C2×C4—102no—
848C2×C4—201no—
849C2×C4—201no—
850C2×C4—201no—
851C2×C4—201no—
852C2×C4—201no—
853C2×C4—201no—
854C2×C4—201no—
855C2×C4—201no—
856C2×C4—201no—
857C2×C4—201no—
858C2×C4—201no—
859C2×C4—201no—
860C2×C4—201no—
861C2×C4—201no—
862C2×C4—201no—
863C2×C4—201no—
864C2×C4—201no—
865C2×C4—201no—
866C2×C4—201no—
867C2×C4D5×C22⋊C414yes—
868C2×C4#403314yes—
869C5#1405311yescharacteristic, complemented, Sylow
870C22C2×D5×C22⋊C411yescharacteristic
871C22C2×#403311yescharacteristic
872C22#6585011yescharacteristic
873C22C4×D4×D511yescharacteristic
874C22#6587911yescharacteristic
875C22C4×Q8×D511yescharacteristic
876C22C4×Q8×D511yescharacteristic
877C22#6592411yescharacteristic
878C22#6593011yescharacteristic
879C22#6593211yescharacteristic
880C22#6593211yescharacteristic
881C22#6594311yescharacteristic
882C22#6594411yescharacteristic
883C22#6595011yescharacteristic
884C22#6595611yescharacteristic
885C22#6595711yescharacteristic
886C22D5×C22⋊Q811yescharacteristic
887C22D5×C22⋊Q811yescharacteristic
888C22#6596611yescharacteristic
889C22#6596611yescharacteristic
890C22#6596611yescharacteristic
891C22#6596911yescharacteristic
892C22#6598811yescharacteristic
893C22#6598911yescharacteristic
894C22#6599611yescharacteristic
895C22D5×#12411yescharacteristic
896C22#6601911yescharacteristic
897C22#6602211yescharacteristic
898C22#6602311yescharacteristic
899C22#6602411yescharacteristic
900C22#6603611yescharacteristic
901C22#6604411yescharacteristic
902C22#6605611yescharacteristic
903C22D5×C4⋊Q811yescharacteristic
904C22D5×C4⋊Q811yescharacteristic
905C4—24no—
906C4—24no—
907C4—42no—
908C4—42no—
909C4—42no—
910C4—42no—
911C4—58no—
912C4—81no—
913C4—104no—
914C4—104no—
915C4—104no—
916C4—202no—
917C4—202no—
918C4—202no—
919C4—401no—
920C2#1060560711yescharacteristic
921C2#1060660911yescharacteristic
922C2#1060668111yescharacteristic
923C2#1060669811yescharacteristic
924C2#1060769811yescharacteristic
925C2#1060771811yescharacteristic
926C2D5×#39111yescharacteristic
927C2#1060866611yescharacteristic
928C2#1060891711yescharacteristic
929C2#1060901911yescharacteristic
930C2#1060902111yescharacteristic
931C2#1060947611yescharacteristic
932C2#1060947911yescharacteristic
933C2#1060951711yescharacteristic
934C2#1060987911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D5
commutatorC23×C5C23×C4
FittingC5×#1441C2
socle, prime radical, cosocleC24×C5C24
hypercenter#1441D5
hypocenterC5#14053
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ #1441

Complements

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

NH ≅ G/Ntype
33. C2×#4034C4semidirect
111. C2×#683Q8semidirect
126. C2×C4×Dic5Q8semidirect
147. #3963Q8semidirect
457. C2×Dic5C4⋊Q8semidirect
598. Dic5#391semidirect
869. C5#14053semidirect

Maximal subgroups

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

subgroupindex
C22×#40342
C2×#652632
C2×#652612
C2×#649352
C2×#649382
C5×#14412
#106023572
#106002172
#106002042
#106002002
#106001972
Dic5×#952
#140535