Finite Group Databasebeta

← #12023025

Subgroups — #12023025

Order 1280.

1530 conjugacy classes of subgroups.

The subgroup lattice has 898 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65261C211yesmaximal, characteristic
2C2×#65261C211yesmaximal, characteristic
3C2×C4×#683C211yesmaximal, characteristic
4C2×#64936C211yesmaximal, characteristic
5C2×#64938C211yesmaximal, characteristic
6C5×C4⋊#95C211yesmaximal, characteristic
7#10602361C211yesmaximal, characteristic
8#10602358C211yesmaximal, characteristic
9#10602329C211yesmaximal, characteristic
10#10600213C211yesmaximal, characteristic
11#10600202C211yesmaximal, characteristic
12#10600198C211yesmaximal, characteristic
13#10600197C211yesmaximal, characteristic
14#10600197C211yesmaximal, characteristic
15#10600197C211yesmaximal, characteristic
16C22×C5×C4⋊C4C2211yescharacteristic
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×#683C2211yescharacteristic
28C22×#683C2211yescharacteristic
29C22×C4×Dic5C2211yescharacteristic
30C22×C4×Dic5C2211yescharacteristic
31C22×C4×Dic5C2211yescharacteristic
32C22×C4×Dic5C2211yescharacteristic
33C2×C5×#95C2211yescharacteristic
34C2×C5×#95C2211yescharacteristic
35C2×C5×#95C2211yescharacteristic
36C2×C5×#95C2211yescharacteristic
37C2×#3963C2211yescharacteristic
38C2×#3963C2211yescharacteristic
39C2×#3963C2211yescharacteristic
40C2×#3963C2211yescharacteristic
41C2×#3963C2211yescharacteristic
42C2×#3963C2211yescharacteristic
43C2×#3963C2211yescharacteristic
44C2×#3963C2211yescharacteristic
45C2×#3963C2211yescharacteristic
46C2×#3963C2211yescharacteristic
47C2×#3963C2211yescharacteristic
48C2×#3963C2211yescharacteristic
49C2×#3963C2211yescharacteristic
50C2×#3963C2211yescharacteristic
51#65261—24no—
52#65261C418yescomplemented
53C4×#683—24no—
54#64938—24no—
55#64936—24no—
56#14045—51nomaximal, Sylow
57C23×C4×C5C2311yescharacteristic
58C23×C4×C5C2311yescharacteristic
59C23×C4×C5C2311yescharacteristic
60C23×C4×C5C2311yescharacteristic
61C23×C4×C5C2311yescharacteristic
62C23×C4×C5C2311yescharacteristic
63C23×C4×C5C2311yescharacteristic
64C23×Dic5C2311yescharacteristic
65C23×Dic5C2311yescharacteristic
66C23×Dic5C2311yescharacteristic
67C23×Dic5C2311yescharacteristic
68C23×Dic5C2311yescharacteristic
69C23×Dic5C2311yescharacteristic
70C23×Dic5C2311yescharacteristic
71C23×Dic5C2311yescharacteristic
72C2×C5×C4⋊C4—22no—
73C2×C5×C4⋊C4—22no—
74C2×C5×C4⋊C4—41no—
75C2×C5×C4⋊C4—41no—
76C2×C5×C4⋊C4—41no—
77C2×C5×C4⋊C4C2×C414yes—
78C2×C42×C5—22no—
79C2×C42×C5—22no—
80C2×C42×C5—41no—
81C2×C4⋊Dic5—22no—
82C2×C4⋊Dic5—41no—
83C2×C4⋊Dic5—41no—
84C2×#683—22no—
85C2×#683—22no—
86C2×#683—22no—
87C2×#683—22no—
88C2×#683—22no—
89C2×#683—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—41no—
100C2×#683—41no—
101C2×#683—41no—
102C2×#683—41no—
103C2×#683—41no—
104C2×#683C2×C414yes—
105C2×#683C2×C414yes—
106C2×#683C2×C414yes—
107C2×#683D414yes—
108C2×#683Q814yes—
109C2×#683Q814yes—
110C2×#683Q814yes—
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—41no—
121C2×C4×Dic5C2×C414yes—
122C2×C4×Dic5D414yes—
123C5×#95—22no—
124C5×#95—22no—
125C5×#95—41no—
126C5×#95—41no—
127#3963—22no—
128#3963—22no—
129#3963—22no—
130#3963—22no—
131#3963—22no—
132#3963—22no—
133#3963—22no—
134#3963—22no—
135#3963—41no—
136#3963—41no—
137#3963—41no—
138#3963—41no—
139#3963C2×C414yes—
140#3963C2×C414yes—
141C2×#389—51no—
142C2×#389—51no—
143C2×#389—51no—
144C2×C4×C4⋊C4—51no—
145C2×C4×C4⋊C4—51no—
146#1444—51no—
147#1444—51no—
148#1441—51no—
149#1441—51no—
150#1436—51no—
151#1436—51no—
152C4⋊#95—51no—
153C4⋊#95—51no—
154C4⋊#95—51no—
155C4⋊#95D511yescharacteristic
156C24×C5C2411yescharacteristic
157C22×C4×C5—21no—
158C22×C4×C5—21no—
159C22×C4×C5—21no—
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×C5C22×C412yes—
197C22×C4×C5C22×C412yes—
198C22×C4×C5C22×C412yes—
199C22×C4×C5C2×D412yes—
200C22×C4×C5C2×D412yes—
201C22×C4×C5C2×Q812yes—
202C22×C4×C5C2×Q812yes—
203C22×C4×C5C2×Q812yes—
204C22×C4×C5#4112yes—
205C22×C4×C5#4112yes—
206C22×Dic5—21no—
207C22×Dic5—21no—
208C22×Dic5—21no—
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×Dic5C22×C412yes—
246C22×Dic5C22×C412yes—
247C22×Dic5C22×C412yes—
248C22×Dic5C22×C412yes—
249C22×Dic5C2×D412yes—
250C22×Dic5C2×D412yes—
251C22×Dic5C2×D412yes—
252C22×Dic5C2×D412yes—
253C22×Dic5C2×Q812yes—
254C22×Dic5C2×Q812yes—
255C22×Dic5C2×Q812yes—
256C22×Dic5C2×Q812yes—
257C22×Dic5C2×Q812yes—
258C22×Dic5C2×Q812yes—
259C22×Dic5#4112yes—
260C22×Dic5#4112yes—
261C22×Dic5#4112yes—
262C5×C4⋊C4—44no—
263C5×C4⋊C4—44no—
264C42×C5—44no—
265C4⋊Dic5—44no—
266#683—28no—
267#683—28no—
268#683—28no—
269#683—28no—
270#683—44no—
271#683—44no—
272#683—44no—
273#683—44no—
274#683C4⋊C4116yescomplemented
275C4×Dic5—28no—
276C4×Dic5—28no—
277C4×Dic5—44no—
278C4×Dic5—44no—
279C22×C4⋊C4—51no—
280C22×C4⋊C4—51no—
281C22×C4⋊C4—51no—
282C22×C4⋊C4—51no—
283C22×C4⋊C4—51no—
284C22×C4⋊C4—51no—
285C22×C4⋊C4—51no—
286C22×C4⋊C4—51no—
287C22×C4⋊C4—51no—
288C22×C4⋊C4—51no—
289C22×C4⋊C4C2×D511yescharacteristic
290C22×C4⋊C4C2×D511yescharacteristic
291C22×C42—51no—
292C22×C42—51no—
293C22×C42—51no—
294C22×C42—51no—
295C22×C42C2×D511yescharacteristic
296#389—58no—
297#389—104no—
298#389—104no—
299C4×C4⋊C4—104no—
300C4×C4⋊C4—104no—
301C2×#95—51no—
302C2×#95—51no—
303C2×#95—51no—
304C2×#95—51no—
305C2×#95—51no—
306C2×#95—51no—
307C2×#95—51no—
308C2×#95—51no—
309C2×#95—51no—
310C2×#95—51no—
311C2×#95—51no—
312C2×#95—51no—
313C2×#95—51no—
314C2×#95—51no—
315C2×#95C2×D511yescharacteristic
316C2×#95C2×D511yescharacteristic
317C2×#95C2×D511yescharacteristic
318C2×#95C2×D511yescharacteristic
319C23×C5C23×C411yescharacteristic
320C23×C5C22×D411yescharacteristic
321C23×C5C22×D411yescharacteristic
322C23×C5C22×Q811yescharacteristic
323C23×C5C22×Q811yescharacteristic
324C23×C5C22×Q811yescharacteristic
325C23×C5C2×#4111yescharacteristic
326C23×C5C2×#4111yescharacteristic
327C23×C5C2×#4111yescharacteristic
328C23×C5C2×#4111yescharacteristic
329C23×C5C2×#4111yescharacteristic
330C23×C5H(5,𝔽2)11yescharacteristic
331C23×C5H(5,𝔽2)11yescharacteristic
332C23×C5H(5,𝔽2)11yescharacteristic
333C23×C52−1+411yescharacteristic
334C2×C4×C5—22no—
335C2×C4×C5—22no—
336C2×C4×C5—22no—
337C2×C4×C5—22no—
338C2×C4×C5—22no—
339C2×C4×C5—22no—
340C2×C4×C5—22no—
341C2×C4×C5—22no—
342C2×C4×C5—22no—
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—41no—
359C2×C4×C5—41no—
360C2×C4×C5—41no—
361C2×C4×C5—41no—
362C2×C4×C5—41no—
363C2×C4×C5—41no—
364C2×C4×C5—41no—
365C2×C4×C5—41no—
366C2×C4×C5—41no—
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×C5C2×C4⋊C414yes—
382C2×C4×C5C22⋊Q814yes—
383C2×Dic5—22no—
384C2×Dic5—22no—
385C2×Dic5—22no—
386C2×Dic5—22no—
387C2×Dic5—22no—
388C2×Dic5—22no—
389C2×Dic5—22no—
390C2×Dic5—22no—
391C2×Dic5—22no—
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—41no—
408C2×Dic5—41no—
409C2×Dic5—41no—
410C2×Dic5—41no—
411C2×Dic5—41no—
412C2×Dic5—41no—
413C2×Dic5—41no—
414C2×Dic5—41no—
415C2×Dic5—41no—
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×Dic5C2×C4⋊C414yes—
431C2×Dic5C2×C4⋊C414yes—
432C2×Dic5C4×D414yes—
433C2×Dic5C4×Q814yes—
434C2×Dic5C4×Q814yes—
435C2×Dic5#12114yes—
436C2×Dic5C22⋊Q814yes—
437C2×Dic5#12514yes—
438C2×Dic5C4⋊Q814yes—
439C23×C4—51no—
440C23×C4—51no—
441C23×C4—51no—
442C23×C4—51no—
443C23×C4—51no—
444C23×C4—51no—
445C23×C4—51no—
446C23×C4—51no—
447C23×C4C22×D511yescharacteristic
448C23×C4C22×D511yescharacteristic
449C23×C4C22×D511yescharacteristic
450C23×C4C22×D511yescharacteristic
451C23×C4C22×D511yescharacteristic
452C23×C4C22×D511yescharacteristic
453C23×C4C22×D511yescharacteristic
454C2×C4⋊C4—22no—
455C2×C4⋊C4—22no—
456C2×C4⋊C4—41no—
457C2×C4⋊C4—41no—
458C2×C4⋊C4—41no—
459C2×C4⋊C4—54no—
460C2×C4⋊C4—54no—
461C2×C4⋊C4—54no—
462C2×C4⋊C4—54no—
463C2×C4⋊C4—54no—
464C2×C4⋊C4—54no—
465C2×C4⋊C4—54no—
466C2×C4⋊C4—102no—
467C2×C4⋊C4—102no—
468C2×C4⋊C4—102no—
469C2×C4⋊C4—102no—
470C2×C4⋊C4—102no—
471C2×C4⋊C4—102no—
472C2×C4⋊C4—102no—
473C2×C4⋊C4—102no—
474C2×C4⋊C4—102no—
475C2×C4⋊C4—102no—
476C2×C4⋊C4—102no—
477C2×C4⋊C4—102no—
478C2×C4⋊C4—102no—
479C2×C4⋊C4—102no—
480C2×C4⋊C4—102no—
481C2×C4⋊C4—102no—
482C2×C4⋊C4—201no—
483C2×C4⋊C4—201no—
484C2×C4⋊C4—201no—
485C2×C4⋊C4—201no—
486C2×C4⋊C4—201no—
487C2×C4⋊C4—201no—
488C2×C4⋊C4—201no—
489C2×C4⋊C4C4×D514yes—
490C2×C42—22no—
491C2×C42—22no—
492C2×C42—41no—
493C2×C42—54no—
494C2×C42—54no—
495C2×C42—102no—
496C2×C42—102no—
497C2×C42—102no—
498C2×C42—102no—
499C2×C42—102no—
500C2×C42—102no—
501C2×C42—102no—
502C2×C42—102no—
503C2×C42—102no—
504C2×C42—201no—
505#95—22no—
506#95—22no—
507#95—41no—
508#95—41no—
509#95—54no—
510#95—54no—
511#95—102no—
512#95—102no—
513#95—102no—
514#95—102no—
515#95—102no—
516#95—102no—
517#95—102no—
518#95—102no—
519#95—201no—
520#95—201no—
521#95—201no—
522#95—201no—
523C22×C5C22×C4⋊C411yescharacteristic
524C22×C5C2×C4×D411yescharacteristic
525C22×C5C2×C4×Q811yescharacteristic
526C22×C5C2×C4×Q811yescharacteristic
527C22×C5C4×#4111yescharacteristic
528C22×C5#51811yescharacteristic
529C22×C5#52011yescharacteristic
530C22×C5C2×#12111yescharacteristic
531C22×C5C2×C22⋊Q811yescharacteristic
532C22×C5C2×C22⋊Q811yescharacteristic
533C22×C5#52511yescharacteristic
534C22×C5C2×#12511yescharacteristic
535C22×C5#52911yescharacteristic
536C22×C5C2×C4⋊Q811yescharacteristic
537C22×C5#53311yescharacteristic
538C22×C5#53511yescharacteristic
539C22×C5#53711yescharacteristic
540C22×C5#54011yescharacteristic
541C22×C5#54211yescharacteristic
542C22×C5#54611yescharacteristic
543C22×C5#54611yescharacteristic
544C22×C5D4×Q811yescharacteristic
545C22×C5#55011yescharacteristic
546C22×C5#55211yescharacteristic
547C22×C5#55311yescharacteristic
548C22×C5#55411yescharacteristic
549C22×C5#55411yescharacteristic
550C22×C5#55411yescharacteristic
551C22×C5#55411yescharacteristic
552C22×C5#55411yescharacteristic
553C22×C5#55511yescharacteristic
554C22×C5#55711yescharacteristic
555C22×C5#55711yescharacteristic
556C22×C5Q8211yescharacteristic
557C22×C5Q8211yescharacteristic
558C4×C5—24no—
559C4×C5—24no—
560C4×C5—42no—
561C4×C5—42no—
562C4×C5—42no—
563C4×C5—42no—
564C4×C5—81no—
565Dic5—24no—
566Dic5—24no—
567Dic5—42no—
568Dic5—42no—
569Dic5—42no—
570Dic5—42no—
571Dic5—81no—
572Dic5#38918yes—
573C24C23×D511yescharacteristic
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
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—52no—
614C22×C4—52no—
615C22×C4—52no—
616C22×C4—52no—
617C22×C4—52no—
618C22×C4—52no—
619C22×C4—52no—
620C22×C4—52no—
621C22×C4—52no—
622C22×C4—52no—
623C22×C4—52no—
624C22×C4—52no—
625C22×C4—52no—
626C22×C4—52no—
627C22×C4—52no—
628C22×C4—52no—
629C22×C4—52no—
630C22×C4—101no—
631C22×C4—101no—
632C22×C4—101no—
633C22×C4—101no—
634C22×C4—101no—
635C22×C4—101no—
636C22×C4—101no—
637C22×C4—101no—
638C22×C4—101no—
639C22×C4—101no—
640C22×C4—101no—
641C22×C4—101no—
642C22×C4—101no—
643C22×C4—101no—
644C22×C4—101no—
645C22×C4—101no—
646C22×C4—101no—
647C22×C4—101no—
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×C4C2×C4×D512yes—
670C22×C4C2×C4×D512yes—
671C22×C4C2×C4×D512yes—
672C22×C4#70912yes—
673C22×C4#70912yes—
674C22×C4D4×D512yes—
675C22×C4D4×D512yes—
676C22×C4Q8×D512yes—
677C22×C4Q8×D512yes—
678C22×C4Q8×D512yes—
679C4⋊C4—44no—
680C4⋊C4—44no—
681C4⋊C4—516no—
682C4⋊C4—108no—
683C4⋊C4—108no—
684C4⋊C4—108no—
685C4⋊C4—108no—
686C4⋊C4—204no—
687C4⋊C4—204no—
688C4⋊C4—204no—
689C4⋊C4—204no—
690C4⋊C4—204no—
691C42—44no—
692C42—108no—
693C42—108no—
694C42—204no—
695C42—204no—
696C2×C5C2×#38911yescharacteristic
697C2×C5C4×C22⋊Q811yescharacteristic
698C2×C5#232411yescharacteristic
699C2×C5#234911yescharacteristic
700C2×C5Q8×C4⋊C411yescharacteristic
701C2×C5#236911yescharacteristic
702C2×C5#237011yescharacteristic
703C2×C5#241411yescharacteristic
704C2×C5#241711yescharacteristic
705C2×C5#245111yescharacteristic
706C2×C5#245411yescharacteristic
707C2×C5#250711yescharacteristic
708C2×C5#250811yescharacteristic
709C2×C5#256711yescharacteristic
710C2×C5#258411yescharacteristic
711C23C22×C4×D511yescharacteristic
712C23C2×#70911yescharacteristic
713C23C2×#70911yescharacteristic
714C23C2×D4×D511yescharacteristic
715C23C2×D4×D511yescharacteristic
716C23#414411yescharacteristic
717C23#414411yescharacteristic
718C23#414411yescharacteristic
719C23C2×Q8×D511yescharacteristic
720C23C2×Q8×D511yescharacteristic
721C23C2×Q8×D511yescharacteristic
722C23D5×#4111yescharacteristic
723C23D5×#4111yescharacteristic
724C23D5×#4111yescharacteristic
725C23#415011yescharacteristic
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
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—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—54no—
774C2×C4—54no—
775C2×C4—54no—
776C2×C4—54no—
777C2×C4—54no—
778C2×C4—54no—
779C2×C4—54no—
780C2×C4—54no—
781C2×C4—54no—
782C2×C4—102no—
783C2×C4—102no—
784C2×C4—102no—
785C2×C4—102no—
786C2×C4—102no—
787C2×C4—102no—
788C2×C4—102no—
789C2×C4—102no—
790C2×C4—102no—
791C2×C4—102no—
792C2×C4—102no—
793C2×C4—102no—
794C2×C4—102no—
795C2×C4—102no—
796C2×C4—102no—
797C2×C4—102no—
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—201no—
807C2×C4—201no—
808C2×C4—201no—
809C2×C4—201no—
810C2×C4—201no—
811C2×C4—201no—
812C2×C4—201no—
813C2×C4—201no—
814C2×C4—201no—
815C2×C4—201no—
816C2×C4—201no—
817C2×C4—201no—
818C2×C4—201no—
819C2×C4—201no—
820C2×C4—201no—
821C2×C4—201no—
822C2×C4—201no—
823C2×C4—201no—
824C2×C4—201no—
825C2×C4—201no—
826C2×C4—201no—
827C2×C4—201no—
828C2×C4—201no—
829C2×C4D5×C4⋊C414yes—
830C2×C4#404214yes—
831C5#1404511yescharacteristic, complemented, Sylow
832C22C4×#70911yescharacteristic
833C22#6582011yescharacteristic
834C22#6582411yescharacteristic
835C22#6582411yescharacteristic
836C22C2×D5×C4⋊C411yescharacteristic
837C22C2×#404211yescharacteristic
838C22#6584511yescharacteristic
839C22#6584511yescharacteristic
840C22#6584511yescharacteristic
841C22#6586211yescharacteristic
842C22#6586511yescharacteristic
843C22#6587411yescharacteristic
844C22C4×D4×D511yescharacteristic
845C22#6588011yescharacteristic
846C22#6588111yescharacteristic
847C22#6590111yescharacteristic
848C22C4×Q8×D511yescharacteristic
849C22C4×Q8×D511yescharacteristic
850C22#6591211yescharacteristic
851C22#6593111yescharacteristic
852C22#6593311yescharacteristic
853C22D5×#12111yescharacteristic
854C22#6594911yescharacteristic
855C22D5×C22⋊Q811yescharacteristic
856C22#6596611yescharacteristic
857C22#6597011yescharacteristic
858C22#6597011yescharacteristic
859C22#6600311yescharacteristic
860C22#6600411yescharacteristic
861C22#6601911yescharacteristic
862C22D5×#12511yescharacteristic
863C22#6604911yescharacteristic
864C22#6605611yescharacteristic
865C22#6605611yescharacteristic
866C22D5×C4⋊Q811yescharacteristic
867C4—24no—
868C4—24no—
869C4—42no—
870C4—42no—
871C4—42no—
872C4—42no—
873C4—58no—
874C4—81no—
875C4—104no—
876C4—104no—
877C4—202no—
878C4—202no—
879C4—202no—
880C4—202no—
881C4—401no—
882C2#1060510011yescharacteristic
883C2#1060539311yescharacteristic
884C2C4×#404211yescharacteristic
885C2#1060562011yescharacteristic
886C2#1060563411yescharacteristic
887C2#1060590111yescharacteristic
888C2#1060607111yescharacteristic
889C2#1060771211yescharacteristic
890C2#1060776711yescharacteristic
891C2#1060781111yescharacteristic
892C2D5×#38911yescharacteristic
893C2#1060802711yescharacteristic
894C2#1060804211yescharacteristic
895C2#1060822511yescharacteristic
896C2#1060824111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D5
commutatorC23×C5C23×C4
FittingC5×C4⋊#95C2
socle, prime radical, cosocleC24×C5C24
hypercenterC4⋊#95D5
hypocenterC5#14045
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
52. #65261C4semidirect
274. #683C4⋊C4semidirect
831. C5#14045semidirect

Maximal subgroups

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

subgroupindex
C2×#652612
C2×C4×#6832
C2×#649362
C2×#649382
C5×C4⋊#952
#106023612
#106023582
#106023292
#106002132
#106002022
#106001982
#106001972
#140455