Finite Group Databasebeta

← #12027282

Subgroups — #12027282

Order 1280.

1390 conjugacy classes of subgroups.

The subgroup lattice has 886 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#389C211yesmaximal, characteristic
2C2×#65262C211yesmaximal, characteristic
3C2×#65270C211yesmaximal, characteristic
4C2×#65270C211yesmaximal, characteristic
5C2×#65265C211yesmaximal, characteristic
6#10602361C211yesmaximal, characteristic
7#10602361C211yesmaximal, characteristic
8#10602361C211yesmaximal, characteristic
9#10602360C211yesmaximal, characteristic
10#10602329C211yesmaximal, characteristic
11#10602329C211yesmaximal, characteristic
12#10600213C211yesmaximal, characteristic
13#10600204C211yesmaximal, characteristic
14#10600199C211yesmaximal, characteristic
15#10600196C211yesmaximal, characteristic
16C22×C5×C4⋊C4C2211yescharacteristic
17C22×C5×C4⋊C4C2211yescharacteristic
18C22×C5×C4⋊C4C2211yescharacteristic
19C22×C5×C4⋊C4C2211yescharacteristic
20C22×C42×C5C2211yescharacteristic
21C22×C4⋊Dic5C2211yescharacteristic
22C22×C4⋊Dic5C2211yescharacteristic
23C22×#683C2211yescharacteristic
24C22×#683C2211yescharacteristic
25C22×#683C2211yescharacteristic
26C22×#683C2211yescharacteristic
27C22×#683C2211yescharacteristic
28C22×#683C2211yescharacteristic
29C22×C4×Dic5C2211yescharacteristic
30C22×C4×Dic5C2211yescharacteristic
31C5×#389—24no—
32C2×C5×#95C2211yescharacteristic
33C2×C5×#95C2211yescharacteristic
34C2×#3963C2211yescharacteristic
35C2×#3963C2211yescharacteristic
36C2×#3963C2211yescharacteristic
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
51C2×#3963C2211yescharacteristic
52#65270—24no—
53#65270C418yescomplemented
54#65265—24no—
55#65262—24no—
56#14406—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—22no—
75C2×C5×C4⋊C4—22no—
76C2×C5×C4⋊C4—22no—
77C2×C5×C4⋊C4—41no—
78C2×C5×C4⋊C4—41no—
79C2×C5×C4⋊C4—41no—
80C2×C5×C4⋊C4—41no—
81C2×C5×C4⋊C4C2×C414yes—
82C2×C5×C4⋊C4D414yes—
83C2×C5×C4⋊C4Q814yes—
84C2×C42×C5—22no—
85C2×C42×C5—41no—
86C2×C42×C5—41no—
87C2×C4⋊Dic5—22no—
88C2×C4⋊Dic5—22no—
89C2×C4⋊Dic5—22no—
90C2×C4⋊Dic5—22no—
91C2×C4⋊Dic5—41no—
92C2×C4⋊Dic5C2×C414yes—
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×#683—41no—
105C2×#683—41no—
106C2×#683—41no—
107C2×#683—41no—
108C2×#683—41no—
109C2×#683—41no—
110C2×#683D414yes—
111C2×C4×Dic5—22no—
112C2×C4×Dic5—22no—
113C2×C4×Dic5—22no—
114C2×C4×Dic5—22no—
115C2×C4×Dic5—41no—
116C2×C4×Dic5C2×C414yes—
117C5×#95—22no—
118C5×#95—22no—
119#3963—22no—
120#3963—22no—
121#3963—22no—
122#3963—22no—
123#3963—22no—
124#3963—22no—
125#3963—22no—
126#3963—22no—
127#3963—41no—
128#3963—41no—
129#3963—41no—
130#3963—41no—
131#3963—41no—
132#3963C2×C414yes—
133#3963C2×C414yes—
134#3963C2×C414yes—
135#3963C2×C414yes—
136#3963Q814yes—
137C2×#389—51no—
138C2×#389D511yescharacteristic
139C2×#387—51no—
140C2×#387—51no—
141C2×#384—51no—
142#1444—51no—
143#1444—51no—
144#1444—51no—
145#1444—51no—
146#1442—51no—
147#1441—51no—
148#1436—51no—
149#1436—51no—
150#1436—51no—
151#1434—51no—
152C24×C5C2411yescharacteristic
153C22×C4×C5—21no—
154C22×C4×C5—21no—
155C22×C4×C5—21no—
156C22×C4×C5—21no—
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×C5C22×C412yes—
192C22×C4×C5C22×C412yes—
193C22×C4×C5C22×C412yes—
194C22×C4×C5C2×D412yes—
195C22×C4×C5C2×D412yes—
196C22×C4×C5C2×D412yes—
197C22×C4×C5C2×D412yes—
198C22×C4×C5C2×Q812yes—
199C22×C4×C5C2×Q812yes—
200C22×C4×C5C2×Q812yes—
201C22×C4×C5C2×Q812yes—
202C22×Dic5—21no—
203C22×Dic5—21no—
204C22×Dic5—21no—
205C22×Dic5—21no—
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×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×Q812yes—
255C22×Dic5C2×Q812yes—
256C22×Dic5#4112yes—
257C22×Dic5#4112yes—
258C5×C4⋊C4—44no—
259C5×C4⋊C4—44no—
260C5×C4⋊C4—44no—
261C5×C4⋊C4C4⋊C4116yescomplemented
262C42×C5—44no—
263C4⋊Dic5—28no—
264C4⋊Dic5—44no—
265#683—44no—
266#683—44no—
267#683—44no—
268#683—44no—
269#683—44no—
270#683—44no—
271C4×Dic5—28no—
272C4×Dic5—44no—
273C22×C4⋊C4—51no—
274C22×C4⋊C4—51no—
275C22×C4⋊C4—51no—
276C22×C4⋊C4—51no—
277C22×C4⋊C4—51no—
278C22×C4⋊C4—51no—
279C22×C4⋊C4—51no—
280C22×C4⋊C4—51no—
281C22×C4⋊C4C2×D511yescharacteristic
282C22×C4⋊C4C2×D511yescharacteristic
283C22×C4⋊C4C2×D511yescharacteristic
284C22×C4⋊C4C2×D511yescharacteristic
285C22×C42—51no—
286C22×C42—51no—
287C22×C42C2×D511yescharacteristic
288#389—24no—
289#389—104no—
290#387—58no—
291#387—104no—
292#384—104no—
293C2×#95—51no—
294C2×#95—51no—
295C2×#95—51no—
296C2×#95—51no—
297C2×#95—51no—
298C2×#95—51no—
299C2×#95—51no—
300C2×#95—51no—
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×#95C2×D511yescharacteristic
312C2×#95C2×D511yescharacteristic
313C23×C5C23×C411yescharacteristic
314C23×C5C22×D411yescharacteristic
315C23×C5C22×D411yescharacteristic
316C23×C5C22×Q811yescharacteristic
317C23×C5C22×Q811yescharacteristic
318C23×C5C2×#4111yescharacteristic
319C23×C5C2×#4111yescharacteristic
320C23×C5H(5,𝔽2)11yescharacteristic
321C23×C5H(5,𝔽2)11yescharacteristic
322C23×C5H(5,𝔽2)11yescharacteristic
323C23×C5H(5,𝔽2)11yescharacteristic
324C23×C52−1+411yescharacteristic
325C23×C52−1+411yescharacteristic
326C23×C52−1+411yescharacteristic
327C23×C52−1+411yescharacteristic
328C2×C4×C5—22no—
329C2×C4×C5—22no—
330C2×C4×C5—22no—
331C2×C4×C5—22no—
332C2×C4×C5—22no—
333C2×C4×C5—22no—
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—41no—
353C2×C4×C5—41no—
354C2×C4×C5—41no—
355C2×C4×C5—41no—
356C2×C4×C5—41no—
357C2×C4×C5—41no—
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×C5C2×C4⋊C414yes—
375C2×C4×C5C2×C4⋊C414yes—
376C2×C4×C5C2×C4⋊C414yes—
377C2×Dic5—22no—
378C2×Dic5—22no—
379C2×Dic5—22no—
380C2×Dic5—22no—
381C2×Dic5—22no—
382C2×Dic5—22no—
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—41no—
402C2×Dic5—41no—
403C2×Dic5—41no—
404C2×Dic5—41no—
405C2×Dic5—41no—
406C2×Dic5—41no—
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×Dic5—41no—
431C2×Dic5C4×D414yes—
432C2×Dic5C4×Q814yes—
433C23×C4—51no—
434C23×C4—51no—
435C23×C4—51no—
436C23×C4—51no—
437C23×C4—51no—
438C23×C4—51no—
439C23×C4—51no—
440C23×C4—51no—
441C23×C4C22×D511yescharacteristic
442C23×C4C22×D511yescharacteristic
443C23×C4C22×D511yescharacteristic
444C23×C4C22×D511yescharacteristic
445C23×C4C22×D511yescharacteristic
446C23×C4C22×D511yescharacteristic
447C23×C4C22×D511yescharacteristic
448C2×C4⋊C4—22no—
449C2×C4⋊C4—22no—
450C2×C4⋊C4—22no—
451C2×C4⋊C4—22no—
452C2×C4⋊C4—22no—
453C2×C4⋊C4—41no—
454C2×C4⋊C4—41no—
455C2×C4⋊C4—41no—
456C2×C4⋊C4—41no—
457C2×C4⋊C4—54no—
458C2×C4⋊C4—54no—
459C2×C4⋊C4—102no—
460C2×C4⋊C4—102no—
461C2×C4⋊C4—102no—
462C2×C4⋊C4—102no—
463C2×C4⋊C4—102no—
464C2×C4⋊C4—102no—
465C2×C4⋊C4—102no—
466C2×C4⋊C4—102no—
467C2×C4⋊C4—102no—
468C2×C4⋊C4—102no—
469C2×C4⋊C4—201no—
470C2×C4⋊C4—201no—
471C2×C4⋊C4—201no—
472C2×C4⋊C4—201no—
473C2×C4⋊C4—201no—
474C2×C4⋊C4—201no—
475C2×C4⋊C4—201no—
476C2×C4⋊C4—201no—
477C2×C4⋊C4—201no—
478C2×C4⋊C4—201no—
479C2×C4⋊C4—201no—
480C2×C4⋊C4—201no—
481C2×C4⋊C4Dic1014yes—
482C2×C4⋊C4C4×D514yes—
483C2×C4⋊C4C22⋊D514yes—
484C2×C42—22no—
485C2×C42—41no—
486C2×C42—41no—
487C2×C42—54no—
488C2×C42—102no—
489C2×C42—102no—
490C2×C42—102no—
491C2×C42—102no—
492C2×C42—201no—
493#95—22no—
494#95—22no—
495#95—54no—
496#95—54no—
497#95—54no—
498#95—54no—
499#95—54no—
500#95—102no—
501#95—102no—
502#95—102no—
503#95—102no—
504#95—102no—
505#95—102no—
506#95—102no—
507#95—102no—
508#95—201no—
509#95—201no—
510#95—201no—
511#95—201no—
512#95—201no—
513C22×C5C22×C4⋊C411yescharacteristic
514C22×C5C2×C4×D411yescharacteristic
515C22×C5C2×C4×Q811yescharacteristic
516C22×C5#52011yescharacteristic
517C22×C5#52011yescharacteristic
518C22×C5#52011yescharacteristic
519C22×C5#52011yescharacteristic
520C22×C5#53411yescharacteristic
521C22×C5#53511yescharacteristic
522C22×C5#53611yescharacteristic
523C22×C5#53611yescharacteristic
524C22×C5#53911yescharacteristic
525C22×C5#53911yescharacteristic
526C22×C5#54011yescharacteristic
527C22×C5#54111yescharacteristic
528C22×C5#54411yescharacteristic
529C22×C5#54411yescharacteristic
530C22×C5#54411yescharacteristic
531C22×C5#54411yescharacteristic
532C22×C5D4211yescharacteristic
533C22×C5#54611yescharacteristic
534C22×C5#54711yescharacteristic
535C22×C5D4×Q811yescharacteristic
536C22×C5D4×Q811yescharacteristic
537C22×C5D4×Q811yescharacteristic
538C22×C5#55011yescharacteristic
539C22×C5#55211yescharacteristic
540C22×C5#55411yescharacteristic
541C22×C5#55411yescharacteristic
542C22×C5#55711yescharacteristic
543C22×C5Q8211yescharacteristic
544C22×C5#56011yescharacteristic
545C22×C5#56311yescharacteristic
546C22×C5#56311yescharacteristic
547C22×C5#56311yescharacteristic
548C4×C5—24no—
549C4×C5—24no—
550C4×C5—24no—
551C4×C5—42no—
552C4×C5—42no—
553C4×C5—81no—
554C4×C5—81no—
555Dic5—24no—
556Dic5—24no—
557Dic5—42no—
558Dic5—42no—
559Dic5—42no—
560Dic5—42no—
561Dic5—81no—
562Dic5—81no—
563C24C23×D511yescharacteristic
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
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—52no—
603C22×C4—52no—
604C22×C4—52no—
605C22×C4—52no—
606C22×C4—52no—
607C22×C4—52no—
608C22×C4—52no—
609C22×C4—52no—
610C22×C4—52no—
611C22×C4—52no—
612C22×C4—101no—
613C22×C4—101no—
614C22×C4—101no—
615C22×C4—101no—
616C22×C4—101no—
617C22×C4—101no—
618C22×C4—101no—
619C22×C4—101no—
620C22×C4—101no—
621C22×C4—101no—
622C22×C4—101no—
623C22×C4—101no—
624C22×C4—101no—
625C22×C4—101no—
626C22×C4—101no—
627C22×C4—101no—
628C22×C4—101no—
629C22×C4—101no—
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×C4C2×Dic1012yes—
659C22×C4C2×Dic1012yes—
660C22×C4C2×Dic1012yes—
661C22×C4C2×C4×D512yes—
662C22×C4C2×C4×D512yes—
663C22×C4C2×C4×D512yes—
664C22×C4D4×D512yes—
665C22×C4Q8×D512yes—
666C22×C4C2×C22⋊D512yes—
667C22×C4C2×C22⋊D512yes—
668C22×C4C2×C22⋊D512yes—
669C4⋊C4—44no—
670C4⋊C4—44no—
671C4⋊C4—44no—
672C4⋊C4—108no—
673C4⋊C4—204no—
674C4⋊C4—204no—
675C4⋊C4—204no—
676C4⋊C4—204no—
677C4⋊C4—204no—
678C4⋊C4—204no—
679C4⋊C4—204no—
680C4⋊C4#683116yescomplemented
681C42—44no—
682C42—108no—
683C42—204no—
684C2×C5#231711yescharacteristic
685C2×C5#232211yescharacteristic
686C2×C5#233011yescharacteristic
687C2×C5D4×C4⋊C411yescharacteristic
688C2×C5Q8×C4⋊C411yescharacteristic
689C2×C5#236011yescharacteristic
690C2×C5#238311yescharacteristic
691C2×C5#267311yescharacteristic
692C2×C5#267711yescharacteristic
693C2×C5#271311yescharacteristic
694C2×C5#272011yescharacteristic
695C2×C5#272111yescharacteristic
696C2×C5#273411yescharacteristic
697C2×C5#279111yescharacteristic
698C2×C5#279211yescharacteristic
699C23C22×Dic1011yescharacteristic
700C23C22×C4×D511yescharacteristic
701C23C2×D4×D511yescharacteristic
702C23#414411yescharacteristic
703C23#414411yescharacteristic
704C23#414411yescharacteristic
705C23C2×Q8×D511yescharacteristic
706C23#414711yescharacteristic
707C23#414711yescharacteristic
708C23#414711yescharacteristic
709C23D5×#4111yescharacteristic
710C23D5×#4111yescharacteristic
711C23#414911yescharacteristic
712C23#415011yescharacteristic
713C23C22×C22⋊D511yescharacteristic
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
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—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
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—54no—
761C2×C4—54no—
762C2×C4—102no—
763C2×C4—102no—
764C2×C4—102no—
765C2×C4—102no—
766C2×C4—102no—
767C2×C4—102no—
768C2×C4—102no—
769C2×C4—102no—
770C2×C4—102no—
771C2×C4—102no—
772C2×C4—102no—
773C2×C4—102no—
774C2×C4—102no—
775C2×C4—102no—
776C2×C4—102no—
777C2×C4—102no—
778C2×C4—102no—
779C2×C4—102no—
780C2×C4—102no—
781C2×C4—102no—
782C2×C4—102no—
783C2×C4—102no—
784C2×C4—102no—
785C2×C4—102no—
786C2×C4—201no—
787C2×C4—201no—
788C2×C4—201no—
789C2×C4—201no—
790C2×C4—201no—
791C2×C4—201no—
792C2×C4—201no—
793C2×C4—201no—
794C2×C4—201no—
795C2×C4—201no—
796C2×C4—201no—
797C2×C4—201no—
798C2×C4—201no—
799C2×C4—201no—
800C2×C4—201no—
801C2×C4—201no—
802C2×C4—201no—
803C2×C4—201no—
804C2×C4—201no—
805C2×C4—201no—
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×C4C2×#68314yes—
817C2×C4C2×#68314yes—
818C2×C4C2×#68314yes—
819C5#1440611yescharacteristic, complemented, Sylow
820C22#6583411yescharacteristic
821C22#6583411yescharacteristic
822C22#6583811yescharacteristic
823C22#6583811yescharacteristic
824C22D4×Dic1011yescharacteristic
825C22#6587311yescharacteristic
826C22C4×D4×D511yescharacteristic
827C22#6588011yescharacteristic
828C22Q8×Dic1011yescharacteristic
829C22#6590311yescharacteristic
830C22C4×Q8×D511yescharacteristic
831C22#6590811yescharacteristic
832C22#6593911yescharacteristic
833C22#6594411yescharacteristic
834C22#6594911yescharacteristic
835C22#6595411yescharacteristic
836C22#6595711yescharacteristic
837C22#6597011yescharacteristic
838C22#6597211yescharacteristic
839C22#6598011yescharacteristic
840C22#6602611yescharacteristic
841C22#6602711yescharacteristic
842C22#6603011yescharacteristic
843C22#6603311yescharacteristic
844C22#6605811yescharacteristic
845C22#6606111yescharacteristic
846C22#6606311yescharacteristic
847C22#6606911yescharacteristic
848C22C22×#68311yescharacteristic
849C22D4×C22⋊D511yescharacteristic
850C22#6613911yescharacteristic
851C22Q8×C22⋊D511yescharacteristic
852C22#6615011yescharacteristic
853C22#6615811yescharacteristic
854C22#6616811yescharacteristic
855C4—24no—
856C4—24no—
857C4—24no—
858C4—42no—
859C4—42no—
860C4—81no—
861C4—81no—
862C4—104no—
863C4—104no—
864C4—202no—
865C4—202no—
866C4—202no—
867C4—202no—
868C4—401no—
869C4—401no—
870C2#1060770411yescharacteristic
871C2#1060771411yescharacteristic
872C2#1060772511yescharacteristic
873C2#1060784611yescharacteristic
874C2#1060786611yescharacteristic
875C2#1060789811yescharacteristic
876C2#1060790011yescharacteristic
877C2#1060792711yescharacteristic
878C2#1061388811yescharacteristic
879C2D4×#68311yescharacteristic
880C2Q8×#68311yescharacteristic
881C2#1061444811yescharacteristic
882C2#1061453411yescharacteristic
883C2#1061478311yescharacteristic
884C2#1061499711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D5
commutatorC23×C5C23×C4
FittingC2×C5×#389C2
socle, prime radical, cosocleC24×C5C24
hypercenterC2×#389D5
hypocenterC5#14406
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
53. #65270C4semidirect
261. C5×C4⋊C4C4⋊C4semidirect
680. C4⋊C4#683semidirect
819. C5#14406semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#3892
C2×#652622
C2×#652702
C2×#652652
#106023612
#106023602
#106023292
#106002132
#106002042
#106001992
#106001962
#144065