Finite Group Databasebeta

← #12066965

Subgroups — #12066965

Order 1280.

944 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3495C211yesmaximal, characteristic
2#10613968C211yesmaximal, characteristic, complemented
3#10613941C211yesmaximal, characteristic, complemented
4#10602631C211yesmaximal, characteristic, complemented
5#10602630C211yesmaximal, characteristic, complemented
6#10602629C211yesmaximal, characteristic, complemented
7#10602628C211yesmaximal, characteristic, complemented
8#10602550C211yesmaximal, characteristic, complemented
9#10602549C211yesmaximal, characteristic, complemented
10#10602548C211yesmaximal, characteristic, complemented
11#10602547C211yesmaximal, characteristic, complemented
12#10602503C211yesmaximal, characteristic
13#10602501C211yesmaximal, characteristic
14#10602482C211yesmaximal, characteristic, complemented
15C2×#64758C211yesmaximal, characteristic, complemented
16C5×#556—21no—
17C5×#554—21no—
18C5×#552—21no—
19C5×#552—21no—
20C5×#552—21no—
21C5×#552—21no—
22C5×#551—21no—
23C5×#551—21no—
24C5×#544C411yescharacteristic, complemented
25C5×#542C411yescharacteristic, complemented
26C5×#542C411yescharacteristic, complemented
27C5×#541C411yescharacteristic, complemented
28C5×#541C411yescharacteristic, complemented
29C5×#536C411yescharacteristic, complemented
30C5×#533C2211yescharacteristic
31C5×#533C2211yescharacteristic
32C5×#529C2211yescharacteristic
33C5×#529C2211yescharacteristic
34C5×#525C2211yescharacteristic
35C2×C5×C22⋊Q8C2211yescharacteristic
36C5×#520C411yescharacteristic, complemented
37C5×#519C411yescharacteristic, complemented
38C2×C5×#117C2211yescharacteristic
39#65500C2211yescharacteristic
40C2×#3963C2211yescharacteristic
41#65496C2211yescharacteristic
42C2×C22⋊#168C2211yescharacteristic
43#65289—21no—
44#65289—21no—
45#65288—21no—
46#65286—21no—
47#65270—21no—
48#65270—21no—
49#65239—21no—
50C22⋊C4×Dic5—21no—
51#65226C2211yescharacteristic
52#65225C2211yescharacteristic
53C4×C4⋊Dic5C2211yescharacteristic
54#65221C2211yescharacteristic
55#65215C2211yescharacteristic
56#65215C2211yescharacteristic
57#65214C2211yescharacteristic
58#65214C2211yescharacteristic
59#64758C2211yescharacteristic
60#64758C2211yescharacteristic
61#64758C2211yescharacteristic
62#64758C2211yescharacteristic
63#64758C2211yescharacteristic
64#64758C2211yescharacteristic
65#64758C2211yescharacteristic
66#64758C2211yescharacteristic
67#64758C2211yescharacteristic
68#64758C2211yescharacteristic
69#64758C2211yescharacteristic
70#64758C2211yescharacteristic
71#64757C2211yescharacteristic
72#64757C2211yescharacteristic
73#64757C2211yescharacteristic
74#64757C2211yescharacteristic
75#17609—51nomaximal, Sylow
76C2×C5×#41C2×C411yescharacteristic
77C22×C5×Q8C2×C411yescharacteristic
78C23×C4×C5C2311yescharacteristic
79C23×Dic5—21no—
80C5×C4⋊Q8—21no—
81C5×C4⋊Q8C2×C411yescharacteristic, complemented
82C5×C4⋊Q8C2×C411yescharacteristic, complemented
83C5×C4⋊Q8C2×C411yescharacteristic, complemented
84C5×C4⋊Q8C2×C411yescharacteristic, complemented
85C5×#126—21no—
86C5×#126—21no—
87C5×#126—21no—
88C5×#126—21no—
89C5×#126—21no—
90C5×#126—21no—
91C5×#126—21no—
92C5×#126—21no—
93C5×#125—21no—
94C5×#125—21no—
95C5×#125—21no—
96C5×#125—21no—
97C5×#125—21no—
98C5×#125—21no—
99C5×#125—21no—
100C5×#125C2×C411yescharacteristic, complemented
101C5×#125C2×C411yescharacteristic, complemented
102C5×#124—21no—
103C5×#124—21no—
104C5×#124C2×C411yescharacteristic, complemented
105C5×#124C2×C411yescharacteristic, complemented
106C5×#123—21no—
107C5×#123—21no—
108C5×#123—21no—
109C5×#123—21no—
110C5×#123—21no—
111C5×#123—21no—
112C5×#123—21no—
113C5×C22⋊Q8—21no—
114C5×C22⋊Q8—21no—
115C5×C22⋊Q8—21no—
116C5×C22⋊Q8—21no—
117C5×C22⋊Q8—21no—
118C5×C22⋊Q8—21no—
119C5×C22⋊Q8—21no—
120C5×C22⋊Q8—21no—
121C5×C22⋊Q8—21no—
122C5×C22⋊Q8—21no—
123C5×C22⋊Q8C2×C411yescharacteristic
124C5×C22⋊Q8C2×C411yescharacteristic
125C5×C22⋊Q8C2×C411yescharacteristic
126C5×C22⋊Q8C2311yescharacteristic
127C5×C22⋊Q8C2311yescharacteristic
128C5×C22⋊Q8C2311yescharacteristic
129C5×#121C2×C411yescharacteristic
130C5×#121C2311yescharacteristic
131C5×#120—21no—
132C4×C5×Q8—21no—
133C4×C5×Q8—21no—
134C4×C5×Q8—21no—
135C4×C5×Q8—21no—
136C4×C5×Q8C2×C411yescharacteristic, complemented
137C4×C5×Q8C2×C411yescharacteristic, complemented
138C4×C5×Q8C2×C411yescharacteristic, complemented
139C4×C5×Q8C2×C411yescharacteristic, complemented
140C4×C5×Q8C2×C411yescharacteristic, complemented
141C4×C5×Q8C2×C411yescharacteristic, complemented
142C4×C5×D4—21no—
143C4×C5×D4—21no—
144C4×C5×D4—21no—
145C4×C5×D4—21no—
146C4×C5×D4—21no—
147C4×C5×D4—21no—
148C4×C5×D4C2×C411yescharacteristic, complemented
149C4×C5×D4C2×C411yescharacteristic, complemented
150C5×#117—21no—
151C5×#117—21no—
152C5×#117—21no—
153C5×#117—21no—
154C5×#117—21no—
155C5×#117—21no—
156C5×#117—21no—
157C5×#117C2×C411yescharacteristic
158C5×#117C2×C411yescharacteristic
159C5×#117C2×C411yescharacteristic
160C5×#117C2×C411yescharacteristic
161C5×#117C2×C411yescharacteristic
162C5×#117D411yescharacteristic
163C5×#117D411yescharacteristic
164C5×#117D411yescharacteristic
165C5×#117D411yescharacteristic
166C2×C5×C4⋊C4—21no—
167C2×C5×C4⋊C4—21no—
168C2×C5×C4⋊C4C2×C411yescharacteristic
169C2×C5×C4⋊C4D411yescharacteristic
170C2×C5×C4⋊C4D411yescharacteristic
171C2×C5×C22⋊C4—21no—
172C2×C5×C22⋊C4D411yescharacteristic
173C2×C5×C22⋊C4D411yescharacteristic
174C2×C42×C5C2311yescharacteristic
175C2×C42×C5C2311yescharacteristic
176C2×C22⋊Dic5—21no—
177C2×C4⋊Dic5—21no—
178C2×C4⋊Dic5—21no—
179C2×C4×Dic5—21no—
180C2×C4×Dic5—21no—
181C2×#681—21no—
182C22×#168—21no—
183#3963—21no—
184#3963—21no—
185#3963—21no—
186#3963—21no—
187#3963—21no—
188#3963—21no—
189#3963C2311yescharacteristic
190#3963C2311yescharacteristic
191#3963C2311yescharacteristic
192#3963C2311yescharacteristic
193C22⋊#168—21no—
194C22⋊#168—21no—
195C22⋊#168C2311yescharacteristic
196C22⋊#168C2311yescharacteristic
197C22⋊#168C2311yescharacteristic
198C22⋊#168C2311yescharacteristic
199C4⋊#168—21no—
200C4⋊#168—21no—
201C4⋊#168—21no—
202C4⋊#168—21no—
203#3935—21no—
204#3935—21no—
205C4×#168—21no—
206C4×#168—21no—
207#3495D511yescharacteristic
208#2924—51no—
209#2343—51no—
210#1521—51no—
211#1518—51no—
212#1516—51no—
213#1515—51no—
214#1512—51no—
215#1511—51no—
216#1509—51no—
217#1506—51no—
218#1504—51no—
219#1503—51no—
220#1500—51no—
221C2×#328—51no—
222C24×C5C2×D411yescharacteristic
223C5×#41—42no—
224C2×C5×Q8—21no—
225C2×C5×Q8—21no—
226C2×C5×Q8—21no—
227C2×C5×Q8—42no—
228C2×C5×Q8C22×C411yescharacteristic
229C2×C5×Q8C22×C411yescharacteristic
230C2×C5×Q8C22×C411yescharacteristic
231C2×C5×D4—21no—
232C2×C5×D4—21no—
233C2×C5×D4—21no—
234C2×C5×D4C22×C411yescharacteristic
235C22×C4×C5—21no—
236C22×C4×C5—21no—
237C22×C4×C5—21no—
238C22×C4×C5—21no—
239C22×C4×C5—21no—
240C22×C4×C5—42no—
241C22×C4×C5C22×C411yescharacteristic
242C22×C4×C5C22×C411yescharacteristic
243C22×C4×C5C2×D411yescharacteristic
244C22×C4×C5C2×D411yescharacteristic
245C22×C4×C5C2×D411yescharacteristic
246C22×C4×C5C2×D411yescharacteristic
247C22×C4×C5C2×D411yescharacteristic
248C22×C4×C5C2×D411yescharacteristic
249C22×C4×C5C2×D411yescharacteristic
250C22×C4×C5C2411yescharacteristic
251C22×Dic5—21no—
252C22×Dic5—21no—
253C22×Dic5—21no—
254C22×Dic5—21no—
255C22×Dic5—42no—
256C22×Dic5—42no—
257C22×Dic5—81no—
258C5×C4⋊C4—21no—
259C5×C4⋊C4—21no—
260C5×C4⋊C4—21no—
261C5×C4⋊C4—21no—
262C5×C4⋊C4—21no—
263C5×C4⋊C4—21no—
264C5×C4⋊C4—21no—
265C5×C4⋊C4—21no—
266C5×C4⋊C4—21no—
267C5×C4⋊C4—21no—
268C5×C4⋊C4—21no—
269C5×C4⋊C4—21no—
270C5×C4⋊C4—21no—
271C5×C4⋊C4—21no—
272C5×C4⋊C4—21no—
273C5×C4⋊C4—21no—
274C5×C4⋊C4—21no—
275C5×C4⋊C4—21no—
276C5×C4⋊C4—21no—
277C5×C4⋊C4—21no—
278C5×C4⋊C4—21no—
279C5×C4⋊C4—21no—
280C5×C4⋊C4—21no—
281C5×C4⋊C4C22⋊C411yescharacteristic
282C5×C4⋊C4C22⋊C411yescharacteristic
283C5×C4⋊C4C22⋊C411yescharacteristic
284C5×C4⋊C4C22⋊C411yescharacteristic
285C5×C4⋊C4C22⋊C411yescharacteristic
286C5×C4⋊C4C22⋊C411yescharacteristic
287C5×C4⋊C4C22⋊C411yescharacteristic
288C5×C4⋊C4C22⋊C411yescharacteristic
289C5×C4⋊C4C22×C411yescharacteristic
290C5×C4⋊C4C22×C411yescharacteristic
291C5×C4⋊C4C22×C411yescharacteristic
292C5×C4⋊C4C22×C411yescharacteristic
293C5×C22⋊C4—21no—
294C5×C22⋊C4—21no—
295C5×C22⋊C4—21no—
296C5×C22⋊C4—21no—
297C5×C22⋊C4—21no—
298C5×C22⋊C4—21no—
299C5×C22⋊C4—21no—
300C5×C22⋊C4—21no—
301C5×C22⋊C4—21no—
302C5×C22⋊C4—21no—
303C5×C22⋊C4—21no—
304C5×C22⋊C4—21no—
305C5×C22⋊C4—21no—
306C5×C22⋊C4—21no—
307C5×C22⋊C4—21no—
308C5×C22⋊C4C22⋊C411yescharacteristic
309C5×C22⋊C4C22⋊C411yescharacteristic
310C5×C22⋊C4C22⋊C411yescharacteristic
311C5×C22⋊C4C22⋊C411yescharacteristic
312C5×C22⋊C4C22⋊C411yescharacteristic
313C5×C22⋊C4C22⋊C411yescharacteristic
314C5×C22⋊C4C22⋊C411yescharacteristic
315C5×C22⋊C4C22⋊C411yescharacteristic
316C42×C5—21no—
317C42×C5—21no—
318C42×C5—21no—
319C42×C5—21no—
320C42×C5—21no—
321C42×C5—21no—
322C42×C5—21no—
323C42×C5C22×C411yescharacteristic
324C42×C5C22×C411yescharacteristic
325C42×C5C22×C411yescharacteristic
326C42×C5C22×C411yescharacteristic
327C42×C5C2×D411yescharacteristic
328C42×C5C2×D411yescharacteristic
329C42×C5C2×D411yescharacteristic
330C42×C5C2×D411yescharacteristic
331C22⋊Dic5—42no—
332C4⋊Dic5—42no—
333C4⋊Dic5—81no—
334C4×Dic5—42no—
335C4×Dic5—81no—
336#681—42no—
337C2×#168—21no—
338C2×#168—21no—
339C2×#168—21no—
340C2×#168—21no—
341C2×#168—42no—
342#556—21no—
343#554—21no—
344#552—21no—
345#552—21no—
346#552—21no—
347#552—21no—
348#551—21no—
349#551—21no—
350#544Dic511yescharacteristic, complemented
351#542Dic511yescharacteristic, complemented
352#542Dic511yescharacteristic, complemented
353#541Dic511yescharacteristic, complemented
354#541Dic511yescharacteristic, complemented
355#536Dic511yescharacteristic, complemented
356#533C2×D511yescharacteristic
357#533C2×D511yescharacteristic
358#529C2×D511yescharacteristic
359#529C2×D511yescharacteristic
360#525C2×D511yescharacteristic
361C2×C22⋊Q8C2×D511yescharacteristic
362#520Dic511yescharacteristic, complemented
363#519Dic511yescharacteristic, complemented
364C2×#117C2×D511yescharacteristic
365#433—101no—
366#433—101no—
367#432—51no—
368#432—51no—
369#431—51no—
370#431—51no—
371#424—101no—
372#407—51no—
373C2×C22⋊C8—51no—
374#405—101no—
375#387—101no—
376#387—101no—
377#385—101no—
378#383—51no—
379#382—51no—
380#381—51no—
381C4×C4⋊C4—51no—
382C4×C22⋊C4—101no—
383#376—51no—
384C2×#95—51no—
385#328—51no—
386#328—51no—
387#328—51no—
388#328—51no—
389#328—51no—
390#328—51no—
391#328—51no—
392#328—51no—
393#328—51no—
394#328—51no—
395#328—51no—
396#328—51no—
397#327—51no—
398#327—51no—
399#327—51no—
400#327—51no—
401C23×C5—21no—
402C23×C5—21no—
403C23×C5—22no—
404C23×C5—21no—
405C23×C5—41no—
406C23×C5C2×C22⋊C411yescharacteristic
407C23×C5C2×C22⋊C411yescharacteristic
408C23×C5C22×D411yescharacteristic
409C5×Q8—41no—
410C5×Q8—41no—
411C5×Q8—41no—
412C5×Q8—42no—
413C5×Q8—81no—
414C5×Q8—81no—
415C5×D4—41no—
416C5×D4—41no—
417C5×D4—41no—
418C5×D4—42no—
419C5×D4—81no—
420C2×C4×C5—21no—
421C2×C4×C5—21no—
422C2×C4×C5—21no—
423C2×C4×C5—21no—
424C2×C4×C5—22no—
425C2×C4×C5—22no—
426C2×C4×C5—21no—
427C2×C4×C5—21no—
428C2×C4×C5—21no—
429C2×C4×C5—21no—
430C2×C4×C5—21no—
431C2×C4×C5—21no—
432C2×C4×C5—21no—
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—42no—
440C2×C4×C5—42no—
441C2×C4×C5—81no—
442C2×C4×C5—81no—
443C2×C4×C5—81no—
444C2×C4×C5C2×C22⋊C411yescharacteristic
445C2×C4×C5C2×C22⋊C411yescharacteristic
446C2×C4×C5C2×C22⋊C411yescharacteristic
447C2×C4×C5C2×C22⋊C411yescharacteristic
448C2×C4×C5C2×C22⋊C411yescharacteristic
449C2×C4×C5C2×C22⋊C411yescharacteristic
450C2×C4×C5C2×C22⋊C411yescharacteristic
451C2×C4×C5C2×C22⋊C411yescharacteristic
452C2×C4×C5C2×C22⋊C411yescharacteristic
453C2×C4×C5C2×C22⋊C411yescharacteristic
454C2×C4×C5C23×C411yescharacteristic
455C2×C4×C5C22×D411yescharacteristic
456C2×Dic5—22no—
457C2×Dic5—41no—
458C2×Dic5—41no—
459C2×Dic5—41no—
460C2×Dic5—41no—
461C2×Dic5—41no—
462C2×Dic5—41no—
463C2×Dic5—41no—
464C2×Dic5—41no—
465C2×Dic5—41no—
466C2×Dic5—41no—
467C2×Dic5—41no—
468C2×Dic5—84no—
469#168—41no—
470#168—41no—
471#168—41no—
472#168—41no—
473C2×#41C2×Dic511yescharacteristic
474C22×Q8C2×Dic511yescharacteristic
475C23×C4—101no—
476C23×C4C22×D511yescharacteristic
477C2×M16—101no—
478C22×C8—101no—
479C4⋊Q8—21no—
480C4⋊Q8C2×Dic511yescharacteristic, complemented
481C4⋊Q8C2×Dic511yescharacteristic, complemented
482C4⋊Q8C2×Dic511yescharacteristic, complemented
483C4⋊Q8C2×Dic511yescharacteristic, complemented
484#126—21no—
485#126—21no—
486#126—21no—
487#126—21no—
488#126—21no—
489#126—21no—
490#126—21no—
491#126—21no—
492#125—21no—
493#125—21no—
494#125—21no—
495#125—21no—
496#125—21no—
497#125—21no—
498#125—21no—
499#125C2×Dic511yescharacteristic, complemented
500#125C2×Dic511yescharacteristic, complemented
501#124—21no—
502#124—21no—
503#124C2×Dic511yescharacteristic, complemented
504#124C2×Dic511yescharacteristic, complemented
505#123—21no—
506#123—21no—
507#123—21no—
508#123—21no—
509#123—21no—
510#123—21no—
511#123—21no—
512C22⋊Q8—21no—
513C22⋊Q8—21no—
514C22⋊Q8—21no—
515C22⋊Q8—21no—
516C22⋊Q8—21no—
517C22⋊Q8—21no—
518C22⋊Q8—21no—
519C22⋊Q8—21no—
520C22⋊Q8—21no—
521C22⋊Q8—21no—
522C22⋊Q8C2×Dic511yescharacteristic
523C22⋊Q8C2×Dic511yescharacteristic
524C22⋊Q8C2×Dic511yescharacteristic
525C22⋊Q8C22×D511yescharacteristic
526C22⋊Q8C22×D511yescharacteristic
527C22⋊Q8C22×D511yescharacteristic
528#121C2×Dic511yescharacteristic
529#121C22×D511yescharacteristic
530#120—21no—
531C4×Q8—21no—
532C4×Q8—21no—
533C4×Q8—21no—
534C4×Q8—21no—
535C4×Q8C2×Dic511yescharacteristic, complemented
536C4×Q8C2×Dic511yescharacteristic, complemented
537C4×Q8C2×Dic511yescharacteristic, complemented
538C4×Q8C2×Dic511yescharacteristic, complemented
539C4×Q8C2×Dic511yescharacteristic, complemented
540C4×Q8C2×Dic511yescharacteristic, complemented
541C4×D4—21no—
542C4×D4—21no—
543C4×D4—21no—
544C4×D4—21no—
545C4×D4—21no—
546C4×D4—21no—
547C4×D4C2×Dic511yescharacteristic, complemented
548C4×D4C2×Dic511yescharacteristic, complemented
549#117—21no—
550#117—21no—
551#117—21no—
552#117—21no—
553#117—21no—
554#117—21no—
555#117—21no—
556#117C2×Dic511yescharacteristic
557#117C2×Dic511yescharacteristic
558#117C2×Dic511yescharacteristic
559#117C2×Dic511yescharacteristic
560#117C2×Dic511yescharacteristic
561#117C22⋊D511yescharacteristic
562#117C22⋊D511yescharacteristic
563#117C22⋊D511yescharacteristic
564#117C22⋊D511yescharacteristic
565C2×C4⋊C4—21no—
566C2×C4⋊C4—21no—
567C2×C4⋊C4—101no—
568C2×C4⋊C4—101no—
569C2×C4⋊C4C2×Dic511yescharacteristic
570C2×C4⋊C4C22⋊D511yescharacteristic
571C2×C4⋊C4C22⋊D511yescharacteristic
572C2×C22⋊C4—21no—
573C2×C22⋊C4—101no—
574C2×C22⋊C4C22⋊D511yescharacteristic
575C2×C22⋊C4C22⋊D511yescharacteristic
576C2×C42—101no—
577C2×C42—101no—
578C2×C42C22×D511yescharacteristic
579C2×C42C22×D511yescharacteristic
580C4⋊C8—101no—
581C4⋊C8—101no—
582C4⋊C8—101no—
583C4⋊C8—101no—
584C22⋊C8—51no—
585C22⋊C8—51no—
586C22⋊C8—51no—
587C22⋊C8—51no—
588C22⋊C8—101no—
589C22⋊C8—101no—
590#97—101no—
591#97—101no—
592C4×C8—101no—
593C4×C8—101no—
594#95—51no—
595#95—51no—
596#95—51no—
597#95—51no—
598#95—101no—
599#95—101no—
600#95—101no—
601#95—101no—
602#95—101no—
603#95—101no—
604C22×C5—21no—
605C22×C5—21no—
606C22×C5—21no—
607C22×C5—21no—
608C22×C5—21no—
609C22×C5—21no—
610C22×C5—21no—
611C22×C5—42no—
612C22×C5—42no—
613C22×C5—41no—
614C22×C5—41no—
615C22×C5—41no—
616C22×C5#41012yes—
617C22×C5C22×C22⋊C411yescharacteristic
618C22×C5#57711yescharacteristic
619C22×C5#57811yescharacteristic
620C4×C5—21no—
621C4×C5—21no—
622C4×C5—21no—
623C4×C5—21no—
624C4×C5—21no—
625C4×C5—21no—
626C4×C5—21no—
627C4×C5—21no—
628C4×C5—21no—
629C4×C5—21no—
630C4×C5—21no—
631C4×C5—21no—
632C4×C5—41no—
633C4×C5—41no—
634C4×C5—41no—
635C4×C5—41no—
636C4×C5—41no—
637C4×C5—41no—
638C4×C5—41no—
639Dic5—42no—
640Dic5—81no—
641Dic5—81no—
642Dic5—81no—
643C24C2×C22⋊D511yescharacteristic
644#41—42no—
645C2×Q8—21no—
646C2×Q8—21no—
647C2×Q8—21no—
648C2×Q8—42no—
649C2×Q8C22×Dic511yescharacteristic
650C2×Q8C22×Dic511yescharacteristic
651C2×Q8C22×Dic511yescharacteristic
652C2×D4—21no—
653C2×D4—21no—
654C2×D4—21no—
655C2×D4C22×Dic511yescharacteristic
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—42no—
662C22×C4—101no—
663C22×C4—101no—
664C22×C4—101no—
665C22×C4—101no—
666C22×C4—202no—
667C22×C4—202no—
668C22×C4—401no—
669C22×C4C22×Dic511yescharacteristic
670C22×C4C22×Dic511yescharacteristic
671C22×C4C2×C22⋊D511yescharacteristic
672C22×C4C2×C22⋊D511yescharacteristic
673C22×C4C2×C22⋊D511yescharacteristic
674C22×C4C2×C22⋊D511yescharacteristic
675C22×C4C2×C22⋊D511yescharacteristic
676C22×C4C2×C22⋊D511yescharacteristic
677C22×C4C2×C22⋊D511yescharacteristic
678C22×C4C23×D511yescharacteristic
679M16—202no—
680C2×C8—101no—
681C2×C8—101no—
682C2×C8—101no—
683C2×C8—101no—
684C2×C8—202no—
685C4⋊C4—21no—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—21no—
692C4⋊C4—21no—
693C4⋊C4—21no—
694C4⋊C4—21no—
695C4⋊C4—21no—
696C4⋊C4—21no—
697C4⋊C4—21no—
698C4⋊C4—21no—
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4—21no—
705C4⋊C4—21no—
706C4⋊C4—21no—
707C4⋊C4—21no—
708C4⋊C4—202no—
709C4⋊C4—401no—
710C4⋊C4C22⋊Dic511yescharacteristic
711C4⋊C4C22⋊Dic511yescharacteristic
712C4⋊C4C22⋊Dic511yescharacteristic
713C4⋊C4C22⋊Dic511yescharacteristic
714C4⋊C4C22⋊Dic511yescharacteristic
715C4⋊C4C22⋊Dic511yescharacteristic
716C4⋊C4C22⋊Dic511yescharacteristic
717C4⋊C4C22⋊Dic511yescharacteristic
718C4⋊C4C22×Dic511yescharacteristic
719C4⋊C4C22×Dic511yescharacteristic
720C4⋊C4C22×Dic511yescharacteristic
721C4⋊C4C22×Dic511yescharacteristic
722C22⋊C4—21no—
723C22⋊C4—21no—
724C22⋊C4—21no—
725C22⋊C4—21no—
726C22⋊C4—21no—
727C22⋊C4—21no—
728C22⋊C4—21no—
729C22⋊C4—21no—
730C22⋊C4—21no—
731C22⋊C4—21no—
732C22⋊C4—21no—
733C22⋊C4—21no—
734C22⋊C4—21no—
735C22⋊C4—21no—
736C22⋊C4—21no—
737C22⋊C4—202no—
738C22⋊C4C22⋊Dic511yescharacteristic
739C22⋊C4C22⋊Dic511yescharacteristic
740C22⋊C4C22⋊Dic511yescharacteristic
741C22⋊C4C22⋊Dic511yescharacteristic
742C22⋊C4C22⋊Dic511yescharacteristic
743C22⋊C4C22⋊Dic511yescharacteristic
744C22⋊C4C22⋊Dic511yescharacteristic
745C22⋊C4C22⋊Dic511yescharacteristic
746C42—21no—
747C42—21no—
748C42—21no—
749C42—21no—
750C42—21no—
751C42—21no—
752C42—21no—
753C42—202no—
754C42—401no—
755C42C22×Dic511yescharacteristic
756C42C22×Dic511yescharacteristic
757C42C22×Dic511yescharacteristic
758C42C22×Dic511yescharacteristic
759C42C2×C22⋊D511yescharacteristic
760C42C2×C22⋊D511yescharacteristic
761C42C2×C22⋊D511yescharacteristic
762C42C2×C22⋊D511yescharacteristic
763C2×C5—21no—
764C2×C5—21no—
765C2×C5—22no—
766C2×C5—41no—
767C2×C5—81no—
768C2×C5C2×#41011yescharacteristic
769C2×C5#289811yescharacteristic
770C2×C5#290111yescharacteristic
771C23—21no—
772C23—21no—
773C23—22no—
774C23—21no—
775C23—41no—
776C23C2×C22⋊Dic511yescharacteristic
777C23C2×C22⋊Dic511yescharacteristic
778C23C22×C22⋊D511yescharacteristic
779Q8—41no—
780Q8—41no—
781Q8—41no—
782Q8—42no—
783Q8—81no—
784Q8—81no—
785D4—41no—
786D4—41no—
787D4—41no—
788D4—42no—
789D4—81no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—21no—
799C2×C4—21no—
800C2×C4—21no—
801C2×C4—21no—
802C2×C4—21no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—81no—
812C2×C4—81no—
813C2×C4—81no—
814C2×C4—102no—
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—404no—
827C2×C4C2×C22⋊Dic511yescharacteristic
828C2×C4C2×C22⋊Dic511yescharacteristic
829C2×C4C2×C22⋊Dic511yescharacteristic
830C2×C4C2×C22⋊Dic511yescharacteristic
831C2×C4C2×C22⋊Dic511yescharacteristic
832C2×C4C2×C22⋊Dic511yescharacteristic
833C2×C4C2×C22⋊Dic511yescharacteristic
834C2×C4C2×C22⋊Dic511yescharacteristic
835C2×C4C2×C22⋊Dic511yescharacteristic
836C2×C4C2×C22⋊Dic511yescharacteristic
837C2×C4C23×Dic511yescharacteristic
838C2×C4C22×C22⋊D511yescharacteristic
839C8—201no—
840C8—201no—
841C8—201no—
842C8—201no—
843C5#1760911yescharacteristic, complemented, Sylow
844C22—21no—
845C22—21no—
846C22—21no—
847C22—21no—
848C22—21no—
849C22—21no—
850C22—21no—
851C22—42no—
852C22—42no—
853C22—41no—
854C22—41no—
855C22—41no—
856C22#6552912yes—
857C22#6617111yescharacteristic
858C22#6617211yescharacteristic
859C22C22×C22⋊Dic511yescharacteristic
860C4—21no—
861C4—21no—
862C4—21no—
863C4—21no—
864C4—21no—
865C4—21no—
866C4—21no—
867C4—21no—
868C4—21no—
869C4—21no—
870C4—21no—
871C4—21no—
872C4—41no—
873C4—41no—
874C4—41no—
875C4—41no—
876C4—41no—
877C4—41no—
878C4—41no—
879C4—202no—
880C4—401no—
881C4—401no—
882C4—401no—
883C2—21no—
884C2—21no—
885C2—22no—
886C2—41no—
887C2—81no—
888C2C2×#6552911yescharacteristic
889C2#1061584211yescharacteristic
890C2#1061585111yescharacteristic
subgroupG/H
centerC22C22×C22⋊Dic5
commutatorC2×C4×C5C23×C4
FrattiniC22×C4C23×D5
FittingC5×#3495C2
socleC22×C5C22×C22⋊C4
prime radicalC5×#525C22
cosocleC22×C4×C5C24
hypercenter#3495D5
hypocenterC5#17609
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ C2×#117 ◁ #3495

Complements

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

NH ≅ G/Ntype
2. #10613968C2semidirect
3. #10613941C2semidirect
4. #10602631C2semidirect
5. #10602630C2semidirect
6. #10602629C2semidirect
7. #10602628C2semidirect
8. #10602550C2semidirect
9. #10602549C2semidirect
10. #10602548C2semidirect
11. #10602547C2semidirect
14. #10602482C2semidirect
15. C2×#64758C2semidirect
24. C5×#544C4semidirect
25. C5×#542C4semidirect
26. C5×#542C4semidirect
27. C5×#541C4semidirect
28. C5×#541C4semidirect
29. C5×#536C4semidirect
36. C5×#520C4semidirect
37. C5×#519C4semidirect
81. C5×C4⋊Q8C2×C4semidirect
82. C5×C4⋊Q8C2×C4semidirect
83. C5×C4⋊Q8C2×C4semidirect
84. C5×C4⋊Q8C2×C4semidirect
100. C5×#125C2×C4semidirect
101. C5×#125C2×C4semidirect
104. C5×#124C2×C4semidirect
105. C5×#124C2×C4semidirect
136. C4×C5×Q8C2×C4semidirect
137. C4×C5×Q8C2×C4semidirect
138. C4×C5×Q8C2×C4semidirect
139. C4×C5×Q8C2×C4semidirect
140. C4×C5×Q8C2×C4semidirect
141. C4×C5×Q8C2×C4semidirect
148. C4×C5×D4C2×C4semidirect
149. C4×C5×D4C2×C4semidirect
350. #544Dic5semidirect
351. #542Dic5semidirect
352. #542Dic5semidirect
353. #541Dic5semidirect
354. #541Dic5semidirect
355. #536Dic5semidirect
362. #520Dic5semidirect
363. #519Dic5semidirect
480. C4⋊Q8C2×Dic5semidirect
481. C4⋊Q8C2×Dic5semidirect
482. C4⋊Q8C2×Dic5semidirect
483. C4⋊Q8C2×Dic5semidirect
499. #125C2×Dic5semidirect
500. #125C2×Dic5semidirect
503. #124C2×Dic5semidirect
504. #124C2×Dic5semidirect
535. C4×Q8C2×Dic5semidirect
536. C4×Q8C2×Dic5semidirect
537. C4×Q8C2×Dic5semidirect
538. C4×Q8C2×Dic5semidirect
539. C4×Q8C2×Dic5semidirect
540. C4×Q8C2×Dic5semidirect
547. C4×D4C2×Dic5semidirect
548. C4×D4C2×Dic5semidirect
843. C5#17609semidirect

Maximal subgroups

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

subgroupindex
C5×#34952
#106139682
#106139412
#106026312
#106026302
#106026292
#106026282
#106025502
#106025492
#106025482
#106025472
#106025032
#106025012
#106024822
C2×#647582
#176095