Finite Group Databasebeta

← #12269185

Subgroups — #12269185

Order 1280.

1892 conjugacy classes of subgroups.

The subgroup lattice has 1402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C5×#123C211yesmaximal, characteristic, complemented
2#10614578C211yesmaximal, characteristic
3#10614575C211yesmaximal, characteristic, complemented
4C4×#4085C211yesmaximal, characteristic
5C4×D4×Dic5C211yesmaximal, characteristic, complemented
6C4×#4075C211yesmaximal, characteristic, complemented
7C2×#65221C211yesmaximal, characteristic, complemented
8#10607316C211yesmaximal, characteristic, complemented
9#10607314C211yesmaximal, characteristic, complemented
10#10607307C211yesmaximal, characteristic, complemented
11#10607305C211yesmaximal, characteristic, complemented
12#10606803C211yesmaximal, characteristic, complemented
13#10606799C211yesmaximal, characteristic, complemented
14#10606796C211yesmaximal, characteristic, complemented
15#10606792C211yesmaximal, characteristic, complemented
16#10606443C211yesmaximal, characteristic, complemented
17#10606437C211yesmaximal, characteristic
18#10606196C211yesmaximal, characteristic, complemented
19#10606194C211yesmaximal, characteristic, complemented
20#10605809C211yesmaximal, characteristic, complemented
21#10605807C211yesmaximal, characteristic, complemented
22#10605510C211yesmaximal, characteristic, complemented
23#10605401C211yesmaximal, characteristic, complemented
24#10605351C211yesmaximal, characteristic, complemented
25#10605350C211yesmaximal, characteristic, complemented
26#10605213C211yesmaximal, characteristic, complemented
27#10605212C211yesmaximal, characteristic, complemented
28C4×#4024C211yesmaximal, characteristic, complemented
29#10605169C211yesmaximal, characteristic, complemented
30#10605169C211yesmaximal, characteristic, complemented
31#10605168C211yesmaximal, characteristic, complemented
32C2×C5×#123C2211yescharacteristic
33C2×C4×C5×D4C2211yescharacteristic
34C22×C42×C5C2211yescharacteristic
35C2×#4085C2211yescharacteristic
36C2×D4×Dic5C2211yescharacteristic
37C2×D4×Dic5C2211yescharacteristic
38C2×#4075C2211yescharacteristic
39C2×C4×C22⋊D5C2211yescharacteristic
40C2×C4×C22⋊D5C2211yescharacteristic
41C22×C4×Dic5C2211yescharacteristic
42C22×C4×Dic5C2211yescharacteristic
43C22×C4×Dic5C2211yescharacteristic
44C2×#4024C2211yescharacteristic
45C2×#4018C2211yescharacteristic
46C2×C4×Dic10C2211yescharacteristic
47C5×#388C2211yescharacteristic
48C5×#388C2211yescharacteristic
49C5×#387C2211yescharacteristic
50C5×#387C2211yescharacteristic
51C5×#386C2211yescharacteristic
52C5×#385C2211yescharacteristic
53C5×#381C2211yescharacteristic
54C4×C5×C4⋊C4C2211yescharacteristic
55C4×C5×C4⋊C4C2211yescharacteristic
56C4×C5×C22⋊C4C2211yescharacteristic
57C4×C5×C22⋊C4C2211yescharacteristic
58C4×C5×C22⋊C4C2211yescharacteristic
59#65509C2211yescharacteristic
60#65502C2211yescharacteristic
61#65500C2211yescharacteristic
62#65499C2211yescharacteristic
63C4×C22⋊Dic5C2211yescharacteristic
64C4×C22⋊Dic5C2211yescharacteristic
65C4×C22⋊Dic5C2211yescharacteristic
66C2×#3963C2211yescharacteristic
67C2×#3963C2211yescharacteristic
68C2×#3963C2211yescharacteristic
69C2×#3963C2211yescharacteristic
70#65283C2211yescharacteristic
71#65282C2211yescharacteristic
72#65279C2211yescharacteristic
73#65279C2211yescharacteristic
74#65279C2211yescharacteristic
75#65275C2211yescharacteristic
76#65273C2211yescharacteristic
77#65272C2211yescharacteristic
78#65271C2211yescharacteristic
79#65271C2211yescharacteristic
80#65269C2211yescharacteristic
81#65267C2211yescharacteristic
82#65267C2211yescharacteristic
83#65267C2211yescharacteristic
84#65267C2211yescharacteristic
85C4⋊C4×Dic5C2211yescharacteristic
86C4⋊C4×Dic5C2211yescharacteristic
87#65261C2211yescharacteristic
88#65261C2211yescharacteristic
89#65261C2211yescharacteristic
90#65250C2211yescharacteristic
91#65248C2211yescharacteristic
92#65247C2211yescharacteristic
93#65247C2211yescharacteristic
94#65247C2211yescharacteristic
95#65247C2211yescharacteristic
96#65247C2211yescharacteristic
97#65246C2211yescharacteristic
98#65242C2211yescharacteristic
99#65241C2211yescharacteristic
100#65241C2211yescharacteristic
101#65241C2211yescharacteristic
102#65239C2211yescharacteristic
103#65237C2211yescharacteristic
104#65236C2211yescharacteristic
105#65235C2211yescharacteristic
106#65235C2211yescharacteristic
107#65235C2211yescharacteristic
108#65235C2211yescharacteristic
109#65235C2211yescharacteristic
110#65234C2211yescharacteristic
111#65232C2211yescharacteristic
112#65232C2211yescharacteristic
113#65231C2211yescharacteristic
114#65231C2211yescharacteristic
115#65231C2211yescharacteristic
116#65231C2211yescharacteristic
117C22⋊C4×Dic5C2211yescharacteristic
118C22⋊C4×Dic5C2211yescharacteristic
119C22⋊C4×Dic5C2211yescharacteristic
120C22⋊C4×Dic5C2211yescharacteristic
121#65229C2211yescharacteristic
122#65229C2211yescharacteristic
123C4×#685C2211yescharacteristic
124C4×#685C2211yescharacteristic
125C4×#685C2211yescharacteristic
126C4×#685C2211yescharacteristic
127C4×C4⋊Dic5C2211yescharacteristic
128C4×C4⋊Dic5C2211yescharacteristic
129#65222C2211yescharacteristic
130#65222C2211yescharacteristic
131#65221C2211yescharacteristic
132#65221C2211yescharacteristic
133#65221C2211yescharacteristic
134#65221C2211yescharacteristic
135#65221C2211yescharacteristic
136#65221C2211yescharacteristic
137#65221C2211yescharacteristic
138#65221C2211yescharacteristic
139#65221C2211yescharacteristic
140C4×#683C2211yescharacteristic
141C4×#683C2211yescharacteristic
142C4×#683C2211yescharacteristic
143C4×#683C2211yescharacteristic
144C4×#683C2211yescharacteristic
145C4×#683C2211yescharacteristic
146C42×Dic5C2211yescharacteristic
147#64964C2211yescharacteristic
148#64964C2211yescharacteristic
149#64963C2211yescharacteristic
150#64962C2211yescharacteristic
151#64959C2211yescharacteristic
152#64959C2211yescharacteristic
153#64958C2211yescharacteristic
154#64958C2211yescharacteristic
155#64958C2211yescharacteristic
156#64958C2211yescharacteristic
157C5⋊#401C2211yescharacteristic
158C5⋊#401C2211yescharacteristic
159#64949C2211yescharacteristic
160#64949C2211yescharacteristic
161#64949C2211yescharacteristic
162#64948C2211yescharacteristic
163#64948C2211yescharacteristic
164#64947C2211yescharacteristic
165#64947C2211yescharacteristic
166#64947C2211yescharacteristic
167#64947C2211yescharacteristic
168#64946C2211yescharacteristic
169#64944C2211yescharacteristic
170#64944C2211yescharacteristic
171#64944C2211yescharacteristic
172#64943C2211yescharacteristic
173#64942C2211yescharacteristic
174#64942C2211yescharacteristic
175#64941C2211yescharacteristic
176#64941C2211yescharacteristic
177#64941C2211yescharacteristic
178#64941C2211yescharacteristic
179#64940C2211yescharacteristic
180#64940C2211yescharacteristic
181#64939C2211yescharacteristic
182#64939C2211yescharacteristic
183#64936C2211yescharacteristic
184#64935C2211yescharacteristic
185#64935C2211yescharacteristic
186#64935C2211yescharacteristic
187#34811—51nomaximal, Sylow
188C22×C5×D4C2311yescharacteristic
189C23×C4×C5C2311yescharacteristic
190C23×C4×C5C2311yescharacteristic
191C23×C4×C5C2311yescharacteristic
192C23×C4×C5C2311yescharacteristic
193C22×C22⋊D5C2311yescharacteristic
194C22×C22⋊D5C2311yescharacteristic
195C23×Dic5C2311yescharacteristic
196C23×Dic5C2311yescharacteristic
197C23×Dic5C2311yescharacteristic
198C23×Dic5C2311yescharacteristic
199C23×Dic5C2311yescharacteristic
200C23×Dic5C2311yescharacteristic
201C22×C4×D5C2311yescharacteristic
202C22×Dic10C2311yescharacteristic
203C5×#123—24no—
204C4×C5×D4—24no—
205C2×C5×C4⋊C4C2311yescharacteristic
206C2×C5×C4⋊C4C2311yescharacteristic
207C2×C5×C4⋊C4C2311yescharacteristic
208C2×C5×C4⋊C4C2311yescharacteristic
209C2×C5×C4⋊C4C2311yescharacteristic
210C2×C5×C22⋊C4C2311yescharacteristic
211C2×C5×C22⋊C4C2311yescharacteristic
212C2×C5×C22⋊C4C2311yescharacteristic
213C2×C5×C22⋊C4C2311yescharacteristic
214C2×C5×C22⋊C4C2311yescharacteristic
215C2×C5×C22⋊C4C2311yescharacteristic
216C2×C5×C22⋊C4C2311yescharacteristic
217C2×C5×C22⋊C4C2311yescharacteristic
218C2×C42×C5—24no—
219C2×C42×C5C2311yescharacteristic
220C2×C42×C5C2311yescharacteristic
221C2×C42×C5C2311yescharacteristic
222C2×C42×C5C2311yescharacteristic
223C2×C42×C5C2311yescharacteristic
224C2×C42×C5C2311yescharacteristic
225C2×C42×C5C2311yescharacteristic
226C2×C22⋊Dic5C2311yescharacteristic
227C2×C22⋊Dic5C2311yescharacteristic
228C2×C22⋊Dic5C2311yescharacteristic
229C2×C22⋊Dic5C2311yescharacteristic
230C2×C22⋊Dic5C2311yescharacteristic
231C2×C22⋊Dic5C2311yescharacteristic
232C2×C22⋊Dic5C2311yescharacteristic
233C2×C22⋊Dic5C2311yescharacteristic
234#4085—24no—
235D4×Dic5—24no—
236D4×Dic5—24no—
237#4075—24no—
238C4×C22⋊D5—24no—
239C4×C22⋊D5—24no—
240C2×#685C2311yescharacteristic
241C2×#685C2311yescharacteristic
242C2×#685C2311yescharacteristic
243C2×#685C2311yescharacteristic
244C2×#685C2311yescharacteristic
245C2×#685C2311yescharacteristic
246C2×#685C2311yescharacteristic
247C2×#685C2311yescharacteristic
248C2×#685C2311yescharacteristic
249C2×#685C2311yescharacteristic
250C2×#685C2311yescharacteristic
251C2×#685C2311yescharacteristic
252C2×C4⋊Dic5C2311yescharacteristic
253C2×C4⋊Dic5C2311yescharacteristic
254C2×C4⋊Dic5C2311yescharacteristic
255C2×C4⋊Dic5C2311yescharacteristic
256C2×C4⋊Dic5C2311yescharacteristic
257C2×#683C2311yescharacteristic
258C2×#683C2311yescharacteristic
259C2×#683C2311yescharacteristic
260C2×#683C2311yescharacteristic
261C2×#683C2311yescharacteristic
262C2×#683C2311yescharacteristic
263C2×#683C2311yescharacteristic
264C2×#683C2311yescharacteristic
265C2×#683C2311yescharacteristic
266C2×#683C2311yescharacteristic
267C2×#683C2311yescharacteristic
268C2×#683C2311yescharacteristic
269C2×#683C2311yescharacteristic
270C2×#683C2311yescharacteristic
271C2×#683C2311yescharacteristic
272C2×#683C2311yescharacteristic
273C2×#683C2311yescharacteristic
274C2×#683C2311yescharacteristic
275C2×C4×Dic5—24no—
276C2×C4×Dic5—24no—
277C2×C4×Dic5—24no—
278C2×C4×Dic5C2311yescharacteristic
279C2×C4×Dic5C2311yescharacteristic
280C2×C4×Dic5C2311yescharacteristic
281C2×C4×Dic5C2311yescharacteristic
282C2×C4×Dic5C2311yescharacteristic
283C2×C4×Dic5C2311yescharacteristic
284C2×C4×Dic5C2311yescharacteristic
285C2×C4×Dic5C2311yescharacteristic
286C2×C4×Dic5C2311yescharacteristic
287C2×C4×Dic5C2311yescharacteristic
288C2×C4×Dic5C2311yescharacteristic
289C2×C4×Dic5C2311yescharacteristic
290C2×C4×Dic5C2311yescharacteristic
291C2×C4×Dic5C2311yescharacteristic
292C2×C4×Dic5C2311yescharacteristic
293C2×C4×Dic5C2311yescharacteristic
294C2×C4×Dic5C2311yescharacteristic
295#4024—24no—
296#4018—24no—
297C4×Dic10—24no—
298C5×#95C2311yescharacteristic
299C5×#95C2311yescharacteristic
300C5×#95C2311yescharacteristic
301C5×#95C2311yescharacteristic
302C5×#95C2311yescharacteristic
303C5×#95C2311yescharacteristic
304C5×#95C2311yescharacteristic
305C5×#95C2311yescharacteristic
306C5×#95C2311yescharacteristic
307C5×#95C2311yescharacteristic
308#3963C2311yescharacteristic
309#3963C2311yescharacteristic
310#3963C2311yescharacteristic
311#3963C2311yescharacteristic
312#3963C2311yescharacteristic
313#3963C2311yescharacteristic
314#3963C2311yescharacteristic
315#3963C2311yescharacteristic
316#3963C2311yescharacteristic
317#3963C2311yescharacteristic
318#3963C2311yescharacteristic
319#3963C2311yescharacteristic
320#3963C2311yescharacteristic
321#3963C2311yescharacteristic
322#3963C2311yescharacteristic
323#3963C2311yescharacteristic
324#3963C2311yescharacteristic
325#3963C2311yescharacteristic
326#3963C2311yescharacteristic
327#3963C2311yescharacteristic
328#3963C2311yescharacteristic
329#3963C2311yescharacteristic
330#3963C2311yescharacteristic
331#3963C2311yescharacteristic
332#3963C2311yescharacteristic
333#3963C2311yescharacteristic
334#3963C2311yescharacteristic
335#3963C2311yescharacteristic
336#3963C2311yescharacteristic
337#3963C2311yescharacteristic
338#3963C2311yescharacteristic
339#3963C2311yescharacteristic
340#3963C2311yescharacteristic
341#3963C2311yescharacteristic
342#3963C2311yescharacteristic
343#3963C2311yescharacteristic
344#3963C2311yescharacteristic
345#3963C2311yescharacteristic
346#3963C2311yescharacteristic
347#3963C2311yescharacteristic
348#3963C2311yescharacteristic
349#3963C2311yescharacteristic
350#3963C2311yescharacteristic
351#3963C2311yescharacteristic
352#3963C2311yescharacteristic
353#3963C2311yescharacteristic
354#3963C2311yescharacteristic
355#3963C2311yescharacteristic
356#3963C2311yescharacteristic
357#3963C2311yescharacteristic
358#2533—51no—
359#2532—51no—
360#2531—51no—
361#2530—51no—
362#2529—51no—
363#2528—51no—
364#2527—51no—
365#2526—51no—
366#2510—51no—
367#2505—51no—
368#2493—51no—
369#2488—51no—
370#2450—51no—
371#2444—51no—
372#2425—51no—
373#2419—51no—
374#2402—51no—
375#2401—51no—
376#2401—51no—
377#2398—51no—
378C4×C22⋊Q8—51no—
379C4×#123—51no—
380C4×#123D511yescharacteristic, complemented
381C4×#121—51no—
382#2298—51no—
383#2295—51no—
384#2290—51no—
385#2290—51no—
386#2283—51no—
387C42×D4—51no—
388C2×#376—51no—
389C24×C5C2411yescharacteristic
390C24×C5C2411yescharacteristic
391C23×D5C2411yescharacteristic
392C2×C5×D4—22no—
393C2×C5×D4—22no—
394C2×C5×D4#4114yes—
395C22×C4×C5—22no—
396C22×C4×C5—22no—
397C22×C4×C5—22no—
398C22×C4×C5—22no—
399C22×C4×C5—22no—
400C22×C4×C5—22no—
401C22×C4×C5—22no—
402C22×C4×C5—22no—
403C22×C4×C5—22no—
404C22×C4×C5—41no—
405C22×C4×C5—41no—
406C22×C4×C5#4114yes—
407C22×C4×C5C2411yescharacteristic
408C22×C4×C5C2411yescharacteristic
409C22×C4×C5C2411yescharacteristic
410C22×C4×C5C2411yescharacteristic
411C22×C4×C5C2411yescharacteristic
412C22×C4×C5C2411yescharacteristic
413C22×C4×C5C2411yescharacteristic
414C22×C4×C5C2411yescharacteristic
415C22×C4×C5C2411yescharacteristic
416C22×C4×C5C2411yescharacteristic
417C22×C4×C5C2411yescharacteristic
418C22×C4×C5C2411yescharacteristic
419C22×C4×C5C2411yescharacteristic
420C2×C22⋊D5—22no—
421C2×C22⋊D5—22no—
422C2×C22⋊D5—22no—
423C2×C22⋊D5—22no—
424C2×C22⋊D5—22no—
425C2×C22⋊D5—41no—
426C22×Dic5—22no—
427C22×Dic5—22no—
428C22×Dic5—22no—
429C22×Dic5—22no—
430C22×Dic5—22no—
431C22×Dic5—22no—
432C22×Dic5—22no—
433C22×Dic5—22no—
434C22×Dic5—22no—
435C22×Dic5—22no—
436C22×Dic5—22no—
437C22×Dic5—22no—
438C22×Dic5—41no—
439C22×Dic5—41no—
440C22×Dic5—41no—
441C22×Dic5—41no—
442C22×Dic5—41no—
443C22×Dic5—41no—
444C22×Dic5C2411yescharacteristic
445C22×Dic5C2411yescharacteristic
446C22×Dic5C2411yescharacteristic
447C22×Dic5C2411yescharacteristic
448C22×Dic5C2411yescharacteristic
449C22×Dic5C2411yescharacteristic
450C22×Dic5C2411yescharacteristic
451C22×Dic5C2411yescharacteristic
452C22×Dic5C2411yescharacteristic
453C22×Dic5C2411yescharacteristic
454C22×Dic5C2411yescharacteristic
455C22×Dic5C2411yescharacteristic
456C22×Dic5C2411yescharacteristic
457C22×Dic5C2411yescharacteristic
458C22×Dic5C2411yescharacteristic
459C2×C4×D5—22no—
460C2×C4×D5—22no—
461C2×C4×D5—22no—
462C2×Dic10—22no—
463C2×Dic10—22no—
464C2×Dic10—41no—
465C5×C4⋊C4—22no—
466C5×C4⋊C4—22no—
467C5×C4⋊C4—22no—
468C5×C4⋊C4—41no—
469C5×C4⋊C4—41no—
470C5×C22⋊C4—22no—
471C5×C22⋊C4—22no—
472C5×C22⋊C4—22no—
473C5×C22⋊C4—22no—
474C5×C22⋊C4—22no—
475C5×C22⋊C4—22no—
476C5×C22⋊C4—41no—
477C5×C22⋊C4—41no—
478C42×C5—22no—
479C42×C5—22no—
480C42×C5—22no—
481C42×C5—22no—
482C42×C5—22no—
483C42×C5—22no—
484C42×C5—22no—
485C22⋊Dic5—22no—
486C22⋊Dic5—22no—
487C22⋊Dic5—22no—
488C22⋊Dic5—22no—
489C22⋊Dic5—22no—
490C22⋊Dic5—22no—
491C22⋊Dic5—41no—
492C22⋊Dic5#4114yes—
493#685—22no—
494#685—22no—
495#685—22no—
496#685—22no—
497#685—22no—
498#685—22no—
499#685—22no—
500#685—41no—
501#685—41no—
502#685—41no—
503#685—41no—
504#685—41no—
505C4⋊Dic5—22no—
506C4⋊Dic5—22no—
507C4⋊Dic5—22no—
508C4⋊Dic5—22no—
509C4⋊Dic5—41no—
510#683—22no—
511#683—22no—
512#683—22no—
513#683—22no—
514#683—22no—
515#683—22no—
516#683—22no—
517#683—22no—
518#683—22no—
519#683—22no—
520#683—22no—
521#683—41no—
522#683—41no—
523#683—41no—
524#683—41no—
525#683—41no—
526#683—41no—
527#683—41no—
528C4×Dic5—22no—
529C4×Dic5—22no—
530C4×Dic5—22no—
531C4×Dic5—22no—
532C4×Dic5—22no—
533C4×Dic5—22no—
534C4×Dic5—22no—
535C4×Dic5—22no—
536C4×Dic5—22no—
537C4×Dic5—22no—
538C4×Dic5—22no—
539C4×Dic5—22no—
540C4×Dic5—22no—
541C4×Dic5—41no—
542C4×Dic5—41no—
543C4×Dic5#4114yes—
544C4×Dic5#4114yes—
545C2×#123—51no—
546C2×#123C2×D511yescharacteristic
547C2×C22⋊Q8—51no—
548C2×#121—51no—
549C2×C4×Q8—51no—
550C2×C4×D4—51no—
551C2×C4×D4—51no—
552C2×C4×D4—51no—
553C2×C4×D4—51no—
554C2×C4×D4C2×D511yescharacteristic
555C2×#117—51no—
556C22×C42—51no—
557C22×C42—51no—
558C22×C42—51no—
559C22×C42C2×D511yescharacteristic
560#401—51no—
561#401—51no—
562#400—51no—
563#400—51no—
564#400—51no—
565#400—51no—
566#400—51no—
567#400—51no—
568#400—51no—
569#400—51no—
570#400—51no—
571#400—51no—
572#400—51no—
573#400—51no—
574#398—51no—
575#398—51no—
576#398—51no—
577#398—51no—
578#397—51no—
579#397—51no—
580#397—51no—
581#397—51no—
582#397—51no—
583#397—51no—
584#397—51no—
585#397—51no—
586#396—51no—
587#396—51no—
588#394—51no—
589#394—51no—
590#393—51no—
591#393—51no—
592#391—51no—
593#391—51no—
594#391—51no—
595#390—51no—
596#389—51no—
597#389—51no—
598#389—51no—
599#389—51no—
600#388—51no—
601#388—51no—
602#388—51no—
603#388—51no—
604#388—51no—
605#388—51no—
606#388—51no—
607#388—51no—
608#388—51no—
609#388—51no—
610#388—51no—
611#388—51no—
612#388C2×D511yescharacteristic
613#388C2×D511yescharacteristic
614#387—51no—
615#387—51no—
616#387—51no—
617#387—51no—
618#387—51no—
619#387—51no—
620#387—51no—
621#387—51no—
622#387—51no—
623#387—51no—
624#387—51no—
625#387—51no—
626#387—51no—
627#387—51no—
628#387—51no—
629#387—51no—
630#387C2×D511yescharacteristic
631#387C2×D511yescharacteristic
632#386—51no—
633#386—51no—
634#386—51no—
635#386—51no—
636#386—51no—
637#386—51no—
638#386—51no—
639#386C2×D511yescharacteristic
640#385—51no—
641#385—51no—
642#385—51no—
643#385—51no—
644#385—51no—
645#385—51no—
646#385—51no—
647#385C2×D511yescharacteristic
648#383—51no—
649#383—51no—
650#382—51no—
651#382—51no—
652#381—51no—
653#381—51no—
654#381—51no—
655#381C2×D511yescharacteristic
656#380—51no—
657#380—51no—
658#380—51no—
659#380—51no—
660C4×C4⋊C4—51no—
661C4×C4⋊C4—51no—
662C4×C4⋊C4—51no—
663C4×C4⋊C4—51no—
664C4×C4⋊C4—51no—
665C4×C4⋊C4—51no—
666C4×C4⋊C4—51no—
667C4×C4⋊C4—51no—
668C4×C4⋊C4—51no—
669C4×C4⋊C4—51no—
670C4×C4⋊C4C2×D511yescharacteristic
671C4×C4⋊C4C2×D511yescharacteristic
672C4×C22⋊C4—51no—
673C4×C22⋊C4—51no—
674C4×C22⋊C4—51no—
675C4×C22⋊C4—51no—
676C4×C22⋊C4—51no—
677C4×C22⋊C4—51no—
678C4×C22⋊C4—51no—
679C4×C22⋊C4—51no—
680C4×C22⋊C4—51no—
681C4×C22⋊C4—51no—
682C4×C22⋊C4—51no—
683C4×C22⋊C4C2×D511yescharacteristic
684C4×C22⋊C4C2×D511yescharacteristic
685C4×C22⋊C4C2×D511yescharacteristic
686#376—51no—
687#376—51no—
688#376—51no—
689#376—51no—
690#376—51no—
691#376—51no—
692#376—51no—
693#376—51no—
694#376—51no—
695C2×#95—51no—
696C2×#95—51no—
697C2×#95—51no—
698C2×#95—51no—
699C43—51no—
700C23×C5—21no—
701C23×C5—21no—
702C23×C5—21no—
703C23×C5—21no—
704C23×C5—21no—
705C23×C5—21no—
706C23×C5—21no—
707C23×C5—21no—
708C23×C5—21no—
709C23×C5—21no—
710C23×C5C2×#4112yes—
711C23×C5C2×#4112yes—
712C23×C5C2×#4112yes—
713C23×C5C2×#4112yes—
714C23×C5C2511yescharacteristic
715C22×D5—21no—
716C22×D5—21no—
717C22×D5—21no—
718C22×D5—21no—
719C22×D5—21no—
720C22×D5—21no—
721C22×D5—21no—
722C5×D4—28no—
723C2×C4×C5—21no—
724C2×C4×C5—21no—
725C2×C4×C5—21no—
726C2×C4×C5—21no—
727C2×C4×C5—28no—
728C2×C4×C5—21no—
729C2×C4×C5—21no—
730C2×C4×C5—21no—
731C2×C4×C5—21no—
732C2×C4×C5—21no—
733C2×C4×C5—21no—
734C2×C4×C5—21no—
735C2×C4×C5—21no—
736C2×C4×C5—21no—
737C2×C4×C5—21no—
738C2×C4×C5—21no—
739C2×C4×C5—21no—
740C2×C4×C5—21no—
741C2×C4×C5—21no—
742C2×C4×C5—21no—
743C2×C4×C5—21no—
744C2×C4×C5—21no—
745C2×C4×C5—21no—
746C2×C4×C5—21no—
747C2×C4×C5—21no—
748C2×C4×C5—21no—
749C2×C4×C5—21no—
750C2×C4×C5—21no—
751C2×C4×C5—21no—
752C2×C4×C5—21no—
753C2×C4×C5—21no—
754C2×C4×C5—21no—
755C2×C4×C5—21no—
756C2×C4×C5—21no—
757C2×C4×C5—21no—
758C2×C4×C5—44no—
759C2×C4×C5—44no—
760C2×C4×C5—44no—
761C2×C4×C5C2×#4112yes—
762C2×C4×C5C2×#4112yes—
763C2×C4×C5C2×#4112yes—
764C2×C4×C5C2×#4112yes—
765C2×C4×C5C2×#4112yes—
766C22⋊D5—44no—
767C22⋊D5—44no—
768C2×Dic5—21no—
769C2×Dic5—21no—
770C2×Dic5—21no—
771C2×Dic5—21no—
772C2×Dic5—21no—
773C2×Dic5—21no—
774C2×Dic5—21no—
775C2×Dic5—21no—
776C2×Dic5—21no—
777C2×Dic5—21no—
778C2×Dic5—21no—
779C2×Dic5—21no—
780C2×Dic5—21no—
781C2×Dic5—21no—
782C2×Dic5—21no—
783C2×Dic5—21no—
784C2×Dic5—21no—
785C2×Dic5—21no—
786C2×Dic5—21no—
787C2×Dic5—21no—
788C2×Dic5—21no—
789C2×Dic5—21no—
790C2×Dic5—21no—
791C2×Dic5—21no—
792C2×Dic5—21no—
793C2×Dic5—21no—
794C2×Dic5—21no—
795C2×Dic5—21no—
796C2×Dic5—21no—
797C2×Dic5—21no—
798C2×Dic5—21no—
799C2×Dic5—21no—
800C2×Dic5—21no—
801C2×Dic5—21no—
802C2×Dic5—21no—
803C2×Dic5—21no—
804C2×Dic5—21no—
805C2×Dic5—21no—
806C2×Dic5—21no—
807C2×Dic5—44no—
808C2×Dic5—44no—
809C2×Dic5—44no—
810C2×Dic5—44no—
811C2×Dic5—44no—
812C2×Dic5—44no—
813C2×Dic5C2×#4112yes—
814C2×Dic5C2×#4112yes—
815C2×Dic5C2×#4112yes—
816C2×Dic5C2×#4112yes—
817C2×Dic5C2×#4112yes—
818C2×Dic5C2×#4112yes—
819C4×D5—44no—
820Dic10—44no—
821C22×Q8—51no—
822C22×D4—51no—
823C22×D4—51no—
824C22×D4C22×D511yescharacteristic
825C23×C4—51no—
826C23×C4—51no—
827C23×C4—51no—
828C23×C4—51no—
829C23×C4—51no—
830C23×C4—51no—
831C23×C4—51no—
832C23×C4C22×D511yescharacteristic
833C23×C4C22×D511yescharacteristic
834C23×C4C22×D511yescharacteristic
835C23×C4C22×D511yescharacteristic
836#123—24no—
837#123—104no—
838C22⋊Q8—104no—
839#121—104no—
840C4×Q8—104no—
841C4×D4—24no—
842C4×D4—104no—
843C4×D4—104no—
844C4×D4—104no—
845C4×D4—104no—
846#117—104no—
847C2×C4⋊C4—51no—
848C2×C4⋊C4—51no—
849C2×C4⋊C4—51no—
850C2×C4⋊C4—51no—
851C2×C4⋊C4—51no—
852C2×C4⋊C4—51no—
853C2×C4⋊C4—51no—
854C2×C4⋊C4—51no—
855C2×C4⋊C4—51no—
856C2×C4⋊C4—51no—
857C2×C4⋊C4—51no—
858C2×C4⋊C4—51no—
859C2×C4⋊C4—51no—
860C2×C4⋊C4—51no—
861C2×C4⋊C4—51no—
862C2×C4⋊C4—51no—
863C2×C4⋊C4—51no—
864C2×C4⋊C4—51no—
865C2×C4⋊C4—51no—
866C2×C4⋊C4—51no—
867C2×C4⋊C4—51no—
868C2×C4⋊C4—51no—
869C2×C4⋊C4—51no—
870C2×C4⋊C4C22×D511yescharacteristic
871C2×C4⋊C4C22×D511yescharacteristic
872C2×C4⋊C4C22×D511yescharacteristic
873C2×C4⋊C4C22×D511yescharacteristic
874C2×C4⋊C4C22×D511yescharacteristic
875C2×C22⋊C4—51no—
876C2×C22⋊C4—51no—
877C2×C22⋊C4—51no—
878C2×C22⋊C4—51no—
879C2×C22⋊C4—51no—
880C2×C22⋊C4—51no—
881C2×C22⋊C4—51no—
882C2×C22⋊C4—51no—
883C2×C22⋊C4—51no—
884C2×C22⋊C4—51no—
885C2×C22⋊C4—51no—
886C2×C22⋊C4—51no—
887C2×C22⋊C4—51no—
888C2×C22⋊C4—51no—
889C2×C22⋊C4—51no—
890C2×C22⋊C4—51no—
891C2×C22⋊C4—51no—
892C2×C22⋊C4—51no—
893C2×C22⋊C4—51no—
894C2×C22⋊C4—51no—
895C2×C22⋊C4C22×D511yescharacteristic
896C2×C22⋊C4C22×D511yescharacteristic
897C2×C22⋊C4C22×D511yescharacteristic
898C2×C22⋊C4C22×D511yescharacteristic
899C2×C22⋊C4C22×D511yescharacteristic
900C2×C22⋊C4C22×D511yescharacteristic
901C2×C22⋊C4C22×D511yescharacteristic
902C2×C22⋊C4C22×D511yescharacteristic
903C2×C42—24no—
904C2×C42—51no—
905C2×C42—51no—
906C2×C42—51no—
907C2×C42—51no—
908C2×C42—51no—
909C2×C42—51no—
910C2×C42—51no—
911C2×C42—51no—
912C2×C42—51no—
913C2×C42—51no—
914C2×C42—51no—
915C2×C42—51no—
916C2×C42—51no—
917C2×C42—51no—
918C2×C42—51no—
919C2×C42—51no—
920C2×C42—51no—
921C2×C42—104no—
922C2×C42—104no—
923C2×C42—104no—
924C2×C42C22×D511yescharacteristic
925C2×C42C22×D511yescharacteristic
926C2×C42C22×D511yescharacteristic
927C2×C42C22×D511yescharacteristic
928C2×C42C22×D511yescharacteristic
929C2×C42C22×D511yescharacteristic
930C2×C42C22×D511yescharacteristic
931#95—51no—
932#95—51no—
933#95—51no—
934#95—51no—
935#95—51no—
936#95—51no—
937#95—51no—
938#95—51no—
939#95—51no—
940#95—51no—
941#95—51no—
942#95—51no—
943#95—51no—
944#95—51no—
945#95—51no—
946#95—51no—
947#95—51no—
948#95—51no—
949#95—51no—
950#95—51no—
951#95—51no—
952#95—51no—
953#95—51no—
954#95—51no—
955#95—51no—
956#95—51no—
957#95—51no—
958#95—51no—
959#95—51no—
960#95—51no—
961#95—51no—
962#95—51no—
963#95—51no—
964#95—51no—
965#95—51no—
966#95—51no—
967#95—51no—
968#95—51no—
969#95—51no—
970#95—51no—
971#95—51no—
972#95—51no—
973#95—51no—
974#95—51no—
975#95—51no—
976#95—51no—
977#95—51no—
978#95—51no—
979#95—51no—
980#95—51no—
981#95C22×D511yescharacteristic
982#95C22×D511yescharacteristic
983#95C22×D511yescharacteristic
984#95C22×D511yescharacteristic
985#95C22×D511yescharacteristic
986#95C22×D511yescharacteristic
987#95C22×D511yescharacteristic
988#95C22×D511yescharacteristic
989#95C22×D511yescharacteristic
990#95C22×D511yescharacteristic
991C22×C5—22no—
992C22×C5—22no—
993C22×C5—22no—
994C22×C5—22no—
995C22×C5—22no—
996C22×C5—22no—
997C22×C5—22no—
998C22×C5—22no—
999C22×C5—22no—
1000C22×C5—41no—
1001C22×C5—41no—
1002C22×C5—41no—
1003C22×C5—41no—
1004C22×C5#52914yes—
1005C22×C5C22×#4111yescharacteristic
1006C22×C5C22×#4111yescharacteristic
1007C22×C5C22×#4111yescharacteristic
1008C22×C5C22×#4111yescharacteristic
1009C22×C5C22×#4111yescharacteristic
1010C22×C5#58511yescharacteristic
1011C22×C5#58511yescharacteristic
1012C2×D5—41no—
1013C2×D5—41no—
1014C2×D5—41no—
1015C2×D5—41no—
1016C2×D5—41no—
1017C2×D5—41no—
1018C2×D5—41no—
1019C4×C5—22no—
1020C4×C5—22no—
1021C4×C5—41no—
1022C4×C5—41no—
1023C4×C5—41no—
1024C4×C5—41no—
1025C4×C5—41no—
1026C4×C5—41no—
1027C4×C5—41no—
1028C4×C5—41no—
1029C4×C5—41no—
1030C4×C5—41no—
1031C4×C5#52914yes—
1032Dic5—22no—
1033Dic5—22no—
1034Dic5—22no—
1035Dic5—22no—
1036Dic5—22no—
1037Dic5—22no—
1038Dic5—41no—
1039Dic5—41no—
1040Dic5—41no—
1041Dic5—41no—
1042Dic5—41no—
1043Dic5—41no—
1044Dic5—41no—
1045Dic5—41no—
1046Dic5—41no—
1047C24—51no—
1048C24C23×D511yescharacteristic
1049C24C23×D511yescharacteristic
1050C2×Q8—102no—
1051C2×Q8—102no—
1052C2×Q8—201no—
1053C2×D4—22no—
1054C2×D4—22no—
1055C2×D4—102no—
1056C2×D4—102no—
1057C2×D4—102no—
1058C2×D4—102no—
1059C2×D4—102no—
1060C2×D4—201no—
1061C2×D4#70914yes—
1062C22×C4—22no—
1063C22×C4—22no—
1064C22×C4—22no—
1065C22×C4—22no—
1066C22×C4—22no—
1067C22×C4—22no—
1068C22×C4—22no—
1069C22×C4—22no—
1070C22×C4—22no—
1071C22×C4—41no—
1072C22×C4—41no—
1073C22×C4—51no—
1074C22×C4—51no—
1075C22×C4—51no—
1076C22×C4—51no—
1077C22×C4—51no—
1078C22×C4—51no—
1079C22×C4—51no—
1080C22×C4—51no—
1081C22×C4—51no—
1082C22×C4—51no—
1083C22×C4—51no—
1084C22×C4—51no—
1085C22×C4—51no—
1086C22×C4—51no—
1087C22×C4—51no—
1088C22×C4—102no—
1089C22×C4—102no—
1090C22×C4—102no—
1091C22×C4—102no—
1092C22×C4—102no—
1093C22×C4—102no—
1094C22×C4—102no—
1095C22×C4—102no—
1096C22×C4—102no—
1097C22×C4—102no—
1098C22×C4—102no—
1099C22×C4—102no—
1100C22×C4—102no—
1101C22×C4—102no—
1102C22×C4—102no—
1103C22×C4—201no—
1104C22×C4—201no—
1105C22×C4—201no—
1106C22×C4—201no—
1107C22×C4—201no—
1108C22×C4—201no—
1109C22×C4#71114yes—
1110C22×C4C23×D511yescharacteristic
1111C22×C4C23×D511yescharacteristic
1112C22×C4C23×D511yescharacteristic
1113C22×C4C23×D511yescharacteristic
1114C22×C4C23×D511yescharacteristic
1115C22×C4C23×D511yescharacteristic
1116C22×C4C23×D511yescharacteristic
1117C22×C4C23×D511yescharacteristic
1118C22×C4C23×D511yescharacteristic
1119C22×C4C23×D511yescharacteristic
1120C22×C4C23×D511yescharacteristic
1121C22×C4C23×D511yescharacteristic
1122C22×C4C23×D511yescharacteristic
1123C4⋊C4—22no—
1124C4⋊C4—22no—
1125C4⋊C4—22no—
1126C4⋊C4—41no—
1127C4⋊C4—41no—
1128C4⋊C4—102no—
1129C4⋊C4—102no—
1130C4⋊C4—102no—
1131C4⋊C4—102no—
1132C4⋊C4—102no—
1133C4⋊C4—102no—
1134C4⋊C4—102no—
1135C4⋊C4—102no—
1136C4⋊C4—102no—
1137C4⋊C4—102no—
1138C4⋊C4—102no—
1139C4⋊C4—102no—
1140C4⋊C4—102no—
1141C4⋊C4—102no—
1142C4⋊C4—102no—
1143C4⋊C4—201no—
1144C4⋊C4—201no—
1145C4⋊C4—201no—
1146C4⋊C4—201no—
1147C4⋊C4—201no—
1148C4⋊C4—201no—
1149C4⋊C4—201no—
1150C4⋊C4—201no—
1151C22⋊C4—22no—
1152C22⋊C4—22no—
1153C22⋊C4—22no—
1154C22⋊C4—22no—
1155C22⋊C4—22no—
1156C22⋊C4—22no—
1157C22⋊C4—41no—
1158C22⋊C4—41no—
1159C22⋊C4—54no—
1160C22⋊C4—102no—
1161C22⋊C4—102no—
1162C22⋊C4—102no—
1163C22⋊C4—102no—
1164C22⋊C4—102no—
1165C22⋊C4—102no—
1166C22⋊C4—102no—
1167C22⋊C4—102no—
1168C22⋊C4—102no—
1169C22⋊C4—102no—
1170C22⋊C4—102no—
1171C22⋊C4—102no—
1172C22⋊C4—102no—
1173C22⋊C4—201no—
1174C22⋊C4—201no—
1175C22⋊C4—201no—
1176C22⋊C4—201no—
1177C22⋊C4—201no—
1178C22⋊C4—201no—
1179C42—22no—
1180C42—22no—
1181C42—22no—
1182C42—22no—
1183C42—22no—
1184C42—22no—
1185C42—22no—
1186C42—54no—
1187C42—54no—
1188C42—102no—
1189C42—102no—
1190C42—102no—
1191C42—102no—
1192C42—102no—
1193C42—102no—
1194C42—102no—
1195C42—102no—
1196C42—102no—
1197C42—102no—
1198C42—102no—
1199C42—102no—
1200C42—102no—
1201C42—201no—
1202C42—201no—
1203C2×C5—24no—
1204C2×C5—42no—
1205C2×C5C2×#52911yescharacteristic
1206C2×C5C2×#52911yescharacteristic
1207C2×C5#345511yescharacteristic
1208C2×C5#347511yescharacteristic
1209C2×C5#347511yescharacteristic
1210C2×C5#347511yescharacteristic
1211C2×C5#347511yescharacteristic
1212D5—81no—
1213C23—21no—
1214C23—21no—
1215C23—21no—
1216C23—21no—
1217C23—21no—
1218C23—21no—
1219C23—21no—
1220C23—21no—
1221C23—21no—
1222C23—21no—
1223C23—101no—
1224C23—101no—
1225C23—101no—
1226C23—101no—
1227C23—101no—
1228C23—101no—
1229C23—101no—
1230C23C2×#70912yes—
1231C23C2×#70912yes—
1232C23C2×#71112yes—
1233C23D5×#4112yes—
1234C23C24×D511yescharacteristic
1235Q8—204no—
1236D4—28no—
1237D4—204no—
1238D4—204no—
1239C2×C4—21no—
1240C2×C4—21no—
1241C2×C4—21no—
1242C2×C4—21no—
1243C2×C4—28no—
1244C2×C4—21no—
1245C2×C4—21no—
1246C2×C4—21no—
1247C2×C4—21no—
1248C2×C4—21no—
1249C2×C4—21no—
1250C2×C4—21no—
1251C2×C4—21no—
1252C2×C4—21no—
1253C2×C4—21no—
1254C2×C4—21no—
1255C2×C4—21no—
1256C2×C4—21no—
1257C2×C4—21no—
1258C2×C4—21no—
1259C2×C4—21no—
1260C2×C4—21no—
1261C2×C4—21no—
1262C2×C4—21no—
1263C2×C4—21no—
1264C2×C4—21no—
1265C2×C4—21no—
1266C2×C4—21no—
1267C2×C4—21no—
1268C2×C4—21no—
1269C2×C4—21no—
1270C2×C4—21no—
1271C2×C4—21no—
1272C2×C4—21no—
1273C2×C4—21no—
1274C2×C4—44no—
1275C2×C4—44no—
1276C2×C4—44no—
1277C2×C4—52no—
1278C2×C4—52no—
1279C2×C4—52no—
1280C2×C4—52no—
1281C2×C4—52no—
1282C2×C4—52no—
1283C2×C4—101no—
1284C2×C4—101no—
1285C2×C4—101no—
1286C2×C4—101no—
1287C2×C4—101no—
1288C2×C4—101no—
1289C2×C4—101no—
1290C2×C4—101no—
1291C2×C4—101no—
1292C2×C4—101no—
1293C2×C4—101no—
1294C2×C4—101no—
1295C2×C4—101no—
1296C2×C4—101no—
1297C2×C4—101no—
1298C2×C4—101no—
1299C2×C4—101no—
1300C2×C4—101no—
1301C2×C4—101no—
1302C2×C4—101no—
1303C2×C4—101no—
1304C2×C4—101no—
1305C2×C4—101no—
1306C2×C4—101no—
1307C2×C4—101no—
1308C2×C4—101no—
1309C2×C4—101no—
1310C2×C4—101no—
1311C2×C4—101no—
1312C2×C4—101no—
1313C2×C4—101no—
1314C2×C4—101no—
1315C2×C4—101no—
1316C2×C4—101no—
1317C2×C4—101no—
1318C2×C4—101no—
1319C2×C4—101no—
1320C2×C4—101no—
1321C2×C4—101no—
1322C2×C4—204no—
1323C2×C4—204no—
1324C2×C4—204no—
1325C2×C4—204no—
1326C2×C4—204no—
1327C2×C4—204no—
1328C2×C4—204no—
1329C2×C4C2×#70912yes—
1330C2×C4C2×#71112yes—
1331C2×C4C2×#71112yes—
1332C2×C4D5×#4112yes—
1333C2×C4D5×#4112yes—
1334C5#3481111yescharacteristic, complemented, Sylow
1335C22—22no—
1336C22—22no—
1337C22—22no—
1338C22—22no—
1339C22—22no—
1340C22—22no—
1341C22—22no—
1342C22—22no—
1343C22—22no—
1344C22—41no—
1345C22—41no—
1346C22—41no—
1347C22—41no—
1348C22—201no—
1349C22—201no—
1350C22—201no—
1351C22—201no—
1352C22—201no—
1353C22—201no—
1354C22—201no—
1355C22#6587214yes—
1356C22C22×#70911yescharacteristic
1357C22C22×#71111yescharacteristic
1358C22C2×D5×#4111yescharacteristic
1359C22C2×D5×#4111yescharacteristic
1360C22C2×D5×#4111yescharacteristic
1361C22#6628311yescharacteristic
1362C22#6628311yescharacteristic
1363C4—22no—
1364C4—22no—
1365C4—41no—
1366C4—41no—
1367C4—41no—
1368C4—41no—
1369C4—41no—
1370C4—41no—
1371C4—41no—
1372C4—41no—
1373C4—41no—
1374C4—41no—
1375C4—102no—
1376C4—102no—
1377C4—102no—
1378C4—102no—
1379C4—102no—
1380C4—102no—
1381C4—201no—
1382C4—201no—
1383C4—201no—
1384C4—201no—
1385C4—201no—
1386C4—201no—
1387C4—201no—
1388C4—201no—
1389C4—201no—
1390C4#6598314yes—
1391C2—24no—
1392C2—42no—
1393C2—401no—
1394C2C2×#6587211yescharacteristic
1395C2#1061774211yescharacteristic
1396C2#1061774211yescharacteristic
1397C2C2×#6598311yescharacteristic
1398C2#1061792011yescharacteristic
1399C2#1061805111yescharacteristic
1400C2#1061805111yescharacteristic
subgroupG/H
centerC22×C4C23×D5
commutator, socle, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC4×C5×#123C2
prime radicalC2×#4085C22
hypercenterC4×#123D5
hypocenterC5#34811
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C22×C4 ◁ C4×#123

Complements

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

NH ≅ G/Ntype
1. C4×C5×#123C2semidirect
3. #10614575C2semidirect
5. C4×D4×Dic5C2semidirect
6. C4×#4075C2semidirect
7. C2×#65221C2semidirect
8. #10607316C2semidirect
9. #10607314C2semidirect
10. #10607307C2semidirect
11. #10607305C2semidirect
12. #10606803C2semidirect
13. #10606799C2semidirect
14. #10606796C2semidirect
15. #10606792C2semidirect
16. #10606443C2semidirect
18. #10606196C2semidirect
19. #10606194C2semidirect
20. #10605809C2semidirect
21. #10605807C2semidirect
22. #10605510C2semidirect
23. #10605401C2semidirect
24. #10605351C2semidirect
25. #10605350C2semidirect
26. #10605213C2semidirect
27. #10605212C2semidirect
28. C4×#4024C2semidirect
29. #10605169C2semidirect
30. #10605169C2semidirect
31. #10605168C2semidirect
380. C4×#123D5semidirect
1334. C5#34811semidirect

Maximal subgroups

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

subgroupindex
C4×C5×#1232
#106145782
#106145752
C4×#40852
C4×D4×Dic52
C4×#40752
C2×#652212
#106073162
#106073142
#106073072
#106073052
#106068032
#106067992
#106067962
#106067922
#106064432
#106064372
#106061962
#106061942
#106058092
#106058072
#106055102
#106054012
#106053512
#106053502
#106052132
#106052122
C4×#40242
#106051692
#106051682
#348115