Finite Group Databasebeta

← #12272496

Subgroups — #12272496

Order 1280.

1766 conjugacy classes of subgroups.

The subgroup lattice has 1398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2593C211yesmaximal, characteristic, complemented
2#10610094C211yesmaximal, characteristic, complemented
3#10609895C211yesmaximal, characteristic, complemented
4#10609695C211yesmaximal, characteristic, complemented
5#10609509C211yesmaximal, characteristic, complemented
6#10608857C211yesmaximal, characteristic
7#10608855C211yesmaximal, characteristic
8#10608654C211yesmaximal, characteristic, complemented
9#10608653C211yesmaximal, characteristic, complemented
10#10608097C211yesmaximal, characteristic, complemented
11#10608022C211yesmaximal, characteristic
12#10607690C211yesmaximal, characteristic, complemented
13#10607690C211yesmaximal, characteristic, complemented
14#10607689C211yesmaximal, characteristic, complemented
15#10607689C211yesmaximal, characteristic, complemented
16#10607559C211yesmaximal, characteristic, complemented
17#10607559C211yesmaximal, characteristic, complemented
18#10607339C211yesmaximal, characteristic, complemented
19#10607338C211yesmaximal, characteristic, complemented
20#10607337C211yesmaximal, characteristic, complemented
21#10607336C211yesmaximal, characteristic, complemented
22#10607304C211yesmaximal, characteristic, complemented
23#10607303C211yesmaximal, characteristic, complemented
24#10607255C211yesmaximal, characteristic, complemented
25#10607254C211yesmaximal, characteristic, complemented
26#10607188C211yesmaximal, characteristic, complemented
27#10607188C211yesmaximal, characteristic, complemented
28C4×#4042C211yesmaximal, characteristic, complemented
29C4×D5×C4⋊C4C211yesmaximal, characteristic, complemented
30#10605460C211yesmaximal, characteristic, complemented
31#10605459C211yesmaximal, characteristic, complemented
32C2×#4084C2211yescharacteristic
33C2×D4×Dic5C2211yescharacteristic
34C2×#4042C2211yescharacteristic
35C2×D5×C4⋊C4C2211yescharacteristic
36C2×D5×C4⋊C4C2211yescharacteristic
37C2×#4029C2211yescharacteristic
38C2×#4029C2211yescharacteristic
39C2×#4027C2211yescharacteristic
40C2×#4027C2211yescharacteristic
41C2×#4025C2211yescharacteristic
42C2×#4025C2211yescharacteristic
43C2×C42×D5C2211yescharacteristic
44C2×C42×D5C2211yescharacteristic
45C2×C42×D5C2211yescharacteristic
46C2×C4×Dic10C2211yescharacteristic
47C5×#400C2211yescharacteristic
48C5×#398C2211yescharacteristic
49C5×#394C2211yescharacteristic
50C5×#394C2211yescharacteristic
51C5×#390C2211yescharacteristic
52C5×#388C2211yescharacteristic
53C5×#388C2211yescharacteristic
54C5×#388C2211yescharacteristic
55C5×#388C2211yescharacteristic
56C5×#388C2211yescharacteristic
57C5×#388C2211yescharacteristic
58C5×#388C2211yescharacteristic
59C5×#388C2211yescharacteristic
60C4×C5×C4⋊C4C2211yescharacteristic
61C4×C5×C4⋊C4C2211yescharacteristic
62#65511C2211yescharacteristic
63#65511C2211yescharacteristic
64#65278C2211yescharacteristic
65#65278C2211yescharacteristic
66#65278C2211yescharacteristic
67#65276C2211yescharacteristic
68#65275C2211yescharacteristic
69#65275C2211yescharacteristic
70#65273C2211yescharacteristic
71#65273C2211yescharacteristic
72#65273C2211yescharacteristic
73#65272C2211yescharacteristic
74#65272C2211yescharacteristic
75#65270C2211yescharacteristic
76#65270C2211yescharacteristic
77#65270C2211yescharacteristic
78#65270C2211yescharacteristic
79#65270C2211yescharacteristic
80#65268C2211yescharacteristic
81#65266C2211yescharacteristic
82#65266C2211yescharacteristic
83C4⋊C4×Dic5C2211yescharacteristic
84C4⋊C4×Dic5C2211yescharacteristic
85C4⋊C4×Dic5C2211yescharacteristic
86#65261C2211yescharacteristic
87#65261C2211yescharacteristic
88#65261C2211yescharacteristic
89#65245C2211yescharacteristic
90#65245C2211yescharacteristic
91#65245C2211yescharacteristic
92#65245C2211yescharacteristic
93#65245C2211yescharacteristic
94#65245C2211yescharacteristic
95#65245C2211yescharacteristic
96#65245C2211yescharacteristic
97#65241C2211yescharacteristic
98#65241C2211yescharacteristic
99#65240C2211yescharacteristic
100#65240C2211yescharacteristic
101#65240C2211yescharacteristic
102#65240C2211yescharacteristic
103#65240C2211yescharacteristic
104#65240C2211yescharacteristic
105#65239C2211yescharacteristic
106#65239C2211yescharacteristic
107#65237C2211yescharacteristic
108#65237C2211yescharacteristic
109#65237C2211yescharacteristic
110#65237C2211yescharacteristic
111#65236C2211yescharacteristic
112#65236C2211yescharacteristic
113#65235C2211yescharacteristic
114#65235C2211yescharacteristic
115#65234C2211yescharacteristic
116#65234C2211yescharacteristic
117#65234C2211yescharacteristic
118#65234C2211yescharacteristic
119#65234C2211yescharacteristic
120#65234C2211yescharacteristic
121#65234C2211yescharacteristic
122#65234C2211yescharacteristic
123#65233C2211yescharacteristic
124#65233C2211yescharacteristic
125#65232C2211yescharacteristic
126#65232C2211yescharacteristic
127#65231C2211yescharacteristic
128#65231C2211yescharacteristic
129C22⋊C4×Dic5C2211yescharacteristic
130C22⋊C4×Dic5C2211yescharacteristic
131C4×#685C2211yescharacteristic
132C4×#685C2211yescharacteristic
133C4×C4⋊Dic5C2211yescharacteristic
134#65222C2211yescharacteristic
135#65222C2211yescharacteristic
136#65222C2211yescharacteristic
137#65222C2211yescharacteristic
138#65222C2211yescharacteristic
139#65222C2211yescharacteristic
140C4×#683C2211yescharacteristic
141C4×#683C2211yescharacteristic
142C4×#683C2211yescharacteristic
143C4×#683C2211yescharacteristic
144#65217C2211yescharacteristic
145#65217C2211yescharacteristic
146#65217C2211yescharacteristic
147#64957C2211yescharacteristic
148#64957C2211yescharacteristic
149#64957C2211yescharacteristic
150#64957C2211yescharacteristic
151#64957C2211yescharacteristic
152#64956C2211yescharacteristic
153#64953C2211yescharacteristic
154#64953C2211yescharacteristic
155D5×#95C2211yescharacteristic
156D5×#95C2211yescharacteristic
157#64950C2211yescharacteristic
158#64950C2211yescharacteristic
159#64949C2211yescharacteristic
160#64948C2211yescharacteristic
161#64948C2211yescharacteristic
162#64947C2211yescharacteristic
163#64947C2211yescharacteristic
164#64946C2211yescharacteristic
165#64946C2211yescharacteristic
166#64945C2211yescharacteristic
167#64944C2211yescharacteristic
168#64944C2211yescharacteristic
169#64944C2211yescharacteristic
170#64944C2211yescharacteristic
171#64943C2211yescharacteristic
172#64943C2211yescharacteristic
173#64943C2211yescharacteristic
174#64943C2211yescharacteristic
175#64942C2211yescharacteristic
176#64942C2211yescharacteristic
177#64941C2211yescharacteristic
178#64941C2211yescharacteristic
179#64941C2211yescharacteristic
180#64940C2211yescharacteristic
181#64940C2211yescharacteristic
182#64940C2211yescharacteristic
183#64940C2211yescharacteristic
184#64938C2211yescharacteristic
185#64938C2211yescharacteristic
186#64935C2211yescharacteristic
187#35021—51nomaximal, Sylow
188C22×C5×D4C2311yescharacteristic
189C22×C22⋊D5C2311yescharacteristic
190C22×C22⋊D5C2311yescharacteristic
191C23×Dic5C2311yescharacteristic
192C23×Dic5C2311yescharacteristic
193C22×C4×D5C2311yescharacteristic
194C22×C4×D5C2311yescharacteristic
195C22×C4×D5C2311yescharacteristic
196C22×C4×D5C2311yescharacteristic
197C22×C4×D5C2311yescharacteristic
198C22×C4×D5C2311yescharacteristic
199C22×C4×D5C2311yescharacteristic
200C22×Dic10C2311yescharacteristic
201C2×C5×C4⋊C4C2311yescharacteristic
202C2×C5×C4⋊C4C2311yescharacteristic
203C2×C5×C4⋊C4C2311yescharacteristic
204C2×C5×C4⋊C4C2311yescharacteristic
205C2×C5×C4⋊C4C2311yescharacteristic
206C2×C5×C4⋊C4C2311yescharacteristic
207C2×C5×C4⋊C4C2311yescharacteristic
208C2×C5×C22⋊C4C2311yescharacteristic
209C2×C5×C22⋊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×C5×C22⋊C4C2311yescharacteristic
219C2×C5×C22⋊C4C2311yescharacteristic
220C2×C42×C5C2311yescharacteristic
221C2×C42×C5C2311yescharacteristic
222C2×C42×C5C2311yescharacteristic
223C2×C42×C5C2311yescharacteristic
224C2×C42×C5C2311yescharacteristic
225C2×C22⋊Dic5C2311yescharacteristic
226C2×C22⋊Dic5C2311yescharacteristic
227C2×C22⋊Dic5C2311yescharacteristic
228C2×C22⋊Dic5C2311yescharacteristic
229C2×C22⋊Dic5C2311yescharacteristic
230C2×C22⋊Dic5C2311yescharacteristic
231C2×C22⋊Dic5C2311yescharacteristic
232C2×C22⋊Dic5C2311yescharacteristic
233C2×C22⋊Dic5C2311yescharacteristic
234C2×C22⋊Dic5C2311yescharacteristic
235C2×C22⋊Dic5C2311yescharacteristic
236C2×C22⋊Dic5C2311yescharacteristic
237#4084—24no—
238D4×Dic5—42no—
239C2×#685C2311yescharacteristic
240C2×#685C2311yescharacteristic
241C2×#685C2311yescharacteristic
242C2×#685C2311yescharacteristic
243C2×#685C2311yescharacteristic
244C2×#685C2311yescharacteristic
245C2×C4⋊Dic5C2311yescharacteristic
246C2×C4⋊Dic5C2311yescharacteristic
247C2×C4⋊Dic5C2311yescharacteristic
248C2×C4⋊Dic5C2311yescharacteristic
249C2×C4⋊Dic5C2311yescharacteristic
250C2×C4⋊Dic5C2311yescharacteristic
251C2×C4⋊Dic5C2311yescharacteristic
252C2×C4⋊Dic5C2311yescharacteristic
253C2×C4⋊Dic5C2311yescharacteristic
254C2×C4⋊Dic5C2311yescharacteristic
255C2×C4⋊Dic5C2311yescharacteristic
256C2×#683C2311yescharacteristic
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×#683C2311yescharacteristic
276C2×C4×Dic5C2311yescharacteristic
277C2×C4×Dic5C2311yescharacteristic
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
289#4042—24no—
290D5×C4⋊C4—24no—
291D5×C4⋊C4—24no—
292#4029—24no—
293#4029—24no—
294#4027—24no—
295#4027—24no—
296#4025—42no—
297#4025—42no—
298C42×D5—24no—
299C42×D5—42no—
300C42×D5—42no—
301C4×Dic10—42no—
302C5×#95C2311yescharacteristic
303C5×#95C2311yescharacteristic
304C5×#95C2311yescharacteristic
305C5×#95C2311yescharacteristic
306C5×#95C2311yescharacteristic
307C5×#95C2311yescharacteristic
308C5×#95C2311yescharacteristic
309C5×#95C2311yescharacteristic
310C5×#95C2311yescharacteristic
311C5×#95C2311yescharacteristic
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#2853—51no—
359#2853—51no—
360#2852—51no—
361#2852—51no—
362#2646—51no—
363#2639—51no—
364#2627—51no—
365#2618—51no—
366#2593—51no—
367#2593D511yescharacteristic, complemented
368#2585—51no—
369#2585—51no—
370#2574—51no—
371#2574—51no—
372#2573—51no—
373#2573—51no—
374#2525—51no—
375#2525—51no—
376#2524—51no—
377#2524—51no—
378#2469—51no—
379#2469—51no—
380#2468—51no—
381#2468—51no—
382#2322—51no—
383#2322—51no—
384#2318—51no—
385#2318—51no—
386C4×C22⋊Q8—51no—
387C4×#121—51no—
388C2×C4×C4⋊C4—51no—
389C24×C5C2411yescharacteristic
390C24×C5C2411yescharacteristic
391C23×D5C2411yescharacteristic
392C2×C5×D4—22no—
393C2×C5×D4—41no—
394C2×C5×D4—41no—
395C22×C4×C5C2411yescharacteristic
396C22×C4×C5C2411yescharacteristic
397C22×C4×C5C2411yescharacteristic
398C22×C4×C5C2411yescharacteristic
399C22×C4×C5C2411yescharacteristic
400C22×C4×C5C2411yescharacteristic
401C22×C4×C5C2411yescharacteristic
402C22×C4×C5C2411yescharacteristic
403C22×C4×C5C2411yescharacteristic
404C22×C4×C5C2411yescharacteristic
405C22×C4×C5C2411yescharacteristic
406C22×C4×C5C2411yescharacteristic
407C22×C4×C5C2411yescharacteristic
408C2×C22⋊D5—22no—
409C2×C22⋊D5—22no—
410C2×C22⋊D5—22no—
411C2×C22⋊D5—22no—
412C2×C22⋊D5—22no—
413C2×C22⋊D5—22no—
414C22×Dic5—22no—
415C22×Dic5—22no—
416C22×Dic5—41no—
417C22×Dic5—41no—
418C22×Dic5—41no—
419C22×Dic5—41no—
420C22×Dic5C2411yescharacteristic
421C22×Dic5C2411yescharacteristic
422C22×Dic5C2411yescharacteristic
423C22×Dic5C2411yescharacteristic
424C22×Dic5C2411yescharacteristic
425C22×Dic5C2411yescharacteristic
426C22×Dic5C2411yescharacteristic
427C22×Dic5C2411yescharacteristic
428C22×Dic5C2411yescharacteristic
429C22×Dic5C2411yescharacteristic
430C22×Dic5C2411yescharacteristic
431C22×Dic5C2411yescharacteristic
432C22×Dic5C2411yescharacteristic
433C22×Dic5C2411yescharacteristic
434C22×Dic5C2411yescharacteristic
435C2×C4×D5—22no—
436C2×C4×D5—22no—
437C2×C4×D5—22no—
438C2×C4×D5—22no—
439C2×C4×D5—22no—
440C2×C4×D5—22no—
441C2×C4×D5—22no—
442C2×C4×D5—22no—
443C2×C4×D5—41no—
444C2×C4×D5—41no—
445C2×C4×D5—41no—
446C2×C4×D5—41no—
447C2×C4×D5—41no—
448C2×C4×D5—41no—
449C2×C4×D5—41no—
450C2×C4×D5—41no—
451C2×C4×D5—41no—
452C2×C4×D5—41no—
453C2×C4×D5#4114yes—
454C2×C4×D5#4114yes—
455C2×C4×D5#4114yes—
456C2×Dic10—22no—
457C2×Dic10—41no—
458C2×Dic10—41no—
459C5×C4⋊C4—22no—
460C5×C4⋊C4—22no—
461C5×C4⋊C4—22no—
462C5×C4⋊C4—22no—
463C5×C4⋊C4—41no—
464C5×C4⋊C4—41no—
465C5×C4⋊C4—41no—
466C5×C22⋊C4—22no—
467C5×C22⋊C4—22no—
468C5×C22⋊C4—22no—
469C5×C22⋊C4—22no—
470C5×C22⋊C4—22no—
471C5×C22⋊C4—22no—
472C5×C22⋊C4—41no—
473C5×C22⋊C4—41no—
474C5×C22⋊C4—41no—
475C5×C22⋊C4—41no—
476C5×C22⋊C4—41no—
477C5×C22⋊C4—41no—
478C42×C5—22no—
479C42×C5—41no—
480C42×C5—41no—
481C42×C5—41no—
482C42×C5—41no—
483C22⋊Dic5—22no—
484C22⋊Dic5—22no—
485C22⋊Dic5—22no—
486C22⋊Dic5—22no—
487C22⋊Dic5—22no—
488C22⋊Dic5—22no—
489C22⋊Dic5—41no—
490C22⋊Dic5—41no—
491C22⋊Dic5—41no—
492C22⋊Dic5—41no—
493C22⋊Dic5—41no—
494C22⋊Dic5—41no—
495#685—22no—
496#685—22no—
497#685—22no—
498#685—22no—
499#685—22no—
500#685—22no—
501C4⋊Dic5—22no—
502C4⋊Dic5—22no—
503C4⋊Dic5—22no—
504C4⋊Dic5—22no—
505C4⋊Dic5—22no—
506C4⋊Dic5—22no—
507C4⋊Dic5—41no—
508C4⋊Dic5—41no—
509C4⋊Dic5—41no—
510C4⋊Dic5—41no—
511C4⋊Dic5—41no—
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—22no—
522#683—22no—
523#683—22no—
524#683—41no—
525#683—41no—
526#683—41no—
527#683—41no—
528#683—41no—
529#683—41no—
530#683—41no—
531#683—41no—
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—41no—
544C4×Dic5—41no—
545C2×#126—51no—
546C2×#126—51no—
547C2×#123—51no—
548C2×#123—51no—
549C2×C22⋊Q8—51no—
550C2×#121—51no—
551C2×C4×Q8—51no—
552C2×C4×D4—51no—
553C2×C4×D4—51no—
554C2×C4×D4—51no—
555C22×C4⋊C4—51no—
556C22×C4⋊C4—51no—
557C22×C42—51no—
558C22×C42—51no—
559C22×C42—51no—
560#400—51no—
561#400—51no—
562#400—51no—
563#400—51no—
564#400—51no—
565#400—51no—
566#400—51no—
567#400C2×D511yescharacteristic
568#398—51no—
569#398—51no—
570#398—51no—
571#398—51no—
572#398—51no—
573#398—51no—
574#398—51no—
575#398—51no—
576#398—51no—
577#398C2×D511yescharacteristic
578#397—51no—
579#397—51no—
580#396—51no—
581#396—51no—
582#396—51no—
583#396—51no—
584#395—51no—
585#395—51no—
586#394—51no—
587#394—51no—
588#394C2×D511yescharacteristic
589#394C2×D511yescharacteristic
590#393—51no—
591#393—51no—
592#391—51no—
593#390C2×D511yescharacteristic
594#389—51no—
595#389—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#388—51no—
613#388—51no—
614#388—51no—
615#388—51no—
616#388C2×D511yescharacteristic
617#388C2×D511yescharacteristic
618#388C2×D511yescharacteristic
619#388C2×D511yescharacteristic
620#388C2×D511yescharacteristic
621#388C2×D511yescharacteristic
622#388C2×D511yescharacteristic
623#388C2×D511yescharacteristic
624#387—51no—
625#387—51no—
626#387—51no—
627#387—51no—
628#387—51no—
629#387—51no—
630#387—51no—
631#387—51no—
632#387—51no—
633#387—51no—
634#387—51no—
635#387—51no—
636#387—51no—
637#387—51no—
638#387—51no—
639#387—51no—
640#387—51no—
641#387—51no—
642#387—51no—
643#387—51no—
644#387—51no—
645#387—51no—
646#387—51no—
647#387—51no—
648#386—51no—
649#386—51no—
650#386—51no—
651#386—51no—
652#386—51no—
653#386—51no—
654#386—51no—
655#386—51no—
656#385—51no—
657#385—51no—
658#385—51no—
659#385—51no—
660#385—51no—
661#385—51no—
662#385—51no—
663#385—51no—
664#385—51no—
665#385—51no—
666#385—51no—
667#385—51no—
668#383—51no—
669#383—51no—
670#383—51no—
671#383—51no—
672#382—51no—
673#382—51no—
674#381—51no—
675#381—51no—
676#381—51no—
677#381—51no—
678#380—51no—
679#380—51no—
680#380—51no—
681#380—51no—
682C4×C4⋊C4—51no—
683C4×C4⋊C4—51no—
684C4×C4⋊C4—51no—
685C4×C4⋊C4—51no—
686C4×C4⋊C4—51no—
687C4×C4⋊C4—51no—
688C4×C4⋊C4—51no—
689C4×C4⋊C4—51no—
690C4×C4⋊C4—51no—
691C4×C4⋊C4—51no—
692C4×C4⋊C4C2×D511yescharacteristic
693C4×C4⋊C4C2×D511yescharacteristic
694C4×C22⋊C4—51no—
695C4×C22⋊C4—51no—
696C4×C22⋊C4—51no—
697C4×C22⋊C4—51no—
698C2×#95—51no—
699C2×#95—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×C5—21no—
711C23×C5—21no—
712C23×C5—21no—
713C23×C5—21no—
714C23×C5C2511yescharacteristic
715C22×D5—21no—
716C22×D5—21no—
717C22×D5—21no—
718C22×D5—21no—
719C22×D5C2×#4112yes—
720C22×D5C2×#4112yes—
721C22×D5C2×#4112yes—
722C5×D4—44no—
723C2×C4×C5—21no—
724C2×C4×C5—21no—
725C2×C4×C5—21no—
726C2×C4×C5—21no—
727C2×C4×C5—21no—
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×C5C2×#4112yes—
759C2×C4×C5C2×#4112yes—
760C2×C4×C5C2×#4112yes—
761C2×C4×C52−1+412yes—
762C22⋊D5—44no—
763C22⋊D5—44no—
764C2×Dic5—21no—
765C2×Dic5—21no—
766C2×Dic5—21no—
767C2×Dic5—21no—
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—82no—
806C2×Dic5—82no—
807C2×Dic5C2×#4112yes—
808C2×Dic5C2×#4112yes—
809C2×Dic5C2×#4112yes—
810C2×Dic5H(5,𝔽2)12yes—
811C4×D5—28no—
812C4×D5—28no—
813C4×D5—44no—
814C4×D5—44no—
815C4×D5—44no—
816C4×D5—44no—
817C4×D5—44no—
818Dic10—44no—
819C22×Q8—51no—
820C22×D4—51no—
821C22×D4—51no—
822C22×D4C22×D511yescharacteristic
823C23×C4—51no—
824C23×C4—51no—
825C23×C4—51no—
826C23×C4—51no—
827C23×C4—51no—
828C23×C4—51no—
829C23×C4—51no—
830C23×C4—51no—
831C23×C4—51no—
832#126—202no—
833#126—202no—
834#123—104no—
835#123—104no—
836C22⋊Q8—104no—
837#121—104no—
838C4×Q8—202no—
839C4×D4—104no—
840C4×D4—104no—
841C4×D4—202no—
842C2×C4⋊C4—51no—
843C2×C4⋊C4—51no—
844C2×C4⋊C4—51no—
845C2×C4⋊C4—51no—
846C2×C4⋊C4—51no—
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⋊C4—51no—
871C2×C4⋊C4—51no—
872C2×C4⋊C4—51no—
873C2×C4⋊C4—104no—
874C2×C4⋊C4—104no—
875C2×C4⋊C4C22×D511yescharacteristic
876C2×C4⋊C4C22×D511yescharacteristic
877C2×C4⋊C4C22×D511yescharacteristic
878C2×C4⋊C4C22×D511yescharacteristic
879C2×C4⋊C4C22×D511yescharacteristic
880C2×C4⋊C4C22×D511yescharacteristic
881C2×C4⋊C4C22×D511yescharacteristic
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⋊C4—51no—
896C2×C22⋊C4—51no—
897C2×C22⋊C4—51no—
898C2×C22⋊C4—51no—
899C2×C22⋊C4—51no—
900C2×C22⋊C4C22×D511yescharacteristic
901C2×C22⋊C4C22×D511yescharacteristic
902C2×C22⋊C4C22×D511yescharacteristic
903C2×C22⋊C4C22×D511yescharacteristic
904C2×C22⋊C4C22×D511yescharacteristic
905C2×C22⋊C4C22×D511yescharacteristic
906C2×C22⋊C4C22×D511yescharacteristic
907C2×C22⋊C4C22×D511yescharacteristic
908C2×C22⋊C4C22×D511yescharacteristic
909C2×C22⋊C4C22×D511yescharacteristic
910C2×C22⋊C4C22×D511yescharacteristic
911C2×C22⋊C4C22×D511yescharacteristic
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—51no—
922C2×C42—51no—
923C2×C42—51no—
924C2×C42—51no—
925C2×C42—104no—
926C2×C42—202no—
927C2×C42—202no—
928C2×C42C22×D511yescharacteristic
929C2×C42C22×D511yescharacteristic
930C2×C42C22×D511yescharacteristic
931C2×C42C22×D511yescharacteristic
932C2×C42C22×D511yescharacteristic
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#95C22×D511yescharacteristic
980#95C22×D511yescharacteristic
981#95C22×D511yescharacteristic
982#95C22×D511yescharacteristic
983#95C22×D511yescharacteristic
984#95C22×D511yescharacteristic
985#95C22×D511yescharacteristic
986#95C22×D511yescharacteristic
987#95C22×D511yescharacteristic
988#95C22×D511yescharacteristic
989C22×C5—41no—
990C22×C5—41no—
991C22×C5—41no—
992C22×C5—41no—
993C22×C5—41no—
994C22×C5—41no—
995C22×C5—41no—
996C22×C5—41no—
997C22×C5—41no—
998C22×C5—41no—
999C22×C5—41no—
1000C22×C5—41no—
1001C22×C5—41no—
1002C22×C5—41no—
1003C22×C5C22×#4111yescharacteristic
1004C22×C5C22×#4111yescharacteristic
1005C22×C5C22×#4111yescharacteristic
1006C22×C5C2×H(5,𝔽2)11yescharacteristic
1007C22×C5C2×2−1+411yescharacteristic
1008C22×C5#58511yescharacteristic
1009C22×C5#58511yescharacteristic
1010C2×D5—22no—
1011C2×D5—22no—
1012C2×D5—22no—
1013C2×D5—22no—
1014C2×D5—22no—
1015C2×D5—22no—
1016C2×D5#52914yes—
1017C4×C5—22no—
1018C4×C5—22no—
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—
1030Dic5—22no—
1031Dic5—22no—
1032Dic5—22no—
1033Dic5—22no—
1034Dic5—41no—
1035Dic5—41no—
1036Dic5—41no—
1037Dic5—41no—
1038Dic5—41no—
1039Dic5—41no—
1040Dic5—41no—
1041Dic5—41no—
1042Dic5—41no—
1043Dic5—41no—
1044Dic5—41no—
1045C24—51no—
1046C24C23×D511yescharacteristic
1047C24C23×D511yescharacteristic
1048C2×Q8—102no—
1049C2×Q8—201no—
1050C2×Q8—201no—
1051C2×D4—22no—
1052C2×D4—41no—
1053C2×D4—41no—
1054C2×D4—102no—
1055C2×D4—102no—
1056C2×D4—102no—
1057C2×D4—102no—
1058C2×D4—102no—
1059C2×D4—102no—
1060C22×C4—51no—
1061C22×C4—51no—
1062C22×C4—51no—
1063C22×C4—51no—
1064C22×C4—54no—
1065C22×C4—54no—
1066C22×C4—54no—
1067C22×C4—51no—
1068C22×C4—51no—
1069C22×C4—51no—
1070C22×C4—51no—
1071C22×C4—51no—
1072C22×C4—51no—
1073C22×C4—51no—
1074C22×C4—51no—
1075C22×C4—51no—
1076C22×C4—51no—
1077C22×C4—51no—
1078C22×C4—102no—
1079C22×C4—102no—
1080C22×C4—102no—
1081C22×C4—102no—
1082C22×C4—102no—
1083C22×C4—102no—
1084C22×C4—102no—
1085C22×C4—102no—
1086C22×C4—102no—
1087C22×C4—102no—
1088C22×C4—201no—
1089C22×C4—201no—
1090C22×C4—201no—
1091C22×C4—201no—
1092C22×C4—201no—
1093C22×C4—201no—
1094C22×C4—201no—
1095C22×C4—201no—
1096C22×C4—201no—
1097C22×C4—201no—
1098C22×C4—201no—
1099C22×C4—201no—
1100C22×C4—201no—
1101C22×C4—201no—
1102C22×C4C23×D511yescharacteristic
1103C22×C4C23×D511yescharacteristic
1104C22×C4C23×D511yescharacteristic
1105C22×C4C23×D511yescharacteristic
1106C22×C4C23×D511yescharacteristic
1107C22×C4C23×D511yescharacteristic
1108C22×C4C23×D511yescharacteristic
1109C22×C4C23×D511yescharacteristic
1110C22×C4C23×D511yescharacteristic
1111C22×C4C23×D511yescharacteristic
1112C22×C4C23×D511yescharacteristic
1113C22×C4C23×D511yescharacteristic
1114C22×C4C23×D511yescharacteristic
1115C4⋊C4—22no—
1116C4⋊C4—22no—
1117C4⋊C4—22no—
1118C4⋊C4—22no—
1119C4⋊C4—41no—
1120C4⋊C4—41no—
1121C4⋊C4—41no—
1122C4⋊C4—102no—
1123C4⋊C4—102no—
1124C4⋊C4—102no—
1125C4⋊C4—102no—
1126C4⋊C4—102no—
1127C4⋊C4—102no—
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—201no—
1141C4⋊C4—201no—
1142C4⋊C4—201no—
1143C4⋊C4—201no—
1144C4⋊C4—201no—
1145C4⋊C4—201no—
1146C4⋊C4—201no—
1147C4⋊C4—201no—
1148C4⋊C4—201no—
1149C4⋊C4—201no—
1150C4⋊C4—201no—
1151C4⋊C4—201no—
1152C4⋊C4—201no—
1153C22⋊C4—22no—
1154C22⋊C4—22no—
1155C22⋊C4—22no—
1156C22⋊C4—22no—
1157C22⋊C4—22no—
1158C22⋊C4—22no—
1159C22⋊C4—41no—
1160C22⋊C4—41no—
1161C22⋊C4—41no—
1162C22⋊C4—41no—
1163C22⋊C4—41no—
1164C22⋊C4—41no—
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—102no—
1174C22⋊C4—102no—
1175C22⋊C4—102no—
1176C22⋊C4—102no—
1177C22⋊C4—201no—
1178C22⋊C4—201no—
1179C22⋊C4—201no—
1180C22⋊C4—201no—
1181C22⋊C4—201no—
1182C22⋊C4—201no—
1183C42—22no—
1184C42—41no—
1185C42—41no—
1186C42—41no—
1187C42—41no—
1188C42—102no—
1189C42—102no—
1190C42—102no—
1191C42—102no—
1192C42—102no—
1193C42—102no—
1194C42—102no—
1195C42—102no—
1196C42—102no—
1197C42—201no—
1198C42—201no—
1199C42—201no—
1200C42—201no—
1201C2×C5—81no—
1202C2×C5—81no—
1203C2×C5C2×#52911yescharacteristic
1204C2×C5#345911yescharacteristic
1205C2×C5#346111yescharacteristic
1206C2×C5#349211yescharacteristic
1207C2×C5#349311yescharacteristic
1208C2×C5#350511yescharacteristic
1209C2×C5#350711yescharacteristic
1210D5—24no—
1211C23—21no—
1212C23—21no—
1213C23—21no—
1214C23—21no—
1215C23—21no—
1216C23—21no—
1217C23—21no—
1218C23—21no—
1219C23—21no—
1220C23—21no—
1221C23—21no—
1222C23—21no—
1223C23—21no—
1224C23—21no—
1225C23—52no—
1226C23—52no—
1227C23—52no—
1228C23—101no—
1229C23—101no—
1230C23—101no—
1231C23—101no—
1232C23C24×D511yescharacteristic
1233Q8—204no—
1234D4—44no—
1235D4—204no—
1236D4—204no—
1237C2×C4—21no—
1238C2×C4—21no—
1239C2×C4—21no—
1240C2×C4—21no—
1241C2×C4—21no—
1242C2×C4—21no—
1243C2×C4—21no—
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—52no—
1273C2×C4—52no—
1274C2×C4—52no—
1275C2×C4—52no—
1276C2×C4—108no—
1277C2×C4—108no—
1278C2×C4—101no—
1279C2×C4—101no—
1280C2×C4—101no—
1281C2×C4—101no—
1282C2×C4—101no—
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—204no—
1320C2×C4—204no—
1321C2×C4—204no—
1322C2×C4—204no—
1323C2×C4—204no—
1324C2×C4—402no—
1325C2×C4—402no—
1326C2×C4D5×#4112yes—
1327C2×C4D5×#4112yes—
1328C2×C4D5×#4112yes—
1329C2×C4#415012yes—
1330C5#3502111yescharacteristic, complemented, Sylow
1331C22—41no—
1332C22—41no—
1333C22—41no—
1334C22—41no—
1335C22—41no—
1336C22—41no—
1337C22—41no—
1338C22—41no—
1339C22—41no—
1340C22—41no—
1341C22—41no—
1342C22—41no—
1343C22—41no—
1344C22—41no—
1345C22—54no—
1346C22—102no—
1347C22—102no—
1348C22—102no—
1349C22—102no—
1350C22—102no—
1351C22—102no—
1352C22C2×D5×#4111yescharacteristic
1353C22C2×D5×#4111yescharacteristic
1354C22C2×D5×#4111yescharacteristic
1355C22C2×#415011yescharacteristic
1356C22#6628311yescharacteristic
1357C22D5×H(5,𝔽2)11yescharacteristic
1358C22#6628511yescharacteristic
1359C4—22no—
1360C4—22no—
1361C4—22no—
1362C4—22no—
1363C4—41no—
1364C4—41no—
1365C4—41no—
1366C4—41no—
1367C4—41no—
1368C4—41no—
1369C4—41no—
1370C4—41no—
1371C4—41no—
1372C4—102no—
1373C4—102no—
1374C4—102no—
1375C4—102no—
1376C4—201no—
1377C4—201no—
1378C4—201no—
1379C4—201no—
1380C4—201no—
1381C4—201no—
1382C4—201no—
1383C4—201no—
1384C4—201no—
1385C4—201no—
1386C4—201no—
1387C2—81no—
1388C2—81no—
1389C2—104no—
1390C2D5×#52911yescharacteristic
1391C2#1061805011yescharacteristic
1392C2#1061828911yescharacteristic
1393C2#1061881011yescharacteristic
1394C2#1061881311yescharacteristic
1395C2#1061887311yescharacteristic
1396C2#1061896511yescharacteristic
subgroupG/H
center, FrattiniC23C24×D5
commutator, socle, cosocleC23×C5C25
FittingC5×#2593C2
prime radicalC2×#4084C22
hypercenter#2593D5
hypocenterC5#35021
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C23 ◁ #2593

Complements

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

NH ≅ G/Ntype
1. C5×#2593C2semidirect
2. #10610094C2semidirect
3. #10609895C2semidirect
4. #10609695C2semidirect
5. #10609509C2semidirect
8. #10608654C2semidirect
9. #10608653C2semidirect
10. #10608097C2semidirect
12. #10607690C2semidirect
13. #10607690C2semidirect
14. #10607689C2semidirect
15. #10607689C2semidirect
16. #10607559C2semidirect
17. #10607559C2semidirect
18. #10607339C2semidirect
19. #10607338C2semidirect
20. #10607337C2semidirect
21. #10607336C2semidirect
22. #10607304C2semidirect
23. #10607303C2semidirect
24. #10607255C2semidirect
25. #10607254C2semidirect
26. #10607188C2semidirect
27. #10607188C2semidirect
28. C4×#4042C2semidirect
29. C4×D5×C4⋊C4C2semidirect
30. #10605460C2semidirect
31. #10605459C2semidirect
367. #2593D5semidirect
1330. C5#35021semidirect

Maximal subgroups

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

subgroupindex
C5×#25932
#106100942
#106098952
#106096952
#106095092
#106088572
#106088552
#106086542
#106086532
#106080972
#106080222
#106076902
#106076892
#106075592
#106073392
#106073382
#106073372
#106073362
#106073042
#106073032
#106072552
#106072542
#106071882
C4×#40422
C4×D5×C4⋊C42
#106054602
#106054592
#350215