Finite Group Databasebeta

← #12272497

Subgroups — #12272497

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×#2318C211yesmaximal, characteristic, complemented
2#10614057C211yesmaximal, characteristic, complemented
3C4×#4085C211yesmaximal, characteristic
4#10607353C211yesmaximal, characteristic, complemented
5#10607351C211yesmaximal, characteristic, complemented
6#10607303C211yesmaximal, characteristic, complemented
7#10607254C211yesmaximal, characteristic, complemented
8#10606827C211yesmaximal, characteristic, complemented
9#10606826C211yesmaximal, characteristic, complemented
10#10606785C211yesmaximal, characteristic, complemented
11#10606737C211yesmaximal, characteristic, complemented
12#10606602C211yesmaximal, characteristic, complemented
13#10606601C211yesmaximal, characteristic, complemented
14#10606516C211yesmaximal, characteristic
15#10606512C211yesmaximal, characteristic
16#10606319C211yesmaximal, characteristic, complemented
17#10606318C211yesmaximal, characteristic, complemented
18#10606235C211yesmaximal, characteristic, complemented
19#10606233C211yesmaximal, characteristic, complemented
20#10606035C211yesmaximal, characteristic, complemented
21#10606002C211yesmaximal, characteristic, complemented
22#10605920C211yesmaximal, characteristic, complemented
23#10605908C211yesmaximal, characteristic, complemented
24#10605816C211yesmaximal, characteristic, complemented
25#10605803C211yesmaximal, characteristic, complemented
26#10605677C211yesmaximal, characteristic, complemented
27#10605638C211yesmaximal, characteristic, complemented
28#10605177C211yesmaximal, characteristic, complemented
29C4×#4024C211yesmaximal, characteristic, complemented
30#10605098C211yesmaximal, characteristic, complemented
31C2×#64938C211yesmaximal, characteristic, complemented
32C2×C4×C5×D4C2211yescharacteristic
33C2×#4085C2211yescharacteristic
34C2×#4081C2211yescharacteristic
35C2×C4×C22⋊D5C2211yescharacteristic
36C2×C4×C22⋊D5C2211yescharacteristic
37C22×#683C2211yescharacteristic
38C22×#683C2211yescharacteristic
39C22×C4×Dic5C2211yescharacteristic
40C22×C4×Dic5C2211yescharacteristic
41C22×C4×Dic5C2211yescharacteristic
42C2×#4044C2211yescharacteristic
43C2×#4032C2211yescharacteristic
44C2×#4025C2211yescharacteristic
45C2×#4024C2211yescharacteristic
46C2×C4×Dic10C2211yescharacteristic
47C5×#388C2211yescharacteristic
48C5×#388C2211yescharacteristic
49C5×#387C2211yescharacteristic
50C5×#387C2211yescharacteristic
51C5×#386C2211yescharacteristic
52C5×#386C2211yescharacteristic
53C5×#385C2211yescharacteristic
54C5×#385C2211yescharacteristic
55C5×#383C2211yescharacteristic
56C5×#382C2211yescharacteristic
57C5×#381C2211yescharacteristic
58C5×#380C2211yescharacteristic
59C4×C5×C22⋊C4C2211yescharacteristic
60C2×C5×#95C2211yescharacteristic
61#65509C2211yescharacteristic
62#65509C2211yescharacteristic
63#65502C2211yescharacteristic
64#65502C2211yescharacteristic
65#65499C2211yescharacteristic
66#65499C2211yescharacteristic
67#65499C2211yescharacteristic
68#65499C2211yescharacteristic
69C4×C22⋊Dic5C2211yescharacteristic
70C4×C22⋊Dic5C2211yescharacteristic
71C2×#3963C2211yescharacteristic
72#65279C2211yescharacteristic
73#65279C2211yescharacteristic
74#65279C2211yescharacteristic
75#65279C2211yescharacteristic
76#65273C2211yescharacteristic
77#65272C2211yescharacteristic
78#65271C2211yescharacteristic
79#65270C2211yescharacteristic
80#65270C2211yescharacteristic
81#65270C2211yescharacteristic
82#65269C2211yescharacteristic
83#65269C2211yescharacteristic
84#65269C2211yescharacteristic
85#65268C2211yescharacteristic
86#65268C2211yescharacteristic
87#65267C2211yescharacteristic
88#65261C2211yescharacteristic
89#65261C2211yescharacteristic
90#65261C2211yescharacteristic
91#65250C2211yescharacteristic
92#65248C2211yescharacteristic
93#65248C2211yescharacteristic
94#65248C2211yescharacteristic
95#65247C2211yescharacteristic
96#65247C2211yescharacteristic
97#65246C2211yescharacteristic
98#65241C2211yescharacteristic
99#65240C2211yescharacteristic
100#65240C2211yescharacteristic
101#65240C2211yescharacteristic
102#65239C2211yescharacteristic
103#65239C2211yescharacteristic
104#65237C2211yescharacteristic
105#65237C2211yescharacteristic
106#65236C2211yescharacteristic
107#65235C2211yescharacteristic
108#65235C2211yescharacteristic
109#65234C2211yescharacteristic
110#65234C2211yescharacteristic
111#65234C2211yescharacteristic
112#65234C2211yescharacteristic
113#65234C2211yescharacteristic
114#65234C2211yescharacteristic
115#65233C2211yescharacteristic
116#65232C2211yescharacteristic
117#65232C2211yescharacteristic
118#65231C2211yescharacteristic
119#65231C2211yescharacteristic
120#65229C2211yescharacteristic
121#65229C2211yescharacteristic
122C4×#685C2211yescharacteristic
123C4×C4⋊Dic5C2211yescharacteristic
124#65222C2211yescharacteristic
125#65222C2211yescharacteristic
126C4×#683C2211yescharacteristic
127C4×#683C2211yescharacteristic
128C4×#683C2211yescharacteristic
129#65217C2211yescharacteristic
130#65217C2211yescharacteristic
131#64965C2211yescharacteristic
132#64965C2211yescharacteristic
133#64964C2211yescharacteristic
134#64962C2211yescharacteristic
135#64959C2211yescharacteristic
136#64958C2211yescharacteristic
137#64958C2211yescharacteristic
138#64958C2211yescharacteristic
139#64958C2211yescharacteristic
140#64958C2211yescharacteristic
141#64957C2211yescharacteristic
142#64957C2211yescharacteristic
143#64956C2211yescharacteristic
144#64953C2211yescharacteristic
145#64949C2211yescharacteristic
146#64948C2211yescharacteristic
147#64947C2211yescharacteristic
148#64947C2211yescharacteristic
149#64947C2211yescharacteristic
150#64947C2211yescharacteristic
151#64947C2211yescharacteristic
152#64946C2211yescharacteristic
153#64946C2211yescharacteristic
154#64946C2211yescharacteristic
155#64946C2211yescharacteristic
156#64946C2211yescharacteristic
157#64944C2211yescharacteristic
158#64944C2211yescharacteristic
159#64944C2211yescharacteristic
160#64944C2211yescharacteristic
161#64943C2211yescharacteristic
162#64943C2211yescharacteristic
163#64943C2211yescharacteristic
164#64943C2211yescharacteristic
165#64942C2211yescharacteristic
166#64942C2211yescharacteristic
167#64942C2211yescharacteristic
168#64941C2211yescharacteristic
169#64941C2211yescharacteristic
170#64941C2211yescharacteristic
171#64941C2211yescharacteristic
172#64941C2211yescharacteristic
173#64940C2211yescharacteristic
174#64940C2211yescharacteristic
175#64940C2211yescharacteristic
176#64939C2211yescharacteristic
177#64938C2211yescharacteristic
178#64938C2211yescharacteristic
179#64938C2211yescharacteristic
180#64938C2211yescharacteristic
181#64938C2211yescharacteristic
182#64938C2211yescharacteristic
183#64938C2211yescharacteristic
184#64938C2211yescharacteristic
185#64936C2211yescharacteristic
186#64935C2211yescharacteristic
187#35021—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
199C22×C4×D5C2311yescharacteristic
200C22×Dic10C2311yescharacteristic
201C4×C5×D4—24no—
202C2×C5×C4⋊C4C2311yescharacteristic
203C2×C5×C4⋊C4C2311yescharacteristic
204C2×C5×C4⋊C4C2311yescharacteristic
205C2×C5×C4⋊C4C2311yescharacteristic
206C2×C5×C4⋊C4C2311yescharacteristic
207C2×C5×C22⋊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×C42×C5C2311yescharacteristic
216C2×C42×C5C2311yescharacteristic
217C2×C42×C5C2311yescharacteristic
218C2×C22⋊Dic5C2311yescharacteristic
219C2×C22⋊Dic5C2311yescharacteristic
220C2×C22⋊Dic5C2311yescharacteristic
221C2×C22⋊Dic5C2311yescharacteristic
222C2×C22⋊Dic5C2311yescharacteristic
223C2×C22⋊Dic5C2311yescharacteristic
224C2×C22⋊Dic5C2311yescharacteristic
225C2×C22⋊Dic5C2311yescharacteristic
226C2×C22⋊Dic5C2311yescharacteristic
227C2×C22⋊Dic5C2311yescharacteristic
228#4085—24no—
229#4081—24no—
230C4×C22⋊D5—24no—
231C4×C22⋊D5—42no—
232C2×#685C2311yescharacteristic
233C2×#685C2311yescharacteristic
234C2×#685C2311yescharacteristic
235C2×#685C2311yescharacteristic
236C2×#685C2311yescharacteristic
237C2×#685C2311yescharacteristic
238C2×#685C2311yescharacteristic
239C2×#685C2311yescharacteristic
240C2×#685C2311yescharacteristic
241C2×#685C2311yescharacteristic
242C2×#685C2311yescharacteristic
243C2×#685C2311yescharacteristic
244C2×C4⋊Dic5C2311yescharacteristic
245C2×C4⋊Dic5C2311yescharacteristic
246C2×C4⋊Dic5C2311yescharacteristic
247C2×C4⋊Dic5C2311yescharacteristic
248C2×C4⋊Dic5C2311yescharacteristic
249C2×C4⋊Dic5C2311yescharacteristic
250C2×C4⋊Dic5C2311yescharacteristic
251C2×#683—24no—
252C2×#683—24no—
253C2×#683C2311yescharacteristic
254C2×#683C2311yescharacteristic
255C2×#683C2311yescharacteristic
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×#683C2311yescharacteristic
277C2×#683C2311yescharacteristic
278C2×#683C2311yescharacteristic
279C2×C4×Dic5—24no—
280C2×C4×Dic5—42no—
281C2×C4×Dic5—42no—
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
295C2×C4×Dic5C2311yescharacteristic
296C2×C4×Dic5C2311yescharacteristic
297#4044—42no—
298#4032—24no—
299#4025—42no—
300#4024—24no—
301C4×Dic10—42no—
302C5×#95C2311yescharacteristic
303C5×#95C2311yescharacteristic
304C5×#95C2311yescharacteristic
305C5×#95C2311yescharacteristic
306C5×#95C2311yescharacteristic
307C5×#95C2311yescharacteristic
308C5×#95C2311yescharacteristic
309C5×#95C2311yescharacteristic
310C5×#95C2311yescharacteristic
311C5×#95C2311yescharacteristic
312C5×#95C2311yescharacteristic
313C5×#95C2311yescharacteristic
314C5×#95C2311yescharacteristic
315C5×#95C2311yescharacteristic
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#2593—51no—
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#2318D511yescharacteristic, complemented
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—22no—
394C2×C5×D4—22no—
395C22×C4×C5—22no—
396C22×C4×C5—22no—
397C22×C4×C5—22no—
398C22×C4×C5—41no—
399C22×C4×C5—41no—
400C22×C4×C5—41no—
401C22×C4×C5—41no—
402C22×C4×C5—41no—
403C22×C4×C5—41no—
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—41no—
425C2×C22⋊D5—41no—
426C22×Dic5—22no—
427C22×Dic5—22no—
428C22×Dic5—22no—
429C22×Dic5—22no—
430C22×Dic5—22no—
431C22×Dic5—22no—
432C22×Dic5—41no—
433C22×Dic5—41no—
434C22×Dic5—41no—
435C22×Dic5—41no—
436C22×Dic5#4114yes—
437C22×Dic5#4114yes—
438C22×Dic5C2411yescharacteristic
439C22×Dic5C2411yescharacteristic
440C22×Dic5C2411yescharacteristic
441C22×Dic5C2411yescharacteristic
442C22×Dic5C2411yescharacteristic
443C22×Dic5C2411yescharacteristic
444C22×Dic5C2411yescharacteristic
445C22×Dic5C2411yescharacteristic
446C22×Dic5C2411yescharacteristic
447C22×Dic5C2411yescharacteristic
448C22×Dic5C2411yescharacteristic
449C22×Dic5C2411yescharacteristic
450C22×Dic5C2411yescharacteristic
451C22×Dic5C2411yescharacteristic
452C22×Dic5C2411yescharacteristic
453C2×C4×D5—22no—
454C2×C4×D5—41no—
455C2×C4×D5—41no—
456C2×Dic10—22no—
457C2×Dic10—41no—
458C2×Dic10—41no—
459C5×C4⋊C4—22no—
460C5×C4⋊C4—41no—
461C5×C4⋊C4—41no—
462C5×C4⋊C4—41no—
463C5×C4⋊C4—41no—
464C5×C22⋊C4—22no—
465C5×C22⋊C4—22no—
466C5×C22⋊C4—22no—
467C5×C22⋊C4—22no—
468C5×C22⋊C4—41no—
469C5×C22⋊C4—41no—
470C5×C22⋊C4—41no—
471C5×C22⋊C4—41no—
472C42×C5—22no—
473C42×C5—41no—
474C42×C5—41no—
475C22⋊Dic5—22no—
476C22⋊Dic5—22no—
477C22⋊Dic5—22no—
478C22⋊Dic5—22no—
479C22⋊Dic5—22no—
480C22⋊Dic5—22no—
481C22⋊Dic5—22no—
482C22⋊Dic5—22no—
483C22⋊Dic5—41no—
484C22⋊Dic5—41no—
485#685—22no—
486#685—22no—
487#685—22no—
488#685—22no—
489#685—22no—
490#685—22no—
491#685—41no—
492#685—41no—
493#685—41no—
494#685—41no—
495#685—41no—
496#685—41no—
497C4⋊Dic5—22no—
498C4⋊Dic5—22no—
499C4⋊Dic5—22no—
500C4⋊Dic5—22no—
501C4⋊Dic5—22no—
502C4⋊Dic5—41no—
503C4⋊Dic5—41no—
504#683—22no—
505#683—22no—
506#683—22no—
507#683—22no—
508#683—22no—
509#683—22no—
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—41no—
521#683—41no—
522#683—41no—
523#683—41no—
524#683—41no—
525#683—41no—
526#683—41no—
527#683—41no—
528#683—41no—
529#683—41no—
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—41no—
540C4×Dic5—41no—
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×D4C2×D511yescharacteristic
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#400—51no—
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#398—51no—
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#394—51no—
589#394—51no—
590#393—51no—
591#393—51no—
592#391—51no—
593#390—51no—
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#388—51no—
617#388—51no—
618#388—51no—
619#388—51no—
620#388—51no—
621#388—51no—
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#387C2×D511yescharacteristic
647#387C2×D511yescharacteristic
648#386—51no—
649#386—51no—
650#386—51no—
651#386—51no—
652#386—51no—
653#386—51no—
654#386C2×D511yescharacteristic
655#386C2×D511yescharacteristic
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#385C2×D511yescharacteristic
667#385C2×D511yescharacteristic
668#383—51no—
669#383—51no—
670#383—51no—
671#383C2×D511yescharacteristic
672#382—51no—
673#382C2×D511yescharacteristic
674#381—51no—
675#381—51no—
676#381—51no—
677#381C2×D511yescharacteristic
678#380—51no—
679#380—51no—
680#380—51no—
681#380C2×D511yescharacteristic
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⋊C4—51no—
693C4×C4⋊C4—51no—
694C4×C22⋊C4—51no—
695C4×C22⋊C4—51no—
696C4×C22⋊C4—51no—
697C4×C22⋊C4C2×D511yescharacteristic
698C2×#95—51no—
699C2×#95C2×D511yescharacteristic
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×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—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×C5—21no—
759C2×C4×C5—21no—
760C2×C4×C5—44no—
761C2×C4×C5—44no—
762C2×C4×C5—44no—
763C2×C4×C5—82no—
764C2×C4×C5C2×#4112yes—
765C2×C4×C5C2×#4112yes—
766C22⋊D5—44no—
767C22⋊D5—44no—
768C2×Dic5—28no—
769C2×Dic5—28no—
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—21no—
808C2×Dic5—21no—
809C2×Dic5—44no—
810C2×Dic5—44no—
811C2×Dic5C2×#4112yes—
812C2×Dic5C2×#4112yes—
813C2×Dic5C2×#4112yes—
814C2×Dic5C2×#4112yes—
815C2×Dic5H(5,𝔽2)12yes—
816C2×Dic52−1+412yes—
817C4×D5—82no—
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×C4C22×D511yescharacteristic
829C23×C4C22×D511yescharacteristic
830C23×C4C22×D511yescharacteristic
831C23×C4C22×D511yescharacteristic
832#126—202no—
833#126—202no—
834#123—104no—
835#123—104no—
836C22⋊Q8—104no—
837#121—104no—
838C4×Q8—202no—
839C4×D4—24no—
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—51no—
874C2×C4⋊C4—51no—
875C2×C4⋊C4—104no—
876C2×C4⋊C4—104no—
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⋊C4—51no—
901C2×C22⋊C4—51no—
902C2×C22⋊C4—51no—
903C2×C22⋊C4—51no—
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—51no—
926C2×C42—51no—
927C2×C42—104no—
928C2×C42—202no—
929C2×C42—202no—
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#95C22×D511yescharacteristic
976#95C22×D511yescharacteristic
977#95C22×D511yescharacteristic
978#95C22×D511yescharacteristic
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—22no—
990C22×C5—22no—
991C22×C5—22no—
992C22×C5—22no—
993C22×C5—22no—
994C22×C5—22no—
995C22×C5—41no—
996C22×C5—41no—
997C22×C5—41no—
998C22×C5—41no—
999C22×C5—41no—
1000C22×C5—41no—
1001C22×C5—41no—
1002C22×C5#52914yes—
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—41no—
1011C2×D5—41no—
1012C2×D5—41no—
1013C2×D5—41no—
1014C2×D5—41no—
1015C2×D5—41no—
1016C2×D5—41no—
1017C4×C5—22no—
1018C4×C5—22no—
1019C4×C5—41no—
1020C4×C5—41no—
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—22no—
1035Dic5—22no—
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—22no—
1053C2×D4—22no—
1054C2×D4—102no—
1055C2×D4—102no—
1056C2×D4—102no—
1057C2×D4—102no—
1058C2×D4—201no—
1059C2×D4—201no—
1060C22×C4—22no—
1061C22×C4—22no—
1062C22×C4—22no—
1063C22×C4—41no—
1064C22×C4—41no—
1065C22×C4—41no—
1066C22×C4—41no—
1067C22×C4—41no—
1068C22×C4—41no—
1069C22×C4—41no—
1070C22×C4—41no—
1071C22×C4—54no—
1072C22×C4—51no—
1073C22×C4—51no—
1074C22×C4—51no—
1075C22×C4—51no—
1076C22×C4—51no—
1077C22×C4—51no—
1078C22×C4—54no—
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—201no—
1096C22×C4—201no—
1097C22×C4—201no—
1098C22×C4—201no—
1099C22×C4—201no—
1100C22×C4—201no—
1101C22×C4#70914yes—
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—41no—
1117C4⋊C4—41no—
1118C4⋊C4—41no—
1119C4⋊C4—41no—
1120C4⋊C4—102no—
1121C4⋊C4—102no—
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—102no—
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—41no—
1158C22⋊C4—41no—
1159C22⋊C4—41no—
1160C22⋊C4—41no—
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—102no—
1174C22⋊C4—102no—
1175C22⋊C4—201no—
1176C22⋊C4—201no—
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—102no—
1187C42—102no—
1188C42—102no—
1189C42—102no—
1190C42—102no—
1191C42—102no—
1192C42—102no—
1193C42—102no—
1194C42—102no—
1195C42—201no—
1196C42—201no—
1197C42—201no—
1198C42—201no—
1199C42—201no—
1200C42—201no—
1201C2×C5—24no—
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—81no—
1211C23—21no—
1212C23—21no—
1213C23—21no—
1214C23—21no—
1215C23—21no—
1216C23—21no—
1217C23—21no—
1218C23—21no—
1219C23—21no—
1220C23—21no—
1221C23—21no—
1222C23—101no—
1223C23—101no—
1224C23—101no—
1225C23—101no—
1226C23—101no—
1227C23—101no—
1228C23—101no—
1229C23C2×#70912yes—
1230C23D5×#4112yes—
1231C23D5×#4112yes—
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—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—82no—
1284C2×C4—108no—
1285C2×C4—108no—
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—101no—
1323C2×C4—101no—
1324C2×C4—101no—
1325C2×C4—204no—
1326C2×C4—204no—
1327C2×C4—402no—
1328C2×C4C2×#70912yes—
1329C2×C4C2×#70912yes—
1330C5#3502111yescharacteristic, complemented, Sylow
1331C22—22no—
1332C22—22no—
1333C22—22no—
1334C22—22no—
1335C22—22no—
1336C22—22no—
1337C22—41no—
1338C22—41no—
1339C22—41no—
1340C22—41no—
1341C22—41no—
1342C22—41no—
1343C22—41no—
1344C22—201no—
1345C22—201no—
1346C22—201no—
1347C22—201no—
1348C22—201no—
1349C22—201no—
1350C22—201no—
1351C22#6586214yes—
1352C22C22×#70911yescharacteristic
1353C22C2×D5×#4111yescharacteristic
1354C22C2×D5×#4111yescharacteristic
1355C22D5×H(5,𝔽2)11yescharacteristic
1356C22#6628511yescharacteristic
1357C22#6628511yescharacteristic
1358C22D5×2−1+411yescharacteristic
1359C4—22no—
1360C4—22no—
1361C4—41no—
1362C4—41no—
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—102no—
1377C4—102no—
1378C4—201no—
1379C4—201no—
1380C4—201no—
1381C4—201no—
1382C4—201no—
1383C4—201no—
1384C4—201no—
1385C4—201no—
1386C4—201no—
1387C2—24no—
1388C2—81no—
1389C2—401no—
1390C2C2×#6586211yescharacteristic
1391C2#1061776211yescharacteristic
1392C2#1061779311yescharacteristic
1393C2#1061828911yescharacteristic
1394C2#1061829111yescharacteristic
1395C2#1061833011yescharacteristic
1396C2#1061833111yescharacteristic
subgroupG/H
center, FrattiniC23C24×D5
commutator, socle, cosocleC23×C5C25
FittingC5×#2318C2
prime radicalC2×#4085C22
hypercenter#2318D5
hypocenterC5#35021
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C23 ◁ #2318

Complements

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

NH ≅ G/Ntype
1. C5×#2318C2semidirect
2. #10614057C2semidirect
4. #10607353C2semidirect
5. #10607351C2semidirect
6. #10607303C2semidirect
7. #10607254C2semidirect
8. #10606827C2semidirect
9. #10606826C2semidirect
10. #10606785C2semidirect
11. #10606737C2semidirect
12. #10606602C2semidirect
13. #10606601C2semidirect
16. #10606319C2semidirect
17. #10606318C2semidirect
18. #10606235C2semidirect
19. #10606233C2semidirect
20. #10606035C2semidirect
21. #10606002C2semidirect
22. #10605920C2semidirect
23. #10605908C2semidirect
24. #10605816C2semidirect
25. #10605803C2semidirect
26. #10605677C2semidirect
27. #10605638C2semidirect
28. #10605177C2semidirect
29. C4×#4024C2semidirect
30. #10605098C2semidirect
31. C2×#64938C2semidirect
385. #2318D5semidirect
1330. C5#35021semidirect

Maximal subgroups

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

subgroupindex
C5×#23182
#106140572
C4×#40852
#106073532
#106073512
#106073032
#106072542
#106068272
#106068262
#106067852
#106067372
#106066022
#106066012
#106065162
#106065122
#106063192
#106063182
#106062352
#106062332
#106060352
#106060022
#106059202
#106059082
#106058162
#106058032
#106056772
#106056382
#106051772
C4×#40242
#106050982
C2×#649382
#350215