Finite Group Databasebeta

← #12270446

Subgroups — #12270446

Order 1280.

1848 conjugacy classes of subgroups.

The subgroup lattice has 1394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2531C211yesmaximal, characteristic, complemented
2#10609535C211yesmaximal, characteristic, complemented
3#10609472C211yesmaximal, characteristic, complemented
4#10609261C211yesmaximal, characteristic, complemented
5#10609253C211yesmaximal, characteristic, complemented
6#10609191C211yesmaximal, characteristic, complemented
7#10609190C211yesmaximal, characteristic, complemented
8#10608683C211yesmaximal, characteristic
9#10608623C211yesmaximal, characteristic, complemented
10#10608062C211yesmaximal, characteristic
11#10608020C211yesmaximal, characteristic, complemented
12#10607370C211yesmaximal, characteristic, complemented
13#10607322C211yesmaximal, characteristic, complemented
14#10607314C211yesmaximal, characteristic, complemented
15#10607268C211yesmaximal, characteristic, complemented
16#10607186C211yesmaximal, characteristic, complemented
17#10607182C211yesmaximal, characteristic, complemented
18#10607180C211yesmaximal, characteristic, complemented
19#10607180C211yesmaximal, characteristic, complemented
20#10606843C211yesmaximal, characteristic, complemented
21#10606748C211yesmaximal, characteristic, complemented
22#10606673C211yesmaximal, characteristic, complemented
23#10606669C211yesmaximal, characteristic, complemented
24#10606493C211yesmaximal, characteristic, complemented
25#10606391C211yesmaximal, characteristic
26#10605679C211yesmaximal, characteristic, complemented
27#10605597C211yesmaximal, characteristic, complemented
28#10605233C211yesmaximal, characteristic, complemented
29C4×#4023C211yesmaximal, characteristic, complemented
30#10605133C211yesmaximal, characteristic, complemented
31#10605113C211yesmaximal, characteristic, complemented
32C2×#4085C2211yescharacteristic
33C2×D4×Dic5C2211yescharacteristic
34C2×#4070C2211yescharacteristic
35C22×C4×Dic5C2211yescharacteristic
36C2×#4044C2211yescharacteristic
37C2×#4033C2211yescharacteristic
38C2×#4027C2211yescharacteristic
39C2×#4027C2211yescharacteristic
40C2×#4025C2211yescharacteristic
41C2×#4023C2211yescharacteristic
42C2×#4023C2211yescharacteristic
43C2×#4023C2211yescharacteristic
44C2×#4018C2211yescharacteristic
45C2×#4018C2211yescharacteristic
46C2×C42×D5C2211yescharacteristic
47C5×#398C2211yescharacteristic
48C5×#397C2211yescharacteristic
49C5×#397C2211yescharacteristic
50C5×#394C2211yescharacteristic
51C5×#390C2211yescharacteristic
52C5×#388C2211yescharacteristic
53C5×#388C2211yescharacteristic
54C5×#388C2211yescharacteristic
55C5×#388C2211yescharacteristic
56C5×#387C2211yescharacteristic
57C5×#387C2211yescharacteristic
58C5×#386C2211yescharacteristic
59C5×#380C2211yescharacteristic
60C4×C5×C22⋊C4C2211yescharacteristic
61C5×#376C2211yescharacteristic
62#65511C2211yescharacteristic
63#65510C2211yescharacteristic
64#65502C2211yescharacteristic
65C4×C22⋊Dic5C2211yescharacteristic
66#65282C2211yescharacteristic
67#65281C2211yescharacteristic
68#65279C2211yescharacteristic
69#65278C2211yescharacteristic
70#65278C2211yescharacteristic
71#65275C2211yescharacteristic
72#65273C2211yescharacteristic
73#65273C2211yescharacteristic
74#65272C2211yescharacteristic
75#65271C2211yescharacteristic
76#65270C2211yescharacteristic
77#65267C2211yescharacteristic
78#65267C2211yescharacteristic
79C4⋊C4×Dic5C2211yescharacteristic
80C4⋊C4×Dic5C2211yescharacteristic
81C4⋊C4×Dic5C2211yescharacteristic
82C4⋊C4×Dic5C2211yescharacteristic
83C4⋊C4×Dic5C2211yescharacteristic
84#65263C2211yescharacteristic
85#65262C2211yescharacteristic
86#65262C2211yescharacteristic
87#65261C2211yescharacteristic
88#65250C2211yescharacteristic
89#65248C2211yescharacteristic
90#65248C2211yescharacteristic
91#65248C2211yescharacteristic
92#65246C2211yescharacteristic
93#65245C2211yescharacteristic
94#65245C2211yescharacteristic
95#65245C2211yescharacteristic
96#65245C2211yescharacteristic
97#65242C2211yescharacteristic
98#65241C2211yescharacteristic
99#65241C2211yescharacteristic
100#65241C2211yescharacteristic
101#65240C2211yescharacteristic
102#65240C2211yescharacteristic
103#65240C2211yescharacteristic
104#65238C2211yescharacteristic
105#65236C2211yescharacteristic
106#65235C2211yescharacteristic
107#65235C2211yescharacteristic
108#65234C2211yescharacteristic
109#65234C2211yescharacteristic
110#65234C2211yescharacteristic
111#65234C2211yescharacteristic
112#65233C2211yescharacteristic
113#65233C2211yescharacteristic
114#65233C2211yescharacteristic
115#65233C2211yescharacteristic
116#65233C2211yescharacteristic
117#65231C2211yescharacteristic
118C22⋊C4×Dic5C2211yescharacteristic
119C22⋊C4×Dic5C2211yescharacteristic
120C22⋊C4×Dic5C2211yescharacteristic
121C22⋊C4×Dic5C2211yescharacteristic
122C22⋊C4×Dic5C2211yescharacteristic
123C22⋊C4×Dic5C2211yescharacteristic
124C22⋊C4×Dic5C2211yescharacteristic
125C22⋊C4×Dic5C2211yescharacteristic
126#65229C2211yescharacteristic
127#65222C2211yescharacteristic
128#65222C2211yescharacteristic
129#65222C2211yescharacteristic
130#65222C2211yescharacteristic
131#65222C2211yescharacteristic
132#65221C2211yescharacteristic
133C4×#683C2211yescharacteristic
134C4×#683C2211yescharacteristic
135C42×Dic5C2211yescharacteristic
136C42×Dic5C2211yescharacteristic
137C42×Dic5C2211yescharacteristic
138#65217C2211yescharacteristic
139#64964C2211yescharacteristic
140#64962C2211yescharacteristic
141#64959C2211yescharacteristic
142#64959C2211yescharacteristic
143#64957C2211yescharacteristic
144#64957C2211yescharacteristic
145#64955C2211yescharacteristic
146#64955C2211yescharacteristic
147#64955C2211yescharacteristic
148#64955C2211yescharacteristic
149#64955C2211yescharacteristic
150#64955C2211yescharacteristic
151#64950C2211yescharacteristic
152#64949C2211yescharacteristic
153#64949C2211yescharacteristic
154#64948C2211yescharacteristic
155#64947C2211yescharacteristic
156#64947C2211yescharacteristic
157#64947C2211yescharacteristic
158#64946C2211yescharacteristic
159#64944C2211yescharacteristic
160#64944C2211yescharacteristic
161#64943C2211yescharacteristic
162#64942C2211yescharacteristic
163#64941C2211yescharacteristic
164#64941C2211yescharacteristic
165#64941C2211yescharacteristic
166#64941C2211yescharacteristic
167#64941C2211yescharacteristic
168#64941C2211yescharacteristic
169#64940C2211yescharacteristic
170#64940C2211yescharacteristic
171#64938C2211yescharacteristic
172#64938C2211yescharacteristic
173#64938C2211yescharacteristic
174#64938C2211yescharacteristic
175#64938C2211yescharacteristic
176#64938C2211yescharacteristic
177#64938C2211yescharacteristic
178#64938C2211yescharacteristic
179#64938C2211yescharacteristic
180#64937C2211yescharacteristic
181#64937C2211yescharacteristic
182#64937C2211yescharacteristic
183#64936C2211yescharacteristic
184#64936C2211yescharacteristic
185#64935C2211yescharacteristic
186#64935C2211yescharacteristic
187#34884—51nomaximal, Sylow
188C22×C5×D4C2311yescharacteristic
189C23×C4×C5C2311yescharacteristic
190C22×C22⋊D5C2311yescharacteristic
191C22×C22⋊D5C2311yescharacteristic
192C23×Dic5C2311yescharacteristic
193C23×Dic5C2311yescharacteristic
194C23×Dic5C2311yescharacteristic
195C22×C4×D5C2311yescharacteristic
196C22×C4×D5C2311yescharacteristic
197C22×C4×D5C2311yescharacteristic
198C22×Dic10C2311yescharacteristic
199C2×C5×C4⋊C4C2311yescharacteristic
200C2×C5×C4⋊C4C2311yescharacteristic
201C2×C5×C4⋊C4C2311yescharacteristic
202C2×C5×C4⋊C4C2311yescharacteristic
203C2×C5×C4⋊C4C2311yescharacteristic
204C2×C5×C4⋊C4C2311yescharacteristic
205C2×C5×C22⋊C4C2311yescharacteristic
206C2×C5×C22⋊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×C5×C22⋊C4C2311yescharacteristic
216C2×C42×C5C2311yescharacteristic
217C2×C42×C5C2311yescharacteristic
218C2×C42×C5C2311yescharacteristic
219C2×C42×C5C2311yescharacteristic
220C2×C22⋊Dic5C2311yescharacteristic
221C2×C22⋊Dic5C2311yescharacteristic
222C2×C22⋊Dic5C2311yescharacteristic
223C2×C22⋊Dic5C2311yescharacteristic
224C2×C22⋊Dic5C2311yescharacteristic
225C2×C22⋊Dic5C2311yescharacteristic
226C2×C22⋊Dic5C2311yescharacteristic
227C2×C22⋊Dic5C2311yescharacteristic
228C2×C22⋊Dic5C2311yescharacteristic
229C2×C22⋊Dic5C2311yescharacteristic
230C2×C22⋊Dic5C2311yescharacteristic
231#4085—24no—
232D4×Dic5—24no—
233C2×#685C2311yescharacteristic
234C2×#685C2311yescharacteristic
235C2×#685C2311yescharacteristic
236C2×#685C2311yescharacteristic
237C2×#685C2311yescharacteristic
238C2×#685C2311yescharacteristic
239C2×#685C2311yescharacteristic
240C2×#685C2311yescharacteristic
241C2×#685C2311yescharacteristic
242C2×#685C2311yescharacteristic
243C2×C4⋊Dic5C2311yescharacteristic
244C2×C4⋊Dic5C2311yescharacteristic
245C2×C4⋊Dic5C2311yescharacteristic
246C2×C4⋊Dic5C2311yescharacteristic
247C2×C4⋊Dic5C2311yescharacteristic
248C2×C4⋊Dic5C2311yescharacteristic
249#4070—24no—
250C2×#683C2311yescharacteristic
251C2×#683C2311yescharacteristic
252C2×#683C2311yescharacteristic
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×C4×Dic5—24no—
271C2×C4×Dic5C2311yescharacteristic
272C2×C4×Dic5C2311yescharacteristic
273C2×C4×Dic5C2311yescharacteristic
274C2×C4×Dic5C2311yescharacteristic
275C2×C4×Dic5C2311yescharacteristic
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
289C2×C4×Dic5C2311yescharacteristic
290C2×C4×Dic5C2311yescharacteristic
291C2×C4×Dic5C2311yescharacteristic
292C2×C4×Dic5C2311yescharacteristic
293C2×C4×Dic5C2311yescharacteristic
294C2×C4×Dic5C2311yescharacteristic
295#4044—24no—
296#4033—24no—
297#4027—24no—
298#4027—24no—
299#4025—24no—
300#4023—24no—
301#4023—24no—
302#4023—24no—
303#4018—24no—
304#4018—24no—
305C42×D5—24no—
306C5×#95C2311yescharacteristic
307C5×#95C2311yescharacteristic
308C5×#95C2311yescharacteristic
309C5×#95C2311yescharacteristic
310C5×#95C2311yescharacteristic
311C5×#95C2311yescharacteristic
312C5×#95C2311yescharacteristic
313C5×#95C2311yescharacteristic
314C5×#95C2311yescharacteristic
315C5×#95C2311yescharacteristic
316C5×#95C2311yescharacteristic
317C5×#95C2311yescharacteristic
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#2597—51no—
359#2596—51no—
360#2590—51no—
361#2589—51no—
362#2578—51no—
363#2577—51no—
364#2560—51no—
365#2559—51no—
366#2533—51no—
367#2532—51no—
368#2531D511yescharacteristic, complemented
369#2530—51no—
370#2479—51no—
371#2478—51no—
372#2477—51no—
373#2476—51no—
374#2402—51no—
375#2398—51no—
376#2395—51no—
377#2395—51no—
378C4×#126—51no—
379C4×#126—51no—
380C4×C22⋊Q8—51no—
381C4×#121—51no—
382#2298—51no—
383#2295—51no—
384#2293—51no—
385#2290—51no—
386#2290—51no—
387C4×#117—51no—
388C4×#117—51no—
389C24×C5C2411yescharacteristic
390C24×C5C2411yescharacteristic
391C23×D5C2411yescharacteristic
392C2×C5×D4—22no—
393C2×C5×D4—22no—
394C2×C5×D4—41no—
395C22×C4×C5—22no—
396C22×C4×C5—22no—
397C22×C4×C5—41no—
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
408C22×C4×C5C2411yescharacteristic
409C22×C4×C5C2411yescharacteristic
410C22×C4×C5C2411yescharacteristic
411C2×C22⋊D5—22no—
412C2×C22⋊D5—22no—
413C2×C22⋊D5—22no—
414C2×C22⋊D5—22no—
415C2×C22⋊D5—41no—
416C2×C22⋊D5—41no—
417C22×Dic5—22no—
418C22×Dic5—22no—
419C22×Dic5—22no—
420C22×Dic5—22no—
421C22×Dic5—22no—
422C22×Dic5—22no—
423C22×Dic5—22no—
424C22×Dic5—41no—
425C22×Dic5#4114yes—
426C22×Dic5C2411yescharacteristic
427C22×Dic5C2411yescharacteristic
428C22×Dic5C2411yescharacteristic
429C22×Dic5C2411yescharacteristic
430C22×Dic5C2411yescharacteristic
431C22×Dic5C2411yescharacteristic
432C22×Dic5C2411yescharacteristic
433C22×Dic5C2411yescharacteristic
434C22×Dic5C2411yescharacteristic
435C22×Dic5C2411yescharacteristic
436C22×Dic5C2411yescharacteristic
437C22×Dic5C2411yescharacteristic
438C22×Dic5C2411yescharacteristic
439C22×Dic5C2411yescharacteristic
440C22×Dic5C2411yescharacteristic
441C2×C4×D5—22no—
442C2×C4×D5—22no—
443C2×C4×D5—22no—
444C2×C4×D5—22no—
445C2×C4×D5—22no—
446C2×C4×D5—22no—
447C2×C4×D5—22no—
448C2×C4×D5—41no—
449C2×C4×D5—41no—
450C2×Dic10—22no—
451C2×Dic10—22no—
452C2×Dic10—41no—
453C5×C4⋊C4—22no—
454C5×C4⋊C4—22no—
455C5×C4⋊C4—41no—
456C5×C4⋊C4—41no—
457C5×C4⋊C4—41no—
458C5×C4⋊C4—41no—
459C5×C22⋊C4—22no—
460C5×C22⋊C4—22no—
461C5×C22⋊C4—22no—
462C5×C22⋊C4—22no—
463C5×C22⋊C4—22no—
464C5×C22⋊C4—22no—
465C5×C22⋊C4—41no—
466C5×C22⋊C4—41no—
467C5×C22⋊C4—41no—
468C5×C22⋊C4—41no—
469C5×C22⋊C4—41no—
470C42×C5—22no—
471C42×C5—22no—
472C42×C5—22no—
473C42×C5—41no—
474C22⋊Dic5—22no—
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—22no—
484C22⋊Dic5—41no—
485#685—22no—
486#685—22no—
487#685—22no—
488#685—22no—
489#685—22no—
490#685—22no—
491#685—22no—
492#685—41no—
493#685—41no—
494#685#4114yes—
495C4⋊Dic5—22no—
496C4⋊Dic5—22no—
497C4⋊Dic5—22no—
498C4⋊Dic5—22no—
499C4⋊Dic5—41no—
500C4⋊Dic5—41no—
501#683—22no—
502#683—22no—
503#683—22no—
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—41no—
519#683—41no—
520#683#4114yes—
521C4×Dic5—22no—
522C4×Dic5—22no—
523C4×Dic5—22no—
524C4×Dic5—22no—
525C4×Dic5—22no—
526C4×Dic5—22no—
527C4×Dic5—22no—
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—41no—
539C4×Dic5—41no—
540C4×Dic5—41no—
541C4×Dic5—41no—
542C4×Dic5—41no—
543C4×Dic5#4114yes—
544C4×Dic5#4114yes—
545C2×#126—51no—
546C2×#126—51no—
547C2×C22⋊Q8—51no—
548C2×#121—51no—
549C2×C4×Q8—51no—
550C2×C4×D4—51no—
551C2×C4×D4—51no—
552C2×C4×D4—51no—
553C2×#117—51no—
554C2×#117—51no—
555C2×#117—51no—
556C2×#117—51no—
557C2×#117—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#399—51no—
569#399—51no—
570#398—51no—
571#398—51no—
572#398—51no—
573#398—51no—
574#398—51no—
575#398C2×D511yescharacteristic
576#397—51no—
577#397—51no—
578#397—51no—
579#397—51no—
580#397—51no—
581#397—51no—
582#397C2×D511yescharacteristic
583#397C2×D511yescharacteristic
584#394—51no—
585#394—51no—
586#394—51no—
587#394—51no—
588#394—51no—
589#394C2×D511yescharacteristic
590#393—51no—
591#393—51no—
592#391—51no—
593#391—51no—
594#391—51no—
595#390—51no—
596#390—51no—
597#390C2×D511yescharacteristic
598#389—51no—
599#389—51no—
600#389—51no—
601#389—51no—
602#389—51no—
603#389—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#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#387C2×D511yescharacteristic
643#387C2×D511yescharacteristic
644#386—51no—
645#386—51no—
646#386—51no—
647#386—51no—
648#386—51no—
649#386C2×D511yescharacteristic
650#385—51no—
651#385—51no—
652#385—51no—
653#385—51no—
654#385—51no—
655#385—51no—
656#383—51no—
657#383—51no—
658#380—51no—
659#380C2×D511yescharacteristic
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⋊C4—51no—
671C4×C4⋊C4—51no—
672C4×C4⋊C4—51no—
673C4×C4⋊C4—51no—
674C4×C4⋊C4—51no—
675C4×C4⋊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⋊C4—51no—
684C4×C22⋊C4—51no—
685C4×C22⋊C4—51no—
686C4×C22⋊C4—51no—
687C4×C22⋊C4—51no—
688C4×C22⋊C4—51no—
689C4×C22⋊C4—51no—
690C4×C22⋊C4—51no—
691C4×C22⋊C4C2×D511yescharacteristic
692#376—51no—
693#376—51no—
694#376—51no—
695#376—51no—
696#376C2×D511yescharacteristic
697C43—51no—
698C43—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×C5—21no—
711C23×C5—21no—
712C23×C5—21no—
713C23×C5C2×#4112yes—
714C23×C5C2511yescharacteristic
715C22×D5—21no—
716C22×D5—21no—
717C22×D5—21no—
718C22×D5—21no—
719C22×D5—21no—
720C22×D5—21no—
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×C5—44no—
759C2×C4×C5C2×#4112yes—
760C2×C4×C5C2×#4112yes—
761C2×C4×C5C2×#4112yes—
762C2×C4×C5C2×#4112yes—
763C22⋊D5—44no—
764C22⋊D5—44no—
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—28no—
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—44no—
803C2×Dic5—44no—
804C2×Dic5C2×#4112yes—
805C2×Dic5C2×#4112yes—
806C2×Dic5C2×#4112yes—
807C2×Dic5C2×#4112yes—
808C2×Dic5C2×#4112yes—
809C2×Dic5C2×#4112yes—
810C2×Dic5C2×#4112yes—
811C2×Dic5C2×#4112yes—
812C2×Dic5C2×#4112yes—
813C4×D5—28no—
814C4×D5—44no—
815C4×D5—44no—
816Dic10—44no—
817C22×Q8—51no—
818C22×D4—51no—
819C22×D4—51no—
820C22×D4C22×D511yescharacteristic
821C23×C4—51no—
822C23×C4—51no—
823C23×C4—51no—
824C23×C4—51no—
825C23×C4—51no—
826C23×C4—51no—
827C23×C4C22×D511yescharacteristic
828#126—104no—
829#126—104no—
830C22⋊Q8—104no—
831#121—104no—
832C4×Q8—104no—
833C4×D4—104no—
834C4×D4—104no—
835C4×D4—104no—
836#117—104no—
837#117—104no—
838#117—104no—
839#117—104no—
840#117—104no—
841C2×C4⋊C4—51no—
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⋊C4C22×D511yescharacteristic
868C2×C4⋊C4C22×D511yescharacteristic
869C2×C4⋊C4C22×D511yescharacteristic
870C2×C4⋊C4C22×D511yescharacteristic
871C2×C4⋊C4C22×D511yescharacteristic
872C2×C4⋊C4C22×D511yescharacteristic
873C2×C22⋊C4—51no—
874C2×C22⋊C4—51no—
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⋊C4C22×D511yescharacteristic
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×C22⋊C4C22×D511yescharacteristic
904C2×C22⋊C4C22×D511yescharacteristic
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—51no—
922C2×C42—51no—
923C2×C42—51no—
924C2×C42—51no—
925C2×C42—51no—
926C2×C42—51no—
927C2×C42—51no—
928C2×C42—51no—
929C2×C42—104no—
930C2×C42—104no—
931C2×C42C22×D511yescharacteristic
932C2×C42C22×D511yescharacteristic
933C2×C42C22×D511yescharacteristic
934C2×C42C22×D511yescharacteristic
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
987C22×C5—22no—
988C22×C5—22no—
989C22×C5—22no—
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×C5C22×#4111yescharacteristic
1002C22×C5C22×#4111yescharacteristic
1003C22×C5C22×#4111yescharacteristic
1004C22×C5C22×#4111yescharacteristic
1005C22×C5C22×#4111yescharacteristic
1006C22×C5#58511yescharacteristic
1007C22×C5#58511yescharacteristic
1008C2×D5—22no—
1009C2×D5—22no—
1010C2×D5—22no—
1011C2×D5—41no—
1012C2×D5—41no—
1013C2×D5—41no—
1014C2×D5—41no—
1015C4×C5—22no—
1016C4×C5—22no—
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—
1028Dic5—22no—
1029Dic5—22no—
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#52914yes—
1043C24—51no—
1044C24C23×D511yescharacteristic
1045C24C23×D511yescharacteristic
1046C2×Q8—102no—
1047C2×Q8—102no—
1048C2×Q8—201no—
1049C2×D4—22no—
1050C2×D4—22no—
1051C2×D4—41no—
1052C2×D4—102no—
1053C2×D4—102no—
1054C2×D4—102no—
1055C2×D4—102no—
1056C2×D4—201no—
1057C2×D4—201no—
1058C22×C4—22no—
1059C22×C4—22no—
1060C22×C4—41no—
1061C22×C4—51no—
1062C22×C4—54no—
1063C22×C4—51no—
1064C22×C4—51no—
1065C22×C4—51no—
1066C22×C4—51no—
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—102no—
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—102no—
1089C22×C4—102no—
1090C22×C4—102no—
1091C22×C4—201no—
1092C22×C4—201no—
1093C22×C4—201no—
1094C22×C4C23×D511yescharacteristic
1095C22×C4C23×D511yescharacteristic
1096C22×C4C23×D511yescharacteristic
1097C22×C4C23×D511yescharacteristic
1098C22×C4C23×D511yescharacteristic
1099C22×C4C23×D511yescharacteristic
1100C22×C4C23×D511yescharacteristic
1101C22×C4C23×D511yescharacteristic
1102C22×C4C23×D511yescharacteristic
1103C22×C4C23×D511yescharacteristic
1104C22×C4C23×D511yescharacteristic
1105C22×C4C23×D511yescharacteristic
1106C22×C4C23×D511yescharacteristic
1107C4⋊C4—22no—
1108C4⋊C4—22no—
1109C4⋊C4—41no—
1110C4⋊C4—41no—
1111C4⋊C4—41no—
1112C4⋊C4—41no—
1113C4⋊C4—54no—
1114C4⋊C4—102no—
1115C4⋊C4—102no—
1116C4⋊C4—102no—
1117C4⋊C4—102no—
1118C4⋊C4—102no—
1119C4⋊C4—102no—
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—201no—
1136C4⋊C4—201no—
1137C4⋊C4—201no—
1138C4⋊C4—201no—
1139C22⋊C4—22no—
1140C22⋊C4—22no—
1141C22⋊C4—22no—
1142C22⋊C4—22no—
1143C22⋊C4—22no—
1144C22⋊C4—22no—
1145C22⋊C4—41no—
1146C22⋊C4—41no—
1147C22⋊C4—41no—
1148C22⋊C4—41no—
1149C22⋊C4—41no—
1150C22⋊C4—54no—
1151C22⋊C4—102no—
1152C22⋊C4—102no—
1153C22⋊C4—102no—
1154C22⋊C4—102no—
1155C22⋊C4—102no—
1156C22⋊C4—102no—
1157C22⋊C4—102no—
1158C22⋊C4—102no—
1159C22⋊C4—102no—
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—201no—
1169C22⋊C4—201no—
1170C22⋊C4—201no—
1171C42—22no—
1172C42—22no—
1173C42—22no—
1174C42—41no—
1175C42—54no—
1176C42—54no—
1177C42—102no—
1178C42—102no—
1179C42—102no—
1180C42—102no—
1181C42—102no—
1182C42—102no—
1183C42—102no—
1184C42—102no—
1185C42—102no—
1186C42—102no—
1187C42—102no—
1188C42—102no—
1189C42—102no—
1190C42—102no—
1191C42—102no—
1192C42—102no—
1193C42—102no—
1194C42—201no—
1195C42—201no—
1196C42—201no—
1197C42—201no—
1198C42—201no—
1199C2×C5—42no—
1200C2×C5—81no—
1201C2×C5C2×#52911yescharacteristic
1202C2×C5#344411yescharacteristic
1203C2×C5#345511yescharacteristic
1204C2×C5#347511yescharacteristic
1205C2×C5#347511yescharacteristic
1206C2×C5#347511yescharacteristic
1207C2×C5#348011yescharacteristic
1208D5—42no—
1209C23—21no—
1210C23—21no—
1211C23—21no—
1212C23—21no—
1213C23—21no—
1214C23—21no—
1215C23—21no—
1216C23—21no—
1217C23—21no—
1218C23—21no—
1219C23—21no—
1220C23—21no—
1221C23—21no—
1222C23—52no—
1223C23—101no—
1224C23—101no—
1225C23—101no—
1226C23—101no—
1227C23—101no—
1228C23—101no—
1229C23D5×#4112yes—
1230C23C24×D511yescharacteristic
1231Q8—204no—
1232D4—44no—
1233D4—204no—
1234D4—204no—
1235C2×C4—21no—
1236C2×C4—21no—
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—44no—
1271C2×C4—52no—
1272C2×C4—52no—
1273C2×C4—52no—
1274C2×C4—52no—
1275C2×C4—52no—
1276C2×C4—52no—
1277C2×C4—52no—
1278C2×C4—52no—
1279C2×C4—52no—
1280C2×C4—108no—
1281C2×C4—108no—
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—204no—
1319C2×C4—204no—
1320C2×C4—204no—
1321C2×C4—204no—
1322C2×C4D5×#4112yes—
1323C2×C4D5×#4112yes—
1324C2×C4D5×#4112yes—
1325C2×C4D5×#4112yes—
1326C5#3488411yescharacteristic, complemented, Sylow
1327C22—22no—
1328C22—22no—
1329C22—22no—
1330C22—41no—
1331C22—41no—
1332C22—41no—
1333C22—41no—
1334C22—41no—
1335C22—41no—
1336C22—41no—
1337C22—41no—
1338C22—41no—
1339C22—41no—
1340C22—41no—
1341C22—102no—
1342C22—102no—
1343C22—102no—
1344C22—201no—
1345C22—201no—
1346C22—201no—
1347C22—201no—
1348C22C2×D5×#4111yescharacteristic
1349C22C2×D5×#4111yescharacteristic
1350C22C2×D5×#4111yescharacteristic
1351C22C2×D5×#4111yescharacteristic
1352C22C2×D5×#4111yescharacteristic
1353C22#6628511yescharacteristic
1354C22#6628511yescharacteristic
1355C4—22no—
1356C4—22no—
1357C4—22no—
1358C4—22no—
1359C4—41no—
1360C4—41no—
1361C4—41no—
1362C4—41no—
1363C4—41no—
1364C4—41no—
1365C4—41no—
1366C4—41no—
1367C4—41no—
1368C4—54no—
1369C4—102no—
1370C4—102no—
1371C4—102no—
1372C4—102no—
1373C4—102no—
1374C4—102no—
1375C4—201no—
1376C4—201no—
1377C4—201no—
1378C4—201no—
1379C4—201no—
1380C4—201no—
1381C4—201no—
1382C4—201no—
1383C2—42no—
1384C2—81no—
1385C2—202no—
1386C2#1061802011yescharacteristic
1387C2D5×#52911yescharacteristic
1388C2#1061836811yescharacteristic
1389C2#1061869111yescharacteristic
1390C2#1061869111yescharacteristic
1391C2#1061877611yescharacteristic
1392C2#1061885911yescharacteristic
subgroupG/H
center, FrattiniC23C24×D5
commutator, socle, cosocleC23×C5C25
FittingC5×#2531C2
prime radicalC2×#4085C22
hypercenter#2531D5
hypocenterC5#34884
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C23 ◁ #2531

Complements

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

NH ≅ G/Ntype
1. C5×#2531C2semidirect
2. #10609535C2semidirect
3. #10609472C2semidirect
4. #10609261C2semidirect
5. #10609253C2semidirect
6. #10609191C2semidirect
7. #10609190C2semidirect
9. #10608623C2semidirect
11. #10608020C2semidirect
12. #10607370C2semidirect
13. #10607322C2semidirect
14. #10607314C2semidirect
15. #10607268C2semidirect
16. #10607186C2semidirect
17. #10607182C2semidirect
18. #10607180C2semidirect
19. #10607180C2semidirect
20. #10606843C2semidirect
21. #10606748C2semidirect
22. #10606673C2semidirect
23. #10606669C2semidirect
24. #10606493C2semidirect
26. #10605679C2semidirect
27. #10605597C2semidirect
28. #10605233C2semidirect
29. C4×#4023C2semidirect
30. #10605133C2semidirect
31. #10605113C2semidirect
368. #2531D5semidirect
1326. C5#34884semidirect

Maximal subgroups

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

subgroupindex
C5×#25312
#106095352
#106094722
#106092612
#106092532
#106091912
#106091902
#106086832
#106086232
#106080622
#106080202
#106073702
#106073222
#106073142
#106072682
#106071862
#106071822
#106071802
#106068432
#106067482
#106066732
#106066692
#106064932
#106063912
#106056792
#106055972
#106052332
C4×#40232
#106051332
#106051132
#348845