Finite Group Databasebeta

← #12259632

Subgroups — #12259632

Order 1280.

3614 conjugacy classes of subgroups.

The subgroup lattice has 1262 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#4085C211yesmaximal, characteristic
2C2×#65820C211yesmaximal, characteristic, complemented
3C22×#4023C211yesmaximal, characteristic, complemented
4C5×D4×C22⋊C4C211yesmaximal, characteristic, complemented
5D4×C22⋊Dic5C211yesmaximal, characteristic, complemented
6#10614071C212yesmaximal, complemented
7C4×#4085C212yesmaximal, complemented
8C22⋊C4×C22⋊D5C211yesmaximal, characteristic, complemented
9#10613829C211yesmaximal, characteristic, complemented
10#10608036C212yesmaximal, complemented
11#10608027C212yesmaximal, complemented
12#10606408C212yesmaximal, complemented
13#10606407C212yesmaximal, complemented
14#10606396C212yesmaximal, complemented
15#10606391C212yesmaximal, complemented
16#10605740C211yesmaximal, characteristic, complemented
17#10605600C211yesmaximal, characteristic, complemented
18#10605581C211yesmaximal, characteristic, complemented
19#10605553C211yesmaximal, characteristic, complemented
20#10605550C211yesmaximal, characteristic, complemented
21#10605548C211yesmaximal, characteristic, complemented
22#10605306C211yesmaximal, characteristic, complemented
23#10605166C211yesmaximal, characteristic, complemented
24C23×C5×D4C2211yescharacteristic
25C23×C22⋊D5C2211yescharacteristic
26C23×C22⋊D5C2211yescharacteristic
27C24×Dic5C2211yescharacteristic
28C2×C4×C5×D4C2212yescomplemented
29C22×C5×C22⋊C4C2211yescharacteristic
30C22×C5×C22⋊C4C2211yescharacteristic
31C22×C22⋊Dic5C2211yescharacteristic
32C22×C22⋊Dic5C2211yescharacteristic
33C22×C22⋊Dic5C2211yescharacteristic
34C2×#4085C4116yescomplemented
35C2×#4085C2211yescharacteristic
36C2×#4085C2211yescharacteristic
37C2×#4085C2211yescharacteristic
38C2×#4085C2211yescharacteristic
39C2×#4085C2211yescharacteristic
40C2×#4085C2211yescharacteristic
41C2×#4085C2211yescharacteristic
42C2×#4085C2211yescharacteristic
43C2×D4×Dic5C2212yescomplemented
44C2×C4×C22⋊D5C2212yescomplemented
45C2×C4×C22⋊D5C2212yescomplemented
46C2×C4×C22⋊D5C2212yescomplemented
47C22×#685C2211yescharacteristic
48C22×#683C2211yescharacteristic
49C22×#683C2212yescomplemented
50C22×C4×Dic5C2212yescomplemented
51#65820—28no—
52C2×#4027C2212yescomplemented
53C2×#4027C2212yescomplemented
54C2×#4027C2212yescomplemented
55C2×D5×C22⋊C4C2211yescharacteristic
56C2×D5×C22⋊C4C2211yescharacteristic
57C2×#4023—28no—
58C2×#4023C2211yescharacteristic
59C2×#4023C2211yescharacteristic
60C2×#4023C2211yescharacteristic
61C2×#4023C2211yescharacteristic
62C2×#4023C2211yescharacteristic
63C2×#4023C2211yescharacteristic
64C2×#4023C2212yescomplemented
65C2×#4023C2212yescomplemented
66C5×#390C2212yescomplemented
67C5×#386C2212yescomplemented
68C5×#386C2212yescomplemented
69C5×#380C2211yescharacteristic
70C5×#379C2211yescharacteristic
71C5×#379C2211yescharacteristic
72C4×C5×C22⋊C4C2211yescharacteristic
73#65536C2211yescharacteristic
74#65536C2211yescharacteristic
75#65510C2212yescomplemented
76#65509C2212yescomplemented
77#65509C2212yescomplemented
78#65502C2212yescomplemented
79#65501C2211yescharacteristic
80#65499C2212yescomplemented
81C4×C22⋊Dic5C2211yescharacteristic
82C4×C22⋊Dic5C2212yescomplemented
83#65279C2212yescomplemented
84#65278C2212yescomplemented
85#65261C2212yescomplemented
86#65261C2212yescomplemented
87#65247C2212yescomplemented
88#65246C2212yescomplemented
89#65246C2212yescomplemented
90#65246C2212yescomplemented
91#65246C2212yescomplemented
92#65246C2212yescomplemented
93#65246C2212yescomplemented
94#65245C2212yescomplemented
95#65245C2212yescomplemented
96#65244C2211yescharacteristic
97#65244C2211yescharacteristic
98#65235C2212yescomplemented
99#65234C2212yescomplemented
100#65234C2212yescomplemented
101#65233C2212yescomplemented
102#65233C2212yescomplemented
103#65232C2211yescharacteristic
104#65232C2211yescharacteristic
105#65231C2211yescharacteristic
106#65231C2211yescharacteristic
107#65231C2212yescomplemented
108#65231C2212yescomplemented
109C22⋊C4×Dic5C2211yescharacteristic
110C22⋊C4×Dic5C2211yescharacteristic
111C22⋊C4×Dic5C2212yescomplemented
112C22⋊C4×Dic5C2212yescomplemented
113C22⋊C4×Dic5C2212yescomplemented
114#65229C2212yescomplemented
115C4×#685C2212yescomplemented
116C4×#683C2212yescomplemented
117C4×#683C2212yescomplemented
118#64959C2212yescomplemented
119#64958C2212yescomplemented
120#64957C2212yescomplemented
121#64955C2212yescomplemented
122#64938C2212yescomplemented
123#64938C2212yescomplemented
124#64936C2212yescomplemented
125#64936C2212yescomplemented
126#34204—51nomaximal, Sylow
127C25×C5C2311yescharacteristic
128C25×C5C2311yescharacteristic
129C24×D5C2311yescharacteristic
130C22×C5×D4—44no—
131C22×C5×D4C2×C418yescomplemented
132C22×C5×D4C2311yescharacteristic
133C22×C5×D4C2311yescharacteristic
134C22×C5×D4C2311yescharacteristic
135C22×C5×D4C2311yescharacteristic
136C23×C4×C5C2312yes—
137C23×C4×C5C2312yes—
138C23×C4×C5C2311yescharacteristic
139C22×C22⋊D5—24no—
140C22×C22⋊D5—24no—
141C22×C22⋊D5—44no—
142C22×C22⋊D5C2×C418yescomplemented
143C22×C22⋊D5C2×C418yescomplemented
144C22×C22⋊D5C2311yescharacteristic
145C22×C22⋊D5C2311yescharacteristic
146C22×C22⋊D5C2311yescharacteristic
147C22×C22⋊D5C2311yescharacteristic
148C22×C22⋊D5C2311yescharacteristic
149C22×C22⋊D5C2311yescharacteristic
150C22×C22⋊D5C2311yescharacteristic
151C22×C22⋊D5C2311yescharacteristic
152C23×Dic5—24no—
153C23×Dic5—24no—
154C23×Dic5C2×C418yescomplemented
155C23×Dic5C2312yes—
156C23×Dic5C2311yescharacteristic
157C23×Dic5C2311yescharacteristic
158C23×Dic5C2311yescharacteristic
159C23×Dic5C2311yescharacteristic
160C23×Dic5C2311yescharacteristic
161C23×Dic5C2312yes—
162C23×Dic5C2311yescharacteristic
163C23×Dic5C2311yescharacteristic
164C22×C4×D5C2312yes—
165C22×C4×D5C2312yes—
166C4×C5×D4—44no—
167C2×C5×C4⋊C4C2312yes—
168C2×C5×C22⋊C4—24no—
169C2×C5×C22⋊C4—24no—
170C2×C5×C22⋊C4C2311yescharacteristic
171C2×C5×C22⋊C4C2311yescharacteristic
172C2×C5×C22⋊C4C2311yescharacteristic
173C2×C5×C22⋊C4C2312yes—
174C2×C5×C22⋊C4C2312yes—
175C2×C5×C22⋊C4C2312yes—
176C2×C5×C22⋊C4C2312yes—
177C2×C5×C22⋊C4C2312yes—
178C2×C5×C22⋊C4C2312yes—
179C2×C5×C22⋊C4C2311yescharacteristic
180C2×C42×C5C2312yes—
181C2×C22⋊Dic5—24no—
182C2×C22⋊Dic5—24no—
183C2×C22⋊Dic5C2×C418yescomplemented
184C2×C22⋊Dic5C2311yescharacteristic
185C2×C22⋊Dic5C2311yescharacteristic
186C2×C22⋊Dic5C2311yescharacteristic
187C2×C22⋊Dic5C2312yes—
188C2×C22⋊Dic5C2312yes—
189C2×C22⋊Dic5C2312yes—
190C2×C22⋊Dic5C2312yes—
191C2×C22⋊Dic5C2312yes—
192C2×C22⋊Dic5C2312yes—
193C2×C22⋊Dic5C2311yescharacteristic
194C2×C22⋊Dic5C2311yescharacteristic
195C2×C22⋊Dic5C2311yescharacteristic
196C2×C22⋊Dic5C2311yescharacteristic
197C2×C22⋊Dic5C2311yescharacteristic
198#4085C2×C418yescomplemented
199#4085C2×C418yescomplemented
200#4085C2×C418yescomplemented
201#4085C2×C418yescomplemented
202#4085C2×C418yescomplemented
203#4085C2×C418yescomplemented
204#4085C2×C418yescomplemented
205#4085C2×C418yescomplemented
206D4×Dic5—44no—
207C4×C22⋊D5—28no—
208C4×C22⋊D5—28no—
209C4×C22⋊D5—44no—
210C2×#685C2×C418yescomplemented
211C2×#685C2312yes—
212C2×#685C2312yes—
213C2×#685C2312yes—
214C2×#685C2312yes—
215C2×#685C2312yes—
216C2×#685C2312yes—
217C2×#685C2311yescharacteristic
218C2×#685C2311yescharacteristic
219C2×#685C2311yescharacteristic
220C2×#685C2311yescharacteristic
221C2×C4⋊Dic5C2312yes—
222C2×#683—28no—
223C2×#683C2×C418yescomplemented
224C2×#683C2312yes—
225C2×#683C2312yes—
226C2×#683C2312yes—
227C2×#683C2312yes—
228C2×#683C2312yes—
229C2×#683C2312yes—
230C2×#683C2312yes—
231C2×#683C2311yescharacteristic
232C2×#683C2311yescharacteristic
233C2×#683C2311yescharacteristic
234C2×#683C2311yescharacteristic
235C2×#683C2312yes—
236C2×C4×Dic5—28no—
237C2×C4×Dic5C2312yes—
238C2×C4×Dic5C2312yes—
239C2×C4×Dic5C2312yes—
240C2×C4×Dic5C2312yes—
241C2×C4×Dic5C2312yes—
242C2×C4×Dic5C2312yes—
243C2×C4×Dic5C2312yes—
244C2×C4×Dic5C2312yes—
245C2×C4×Dic5C2312yes—
246#4027—28no—
247#4027—28no—
248#4027—44no—
249D5×C22⋊C4—24no—
250D5×C22⋊C4—24no—
251#4023—24no—
252#4023—24no—
253#4023—24no—
254#4023—24no—
255#4023—24no—
256#4023—28no—
257#4023—28no—
258#4023D418yescomplemented
259C5×#95C2312yes—
260C5×#95C2312yes—
261#3963C2312yes—
262#3963C2312yes—
263#3963C2312yes—
264#3963C2312yes—
265#3963C2312yes—
266#3963C2312yes—
267#3963C2312yes—
268#3963C2312yes—
269#3963C2312yes—
270#3963C2312yes—
271C22×#121—51no—
272C2×#518—51no—
273C22×#117—51no—
274#2363—52no—
275#2363—52no—
276#2361—52no—
277#2361—52no—
278#2342—51no—
279#2342—51no—
280#2342—51no—
281#2342—51no—
282D4×C22⋊C4—51no—
283D4×C22⋊C4—51no—
284D4×C22⋊C4—51no—
285D4×C22⋊C4D511yescharacteristic, complemented
286#2324—52no—
287#2324—52no—
288#2316—51no—
289#2309—51no—
290C4×#121—52no—
291C4×#121—52no—
292#2280—51no—
293#2274—51no—
294C24×C5—22no—
295C24×C5—22no—
296C24×C5—24no—
297C24×C5—22no—
298C24×C5—22no—
299C24×C5—42no—
300C24×C5—42no—
301C24×C5—42no—
302C24×C5C22×C414yes—
303C24×C5C22×C414yes—
304C24×C5C2411yescharacteristic
305C24×C5C2411yescharacteristic
306C24×C5C2411yescharacteristic
307C24×C5C2411yescharacteristic
308C24×C5C2411yescharacteristic
309C23×D5—22no—
310C23×D5—22no—
311C23×D5—42no—
312C23×D5—42no—
313C23×D5C22×C414yes—
314C23×D5C2411yescharacteristic
315C23×D5C2411yescharacteristic
316C2×C5×D4—24no—
317C2×C5×D4—24no—
318C2×C5×D4—42no—
319C2×C5×D4—42no—
320C2×C5×D4—416no—
321C2×C5×D4C22×C414yes—
322C2×C5×D4C22×C414yes—
323C2×C5×D4C22×C414yes—
324C2×C5×D4C22×C414yes—
325C22×C4×C5—24no—
326C22×C4×C5—24no—
327C22×C4×C5—24no—
328C22×C4×C5—42no—
329C22×C4×C5—42no—
330C22×C4×C5—42no—
331C22×C4×C5—42no—
332C22×C4×C5C22×C414yes—
333C22×C4×C5C2412yes—
334C22×C4×C5C2412yes—
335C22×C4×C5C2412yes—
336C22×C4×C5C2411yescharacteristic
337C22×C4×C5C2411yescharacteristic
338C22×C4×C5C2412yes—
339C2×C22⋊D5—24no—
340C2×C22⋊D5—24no—
341C2×C22⋊D5—232no—
342C2×C22⋊D5—22no—
343C2×C22⋊D5—22no—
344C2×C22⋊D5—22no—
345C2×C22⋊D5—22no—
346C2×C22⋊D5—22no—
347C2×C22⋊D5—22no—
348C2×C22⋊D5—22no—
349C2×C22⋊D5—22no—
350C2×C22⋊D5—42no—
351C2×C22⋊D5—42no—
352C2×C22⋊D5—416no—
353C2×C22⋊D5C22×C414yes—
354C2×C22⋊D5C22×C414yes—
355C2×C22⋊D5C22×C414yes—
356C2×C22⋊D5C22×C414yes—
357C2×C22⋊D5C22×C414yes—
358C2×C22⋊D5C22×C414yes—
359C2×C22⋊D5C22×C414yes—
360C2×C22⋊D5C22×C414yes—
361C22×Dic5—22no—
362C22×Dic5—22no—
363C22×Dic5—232no—
364C22×Dic5—22no—
365C22×Dic5—22no—
366C22×Dic5—22no—
367C22×Dic5—22no—
368C22×Dic5—22no—
369C22×Dic5—22no—
370C22×Dic5—22no—
371C22×Dic5—22no—
372C22×Dic5—24no—
373C22×Dic5—24no—
374C22×Dic5—24no—
375C22×Dic5—42no—
376C22×Dic5—42no—
377C22×Dic5—42no—
378C22×Dic5—42no—
379C22×Dic5C22×C414yes—
380C22×Dic5C22×C414yes—
381C22×Dic5C22×C414yes—
382C22×Dic5C22×C414yes—
383C22×Dic5C22×C414yes—
384C22×Dic5C22×C414yes—
385C22×Dic5C22×C414yes—
386C22×Dic5C2×D414yes—
387C22×Dic5#4114yes—
388C22×Dic5C2412yes—
389C22×Dic5C2412yes—
390C22×Dic5C2412yes—
391C22×Dic5C2411yescharacteristic
392C22×Dic5C2411yescharacteristic
393C22×Dic5C2411yescharacteristic
394C22×Dic5C2411yescharacteristic
395C22×Dic5C2412yes—
396C22×Dic5C2411yescharacteristic
397C22×Dic5C2411yescharacteristic
398C2×C4×D5—24no—
399C2×C4×D5—24no—
400C2×C4×D5—42no—
401C2×C4×D5—42no—
402C2×C4×D5—42no—
403C2×C4×D5—42no—
404C5×C4⋊C4—42no—
405C5×C22⋊C4—22no—
406C5×C22⋊C4—22no—
407C5×C22⋊C4—22no—
408C5×C22⋊C4—24no—
409C5×C22⋊C4—24no—
410C5×C22⋊C4—24no—
411C5×C22⋊C4—42no—
412C5×C22⋊C4—42no—
413C5×C22⋊C4—42no—
414C5×C22⋊C4C2×D414yes—
415C42×C5—42no—
416C22⋊Dic5—22no—
417C22⋊Dic5—22no—
418C22⋊Dic5—22no—
419C22⋊Dic5—24no—
420C22⋊Dic5—24no—
421C22⋊Dic5—24no—
422C22⋊Dic5—42no—
423C22⋊Dic5—42no—
424C22⋊Dic5—42no—
425C22⋊Dic5C22×C414yes—
426C22⋊Dic5C22×C414yes—
427C22⋊Dic5C22×C414yes—
428C22⋊Dic5C22×C414yes—
429C22⋊Dic5C2×D414yes—
430#685—24no—
431#685—24no—
432#685—42no—
433#685—42no—
434#685—42no—
435#685—42no—
436#685C22×C414yes—
437#685C22×C414yes—
438#685C22×C414yes—
439#685C22×C414yes—
440C4⋊Dic5—42no—
441#683—24no—
442#683—24no—
443#683—24no—
444#683—24no—
445#683—24no—
446#683—42no—
447#683—42no—
448#683C22×C414yes—
449#683C22×C414yes—
450#683C22×C414yes—
451#683C22×C414yes—
452#683C2×D418yescomplemented
453C4×Dic5—24no—
454C4×Dic5—24no—
455C4×Dic5—24no—
456C4×Dic5—24no—
457C4×Dic5—24no—
458C4×Dic5—42no—
459C4×Dic5—42no—
460C4×Dic5—42no—
461C4×Dic5C2×D418yescomplemented
462C23×D4—51no—
463C23×D4—51no—
464C23×D4C2×D511yescharacteristic
465C24×C4—51no—
466C2×#121—516no—
467C2×#121—51no—
468C2×#121—51no—
469C2×#121—51no—
470C2×#121—51no—
471C2×#121—51no—
472C2×#121—51no—
473C2×#121—51no—
474C2×#121—51no—
475#518—108no—
476C2×C4×D4—52no—
477C2×C4×D4—52no—
478C2×C4×D4—52no—
479C2×C4×D4—52no—
480C2×C4×D4—52no—
481C2×C4×D4—52no—
482C2×C4×D4—52no—
483C2×C4×D4C2×D512yescomplemented
484C2×#117—51no—
485C2×#117—51no—
486C2×#117—51no—
487C2×#117—51no—
488C2×#117—52no—
489C2×#117—51no—
490C2×#117—51no—
491C2×#117—52no—
492C2×#117—108no—
493C22×C4⋊C4—51no—
494C22×C4⋊C4—52no—
495C22×C22⋊C4—51no—
496C22×C22⋊C4—51no—
497C22×C22⋊C4—51no—
498C22×C22⋊C4—51no—
499C22×C22⋊C4—51no—
500C22×C22⋊C4—51no—
501C22×C22⋊C4C2×D511yescharacteristic
502C22×C22⋊C4C2×D511yescharacteristic
503C22×C42—52no—
504#390—52no—
505#390—52no—
506#390—52no—
507#390—52no—
508#390—52no—
509#390—52no—
510#390—52no—
511#390C2×D512yescomplemented
512#389—52no—
513#389—52no—
514#389—52no—
515#389—52no—
516#388—52no—
517#388—52no—
518#388—52no—
519#388—52no—
520#388—52no—
521#388—52no—
522#388—52no—
523#388—52no—
524#386—52no—
525#386—52no—
526#386—52no—
527#386—52no—
528#386—52no—
529#386—52no—
530#386C2×D512yescomplemented
531#386C2×D512yescomplemented
532#385—52no—
533#385—52no—
534#385—52no—
535#385—52no—
536#381—51no—
537#381—51no—
538#380—51no—
539#380—51no—
540#380—51no—
541#380—52no—
542#380—52no—
543#380C2×D511yescharacteristic
544#379—51no—
545#379—51no—
546#379—51no—
547#379—51no—
548#379C2×D511yescharacteristic
549#379C2×D511yescharacteristic
550C4×C4⋊C4—52no—
551C4×C4⋊C4—52no—
552C4×C4⋊C4—52no—
553C4×C4⋊C4—52no—
554C4×C22⋊C4—51no—
555C4×C22⋊C4—52no—
556C4×C22⋊C4—51no—
557C4×C22⋊C4—51no—
558C4×C22⋊C4—52no—
559C4×C22⋊C4—52no—
560C4×C22⋊C4—52no—
561C4×C22⋊C4—52no—
562C4×C22⋊C4—52no—
563C4×C22⋊C4C2×D511yescharacteristic
564C23×C5—21no—
565C23×C5—21no—
566C23×C5—22no—
567C23×C5—22no—
568C23×C5—22no—
569C23×C5—28no—
570C23×C5—28no—
571C23×C5—21no—
572C23×C5—21no—
573C23×C5—21no—
574C23×C5—21no—
575C23×C5—21no—
576C23×C5—21no—
577C23×C5—22no—
578C23×C5—22no—
579C23×C5—22no—
580C23×C5—22no—
581C23×C5—22no—
582C23×C5—22no—
583C23×C5—28no—
584C23×C5—44no—
585C23×C5—44no—
586C23×C5—44no—
587C23×C5—48no—
588C23×C5—48no—
589C23×C5—84no—
590C23×C5—84no—
591C23×C5C23×C412yes—
592C23×C5C23×C412yes—
593C23×C5C23×C412yes—
594C23×C5C23×C412yes—
595C23×C5C23×C412yes—
596C23×C5C22×D412yes—
597C23×C5C2×#4112yes—
598C23×C5H(5,𝔽2)14yes—
599C23×C5C2511yescharacteristic
600C22×D5—21no—
601C22×D5—21no—
602C22×D5—21no—
603C22×D5—21no—
604C22×D5—22no—
605C22×D5—22no—
606C22×D5—22no—
607C22×D5—22no—
608C22×D5—28no—
609C22×D5—44no—
610C22×D5—44no—
611C22×D5—84no—
612C22×D5—84no—
613C22×D5C23×C412yes—
614C22×D5C23×C412yes—
615C5×D4—28no—
616C5×D4—28no—
617C5×D4—44no—
618C5×D4—44no—
619C2×C4×C5—22no—
620C2×C4×C5—22no—
621C2×C4×C5—22no—
622C2×C4×C5—22no—
623C2×C4×C5—22no—
624C2×C4×C5—22no—
625C2×C4×C5—22no—
626C2×C4×C5—22no—
627C2×C4×C5—22no—
628C2×C4×C5—22no—
629C2×C4×C5—22no—
630C2×C4×C5—22no—
631C2×C4×C5—22no—
632C2×C4×C5—44no—
633C2×C4×C5—48no—
634C2×C4×C5—84no—
635C2×C4×C5C23×C412yes—
636C2×C4×C5C23×C412yes—
637C2×C4×C5C22×D414yes—
638C22⋊D5—28no—
639C22⋊D5—28no—
640C22⋊D5—28no—
641C22⋊D5—28no—
642C22⋊D5—28no—
643C22⋊D5—28no—
644C22⋊D5—44no—
645C22⋊D5—44no—
646C2×Dic5—28no—
647C2×Dic5—21no—
648C2×Dic5—21no—
649C2×Dic5—21no—
650C2×Dic5—21no—
651C2×Dic5—22no—
652C2×Dic5—22no—
653C2×Dic5—22no—
654C2×Dic5—22no—
655C2×Dic5—28no—
656C2×Dic5—28no—
657C2×Dic5—28no—
658C2×Dic5—28no—
659C2×Dic5—22no—
660C2×Dic5—22no—
661C2×Dic5—22no—
662C2×Dic5—22no—
663C2×Dic5—22no—
664C2×Dic5—22no—
665C2×Dic5—22no—
666C2×Dic5—22no—
667C2×Dic5—22no—
668C2×Dic5—44no—
669C2×Dic5—48no—
670C2×Dic5—84no—
671C2×Dic5C4×D4116yescomplemented
672C2×Dic5C23×C412yes—
673C2×Dic5C23×C412yes—
674C2×Dic5C23×C412yes—
675C2×Dic5C23×C412yes—
676C2×Dic5C23×C412yes—
677C2×Dic5C23×C412yes—
678C2×Dic5C22×D414yes—
679C2×Dic5C22×D412yes—
680C2×Dic5C22×D412yes—
681C2×Dic5C2×#4112yes—
682C2×Dic5C2×#4112yes—
683C4×D5—84no—
684C4×D5—84no—
685C25—51no—
686C25C22×D511yescharacteristic
687C25C22×D511yescharacteristic
688C22×D4—44no—
689C22×D4—58no—
690C22×D4—51no—
691C22×D4—51no—
692C22×D4—51no—
693C22×D4—51no—
694C22×D4—51no—
695C22×D4—51no—
696C22×D4—58no—
697C22×D4—51no—
698C22×D4—51no—
699C22×D4—104no—
700C22×D4—104no—
701C22×D4—204no—
702C22×D4C4×D518yescomplemented
703C22×D4C22×D511yescharacteristic
704C22×D4C22×D511yescharacteristic
705C22×D4C22×D511yescharacteristic
706C22×D4C22×D511yescharacteristic
707C23×C4—51no—
708C23×C4—58no—
709C23×C4—51no—
710C23×C4—51no—
711C23×C4—51no—
712C23×C4—51no—
713C23×C4—51no—
714C23×C4—51no—
715C23×C4—52no—
716C23×C4—52no—
717C23×C4—52no—
718C23×C4—52no—
719C23×C4—104no—
720C23×C4—104no—
721C23×C4C22×D512yes—
722C23×C4C22×D512yes—
723C23×C4C22×D511yescharacteristic
724#121—58no—
725#121—58no—
726#121—58no—
727#121—58no—
728#121—58no—
729#121—58no—
730#121—58no—
731#121—58no—
732C4×D4—44no—
733C4×D4—108no—
734C4×D4—108no—
735C4×D4—108no—
736C4×D4—108no—
737C4×D4—204no—
738C4×D4—204no—
739C4×D4—204no—
740#117—58no—
741#117—108no—
742#117—104no—
743#117—108no—
744#117—104no—
745#117—104no—
746#117—104no—
747#117—104no—
748C2×C4⋊C4—58no—
749C2×C4⋊C4—52no—
750C2×C4⋊C4—51no—
751C2×C4⋊C4—51no—
752C2×C4⋊C4—51no—
753C2×C4⋊C4—51no—
754C2×C4⋊C4—52no—
755C2×C4⋊C4—52no—
756C2×C4⋊C4—52no—
757C2×C4⋊C4—52no—
758C2×C4⋊C4—52no—
759C2×C4⋊C4—52no—
760C2×C4⋊C4—52no—
761C2×C4⋊C4—52no—
762C2×C4⋊C4—108no—
763C2×C4⋊C4C22×D512yes—
764C2×C22⋊C4—24no—
765C2×C22⋊C4—24no—
766C2×C22⋊C4—58no—
767C2×C22⋊C4—51no—
768C2×C22⋊C4—51no—
769C2×C22⋊C4—51no—
770C2×C22⋊C4—51no—
771C2×C22⋊C4—51no—
772C2×C22⋊C4—58no—
773C2×C22⋊C4—51no—
774C2×C22⋊C4—51no—
775C2×C22⋊C4—51no—
776C2×C22⋊C4—51no—
777C2×C22⋊C4—51no—
778C2×C22⋊C4—51no—
779C2×C22⋊C4—52no—
780C2×C22⋊C4—52no—
781C2×C22⋊C4—51no—
782C2×C22⋊C4—52no—
783C2×C22⋊C4—52no—
784C2×C22⋊C4—52no—
785C2×C22⋊C4—52no—
786C2×C22⋊C4—52no—
787C2×C22⋊C4—52no—
788C2×C22⋊C4—52no—
789C2×C22⋊C4—52no—
790C2×C22⋊C4—52no—
791C2×C22⋊C4—52no—
792C2×C22⋊C4—104no—
793C2×C22⋊C4—104no—
794C2×C22⋊C4—104no—
795C2×C22⋊C4—104no—
796C2×C22⋊C4C22×D511yescharacteristic
797C2×C22⋊C4C22×D511yescharacteristic
798C2×C22⋊C4C22×D512yes—
799C2×C22⋊C4C22×D512yes—
800C2×C22⋊C4C22×D511yescharacteristic
801C2×C22⋊C4C22×D512yes—
802C2×C22⋊C4C22×D512yes—
803C2×C22⋊C4C22×D512yes—
804C2×C22⋊C4C22×D512yes—
805C2×C22⋊C4C22×D511yescharacteristic
806C2×C42—52no—
807C2×C42—52no—
808C2×C42—52no—
809C2×C42—52no—
810C2×C42—52no—
811C2×C42—52no—
812C2×C42—52no—
813C2×C42—52no—
814C2×C42—52no—
815C2×C42—108no—
816C2×C42C22×D512yes—
817#95—52no—
818#95—52no—
819#95—52no—
820#95—52no—
821#95—52no—
822#95—52no—
823#95—52no—
824#95—52no—
825#95—52no—
826#95—52no—
827#95C22×D512yes—
828#95C22×D512yes—
829C22×C5—22no—
830C22×C5—22no—
831C22×C5—22no—
832C22×C5—22no—
833C22×C5—24no—
834C22×C5—24no—
835C22×C5—24no—
836C22×C5—24no—
837C22×C5—22no—
838C22×C5—22no—
839C22×C5—22no—
840C22×C5—22no—
841C22×C5—22no—
842C22×C5—22no—
843C22×C5—22no—
844C22×C5—22no—
845C22×C5—22no—
846C22×C5—416no—
847C22×C5—42no—
848C22×C5—42no—
849C22×C5—42no—
850C22×C5—42no—
851C22×C5—42no—
852C22×C5—42no—
853C22×C5—88no—
854C22×C5C2×C4×D414yes—
855C22×C5#51814yescomplemented
856C22×C5C24×C411yescharacteristic
857C22×C5C23×D411yescharacteristic
858C22×C5C22×#4111yescharacteristic
859C22×C5C2×H(5,𝔽2)12yes—
860C22×C5#58512yes—
861C2×D5—22no—
862C2×D5—22no—
863C2×D5—22no—
864C2×D5—22no—
865C2×D5—22no—
866C2×D5—22no—
867C2×D5—42no—
868C2×D5—42no—
869C2×D5—42no—
870C2×D5—42no—
871C2×D5—88no—
872C4×C5—22no—
873C4×C5—22no—
874C4×C5—24no—
875C4×C5—42no—
876C4×C5—42no—
877C4×C5—42no—
878Dic5—22no—
879Dic5—22no—
880Dic5—22no—
881Dic5—22no—
882Dic5—24no—
883Dic5—42no—
884Dic5—42no—
885Dic5—42no—
886Dic5C2×C4×D414yes—
887Dic5C2×C4×D414yes—
888C24—22no—
889C24—24no—
890C24—22no—
891C24—22no—
892C24—22no—
893C24—42no—
894C24—42no—
895C24—42no—
896C24—51no—
897C24—51no—
898C24—54no—
899C24—102no—
900C24—102no—
901C24—202no—
902C24—202no—
903C24C2×C4×D514yes—
904C24C2×C4×D514yes—
905C24C23×D511yescharacteristic
906C24C23×D511yescharacteristic
907C24C23×D511yescharacteristic
908C24C23×D511yescharacteristic
909C24C23×D511yescharacteristic
910C2×D4—24no—
911C2×D4—24no—
912C2×D4—42no—
913C2×D4—42no—
914C2×D4—416no—
915C2×D4—54no—
916C2×D4—54no—
917C2×D4—54no—
918C2×D4—54no—
919C2×D4—54no—
920C2×D4—54no—
921C2×D4—54no—
922C2×D4—54no—
923C2×D4—102no—
924C2×D4—102no—
925C2×D4—102no—
926C2×D4—102no—
927C2×D4—1032no—
928C2×D4—102no—
929C2×D4—102no—
930C2×D4—102no—
931C2×D4—102no—
932C2×D4—104no—
933C2×D4—104no—
934C2×D4—202no—
935C2×D4—202no—
936C2×D4—2016no—
937C2×D4C2×C4×D514yes—
938C2×D4C2×C4×D514yes—
939C2×D4C2×C4×D514yes—
940C2×D4C2×C4×D514yes—
941C22×C4—24no—
942C22×C4—24no—
943C22×C4—24no—
944C22×C4—42no—
945C22×C4—42no—
946C22×C4—42no—
947C22×C4—42no—
948C22×C4—54no—
949C22×C4—54no—
950C22×C4—54no—
951C22×C4—51no—
952C22×C4—51no—
953C22×C4—54no—
954C22×C4—54no—
955C22×C4—54no—
956C22×C4—54no—
957C22×C4—54no—
958C22×C4—51no—
959C22×C4—51no—
960C22×C4—51no—
961C22×C4—51no—
962C22×C4—52no—
963C22×C4—54no—
964C22×C4—52no—
965C22×C4—52no—
966C22×C4—52no—
967C22×C4—104no—
968C22×C4—102no—
969C22×C4—102no—
970C22×C4—102no—
971C22×C4—102no—
972C22×C4—1032no—
973C22×C4—102no—
974C22×C4—102no—
975C22×C4—102no—
976C22×C4—102no—
977C22×C4—104no—
978C22×C4—104no—
979C22×C4—102no—
980C22×C4—102no—
981C22×C4—104no—
982C22×C4—104no—
983C22×C4—202no—
984C22×C4—202no—
985C22×C4—202no—
986C22×C4—202no—
987C22×C4—202no—
988C22×C4—202no—
989C22×C4—202no—
990C22×C4—202no—
991C22×C4C2×C4×D514yes—
992C22×C4C23×D512yes—
993C22×C4C23×D512yes—
994C22×C4C23×D512yes—
995C22×C4C23×D511yescharacteristic
996C22×C4C23×D511yescharacteristic
997C22×C4C23×D512yes—
998C4⋊C4—42no—
999C4⋊C4—54no—
1000C4⋊C4—54no—
1001C4⋊C4—54no—
1002C4⋊C4—54no—
1003C4⋊C4—58no—
1004C4⋊C4—104no—
1005C4⋊C4—104no—
1006C4⋊C4—104no—
1007C4⋊C4—104no—
1008C4⋊C4—104no—
1009C4⋊C4—202no—
1010C4⋊C4—202no—
1011C4⋊C4—202no—
1012C22⋊C4—22no—
1013C22⋊C4—22no—
1014C22⋊C4—24no—
1015C22⋊C4—22no—
1016C22⋊C4—24no—
1017C22⋊C4—24no—
1018C22⋊C4—42no—
1019C22⋊C4—42no—
1020C22⋊C4—42no—
1021C22⋊C4—54no—
1022C22⋊C4—54no—
1023C22⋊C4—54no—
1024C22⋊C4—54no—
1025C22⋊C4—54no—
1026C22⋊C4—54no—
1027C22⋊C4—54no—
1028C22⋊C4—54no—
1029C22⋊C4—54no—
1030C22⋊C4—104no—
1031C22⋊C4—104no—
1032C22⋊C4—104no—
1033C22⋊C4—102no—
1034C22⋊C4—102no—
1035C22⋊C4—104no—
1036C22⋊C4—102no—
1037C22⋊C4—104no—
1038C22⋊C4—202no—
1039C22⋊C4—202no—
1040C22⋊C4—202no—
1041C22⋊C4—202no—
1042C22⋊C4—202no—
1043C22⋊C4—202no—
1044C22⋊C4—202no—
1045C22⋊C4D4×D514yes—
1046C42—42no—
1047C42—58no—
1048C42—104no—
1049C42—104no—
1050C42—104no—
1051C42—104no—
1052C42—104no—
1053C42—202no—
1054C42—202no—
1055C42—202no—
1056C2×C5—24no—
1057C2×C5—24no—
1058C2×C5—42no—
1059C2×C5—42no—
1060C2×C5—42no—
1061C2×C5C22×C4×D411yescharacteristic
1062C2×C5C2×#51811yescharacteristic
1063C2×C5#342811yescharacteristic
1064C2×C5#348812yes—
1065C2×C5#349412yes—
1066D5—42no—
1067D5—42no—
1068C23—21no—
1069C23—22no—
1070C23—21no—
1071C23—22no—
1072C23—22no—
1073C23—28no—
1074C23—28no—
1075C23—21no—
1076C23—21no—
1077C23—21no—
1078C23—22no—
1079C23—22no—
1080C23—22no—
1081C23—21no—
1082C23—21no—
1083C23—21no—
1084C23—22no—
1085C23—22no—
1086C23—22no—
1087C23—28no—
1088C23—44no—
1089C23—44no—
1090C23—44no—
1091C23—48no—
1092C23—48no—
1093C23—52no—
1094C23—52no—
1095C23—84no—
1096C23—84no—
1097C23—101no—
1098C23—101no—
1099C23—102no—
1100C23—102no—
1101C23—101no—
1102C23—101no—
1103C23—102no—
1104C23—102no—
1105C23—108no—
1106C23—204no—
1107C23—204no—
1108C23—404no—
1109C23—404no—
1110C23C22×C4×D512yes—
1111C23C22×C4×D512yes—
1112C23C22×C4×D512yes—
1113C23C22×C4×D512yes—
1114C23C22×C4×D512yes—
1115C23C2×D4×D512yes—
1116C23#414414yes—
1117C23D5×#4112yes—
1118C23C24×D511yescharacteristic
1119D4—28no—
1120D4—28no—
1121D4—44no—
1122D4—44no—
1123D4—108no—
1124D4—108no—
1125D4—108no—
1126D4—108no—
1127D4—108no—
1128D4—108no—
1129D4—204no—
1130D4—204no—
1131C2×C4—22no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—44no—
1145C2×C4—48no—
1146C2×C4—516no—
1147C2×C4—52no—
1148C2×C4—52no—
1149C2×C4—52no—
1150C2×C4—52no—
1151C2×C4—52no—
1152C2×C4—52no—
1153C2×C4—52no—
1154C2×C4—52no—
1155C2×C4—52no—
1156C2×C4—52no—
1157C2×C4—54no—
1158C2×C4—84no—
1159C2×C4—108no—
1160C2×C4—108no—
1161C2×C4—108no—
1162C2×C4—108no—
1163C2×C4—108no—
1164C2×C4—101no—
1165C2×C4—101no—
1166C2×C4—102no—
1167C2×C4—102no—
1168C2×C4—102no—
1169C2×C4—101no—
1170C2×C4—101no—
1171C2×C4—102no—
1172C2×C4—102no—
1173C2×C4—102no—
1174C2×C4—102no—
1175C2×C4—102no—
1176C2×C4—102no—
1177C2×C4—102no—
1178C2×C4—102no—
1179C2×C4—102no—
1180C2×C4—102no—
1181C2×C4—204no—
1182C2×C4—208no—
1183C2×C4—404no—
1184C2×C4—404no—
1185C2×C4—404no—
1186C2×C4C22×C4×D512yes—
1187C2×C4C22×C4×D512yes—
1188C2×C4C2×D4×D514yes—
1189C5#3420411yescharacteristic, complemented, Sylow
1190C22—22no—
1191C22—24no—
1192C22—24no—
1193C22—22no—
1194C22—22no—
1195C22—24no—
1196C22—24no—
1197C22—22no—
1198C22—22no—
1199C22—22no—
1200C22—22no—
1201C22—22no—
1202C22—22no—
1203C22—22no—
1204C22—22no—
1205C22—22no—
1206C22—22no—
1207C22—416no—
1208C22—42no—
1209C22—42no—
1210C22—42no—
1211C22—42no—
1212C22—42no—
1213C22—42no—
1214C22—88no—
1215C22—102no—
1216C22—102no—
1217C22—102no—
1218C22—102no—
1219C22—102no—
1220C22—102no—
1221C22—202no—
1222C22—202no—
1223C22—202no—
1224C22—202no—
1225C22—408no—
1226C22#6582014yescomplemented
1227C22C4×D4×D514yes—
1228C22C23×C4×D511yescharacteristic
1229C22C22×D4×D511yescharacteristic
1230C22C2×#414412yes—
1231C22C2×D5×#4111yescharacteristic
1232C22#6628512yes—
1233C4—24no—
1234C4—22no—
1235C4—22no—
1236C4—42no—
1237C4—42no—
1238C4—42no—
1239C4—54no—
1240C4—54no—
1241C4—102no—
1242C4—102no—
1243C4—104no—
1244C4—102no—
1245C4—102no—
1246C4—202no—
1247C4—202no—
1248C4—202no—
1249C2—24no—
1250C2—24no—
1251C2—42no—
1252C2—42no—
1253C2—42no—
1254C2—202no—
1255C2—202no—
1256C2C2×#6582011yescharacteristic
1257C2C2×C4×D4×D511yescharacteristic
1258C2#1061775711yescharacteristic
1259C2#1061850812yes—
1260C2#1061853212yes—
subgroupG/H
center, FrattiniC23C24×D5
commutatorC22×C5C24×C4
FittingC5×D4×C22⋊C4C2
socle, cosocleC23×C5C25
prime radicalC22×#4085C2
hypercenterD4×C22⋊C4D5
hypocenterC5#34204
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ D4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#65820C2semidirect
3. C22×#4023C2semidirect
4. C5×D4×C22⋊C4C2semidirect
5. D4×C22⋊Dic5C2semidirect
6. #10614071C2semidirect
7. C4×#4085C2semidirect
8. C22⋊C4×C22⋊D5C2semidirect
9. #10613829C2semidirect
10. #10608036C2semidirect
11. #10608027C2semidirect
12. #10606408C2semidirect
13. #10606407C2semidirect
14. #10606396C2semidirect
15. #10606391C2semidirect
16. #10605740C2semidirect
17. #10605600C2semidirect
18. #10605581C2semidirect
19. #10605553C2semidirect
20. #10605550C2semidirect
21. #10605548C2semidirect
22. #10605306C2semidirect
23. #10605166C2semidirect
28. C2×C4×C5×D4C22semidirect
34. C2×#4085C4semidirect
43. C2×D4×Dic5C22semidirect
44. C2×C4×C22⋊D5C22semidirect
45. C2×C4×C22⋊D5C22semidirect
46. C2×C4×C22⋊D5C22semidirect
49. C22×#683C22semidirect
50. C22×C4×Dic5C22semidirect
52. C2×#4027C22semidirect
53. C2×#4027C22semidirect
54. C2×#4027C22semidirect
64. C2×#4023C22semidirect
65. C2×#4023C22semidirect
66. C5×#390C22semidirect
67. C5×#386C22semidirect
68. C5×#386C22semidirect
75. #65510C22semidirect
76. #65509C22semidirect
77. #65509C22semidirect
78. #65502C22semidirect
80. #65499C22semidirect
82. C4×C22⋊Dic5C22semidirect
83. #65279C22semidirect
84. #65278C22semidirect
85. #65261C22semidirect
86. #65261C22semidirect
87. #65247C22semidirect
88. #65246C22semidirect
89. #65246C22semidirect
90. #65246C22semidirect
91. #65246C22semidirect
92. #65246C22semidirect
93. #65246C22semidirect
94. #65245C22semidirect
95. #65245C22semidirect
98. #65235C22semidirect
99. #65234C22semidirect
100. #65234C22semidirect
101. #65233C22semidirect
102. #65233C22semidirect
107. #65231C22semidirect
108. #65231C22semidirect
111. C22⋊C4×Dic5C22semidirect
112. C22⋊C4×Dic5C22semidirect
113. C22⋊C4×Dic5C22semidirect
114. #65229C22semidirect
115. C4×#685C22semidirect
116. C4×#683C22semidirect
117. C4×#683C22semidirect
118. #64959C22semidirect
119. #64958C22semidirect
120. #64957C22semidirect
121. #64955C22semidirect
122. #64938C22semidirect
123. #64938C22semidirect
124. #64936C22semidirect
125. #64936C22semidirect
131. C22×C5×D4C2×C4semidirect
142. C22×C22⋊D5C2×C4semidirect
143. C22×C22⋊D5C2×C4semidirect
154. C23×Dic5C2×C4semidirect
183. C2×C22⋊Dic5C2×C4semidirect
198. #4085C2×C4semidirect
199. #4085C2×C4semidirect
200. #4085C2×C4semidirect
201. #4085C2×C4semidirect
202. #4085C2×C4semidirect
203. #4085C2×C4semidirect
204. #4085C2×C4semidirect
205. #4085C2×C4semidirect
210. C2×#685C2×C4semidirect
223. C2×#683C2×C4semidirect
258. #4023D4semidirect
285. D4×C22⋊C4D5semidirect
452. #683C2×D4semidirect
461. C4×Dic5C2×D4semidirect
483. C2×C4×D4C2×D5semidirect
511. #390C2×D5semidirect
530. #386C2×D5semidirect
531. #386C2×D5semidirect
671. C2×Dic5C4×D4semidirect
702. C22×D4C4×D5semidirect
855. C22×C5#518semidirect
1189. C5#34204semidirect
1226. C22#65820semidirect

Maximal subgroups

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

subgroupindex
C22×#40852
C2×#658202
C22×#40232
C5×D4×C22⋊C42
D4×C22⋊Dic52
#106140712
C4×#40852
C22⋊C4×C22⋊D52
#106138292
#106080362
#106080272
#106064082
#106064072
#106063962
#106063912
#106057402
#106056002
#106055812
#106055532
#106055502
#106055482
#106053062
#106051662
#342045