Finite Group Databasebeta

← #12267215

Subgroups — #12267215

Order 1280.

3700 conjugacy classes of subgroups.

The subgroup lattice has 1278 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D4×Dic5C211yesmaximal, characteristic, complemented
2C2×#65930C211yesmaximal, characteristic, complemented
3C2×#65920C212yesmaximal, complemented
4C5×#2408C211yesmaximal, characteristic, complemented
5#10615780C211yesmaximal, characteristic, complemented
6#10614380C211yesmaximal, characteristic, complemented
7#10614375C211yesmaximal, characteristic, complemented
8Dic5×#121C211yesmaximal, characteristic, complemented
9#10614318C212yesmaximal, complemented
10#10614083C211yesmaximal, characteristic, complemented
11C4×D4×Dic5C211yesmaximal, characteristic, complemented
12#10608646C212yesmaximal, complemented
13#10608621C212yesmaximal, complemented
14#10608413C212yesmaximal, complemented
15#10608396C212yesmaximal, complemented
16#10608054C211yesmaximal, characteristic, complemented
17#10608048C211yesmaximal, characteristic, complemented
18#10608024C211yesmaximal, characteristic, complemented
19#10608020C211yesmaximal, characteristic, complemented
20#10605630C211yesmaximal, characteristic, complemented
21#10605596C211yesmaximal, characteristic, complemented
22#10605560C212yesmaximal, complemented
23#10605549C212yesmaximal, complemented
24C23×C5×D4C2211yescharacteristic
25C24×Dic5C2212yes—
26C22×#711C2212yescomplemented
27C2×C5×#121C2211yescharacteristic
28C2×C5×#121C2211yescharacteristic
29C2×C5×#120C2212yes—
30C2×C4×C5×D4C2211yescharacteristic
31C2×#4099C2212yes—
32C2×#4099C2212yes—
33C22×C22⋊Dic5C2212yes—
34C2×#4086C2211yescharacteristic
35C2×#4086C2211yescharacteristic
36C2×#4085C2212yes—
37C2×#4085C2212yescomplemented
38C2×#4085C2212yescomplemented
39C2×#4081C2212yescomplemented
40C2×D4×Dic5—28no—
41C2×D4×Dic5C2212yes—
42C2×D4×Dic5C2212yes—
43C2×D4×Dic5C2211yescharacteristic
44C2×D4×Dic5C2211yescharacteristic
45C2×D4×Dic5C2211yescharacteristic
46C2×D4×Dic5C2211yescharacteristic
47C2×D4×Dic5C2211yescharacteristic
48C2×D4×Dic5C2211yescharacteristic
49C2×D4×Dic5C2212yescomplemented
50C2×#4076C2211yescharacteristic
51C2×#4076C2211yescharacteristic, complemented
52C22×C4⋊Dic5C2211yescharacteristic
53C22×C4×Dic5C2211yescharacteristic
54C22×C4×Dic5C2211yescharacteristic, complemented
55#65930—28no—
56#65920—216no—
57C2×#4039C2211yescharacteristic, complemented
58C2×#4034C2211yescharacteristic, complemented
59C2×#4032C2212yescomplemented
60C2×#4031C2212yescomplemented
61C2×#4027C2212yes—
62C2×#4027C2212yescomplemented
63C2×#4027C2212yescomplemented
64C2×#4027C2212yescomplemented
65C2×#4024C2212yes—
66C2×#4024C2212yescomplemented
67C2×#4023C2212yescomplemented
68C5×#394C2212yes—
69C5×#392C2212yes—
70C5×#390C2211yescharacteristic
71C5×#390C2211yescharacteristic
72C5×#380C2211yescharacteristic
73C5×#379C2212yes—
74#65512C2212yes—
75#65512C2212yes—
76#65512C2212yescomplemented
77#65511C2212yescomplemented
78#65510C2211yescharacteristic
79#65510C2211yescharacteristic
80#65509C2212yescomplemented
81#65501C2211yescharacteristic, complemented
82C4×C22⋊Dic5C2211yescharacteristic
83C4×C22⋊Dic5C2211yescharacteristic, complemented
84#65283C2212yescomplemented
85#65277C2211yescharacteristic, complemented
86#65274C2211yescharacteristic, complemented
87#65265C2211yescharacteristic, complemented
88C4⋊C4×Dic5C2211yescharacteristic, complemented
89C4⋊C4×Dic5C2211yescharacteristic, complemented
90C4⋊C4×Dic5C2211yescharacteristic, complemented
91#65262C2211yescharacteristic, complemented
92#65262C2211yescharacteristic, complemented
93#65250C2212yescomplemented
94#65250C2212yescomplemented
95#65250C2212yescomplemented
96#65248C2212yescomplemented
97#65247C2212yes—
98#65247C2212yes—
99#65247C2212yescomplemented
100#65247C2212yescomplemented
101#65246C2212yescomplemented
102#65246C2212yescomplemented
103#65241C2212yescomplemented
104#65240C2212yescomplemented
105#65237C2212yescomplemented
106#65236C2212yescomplemented
107#65235C2212yes—
108#65235C2212yescomplemented
109#65235C2212yescomplemented
110#65234C2212yescomplemented
111#65233C2212yescomplemented
112C22⋊C4×Dic5C2211yescharacteristic
113C22⋊C4×Dic5C2211yescharacteristic
114C22⋊C4×Dic5C2211yescharacteristic, complemented
115C22⋊C4×Dic5C2212yescomplemented
116C22⋊C4×Dic5C2211yescharacteristic, complemented
117C22⋊C4×Dic5C2212yescomplemented
118#65228C2211yescharacteristic, complemented
119C4×C4⋊Dic5C2211yescharacteristic, complemented
120C42×Dic5C2211yescharacteristic, complemented
121#65217C2211yescharacteristic, complemented
122#64958C2212yescomplemented
123#64955C2212yescomplemented
124#64946C2212yescomplemented
125#64945C2212yescomplemented
126#34681—51nomaximal, Sylow
127C25×C5C2312yes—
128C22×C5×D4—24no—
129C22×C5×D4—24no—
130C22×C5×D4—24no—
131C22×C5×D4C2312yes—
132C22×C5×D4C2312yes—
133C22×C5×D4C2312yes—
134C22×C5×D4C2311yescharacteristic
135C22×C5×D4C2311yescharacteristic
136C22×C5×D4C2311yescharacteristic
137C23×C4×C5C2311yescharacteristic
138C23×C4×C5C2311yescharacteristic
139C22×C22⋊D5C2312yes—
140C22×C22⋊D5C2312yes—
141C22×C22⋊D5C2312yes—
142C22×C22⋊D5C2312yes—
143C22×C22⋊D5C2312yes—
144C22×C22⋊D5C2312yes—
145C23×Dic5—28no—
146C23×Dic5—28no—
147C23×Dic5—44no—
148C23×Dic5C2312yes—
149C23×Dic5C2312yes—
150C23×Dic5C2312yes—
151C23×Dic5C2312yes—
152C23×Dic5C2311yescharacteristic
153C23×Dic5C2311yescharacteristic
154C23×Dic5C2312yes—
155C23×Dic5C2311yescharacteristic
156C23×Dic5C2311yescharacteristic
157C2×#711—28no—
158C2×#711—28no—
159C2×#711—44no—
160C22×D20C2311yescharacteristic
161C22×C4×D5C2312yes—
162C22×Dic10C2312yes—
163C5×#121—24no—
164C5×#121—24no—
165C5×#120—28no—
166C4×C5×D4—24no—
167C2×C5×C4⋊C4C2311yescharacteristic
168C2×C5×C4⋊C4C2311yescharacteristic
169C2×C5×C4⋊C4C2311yescharacteristic
170C2×C5×C22⋊C4C2311yescharacteristic
171C2×C5×C22⋊C4C2312yes—
172C2×C5×C22⋊C4C2312yes—
173C2×C5×C22⋊C4C2312yes—
174C2×C5×C22⋊C4C2312yes—
175C2×C5×C22⋊C4C2312yes—
176C2×C5×C22⋊C4C2311yescharacteristic
177C2×C5×C22⋊C4C2312yes—
178C2×C5×C22⋊C4C2312yes—
179C2×C42×C5C2311yescharacteristic
180#4099—28no—
181#4099—28no—
182C2×C22⋊Dic5—28no—
183C2×C22⋊Dic5C2312yes—
184C2×C22⋊Dic5C2312yes—
185C2×C22⋊Dic5C2312yes—
186C2×C22⋊Dic5C2312yes—
187C2×C22⋊Dic5C2312yes—
188C2×C22⋊Dic5C2311yescharacteristic
189C2×C22⋊Dic5C2312yes—
190C2×C22⋊Dic5C2312yes—
191C2×C22⋊Dic5C2312yes—
192C2×C22⋊Dic5C2311yescharacteristic
193C2×C22⋊Dic5C2312yes—
194C2×C22⋊Dic5C2311yescharacteristic
195C2×C22⋊Dic5C2311yescharacteristic
196#4086—24no—
197#4086—24no—
198#4085—28no—
199#4085—28no—
200#4085—28no—
201#4081—28no—
202D4×Dic5—24no—
203D4×Dic5—28no—
204D4×Dic5—28no—
205D4×Dic5—28no—
206D4×Dic5—24no—
207D4×Dic5—24no—
208D4×Dic5—24no—
209D4×Dic5D418yescomplemented
210D4×Dic5D418yescomplemented
211#4076—24no—
212#4076—24no—
213C2×#685C2312yes—
214C2×#685C2312yes—
215C2×#685C2312yes—
216C2×#685C2312yes—
217C2×#685C2312yes—
218C2×#685C2312yes—
219C2×#685C2312yes—
220C2×C4⋊Dic5—24no—
221C2×C4⋊Dic5C2312yes—
222C2×C4⋊Dic5C2312yes—
223C2×C4⋊Dic5C2311yescharacteristic
224C2×C4⋊Dic5C2311yescharacteristic
225C2×C4⋊Dic5C2311yescharacteristic
226C2×C4⋊Dic5C2311yescharacteristic
227C2×C4⋊Dic5C2311yescharacteristic
228C2×#683C2312yes—
229C2×#683C2312yes—
230C2×#683C2312yes—
231C2×#683C2312yes—
232C2×#683C2312yes—
233C2×#683C2312yes—
234C2×C4×Dic5—24no—
235C2×C4×Dic5—24no—
236C2×C4×Dic5C2312yes—
237C2×C4×Dic5C2311yescharacteristic
238C2×C4×Dic5C2311yescharacteristic
239C2×C4×Dic5C2311yescharacteristic
240C2×C4×Dic5C2311yescharacteristic
241C2×C4×Dic5C2311yescharacteristic
242C2×C4×Dic5C2311yescharacteristic
243C2×C4×Dic5C2311yescharacteristic
244C2×C4×Dic5C2311yescharacteristic
245C2×C4×Dic5C2311yescharacteristic
246C2×C4×Dic5C2311yescharacteristic
247C2×C4×Dic5C2311yescharacteristic
248C2×C4×Dic5C2311yescharacteristic
249#4039—24no—
250#4034—24no—
251#4032—28no—
252#4031—28no—
253#4027—28no—
254#4027—28no—
255#4027—28no—
256#4027—44no—
257#4024—28no—
258#4024—28no—
259#4023—28no—
260C5×#95C2312yes—
261#3963C2312yes—
262#3963C2311yescharacteristic
263#3963C2312yes—
264#3963C2311yescharacteristic
265#3963C2312yes—
266#3963C2312yes—
267#3963C2312yes—
268#3963C2312yes—
269#3963C2311yescharacteristic
270#3963C2311yescharacteristic
271#3963C2311yescharacteristic
272#3963C2311yescharacteristic
273C2×#532—51no—
274C2×#525—52no—
275C22×C4×D4—51no—
276#2472—52no—
277#2464—52no—
278#2461—52no—
279#2452—51no—
280#2445—51no—
281#2440—51no—
282#2433—51no—
283#2428—51no—
284#2424—52no—
285#2422—51no—
286#2416—51no—
287#2408D511yescharacteristic, complemented
288#2392—52no—
289#2388—52no—
290C4×#127—51no—
291C4×#121—51no—
292C4×#121—51no—
293C4×#120—52no—
294#2293—51no—
295C42×D4—51no—
296C24×C5—24no—
297C24×C5—24no—
298C24×C5—24no—
299C24×C5—24no—
300C24×C5—24no—
301C24×C5—42no—
302C24×C5—42no—
303C24×C5C2412yes—
304C24×C5C2411yescharacteristic
305C24×C5C2412yes—
306C24×C5C2411yescharacteristic
307C23×D5C2412yes—
308C2×C5×D4—232no—
309C2×C5×D4—24no—
310C2×C5×D4—22no—
311C2×C5×D4—24no—
312C2×C5×D4—22no—
313C2×C5×D4—24no—
314C2×C5×D4—24no—
315C2×C5×D4—24no—
316C2×C5×D4—24no—
317C2×C5×D4—22no—
318C2×C5×D4—24no—
319C2×C5×D4—22no—
320C2×C5×D4—22no—
321C2×C5×D4—22no—
322C2×C5×D4—42no—
323C2×C5×D4—42no—
324C2×C5×D4C2×D414yes—
325C2×C5×D4C2×D414yes—
326C2×C5×D4#4114yescomplemented
327C22×C4×C5—22no—
328C22×C4×C5—22no—
329C22×C4×C5—22no—
330C22×C4×C5—22no—
331C22×C4×C5—22no—
332C22×C4×C5#4114yescomplemented
333C22×C4×C5C2411yescharacteristic
334C22×C4×C5C2411yescharacteristic
335C22×C4×C5C2412yes—
336C22×C4×C5C2412yes—
337C22×C4×C5C2411yescharacteristic
338C22×C4×C5C2411yescharacteristic
339C22×C4×C5C2411yescharacteristic
340C2×C22⋊D5—24no—
341C2×C22⋊D5—24no—
342C2×C22⋊D5—24no—
343C2×C22⋊D5—24no—
344C2×C22⋊D5—24no—
345C2×C22⋊D5—24no—
346C2×C22⋊D5—24no—
347C2×C22⋊D5—24no—
348C2×C22⋊D5—24no—
349C2×C22⋊D5—24no—
350C2×C22⋊D5—24no—
351C2×C22⋊D5—24no—
352C2×C22⋊D5—24no—
353C2×C22⋊D5—42no—
354C2×C22⋊D5—42no—
355C2×C22⋊D5—42no—
356C2×C22⋊D5—42no—
357C2×C22⋊D5—42no—
358C22×Dic5—22no—
359C22×Dic5—24no—
360C22×Dic5—22no—
361C22×Dic5—22no—
362C22×Dic5—24no—
363C22×Dic5—22no—
364C22×Dic5—24no—
365C22×Dic5—24no—
366C22×Dic5—22no—
367C22×Dic5—22no—
368C22×Dic5—24no—
369C22×Dic5—24no—
370C22×Dic5—24no—
371C22×Dic5—24no—
372C22×Dic5—24no—
373C22×Dic5—24no—
374C22×Dic5—22no—
375C22×Dic5—22no—
376C22×Dic5—24no—
377C22×Dic5—42no—
378C22×Dic5—42no—
379C22×Dic5—42no—
380C22×Dic5—41no—
381C22×Dic5—41no—
382C22×Dic5—432no—
383C22×Dic5C2×D418yes—
384C22×Dic5C2×D414yes—
385C22×Dic5C2×D414yescomplemented
386C22×Dic5C2411yescharacteristic
387C22×Dic5C2412yes—
388C22×Dic5C2412yes—
389C22×Dic5C2411yescharacteristic
390C22×Dic5C2411yescharacteristic
391C22×Dic5C2411yescharacteristic
392C22×Dic5C2412yes—
393C22×Dic5C2411yescharacteristic
394C22×Dic5C2411yescharacteristic
395C22×Dic5C2411yescharacteristic
396C22×Dic5C2411yescharacteristic
397#711—432no—
398C2×D20—22no—
399C2×D20—22no—
400C2×D20—22no—
401C2×C4×D5—24no—
402C2×C4×D5—24no—
403C2×C4×D5—24no—
404C2×Dic10—24no—
405C2×Dic10—24no—
406C2×Dic10—42no—
407C5×C4⋊C4—22no—
408C5×C4⋊C4—22no—
409C5×C4⋊C4—22no—
410C5×C22⋊C4—24no—
411C5×C22⋊C4—24no—
412C5×C22⋊C4—22no—
413C5×C22⋊C4—24no—
414C5×C22⋊C4—24no—
415C5×C22⋊C4—24no—
416C5×C22⋊C4—22no—
417C5×C22⋊C4—42no—
418C5×C22⋊C4—42no—
419C42×C5—22no—
420C22⋊Dic5—24no—
421C22⋊Dic5—24no—
422C22⋊Dic5—24no—
423C22⋊Dic5—24no—
424C22⋊Dic5—24no—
425C22⋊Dic5—24no—
426C22⋊Dic5—24no—
427C22⋊Dic5—24no—
428C22⋊Dic5—22no—
429C22⋊Dic5C2×D418yes—
430C22⋊Dic5C2×D414yes—
431C22⋊Dic5C2×D414yescomplemented
432C22⋊Dic5#4114yescomplemented
433#685—24no—
434#685—24no—
435#685—24no—
436#685—24no—
437#685—24no—
438#685—42no—
439#685—42no—
440C4⋊Dic5—22no—
441C4⋊Dic5—22no—
442C4⋊Dic5—24no—
443C4⋊Dic5—24no—
444C4⋊Dic5—22no—
445C4⋊Dic5C2×D414yes—
446C4⋊Dic5C2×D414yescomplemented
447#683—24no—
448#683—24no—
449#683—24no—
450#683—24no—
451#683—24no—
452#683—42no—
453C4×Dic5—22no—
454C4×Dic5—22no—
455C4×Dic5—22no—
456C4×Dic5—24no—
457C4×Dic5—22no—
458C4×Dic5—22no—
459C4×Dic5—22no—
460C4×Dic5—22no—
461C4×Dic5—22no—
462C4×Dic5—22no—
463C4×Dic5—41no—
464C4×Dic5C2×D414yes—
465C4×Dic5C2×D414yescomplemented
466C22×#41—52no—
467C23×D4C2×D511yescharacteristic
468C24×C4—52no—
469#532—108no—
470C2×C4⋊Q8—51no—
471C2×#127—51no—
472C2×#127—51no—
473C2×#124—52no—
474#525—1016no—
475C2×#123—52no—
476C2×#123—52no—
477C2×C22⋊Q8—52no—
478C2×C22⋊Q8—52no—
479C2×#121—52no—
480C2×#121—52no—
481C2×#121—52no—
482C2×#121—51no—
483C2×#121—51no—
484C2×#121C2×D511yescharacteristic
485C2×#121C2×D511yescharacteristic
486C2×#120—52no—
487C2×#120—52no—
488C2×#120C2×D512yes—
489C2×C4×D4—51no—
490C2×C4×D4—51no—
491C2×C4×D4—51no—
492C2×C4×D4—52no—
493C2×C4×D4—51no—
494C2×C4×D4—51no—
495C2×C4×D4—52no—
496C2×C4×D4—51no—
497C2×C4×D4—52no—
498C2×C4×D4—51no—
499C2×C4×D4—52no—
500C2×C4×D4—52no—
501C2×C4×D4—52no—
502C2×C4×D4—52no—
503C2×C4×D4—108no—
504C2×C4×D4C2×D511yescharacteristic
505C2×#117—52no—
506C22×C4⋊C4—51no—
507C22×C22⋊C4—52no—
508C22×C42—51no—
509C22×C42—51no—
510#398—52no—
511#397—52no—
512#396—52no—
513#396—52no—
514#395—52no—
515#394—52no—
516#394—52no—
517#394—52no—
518#394—52no—
519#394—52no—
520#394C2×D512yes—
521#393—52no—
522#392—52no—
523#392—52no—
524#392—52no—
525#392C2×D512yes—
526#390—51no—
527#390—51no—
528#390—51no—
529#390—52no—
530#390—52no—
531#390—51no—
532#390C2×D511yescharacteristic
533#390C2×D511yescharacteristic
534#389—51no—
535#389—51no—
536#389—51no—
537#389—51no—
538#388—52no—
539#388—52no—
540#388—52no—
541#388—52no—
542#386—52no—
543#386—52no—
544#386—52no—
545#386—52no—
546#386—52no—
547#385—52no—
548#385—52no—
549#385—52no—
550#384—51no—
551#380—51no—
552#380C2×D511yescharacteristic
553#379C2×D512yes—
554C4×C4⋊C4—51no—
555C4×C4⋊C4—51no—
556C4×C4⋊C4—51no—
557C4×C4⋊C4—51no—
558C4×C22⋊C4—51no—
559C4×C22⋊C4—51no—
560C4×C22⋊C4—51no—
561C4×C22⋊C4—52no—
562C4×C22⋊C4—52no—
563C4×C22⋊C4—51no—
564C4×C22⋊C4—51no—
565C4×C22⋊C4—51no—
566C4×C22⋊C4—52no—
567C43—51no—
568C23×C5—21no—
569C23×C5—21no—
570C23×C5—21no—
571C23×C5—21no—
572C23×C5—216no—
573C23×C5—22no—
574C23×C5—22no—
575C23×C5—22no—
576C23×C5—21no—
577C23×C5—21no—
578C23×C5—22no—
579C23×C5—22no—
580C23×C5—21no—
581C23×C5—21no—
582C23×C5—22no—
583C23×C5—22no—
584C23×C5—22no—
585C23×C5—22no—
586C23×C5—22no—
587C23×C5—21no—
588C23×C5—22no—
589C23×C5—21no—
590C23×C5—22no—
591C23×C5—48no—
592C23×C5—48no—
593C23×C5—48no—
594C23×C5—48no—
595C23×C5—48no—
596C23×C5—48no—
597C23×C5C22×D412yes—
598C23×C5C22×D414yes—
599C23×C5C22×D412yes—
600C23×C5C2×#4114yes—
601C23×C5C2×#4112yes—
602C23×C5C2×#4112yes—
603C23×C5C2511yescharacteristic
604C22×D5—22no—
605C22×D5—22no—
606C22×D5—22no—
607C22×D5—22no—
608C22×D5—22no—
609C22×D5—22no—
610C22×D5—22no—
611C5×D4—216no—
612C5×D4—28no—
613C5×D4—28no—
614C5×D4—28no—
615C5×D4—48no—
616C5×D4—48no—
617C2×C4×C5—21no—
618C2×C4×C5—21no—
619C2×C4×C5—21no—
620C2×C4×C5—21no—
621C2×C4×C5—28no—
622C2×C4×C5—21no—
623C2×C4×C5—22no—
624C2×C4×C5—22no—
625C2×C4×C5—22no—
626C2×C4×C5—21no—
627C2×C4×C5—21no—
628C2×C4×C5—21no—
629C2×C4×C5—22no—
630C2×C4×C5—21no—
631C2×C4×C5—22no—
632C2×C4×C5—21no—
633C2×C4×C5—22no—
634C2×C4×C5—44no—
635C2×C4×C5C22×D412yes—
636C2×C4×C5C22×D412yes—
637C2×C4×C5C2×#4112yes—
638C2×C4×C5C2×#4112yes—
639C2×C4×C5C2×#4112yes—
640C22⋊D5—48no—
641C22⋊D5—48no—
642C22⋊D5—48no—
643C22⋊D5—48no—
644C22⋊D5—48no—
645C22⋊D5—48no—
646C2×Dic5—21no—
647C2×Dic5—21no—
648C2×Dic5—21no—
649C2×Dic5—22no—
650C2×Dic5—21no—
651C2×Dic5—21no—
652C2×Dic5—21no—
653C2×Dic5—21no—
654C2×Dic5—21no—
655C2×Dic5—22no—
656C2×Dic5—21no—
657C2×Dic5—21no—
658C2×Dic5—21no—
659C2×Dic5—21no—
660C2×Dic5—28no—
661C2×Dic5—216no—
662C2×Dic5—28no—
663C2×Dic5—21no—
664C2×Dic5—22no—
665C2×Dic5—22no—
666C2×Dic5—22no—
667C2×Dic5—22no—
668C2×Dic5—21no—
669C2×Dic5—22no—
670C2×Dic5—22no—
671C2×Dic5—21no—
672C2×Dic5—44no—
673C2×Dic5—48no—
674C2×Dic5—44no—
675C2×Dic5—48no—
676C2×Dic5—48no—
677C2×Dic5—48no—
678C2×Dic5C22×D412yes—
679C2×Dic5C22×D412yes—
680C2×Dic5C22×D412yes—
681C2×Dic5C22×D414yes—
682C2×Dic5C22×D412yes—
683C2×Dic5C22×D412yes—
684C2×Dic5C22×D412yes—
685C2×Dic5C2×#4112yes—
686C2×Dic5C2×#4112yes—
687C2×Dic5H(5,𝔽2)12yes—
688D20—44no—
689C4×D5—48no—
690Dic10—48no—
691C25C22×D512yes—
692C2×#41—108no—
693C2×#41—108no—
694C2×#41—204no—
695C22×Q8—52no—
696C22×D4—24no—
697C22×D4—24no—
698C22×D4—24no—
699C22×D4—52no—
700C22×D4—52no—
701C22×D4—52no—
702C22×D4—52no—
703C22×D4—52no—
704C22×D4—52no—
705C22×D4—51no—
706C22×D4C22×D512yes—
707C22×D4C22×D512yes—
708C22×D4C22×D512yes—
709C22×D4C22×D511yescharacteristic
710C22×D4C22×D511yescharacteristic
711C22×D4C22×D511yescharacteristic
712C23×C4—52no—
713C23×C4—51no—
714C23×C4—51no—
715C23×C4—52no—
716C23×C4—51no—
717C23×C4—52no—
718C23×C4—52no—
719C23×C4—52no—
720C23×C4—51no—
721C23×C4—52no—
722C23×C4—108no—
723C23×C4—108no—
724C23×C4—204no—
725C23×C4C22×D511yescharacteristic
726C23×C4C22×D511yescharacteristic
727C4⋊Q8—104no—
728#127—104no—
729#127—104no—
730#124—108no—
731#123—108no—
732#123—108no—
733C22⋊Q8—108no—
734C22⋊Q8—108no—
735#121—24no—
736#121—24no—
737#121—108no—
738#121—108no—
739#121—104no—
740#121—108no—
741#121—104no—
742#120—28no—
743#120—108no—
744#120—108no—
745C4×D4—24no—
746C4×D4—58no—
747C4×D4—58no—
748C4×D4—108no—
749C4×D4—104no—
750C4×D4—104no—
751C4×D4—108no—
752C4×D4—108no—
753C4×D4—108no—
754C4×D4—104no—
755C4×D4—104no—
756C4×D4—108no—
757C4×D4—108no—
758C4×D4—104no—
759C4×D4—204no—
760#117—108no—
761C2×C4⋊C4—51no—
762C2×C4⋊C4—51no—
763C2×C4⋊C4—51no—
764C2×C4⋊C4—52no—
765C2×C4⋊C4—52no—
766C2×C4⋊C4—52no—
767C2×C4⋊C4—52no—
768C2×C4⋊C4—52no—
769C2×C4⋊C4—52no—
770C2×C4⋊C4—52no—
771C2×C4⋊C4—51no—
772C2×C4⋊C4—51no—
773C2×C4⋊C4—52no—
774C2×C4⋊C4—104no—
775C2×C4⋊C4C22×D511yescharacteristic
776C2×C4⋊C4C22×D511yescharacteristic
777C2×C4⋊C4C22×D511yescharacteristic
778C2×C22⋊C4—52no—
779C2×C22⋊C4—51no—
780C2×C22⋊C4—51no—
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—51no—
789C2×C22⋊C4—52no—
790C2×C22⋊C4—52no—
791C2×C22⋊C4—52no—
792C2×C22⋊C4—52no—
793C2×C22⋊C4—52no—
794C2×C22⋊C4—52no—
795C2×C22⋊C4—52no—
796C2×C22⋊C4—52no—
797C2×C22⋊C4—52no—
798C2×C22⋊C4—108no—
799C2×C22⋊C4C22×D512yes—
800C2×C22⋊C4C22×D512yes—
801C2×C22⋊C4C22×D512yes—
802C2×C22⋊C4C22×D512yes—
803C2×C22⋊C4C22×D511yescharacteristic
804C2×C22⋊C4C22×D511yescharacteristic
805C2×C22⋊C4C22×D512yes—
806C2×C22⋊C4C22×D512yes—
807C2×C22⋊C4C22×D512yes—
808C2×C42—51no—
809C2×C42—51no—
810C2×C42—52no—
811C2×C42—51no—
812C2×C42—51no—
813C2×C42—51no—
814C2×C42—51no—
815C2×C42—51no—
816C2×C42—51no—
817C2×C42—51no—
818C2×C42—51no—
819C2×C42—51no—
820C2×C42—51no—
821C2×C42—104no—
822C2×C42—104no—
823C2×C42C22×D511yescharacteristic
824#95—51no—
825#95—51no—
826#95—51no—
827#95—51no—
828#95—51no—
829#95—51no—
830#95—52no—
831#95—52no—
832#95—52no—
833#95—52no—
834#95—52no—
835#95—52no—
836#95C22×D512yes—
837C22×C5—22no—
838C22×C5—22no—
839C22×C5—22no—
840C22×C5—22no—
841C22×C5—22no—
842C22×C5—22no—
843C22×C5—24no—
844C22×C5—24no—
845C22×C5—22no—
846C22×C5—24no—
847C22×C5—22no—
848C22×C5—24no—
849C22×C5—24no—
850C22×C5—22no—
851C22×C5—24no—
852C22×C5—432no—
853C22×C5—41no—
854C22×C5—42no—
855C22×C5—42no—
856C22×C5—41no—
857C22×C5—42no—
858C22×C5—42no—
859C22×C5—42no—
860C22×C5—41no—
861C22×C5—42no—
862C22×C5—42no—
863C22×C5—41no—
864C22×C5—42no—
865C22×C5#53214yescomplemented
866C22×C5C23×D411yescharacteristic
867C22×C5C23×D411yescharacteristic
868C22×C5C22×#4111yescharacteristic
869C22×C5C22×#4111yescharacteristic
870C22×C5C22×#4111yescharacteristic
871C22×C5C2×H(5,𝔽2)11yescharacteristic
872C22×C5#58511yescharacteristic
873C2×D5—42no—
874C2×D5—42no—
875C2×D5—42no—
876C2×D5—42no—
877C2×D5—42no—
878C2×D5—42no—
879C2×D5—42no—
880C4×C5—22no—
881C4×C5—22no—
882C4×C5—41no—
883C4×C5—41no—
884C4×C5—42no—
885C4×C5—42no—
886C4×C5#52514yescomplemented
887Dic5—22no—
888Dic5—24no—
889Dic5—22no—
890Dic5—22no—
891Dic5—22no—
892Dic5—22no—
893Dic5—22no—
894Dic5—42no—
895Dic5—42no—
896Dic5—41no—
897Dic5D4214yes—
898C24—24no—
899C24—24no—
900C24—24no—
901C24—24no—
902C24—24no—
903C24—42no—
904C24—42no—
905C24—52no—
906C24C23×D512yes—
907C24C23×D511yescharacteristic
908C24C23×D512yes—
909C24C23×D511yescharacteristic
910#41—2032no—
911C2×Q8—104no—
912C2×Q8—104no—
913C2×Q8—202no—
914C2×D4—232no—
915C2×D4—24no—
916C2×D4—22no—
917C2×D4—24no—
918C2×D4—22no—
919C2×D4—24no—
920C2×D4—24no—
921C2×D4—24no—
922C2×D4—24no—
923C2×D4—22no—
924C2×D4—24no—
925C2×D4—22no—
926C2×D4—22no—
927C2×D4—22no—
928C2×D4—42no—
929C2×D4—42no—
930C2×D4—104no—
931C2×D4—104no—
932C2×D4—104no—
933C2×D4—104no—
934C2×D4—104no—
935C2×D4—104no—
936C2×D4—104no—
937C2×D4—104no—
938C2×D4—104no—
939C2×D4—104no—
940C2×D4—104no—
941C2×D4—104no—
942C2×D4—104no—
943C2×D4—102no—
944C2×D4—102no—
945C2×D4—102no—
946C2×D4—202no—
947C2×D4—202no—
948C2×D4—202no—
949C2×D4—202no—
950C2×D4—202no—
951C2×D4D4×D514yes—
952C2×D4D4×D514yes—
953C2×D4#71114yescomplemented
954C22×C4—22no—
955C22×C4—22no—
956C22×C4—22no—
957C22×C4—22no—
958C22×C4—22no—
959C22×C4—51no—
960C22×C4—54no—
961C22×C4—58no—
962C22×C4—54no—
963C22×C4—51no—
964C22×C4—51no—
965C22×C4—51no—
966C22×C4—51no—
967C22×C4—51no—
968C22×C4—51no—
969C22×C4—52no—
970C22×C4—51no—
971C22×C4—52no—
972C22×C4—52no—
973C22×C4—104no—
974C22×C4—104no—
975C22×C4—104no—
976C22×C4—102no—
977C22×C4—102no—
978C22×C4—104no—
979C22×C4—102no—
980C22×C4—104no—
981C22×C4—102no—
982C22×C4—102no—
983C22×C4—102no—
984C22×C4—104no—
985C22×C4—104no—
986C22×C4—104no—
987C22×C4—104no—
988C22×C4—102no—
989C22×C4—104no—
990C22×C4—104no—
991C22×C4—104no—
992C22×C4—104no—
993C22×C4—104no—
994C22×C4—102no—
995C22×C4—202no—
996C22×C4—202no—
997C22×C4—202no—
998C22×C4—201no—
999C22×C4—201no—
1000C22×C4—2032no—
1001C22×C4#71114yescomplemented
1002C22×C4C23×D511yescharacteristic
1003C22×C4C23×D511yescharacteristic
1004C22×C4C23×D512yes—
1005C22×C4C23×D512yes—
1006C22×C4C23×D511yescharacteristic
1007C22×C4C23×D511yescharacteristic
1008C22×C4C23×D511yescharacteristic
1009C4⋊C4—22no—
1010C4⋊C4—22no—
1011C4⋊C4—22no—
1012C4⋊C4—54no—
1013C4⋊C4—54no—
1014C4⋊C4—104no—
1015C4⋊C4—104no—
1016C4⋊C4—104no—
1017C4⋊C4—104no—
1018C4⋊C4—104no—
1019C4⋊C4—104no—
1020C4⋊C4—102no—
1021C4⋊C4—102no—
1022C4⋊C4—104no—
1023C4⋊C4—102no—
1024C4⋊C4—202no—
1025C22⋊C4—24no—
1026C22⋊C4—24no—
1027C22⋊C4—22no—
1028C22⋊C4—24no—
1029C22⋊C4—24no—
1030C22⋊C4—24no—
1031C22⋊C4—22no—
1032C22⋊C4—42no—
1033C22⋊C4—42no—
1034C22⋊C4—58no—
1035C22⋊C4—54no—
1036C22⋊C4—54no—
1037C22⋊C4—54no—
1038C22⋊C4—104no—
1039C22⋊C4—104no—
1040C22⋊C4—104no—
1041C22⋊C4—104no—
1042C22⋊C4—104no—
1043C22⋊C4—104no—
1044C22⋊C4—104no—
1045C22⋊C4—102no—
1046C22⋊C4—104no—
1047C22⋊C4—104no—
1048C22⋊C4—104no—
1049C22⋊C4—104no—
1050C22⋊C4—104no—
1051C22⋊C4—104no—
1052C22⋊C4—202no—
1053C22⋊C4—202no—
1054C42—22no—
1055C42—54no—
1056C42—54no—
1057C42—102no—
1058C42—102no—
1059C42—102no—
1060C42—102no—
1061C42—104no—
1062C42—102no—
1063C42—102no—
1064C42—102no—
1065C42—102no—
1066C42—102no—
1067C42—201no—
1068C2×C5—24no—
1069C2×C5—42no—
1070C2×C5—44no—
1071C2×C5—44no—
1072C2×C5C2×#52511yescharacteristic
1073C2×C5C2×#53211yescharacteristic
1074C2×C5#346011yescharacteristic
1075C2×C5C2×D4211yescharacteristic
1076C2×C5D4×#4111yescharacteristic
1077C2×C5D4×#4111yescharacteristic
1078C2×C5#348111yescharacteristic
1079D5—82no—
1080C23—21no—
1081C23—21no—
1082C23—21no—
1083C23—21no—
1084C23—216no—
1085C23—22no—
1086C23—22no—
1087C23—22no—
1088C23—21no—
1089C23—21no—
1090C23—21no—
1091C23—22no—
1092C23—22no—
1093C23—22no—
1094C23—21no—
1095C23—22no—
1096C23—22no—
1097C23—22no—
1098C23—22no—
1099C23—21no—
1100C23—22no—
1101C23—21no—
1102C23—22no—
1103C23—48no—
1104C23—48no—
1105C23—48no—
1106C23—48no—
1107C23—48no—
1108C23—48no—
1109C23—102no—
1110C23—102no—
1111C23—102no—
1112C23—102no—
1113C23—102no—
1114C23—102no—
1115C23—102no—
1116C23C2×D4×D514yes—
1117C23C2×D4×D512yes—
1118C23C2×D4×D512yes—
1119C23C2×#71114yes—
1120C23C2×#71112yes—
1121C23D5×#4112yes—
1122C23C24×D511yescharacteristic
1123Q8—208no—
1124D4—216no—
1125D4—28no—
1126D4—28no—
1127D4—28no—
1128D4—48no—
1129D4—48no—
1130D4—208no—
1131D4—208no—
1132D4—208no—
1133D4—208no—
1134D4—208no—
1135D4—208no—
1136D4—204no—
1137C2×C4—21no—
1138C2×C4—21no—
1139C2×C4—21no—
1140C2×C4—21no—
1141C2×C4—28no—
1142C2×C4—21no—
1143C2×C4—22no—
1144C2×C4—22no—
1145C2×C4—22no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—22no—
1150C2×C4—21no—
1151C2×C4—22no—
1152C2×C4—21no—
1153C2×C4—22no—
1154C2×C4—44no—
1155C2×C4—52no—
1156C2×C4—52no—
1157C2×C4—52no—
1158C2×C4—52no—
1159C2×C4—52no—
1160C2×C4—52no—
1161C2×C4—54no—
1162C2×C4—52no—
1163C2×C4—52no—
1164C2×C4—52no—
1165C2×C4—108no—
1166C2×C4—1016no—
1167C2×C4—108no—
1168C2×C4—101no—
1169C2×C4—101no—
1170C2×C4—101no—
1171C2×C4—102no—
1172C2×C4—101no—
1173C2×C4—101no—
1174C2×C4—101no—
1175C2×C4—101no—
1176C2×C4—101no—
1177C2×C4—102no—
1178C2×C4—101no—
1179C2×C4—101no—
1180C2×C4—101no—
1181C2×C4—101no—
1182C2×C4—101no—
1183C2×C4—102no—
1184C2×C4—102no—
1185C2×C4—102no—
1186C2×C4—102no—
1187C2×C4—102no—
1188C2×C4—101no—
1189C2×C4—102no—
1190C2×C4—101no—
1191C2×C4—208no—
1192C2×C4—208no—
1193C2×C4—208no—
1194C2×C4—204no—
1195C2×C4—208no—
1196C2×C4—208no—
1197C2×C4—204no—
1198C2×C4C2×D4×D512yes—
1199C2×C4C2×D4×D512yes—
1200C2×C4C2×#71112yes—
1201C2×C4C2×#71112yes—
1202C2×C4C2×#71112yes—
1203C5#3468111yescharacteristic, complemented, Sylow
1204C22—22no—
1205C22—22no—
1206C22—22no—
1207C22—22no—
1208C22—22no—
1209C22—22no—
1210C22—22no—
1211C22—24no—
1212C22—24no—
1213C22—22no—
1214C22—24no—
1215C22—24no—
1216C22—24no—
1217C22—24no—
1218C22—22no—
1219C22—432no—
1220C22—42no—
1221C22—42no—
1222C22—41no—
1223C22—42no—
1224C22—42no—
1225C22—41no—
1226C22—42no—
1227C22—42no—
1228C22—41no—
1229C22—41no—
1230C22—42no—
1231C22—42no—
1232C22—202no—
1233C22—202no—
1234C22—202no—
1235C22—202no—
1236C22—202no—
1237C22—202no—
1238C22—202no—
1239C22#6593014yescomplemented
1240C22C22×D4×D511yescharacteristic
1241C22C22×D4×D511yescharacteristic
1242C22C22×#71111yescharacteristic
1243C22C22×#71111yescharacteristic
1244C22C2×D5×#4111yescharacteristic
1245C22D5×H(5,𝔽2)11yescharacteristic
1246C22#6628511yescharacteristic
1247C4—22no—
1248C4—22no—
1249C4—41no—
1250C4—42no—
1251C4—42no—
1252C4—41no—
1253C4—54no—
1254C4—102no—
1255C4—102no—
1256C4—104no—
1257C4—102no—
1258C4—102no—
1259C4—102no—
1260C4—102no—
1261C4—202no—
1262C4—201no—
1263C4—202no—
1264C4#6592014yescomplemented
1265C2—24no—
1266C2—44no—
1267C2—44no—
1268C2—42no—
1269C2—402no—
1270C2C2×#6592011yescharacteristic
1271C2C2×#6593011yescharacteristic
1272C2#1061821511yescharacteristic
1273C2D4×#71111yescharacteristic
1274C2D42×D511yescharacteristic
1275C2#1061852711yescharacteristic
1276C2#1061852911yescharacteristic
subgroupG/H
center, FrattiniC23C24×D5
commutator, socle, cosocleC23×C5C25
FittingC5×#2408C2
hypercenter#2408D5
hypocenterC5#34681
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C23 ◁ #2408

Complements

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

NH ≅ G/Ntype
1. C22×D4×Dic5C2semidirect
2. C2×#65930C2semidirect
3. C2×#65920C2semidirect
4. C5×#2408C2semidirect
5. #10615780C2semidirect
6. #10614380C2semidirect
7. #10614375C2semidirect
8. Dic5×#121C2semidirect
9. #10614318C2semidirect
10. #10614083C2semidirect
11. C4×D4×Dic5C2semidirect
12. #10608646C2semidirect
13. #10608621C2semidirect
14. #10608413C2semidirect
15. #10608396C2semidirect
16. #10608054C2semidirect
17. #10608048C2semidirect
18. #10608024C2semidirect
19. #10608020C2semidirect
20. #10605630C2semidirect
21. #10605596C2semidirect
22. #10605560C2semidirect
23. #10605549C2semidirect
26. C22×#711C22semidirect
37. C2×#4085C22semidirect
38. C2×#4085C22semidirect
39. C2×#4081C22semidirect
49. C2×D4×Dic5C22semidirect
51. C2×#4076C22semidirect
54. C22×C4×Dic5C22semidirect
57. C2×#4039C22semidirect
58. C2×#4034C22semidirect
59. C2×#4032C22semidirect
60. C2×#4031C22semidirect
62. C2×#4027C22semidirect
63. C2×#4027C22semidirect
64. C2×#4027C22semidirect
66. C2×#4024C22semidirect
67. C2×#4023C22semidirect
76. #65512C22semidirect
77. #65511C22semidirect
80. #65509C22semidirect
81. #65501C22semidirect
83. C4×C22⋊Dic5C22semidirect
84. #65283C22semidirect
85. #65277C22semidirect
86. #65274C22semidirect
87. #65265C22semidirect
88. C4⋊C4×Dic5C22semidirect
89. C4⋊C4×Dic5C22semidirect
90. C4⋊C4×Dic5C22semidirect
91. #65262C22semidirect
92. #65262C22semidirect
93. #65250C22semidirect
94. #65250C22semidirect
95. #65250C22semidirect
96. #65248C22semidirect
99. #65247C22semidirect
100. #65247C22semidirect
101. #65246C22semidirect
102. #65246C22semidirect
103. #65241C22semidirect
104. #65240C22semidirect
105. #65237C22semidirect
106. #65236C22semidirect
108. #65235C22semidirect
109. #65235C22semidirect
110. #65234C22semidirect
111. #65233C22semidirect
114. C22⋊C4×Dic5C22semidirect
115. C22⋊C4×Dic5C22semidirect
116. C22⋊C4×Dic5C22semidirect
117. C22⋊C4×Dic5C22semidirect
118. #65228C22semidirect
119. C4×C4⋊Dic5C22semidirect
120. C42×Dic5C22semidirect
121. #65217C22semidirect
122. #64958C22semidirect
123. #64955C22semidirect
124. #64946C22semidirect
125. #64945C22semidirect
209. D4×Dic5D4semidirect
210. D4×Dic5D4semidirect
287. #2408D5semidirect
326. C2×C5×D4#41semidirect
332. C22×C4×C5#41semidirect
385. C22×Dic5C2×D4semidirect
431. C22⋊Dic5C2×D4semidirect
432. C22⋊Dic5#41semidirect
446. C4⋊Dic5C2×D4semidirect
465. C4×Dic5C2×D4semidirect
865. C22×C5#532semidirect
886. C4×C5#525semidirect
953. C2×D4#711semidirect
1001. C22×C4#711semidirect
1203. C5#34681semidirect
1239. C22#65930semidirect
1264. C4#65920semidirect

Maximal subgroups

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

subgroupindex
C22×D4×Dic52
C2×#659302
C2×#659202
C5×#24082
#106157802
#106143802
#106143752
Dic5×#1212
#106143182
#106140832
C4×D4×Dic52
#106086462
#106086212
#106084132
#106083962
#106080542
#106080482
#106080242
#106080202
#106056302
#106055962
#106055602
#106055492
#346815