Finite Group Databasebeta

← #12267234

Subgroups — #12267234

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
1C2×#65882C211yesmaximal, characteristic, complemented
2C2×#65881C212yesmaximal, complemented
3C22×C4×D20C211yesmaximal, characteristic, complemented
4C4×C5×#121C211yesmaximal, characteristic, complemented
5#10614436C211yesmaximal, characteristic, complemented
6#10614384C211yesmaximal, characteristic, complemented
7C4×#4083C212yesmaximal, complemented
8C4×#4086C211yesmaximal, characteristic, complemented
9C42×C22⋊D5C211yesmaximal, characteristic, complemented
10#10608175C211yesmaximal, characteristic, complemented
11#10608047C211yesmaximal, characteristic, complemented
12#10607946C211yesmaximal, characteristic, complemented
13#10607741C211yesmaximal, characteristic, complemented
14#10607588C212yesmaximal, complemented
15#10607243C212yesmaximal, complemented
16#10606624C212yesmaximal, complemented
17#10606458C212yesmaximal, complemented
18#10605747C211yesmaximal, characteristic, complemented
19#10605630C211yesmaximal, characteristic, complemented
20C4×#4041C211yesmaximal, characteristic, complemented
21#10605348C211yesmaximal, characteristic, complemented
22#10605312C212yesmaximal, complemented
23#10605311C212yesmaximal, complemented
24C22×#709C2212yescomplemented
25C23×D20C2211yescharacteristic
26C23×C4×D5C2212yes—
27C2×C5×#121C2211yescharacteristic
28C2×C4×C5×D4C2212yes—
29C2×C4×C5×D4C2211yescharacteristic, complemented
30C22×C42×C5C2211yescharacteristic
31C2×#4086C2211yescharacteristic
32C2×#4086C2211yescharacteristic
33C2×#4085C2212yes—
34C2×#4084C2211yescharacteristic, complemented
35C2×#4083C2212yes—
36C2×#4083C2212yes—
37C2×C4×C22⋊D5C2211yescharacteristic
38C2×C4×C22⋊D5C2211yescharacteristic
39C2×C4×C22⋊D5C2211yescharacteristic
40C2×C4×C22⋊D5C2212yescomplemented
41C2×C4×C22⋊D5C2212yescomplemented
42C2×C4×C22⋊D5C2212yescomplemented
43C22×#685C2212yes—
44C22×C4⋊Dic5C2211yescharacteristic
45#65882—28no—
46#65881—216no—
47C2×#4042C2212yescomplemented
48C2×#4041C2211yescharacteristic
49C2×#4041C2211yescharacteristic
50C2×#4040C2212yescomplemented
51C2×#4034C2211yescharacteristic, complemented
52C2×#4031C2212yescomplemented
53C2×#4030C2212yescomplemented
54C2×#4030C2212yescomplemented
55C2×#4029C2212yescomplemented
56C2×#4028C2212yes—
57C2×#4024C2212yes—
58C2×C4×D20—28no—
59C2×C4×D20C2212yes—
60C2×C4×D20C2211yescharacteristic
61C2×C4×D20C2211yescharacteristic
62C2×C4×D20C2211yescharacteristic
63C2×C4×D20C2212yes—
64C2×C4×D20C2211yescharacteristic
65C2×C4×D20C2212yescomplemented
66C2×#4018C2212yescomplemented
67C2×C42×D5C2211yescharacteristic, complemented
68C5×#390C2211yescharacteristic, complemented
69C5×#389C2211yescharacteristic, complemented
70C5×#388C2212yescomplemented
71C5×#386C2212yes—
72C5×#380C2211yescharacteristic
73C4×C5×C4⋊C4C2211yescharacteristic, complemented
74C4×C5×C22⋊C4C2212yescomplemented
75#65510C2211yescharacteristic, complemented
76#65509C2212yes—
77C4×C22⋊Dic5C2211yescharacteristic
78C4×C22⋊Dic5C2211yescharacteristic
79C4×C22⋊Dic5C2211yescharacteristic
80#65278C2212yescomplemented
81#65278C2212yescomplemented
82#65277C2211yescharacteristic
83#65277C2211yescharacteristic
84#65277C2211yescharacteristic
85#65277C2211yescharacteristic
86#65276C2211yescharacteristic, complemented
87#65274C2211yescharacteristic, complemented
88#65265C2211yescharacteristic, complemented
89#65262C2211yescharacteristic, complemented
90#65262C2211yescharacteristic, complemented
91#65250C2212yescomplemented
92#65250C2212yescomplemented
93#65249C2212yes—
94#65249C2212yes—
95#65249C2212yescomplemented
96#65248C2212yescomplemented
97#65248C2212yescomplemented
98#65246C2212yescomplemented
99#65246C2212yescomplemented
100#65245C2212yescomplemented
101#65245C2212yescomplemented
102#65244C2212yes—
103#65237C2212yescomplemented
104#65235C2212yes—
105C4×#685C2212yescomplemented
106C4×#685C2211yescharacteristic, complemented
107C4×#685C2211yescharacteristic, complemented
108C4×#685C2211yescharacteristic, complemented
109C4×#685C2212yescomplemented
110C4×#683C2211yescharacteristic, complemented
111C4×#683C2211yescharacteristic, complemented
112C4×#683C2211yescharacteristic, complemented
113C42×Dic5C2211yescharacteristic, complemented
114#64965C2212yescomplemented
115#64964C2212yescomplemented
116#64962C2212yescomplemented
117#64961C2212yes—
118#64961C2212yescomplemented
119#64960C2212yes—
120#64959C2212yescomplemented
121#64958C2212yescomplemented
122#64958C2212yescomplemented
123#64954C2212yescomplemented
124#64946C2212yescomplemented
125#64945C2212yescomplemented
126#34681—51nomaximal, Sylow
127C24×D5C2312yes—
128C22×C5×D4C2312yes—
129C22×C5×D4C2311yescharacteristic
130C23×C4×C5C2312yes—
131C23×C4×C5C2311yescharacteristic
132C23×C4×C5C2311yescharacteristic
133C23×C4×C5C2311yescharacteristic
134C22×C22⋊D5C2312yes—
135C22×C22⋊D5C2312yes—
136C22×C22⋊D5C2312yes—
137C22×C22⋊D5C2312yes—
138C22×C22⋊D5C2312yes—
139C22×C22⋊D5C2311yescharacteristic
140C23×Dic5C2312yes—
141C2×#709—28no—
142C2×#709—28no—
143C2×#709—44no—
144C22×D20—24no—
145C22×D20—24no—
146C22×D20—24no—
147C22×D20C2312yes—
148C22×D20C2312yes—
149C22×D20C2312yes—
150C22×D20C2311yescharacteristic
151C22×D20C2311yescharacteristic
152C22×C4×D5—28no—
153C22×C4×D5—28no—
154C22×C4×D5—44no—
155C22×C4×D5C2311yescharacteristic
156C22×C4×D5C2312yes—
157C22×C4×D5C2311yescharacteristic
158C22×C4×D5C2312yes—
159C22×C4×D5C2312yes—
160C22×C4×D5C2312yes—
161C22×C4×D5C2311yescharacteristic
162C22×Dic10C2312yes—
163C5×#121—24no—
164C4×C5×D4—28no—
165C4×C5×D4—24no—
166C2×C5×C4⋊C4C2311yescharacteristic
167C2×C5×C4⋊C4C2311yescharacteristic
168C2×C5×C4⋊C4C2311yescharacteristic
169C2×C5×C4⋊C4C2312yes—
170C2×C5×C22⋊C4C2312yes—
171C2×C5×C22⋊C4C2312yes—
172C2×C5×C22⋊C4C2312yes—
173C2×C5×C22⋊C4C2312yes—
174C2×C5×C22⋊C4C2312yes—
175C2×C42×C5—24no—
176C2×C42×C5C2311yescharacteristic
177C2×C42×C5C2312yes—
178C2×C42×C5C2311yescharacteristic
179C2×C42×C5C2311yescharacteristic
180C2×C42×C5C2311yescharacteristic
181C2×C22⋊Dic5C2312yes—
182C2×C22⋊Dic5C2312yes—
183C2×C22⋊Dic5C2311yescharacteristic
184C2×C22⋊Dic5C2312yes—
185C2×C22⋊Dic5C2311yescharacteristic
186C2×C22⋊Dic5C2311yescharacteristic
187#4086—24no—
188#4086—24no—
189#4085—28no—
190#4084—24no—
191#4083—28no—
192#4083—28no—
193C4×C22⋊D5—24no—
194C4×C22⋊D5—28no—
195C4×C22⋊D5—24no—
196C4×C22⋊D5—28no—
197C4×C22⋊D5—44no—
198C4×C22⋊D5D418yescomplemented
199C2×#685—28no—
200C2×#685C2312yes—
201C2×#685C2312yes—
202C2×#685C2312yes—
203C2×#685C2312yes—
204C2×#685C2312yes—
205C2×#685C2312yes—
206C2×#685C2312yes—
207C2×#685C2312yes—
208C2×#685C2312yes—
209C2×#685C2312yes—
210C2×#685C2311yescharacteristic
211C2×#685C2311yescharacteristic
212C2×#685C2312yes—
213C2×#685C2312yes—
214C2×#685C2312yes—
215C2×#685C2312yes—
216C2×#685C2312yes—
217C2×#685C2311yescharacteristic
218C2×C4⋊Dic5—24no—
219C2×C4⋊Dic5C2312yes—
220C2×C4⋊Dic5C2311yescharacteristic
221C2×C4⋊Dic5C2312yes—
222C2×C4⋊Dic5C2311yescharacteristic
223C2×#683C2312yes—
224C2×#683C2312yes—
225C2×#683C2312yes—
226C2×#683C2312yes—
227C2×#683C2311yescharacteristic
228C2×#683C2311yescharacteristic
229C2×#683C2312yes—
230C2×#683C2311yescharacteristic
231C2×C4×Dic5C2311yescharacteristic
232C2×C4×Dic5C2311yescharacteristic
233C2×C4×Dic5C2311yescharacteristic
234C2×C4×Dic5C2311yescharacteristic
235C2×C4×Dic5C2311yescharacteristic
236C2×C4×Dic5C2311yescharacteristic
237C2×C4×Dic5C2311yescharacteristic
238C2×C4×Dic5C2311yescharacteristic
239C2×C4×Dic5C2311yescharacteristic
240#4042—28no—
241#4041—24no—
242#4041—24no—
243#4040—28no—
244#4034—24no—
245#4031—28no—
246#4030—28no—
247#4030—28no—
248#4029—28no—
249#4028—28no—
250#4024—28no—
251C4×D20—24no—
252C4×D20—28no—
253C4×D20—28no—
254C4×D20—24no—
255C4×D20—28no—
256C4×D20—24no—
257C4×D20D418yescomplemented
258#4018—28no—
259C42×D5—24no—
260C5×#95C2312yes—
261C5×#95C2312yes—
262C5×#95C2312yes—
263#3963C2311yescharacteristic
264#3963C2312yes—
265#3963C2311yescharacteristic
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#2408—51no—
288#2392—52no—
289#2388—52no—
290C4×#127—51no—
291C4×#121—51no—
292C4×#121D511yescharacteristic, complemented
293C4×#120—52no—
294#2293—51no—
295C42×D4—51no—
296C24×C5C2412yes—
297C24×C5C2411yescharacteristic
298C23×D5—24no—
299C23×D5—24no—
300C23×D5—24no—
301C23×D5—24no—
302C23×D5—24no—
303C23×D5—42no—
304C23×D5—42no—
305C23×D5C2411yescharacteristic
306C23×D5C2412yes—
307C23×D5C2412yes—
308C2×C5×D4—24no—
309C2×C5×D4—24no—
310C2×C5×D4—24no—
311C2×C5×D4—22no—
312C2×C5×D4—22no—
313C2×C5×D4—22no—
314C22×C4×C5—22no—
315C22×C4×C5—22no—
316C22×C4×C5—22no—
317C22×C4×C5—22no—
318C22×C4×C5—22no—
319C22×C4×C5—22no—
320C22×C4×C5—24no—
321C22×C4×C5—24no—
322C22×C4×C5—24no—
323C22×C4×C5—41no—
324C22×C4×C5C2×D414yes—
325C22×C4×C5#4114yescomplemented
326C22×C4×C5C2411yescharacteristic
327C22×C4×C5C2412yes—
328C22×C4×C5C2412yes—
329C22×C4×C5C2412yes—
330C22×C4×C5C2411yescharacteristic
331C22×C4×C5C2411yescharacteristic
332C22×C4×C5C2411yescharacteristic
333C22×C4×C5C2411yescharacteristic
334C22×C4×C5C2411yescharacteristic
335C2×C22⋊D5—22no—
336C2×C22⋊D5—22no—
337C2×C22⋊D5—24no—
338C2×C22⋊D5—24no—
339C2×C22⋊D5—24no—
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—42no—
348C2×C22⋊D5—42no—
349C2×C22⋊D5—42no—
350C2×C22⋊D5—42no—
351C2×C22⋊D5—42no—
352C2×C22⋊D5C2×D414yes—
353C22×Dic5—24no—
354C22×Dic5—24no—
355C22×Dic5—42no—
356C22×Dic5C2411yescharacteristic
357C22×Dic5C2411yescharacteristic
358C22×Dic5C2412yes—
359C22×Dic5C2411yescharacteristic
360C22×Dic5C2411yescharacteristic
361C22×Dic5C2412yes—
362C22×Dic5C2411yescharacteristic
363C22×Dic5C2411yescharacteristic
364C22×Dic5C2411yescharacteristic
365#709—432no—
366C2×D20—232no—
367C2×D20—24no—
368C2×D20—24no—
369C2×D20—22no—
370C2×D20—24no—
371C2×D20—22no—
372C2×D20—22no—
373C2×D20—22no—
374C2×D20—24no—
375C2×D20—24no—
376C2×D20—24no—
377C2×D20—24no—
378C2×D20—42no—
379C2×D20—42no—
380C2×D20C2×D414yes—
381C2×D20#4114yescomplemented
382C2×C4×D5—24no—
383C2×C4×D5—22no—
384C2×C4×D5—24no—
385C2×C4×D5—22no—
386C2×C4×D5—24no—
387C2×C4×D5—24no—
388C2×C4×D5—24no—
389C2×C4×D5—24no—
390C2×C4×D5—24no—
391C2×C4×D5—22no—
392C2×C4×D5—22no—
393C2×C4×D5—22no—
394C2×C4×D5—22no—
395C2×C4×D5—24no—
396C2×C4×D5—24no—
397C2×C4×D5—22no—
398C2×C4×D5—432no—
399C2×C4×D5—42no—
400C2×C4×D5—42no—
401C2×C4×D5—41no—
402C2×C4×D5C2×D418yes—
403C2×C4×D5C2×D414yescomplemented
404C2×Dic10—24no—
405C2×Dic10—24no—
406C2×Dic10—42no—
407C5×C4⋊C4—22no—
408C5×C4⋊C4—24no—
409C5×C4⋊C4—22no—
410C5×C4⋊C4—22no—
411C5×C22⋊C4—24no—
412C5×C22⋊C4—24no—
413C5×C22⋊C4—24no—
414C5×C22⋊C4—24no—
415C5×C22⋊C4—42no—
416C42×C5—22no—
417C42×C5—22no—
418C42×C5—22no—
419C42×C5—24no—
420C42×C5C2×D414yes—
421C22⋊Dic5—22no—
422C22⋊Dic5—24no—
423C22⋊Dic5—24no—
424C22⋊Dic5—42no—
425C22⋊Dic5C2×D414yes—
426C22⋊Dic5#4114yescomplemented
427#685—24no—
428#685—24no—
429#685—24no—
430#685—24no—
431#685—24no—
432#685—22no—
433#685—24no—
434#685—24no—
435#685—24no—
436#685—24no—
437#685—24no—
438#685—22no—
439#685—24no—
440#685—24no—
441#685—42no—
442#685—42no—
443#685C2×D418yes—
444#685C2×D414yescomplemented
445C4⋊Dic5—22no—
446C4⋊Dic5—24no—
447C4⋊Dic5—24no—
448C4⋊Dic5C2×D414yes—
449#683—22no—
450#683—24no—
451#683—24no—
452#683—24no—
453#683—24no—
454#683—22no—
455#683—42no—
456#683C2×D414yescomplemented
457C4×Dic5—22no—
458C4×Dic5—22no—
459C4×Dic5—22no—
460C4×Dic5—22no—
461C4×Dic5—22no—
462C4×Dic5—22no—
463C4×Dic5—22no—
464C4×Dic5—41no—
465C4×Dic5C2×D414yescomplemented
466C22×#41—52no—
467C23×D4—51no—
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—51no—
480C2×#121—52no—
481C2×#121—51no—
482C2×#121—51no—
483C2×#121—52no—
484C2×#121—52no—
485C2×#121C2×D511yescharacteristic
486C2×#120—52no—
487C2×#120—52no—
488C2×#120—52no—
489C2×C4×D4—51no—
490C2×C4×D4—52no—
491C2×C4×D4—51no—
492C2×C4×D4—51no—
493C2×C4×D4—52no—
494C2×C4×D4—52no—
495C2×C4×D4—51no—
496C2×C4×D4—51no—
497C2×C4×D4—52no—
498C2×C4×D4—51no—
499C2×C4×D4—51no—
500C2×C4×D4—52no—
501C2×C4×D4—52no—
502C2×C4×D4—108no—
503C2×C4×D4C2×D512yes—
504C2×C4×D4C2×D511yescharacteristic, complemented
505C2×#117—52no—
506C22×C4⋊C4—51no—
507C22×C22⋊C4—52no—
508C22×C42—51no—
509C22×C42C2×D511yescharacteristic
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#394—52no—
521#393—52no—
522#392—52no—
523#392—52no—
524#392—52no—
525#392—52no—
526#390—51no—
527#390—51no—
528#390—51no—
529#390—51no—
530#390—51no—
531#390—52no—
532#390—52no—
533#390C2×D511yescharacteristic, complemented
534#389—51no—
535#389—51no—
536#389—51no—
537#389C2×D511yescharacteristic, complemented
538#388—52no—
539#388—52no—
540#388—52no—
541#388C2×D512yescomplemented
542#386—52no—
543#386—52no—
544#386—52no—
545#386—52no—
546#386C2×D512yes—
547#385—52no—
548#385—52no—
549#385—52no—
550#384—51no—
551#380—51no—
552#380C2×D511yescharacteristic
553#379—52no—
554C4×C4⋊C4—51no—
555C4×C4⋊C4—51no—
556C4×C4⋊C4—51no—
557C4×C4⋊C4C2×D511yescharacteristic, complemented
558C4×C22⋊C4—51no—
559C4×C22⋊C4—51no—
560C4×C22⋊C4—51no—
561C4×C22⋊C4—51no—
562C4×C22⋊C4—52no—
563C4×C22⋊C4—52no—
564C4×C22⋊C4—51no—
565C4×C22⋊C4—51no—
566C4×C22⋊C4C2×D512yescomplemented
567C43—51no—
568C23×C5—21no—
569C23×C5—21no—
570C23×C5—21no—
571C23×C5—21no—
572C23×C5—22no—
573C23×C5—22no—
574C23×C5—22no—
575C23×C5—22no—
576C23×C5—22no—
577C23×C5—22no—
578C23×C5—22no—
579C23×C5C22×D412yes—
580C23×C5C2×#4112yes—
581C23×C5C2×#4112yes—
582C23×C5C2511yescharacteristic
583C22×D5—216no—
584C22×D5—22no—
585C22×D5—22no—
586C22×D5—22no—
587C22×D5—21no—
588C22×D5—21no—
589C22×D5—21no—
590C22×D5—22no—
591C22×D5—22no—
592C22×D5—21no—
593C22×D5—22no—
594C22×D5—22no—
595C22×D5—22no—
596C22×D5—22no—
597C22×D5—22no—
598C22×D5—21no—
599C22×D5—22no—
600C22×D5—21no—
601C22×D5—22no—
602C22×D5—48no—
603C22×D5—48no—
604C22×D5—48no—
605C22×D5—48no—
606C22×D5—48no—
607C22×D5—48no—
608C22×D5C22×D414yes—
609C22×D5C22×D412yes—
610C22×D5C2×#4114yes—
611C5×D4—48no—
612C5×D4—44no—
613C2×C4×C5—21no—
614C2×C4×C5—21no—
615C2×C4×C5—21no—
616C2×C4×C5—21no—
617C2×C4×C5—21no—
618C2×C4×C5—21no—
619C2×C4×C5—28no—
620C2×C4×C5—28no—
621C2×C4×C5—22no—
622C2×C4×C5—22no—
623C2×C4×C5—22no—
624C2×C4×C5—22no—
625C2×C4×C5—21no—
626C2×C4×C5—21no—
627C2×C4×C5—22no—
628C2×C4×C5—22no—
629C2×C4×C5—22no—
630C2×C4×C5—22no—
631C2×C4×C5—22no—
632C2×C4×C5—21no—
633C2×C4×C5—44no—
634C2×C4×C5—48no—
635C2×C4×C5C22×D412yes—
636C2×C4×C5C22×D412yes—
637C2×C4×C5C22×D412yes—
638C2×C4×C5C22×D412yes—
639C2×C4×C5C22×D412yes—
640C2×C4×C5C2×#4112yes—
641C2×C4×C5C2×#4112yes—
642C2×C4×C5C2×#4112yes—
643C2×C4×C5H(5,𝔽2)12yes—
644C22⋊D5—28no—
645C22⋊D5—48no—
646C22⋊D5—48no—
647C22⋊D5—48no—
648C22⋊D5—48no—
649C22⋊D5—48no—
650C2×Dic5—21no—
651C2×Dic5—21no—
652C2×Dic5—22no—
653C2×Dic5—21no—
654C2×Dic5—21no—
655C2×Dic5—21no—
656C2×Dic5—21no—
657C2×Dic5—21no—
658C2×Dic5—21no—
659C2×Dic5—22no—
660C2×Dic5—21no—
661C2×Dic5—21no—
662C2×Dic5—21no—
663C2×Dic5—22no—
664C2×Dic5—22no—
665C2×Dic5—21no—
666C2×Dic5—21no—
667C2×Dic5—21no—
668C2×Dic5—21no—
669C2×Dic5—22no—
670C2×Dic5—21no—
671C2×Dic5—48no—
672C2×Dic5C22×D412yes—
673C2×Dic5C22×D412yes—
674C2×Dic5C22×D414yes—
675C2×Dic5C22×D412yes—
676C2×Dic5C2×#4112yes—
677C2×Dic5C2×#4112yes—
678D20—216no—
679D20—28no—
680D20—28no—
681D20—48no—
682D20—48no—
683C4×D5—216no—
684C4×D5—28no—
685C4×D5—44no—
686C4×D5—48no—
687C4×D5—48no—
688C4×D5—44no—
689C4×D5—48no—
690Dic10—48no—
691C25—52no—
692C2×#41—108no—
693C2×#41—108no—
694C2×#41—204no—
695C22×Q8—52no—
696C22×D4—51no—
697C22×D4—52no—
698C22×D4—52no—
699C22×D4—52no—
700C22×D4—52no—
701C22×D4—52no—
702C22×D4—51no—
703C22×D4—51no—
704C22×D4—52no—
705C22×D4—52no—
706C22×D4—52no—
707C22×D4—104no—
708C22×D4—104no—
709C22×D4—104no—
710C22×D4C22×D512yes—
711C22×D4C22×D511yescharacteristic
712C23×C4—52no—
713C23×C4—51no—
714C23×C4—52no—
715C23×C4—51no—
716C23×C4—52no—
717C23×C4—52no—
718C23×C4—52no—
719C23×C4—51no—
720C23×C4—108no—
721C23×C4—108no—
722C23×C4—204no—
723C23×C4C22×D512yes—
724C23×C4C22×D511yescharacteristic
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—108no—
737#121—108no—
738#121—104no—
739#121—104no—
740#121—104no—
741#121—108no—
742#120—108no—
743#120—108no—
744#120—108no—
745C4×D4—28no—
746C4×D4—24no—
747C4×D4—58no—
748C4×D4—58no—
749C4×D4—108no—
750C4×D4—104no—
751C4×D4—108no—
752C4×D4—108no—
753C4×D4—104no—
754C4×D4—108no—
755C4×D4—104no—
756C4×D4—108no—
757C4×D4—104no—
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—51no—
771C2×C4⋊C4—51no—
772C2×C4⋊C4—52no—
773C2×C4⋊C4—104no—
774C2×C4⋊C4C22×D512yes—
775C2×C4⋊C4C22×D511yescharacteristic
776C2×C4⋊C4C22×D511yescharacteristic
777C2×C4⋊C4C22×D511yescharacteristic
778C2×C22⋊C4—51no—
779C2×C22⋊C4—51no—
780C2×C22⋊C4—52no—
781C2×C22⋊C4—51no—
782C2×C22⋊C4—52no—
783C2×C22⋊C4—52no—
784C2×C22⋊C4—51no—
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—52no—
793C2×C22⋊C4—52no—
794C2×C22⋊C4—51no—
795C2×C22⋊C4—51no—
796C2×C22⋊C4—52no—
797C2×C22⋊C4—52no—
798C2×C22⋊C4—52no—
799C2×C22⋊C4—52no—
800C2×C22⋊C4—52no—
801C2×C22⋊C4—52no—
802C2×C22⋊C4—108no—
803C2×C22⋊C4C22×D512yes—
804C2×C22⋊C4C22×D512yes—
805C2×C22⋊C4C22×D512yes—
806C2×C22⋊C4C22×D512yes—
807C2×C22⋊C4C22×D512yes—
808C2×C42—24no—
809C2×C42—51no—
810C2×C42—51no—
811C2×C42—51no—
812C2×C42—51no—
813C2×C42—51no—
814C2×C42—51no—
815C2×C42—51no—
816C2×C42—51no—
817C2×C42—51no—
818C2×C42—104no—
819C2×C42C22×D511yescharacteristic
820C2×C42C22×D511yescharacteristic
821C2×C42C22×D512yes—
822C2×C42C22×D511yescharacteristic
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#95C22×D512yes—
835#95C22×D512yes—
836#95C22×D512yes—
837C22×C5—22no—
838C22×C5—22no—
839C22×C5—22no—
840C22×C5—22no—
841C22×C5—22no—
842C22×C5—22no—
843C22×C5—42no—
844C22×C5—42no—
845C22×C5—42no—
846C22×C5—42no—
847C22×C5—42no—
848C22×C5—42no—
849C22×C5—42no—
850C22×C5#53214yescomplemented
851C22×C5C23×D411yescharacteristic
852C22×C5C23×D411yescharacteristic
853C22×C5C22×#4111yescharacteristic
854C22×C5C22×#4111yescharacteristic
855C22×C5C22×#4111yescharacteristic
856C22×C5C2×H(5,𝔽2)11yescharacteristic
857C22×C5#58511yescharacteristic
858C2×D5—24no—
859C2×D5—24no—
860C2×D5—22no—
861C2×D5—24no—
862C2×D5—22no—
863C2×D5—22no—
864C2×D5—24no—
865C2×D5—24no—
866C2×D5—24no—
867C2×D5—432no—
868C2×D5—41no—
869C2×D5—42no—
870C2×D5—42no—
871C2×D5—41no—
872C2×D5—42no—
873C2×D5—42no—
874C2×D5—42no—
875C2×D5—41no—
876C2×D5—42no—
877C2×D5—42no—
878C2×D5—41no—
879C2×D5—42no—
880C4×C5—22no—
881C4×C5—22no—
882C4×C5—22no—
883C4×C5—42no—
884C4×C5—42no—
885C4×C5—42no—
886C4×C5—41no—
887C4×C5#52514yescomplemented
888C4×C5D4214yes—
889Dic5—22no—
890Dic5—22no—
891Dic5—24no—
892Dic5—22no—
893Dic5—22no—
894Dic5—22no—
895Dic5—41no—
896Dic5—41no—
897Dic5—42no—
898C24—52no—
899C24—52no—
900C24—51no—
901C24—104no—
902C24—104no—
903C24—104no—
904C24—104no—
905C24—104no—
906C24—202no—
907C24—202no—
908C24C23×D512yes—
909C24C23×D511yescharacteristic
910#41—2032no—
911C2×Q8—104no—
912C2×Q8—104no—
913C2×Q8—202no—
914C2×D4—24no—
915C2×D4—24no—
916C2×D4—24no—
917C2×D4—22no—
918C2×D4—22no—
919C2×D4—22no—
920C2×D4—54no—
921C2×D4—54no—
922C2×D4—54no—
923C2×D4—104no—
924C2×D4—104no—
925C2×D4—1032no—
926C2×D4—104no—
927C2×D4—104no—
928C2×D4—104no—
929C2×D4—104no—
930C2×D4—104no—
931C2×D4—104no—
932C2×D4—104no—
933C2×D4—104no—
934C2×D4—104no—
935C2×D4—102no—
936C2×D4—102no—
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—102no—
947C2×D4—202no—
948C2×D4—202no—
949C2×D4—202no—
950C2×D4—202no—
951C2×D4—202no—
952C2×D4—202no—
953C2×D4—202no—
954C22×C4—22no—
955C22×C4—22no—
956C22×C4—22no—
957C22×C4—22no—
958C22×C4—22no—
959C22×C4—22no—
960C22×C4—24no—
961C22×C4—24no—
962C22×C4—24no—
963C22×C4—41no—
964C22×C4—51no—
965C22×C4—51no—
966C22×C4—51no—
967C22×C4—51no—
968C22×C4—52no—
969C22×C4—51no—
970C22×C4—58no—
971C22×C4—54no—
972C22×C4—51no—
973C22×C4—51no—
974C22×C4—52no—
975C22×C4—104no—
976C22×C4—102no—
977C22×C4—104no—
978C22×C4—104no—
979C22×C4—102no—
980C22×C4—104no—
981C22×C4—104no—
982C22×C4—102no—
983C22×C4—104no—
984C22×C4—102no—
985C22×C4—102no—
986C22×C4—102no—
987C22×C4—104no—
988C22×C4—104no—
989C22×C4—104no—
990C22×C4—104no—
991C22×C4—102no—
992C22×C4—104no—
993C22×C4—202no—
994C22×C4—202no—
995C22×C4—201no—
996C22×C4—2032no—
997C22×C4—202no—
998C22×C4#70914yescomplemented
999C22×C4D4×D514yes—
1000C22×C4C23×D511yescharacteristic
1001C22×C4C23×D512yes—
1002C22×C4C23×D512yes—
1003C22×C4C23×D512yes—
1004C22×C4C23×D511yescharacteristic
1005C22×C4C23×D511yescharacteristic
1006C22×C4C23×D511yescharacteristic
1007C22×C4C23×D511yescharacteristic
1008C22×C4C23×D511yescharacteristic
1009C4⋊C4—22no—
1010C4⋊C4—22no—
1011C4⋊C4—24no—
1012C4⋊C4—22no—
1013C4⋊C4—54no—
1014C4⋊C4—54no—
1015C4⋊C4—104no—
1016C4⋊C4—104no—
1017C4⋊C4—104no—
1018C4⋊C4—104no—
1019C4⋊C4—104no—
1020C4⋊C4—104no—
1021C4⋊C4—102no—
1022C4⋊C4—102no—
1023C4⋊C4—102no—
1024C4⋊C4—202no—
1025C22⋊C4—24no—
1026C22⋊C4—24no—
1027C22⋊C4—24no—
1028C22⋊C4—24no—
1029C22⋊C4—42no—
1030C22⋊C4—54no—
1031C22⋊C4—54no—
1032C22⋊C4—58no—
1033C22⋊C4—54no—
1034C22⋊C4—104no—
1035C22⋊C4—104no—
1036C22⋊C4—104no—
1037C22⋊C4—104no—
1038C22⋊C4—104no—
1039C22⋊C4—102no—
1040C22⋊C4—104no—
1041C22⋊C4—104no—
1042C22⋊C4—104no—
1043C22⋊C4—104no—
1044C22⋊C4—104no—
1045C22⋊C4—104no—
1046C22⋊C4—104no—
1047C22⋊C4—104no—
1048C22⋊C4—102no—
1049C22⋊C4—102no—
1050C22⋊C4—104no—
1051C22⋊C4—202no—
1052C22⋊C4—202no—
1053C22⋊C4—202no—
1054C42—22no—
1055C42—22no—
1056C42—22no—
1057C42—24no—
1058C42—54no—
1059C42—102no—
1060C42—102no—
1061C42—102no—
1062C42—102no—
1063C42—102no—
1064C42—102no—
1065C42—102no—
1066C42—201no—
1067C42D4×D514yes—
1068C2×C5—24no—
1069C2×C5—82no—
1070C2×C5C2×#52511yescharacteristic
1071C2×C5C2×#53211yescharacteristic
1072C2×C5#346011yescharacteristic
1073C2×C5C2×D4211yescharacteristic
1074C2×C5D4×#4111yescharacteristic
1075C2×C5D4×#4111yescharacteristic
1076C2×C5#348111yescharacteristic
1077D5—42no—
1078D5—44no—
1079D5—44no—
1080C23—21no—
1081C23—21no—
1082C23—21no—
1083C23—21no—
1084C23—22no—
1085C23—22no—
1086C23—22no—
1087C23—22no—
1088C23—22no—
1089C23—22no—
1090C23—22no—
1091C23—54no—
1092C23—52no—
1093C23—54no—
1094C23—1016no—
1095C23—101no—
1096C23—102no—
1097C23—102no—
1098C23—102no—
1099C23—102no—
1100C23—102no—
1101C23—101no—
1102C23—101no—
1103C23—102no—
1104C23—102no—
1105C23—101no—
1106C23—102no—
1107C23—102no—
1108C23—102no—
1109C23—101no—
1110C23—102no—
1111C23—101no—
1112C23—102no—
1113C23—208no—
1114C23—208no—
1115C23—208no—
1116C23—208no—
1117C23—208no—
1118C23—208no—
1119C23C2×#70912yes—
1120C23C2×D4×D512yes—
1121C23D5×#4112yes—
1122C23C24×D511yescharacteristic
1123Q8—208no—
1124D4—48no—
1125D4—44no—
1126D4—1016no—
1127D4—108no—
1128D4—108no—
1129D4—108no—
1130D4—208no—
1131D4—208no—
1132D4—208no—
1133D4—208no—
1134D4—208no—
1135D4—208no—
1136D4—208no—
1137C2×C4—21no—
1138C2×C4—21no—
1139C2×C4—21no—
1140C2×C4—21no—
1141C2×C4—21no—
1142C2×C4—21no—
1143C2×C4—28no—
1144C2×C4—28no—
1145C2×C4—22no—
1146C2×C4—21no—
1147C2×C4—22no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—22no—
1152C2×C4—22no—
1153C2×C4—21no—
1154C2×C4—22no—
1155C2×C4—21no—
1156C2×C4—22no—
1157C2×C4—44no—
1158C2×C4—48no—
1159C2×C4—52no—
1160C2×C4—52no—
1161C2×C4—54no—
1162C2×C4—52no—
1163C2×C4—52no—
1164C2×C4—52no—
1165C2×C4—101no—
1166C2×C4—101no—
1167C2×C4—101no—
1168C2×C4—102no—
1169C2×C4—101no—
1170C2×C4—101no—
1171C2×C4—101no—
1172C2×C4—101no—
1173C2×C4—102no—
1174C2×C4—101no—
1175C2×C4—101no—
1176C2×C4—101no—
1177C2×C4—1016no—
1178C2×C4—108no—
1179C2×C4—101no—
1180C2×C4—101no—
1181C2×C4—101no—
1182C2×C4—102no—
1183C2×C4—102no—
1184C2×C4—101no—
1185C2×C4—101no—
1186C2×C4—102no—
1187C2×C4—101no—
1188C2×C4—208no—
1189C2×C4—204no—
1190C2×C4—208no—
1191C2×C4—208no—
1192C2×C4—204no—
1193C2×C4—208no—
1194C2×C4C2×#70912yes—
1195C2×C4C2×#70912yes—
1196C2×C4C2×D4×D512yes—
1197C2×C4C2×D4×D512yes—
1198C2×C4C2×D4×D512yes—
1199C2×C4C2×D4×D512yes—
1200C2×C4C2×D4×D512yes—
1201C2×C4D5×#4112yes—
1202C2×C4#414912yes—
1203C5#3468111yescharacteristic, complemented, Sylow
1204C22—22no—
1205C22—22no—
1206C22—22no—
1207C22—22no—
1208C22—22no—
1209C22—22no—
1210C22—42no—
1211C22—42no—
1212C22—42no—
1213C22—42no—
1214C22—42no—
1215C22—42no—
1216C22—42no—
1217C22—104no—
1218C22—102no—
1219C22—104no—
1220C22—104no—
1221C22—102no—
1222C22—104no—
1223C22—104no—
1224C22—104no—
1225C22—102no—
1226C22—2032no—
1227C22—202no—
1228C22—201no—
1229C22—202no—
1230C22—202no—
1231C22—201no—
1232C22—202no—
1233C22—202no—
1234C22—202no—
1235C22—201no—
1236C22—202no—
1237C22—201no—
1238C22—202no—
1239C22#6588214yescomplemented
1240C22C22×#70911yescharacteristic
1241C22C22×D4×D511yescharacteristic
1242C22C22×D4×D511yescharacteristic
1243C22C2×D5×#4111yescharacteristic
1244C22C2×D5×#4111yescharacteristic
1245C22C2×#414911yescharacteristic
1246C22#6628311yescharacteristic
1247C4—22no—
1248C4—22no—
1249C4—22no—
1250C4—42no—
1251C4—42no—
1252C4—41no—
1253C4—42no—
1254C4—102no—
1255C4—102no—
1256C4—102no—
1257C4—102no—
1258C4—104no—
1259C4—102no—
1260C4—201no—
1261C4—201no—
1262C4—202no—
1263C4#6588114yescomplemented
1264C4#6594314yes—
1265C2—24no—
1266C2—82no—
1267C2—204no—
1268C2—204no—
1269C2—202no—
1270C2C2×#6588111yescharacteristic
1271C2C2×#6588211yescharacteristic
1272C2#1061773911yescharacteristic
1273C2C2×#6594311yescharacteristic
1274C2#1061793811yescharacteristic
1275C2#1061805411yescharacteristic
1276C2#1061813911yescharacteristic
subgroupG/H
centerC22×C4C23×D5
commutator, socle, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC4×C5×#121C2
hypercenterC4×#121D5
hypocenterC5#34681
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C22×C4 ◁ C4×#121

Complements

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

NH ≅ G/Ntype
1. C2×#65882C2semidirect
2. C2×#65881C2semidirect
3. C22×C4×D20C2semidirect
4. C4×C5×#121C2semidirect
5. #10614436C2semidirect
6. #10614384C2semidirect
7. C4×#4083C2semidirect
8. C4×#4086C2semidirect
9. C42×C22⋊D5C2semidirect
10. #10608175C2semidirect
11. #10608047C2semidirect
12. #10607946C2semidirect
13. #10607741C2semidirect
14. #10607588C2semidirect
15. #10607243C2semidirect
16. #10606624C2semidirect
17. #10606458C2semidirect
18. #10605747C2semidirect
19. #10605630C2semidirect
20. C4×#4041C2semidirect
21. #10605348C2semidirect
22. #10605312C2semidirect
23. #10605311C2semidirect
24. C22×#709C22semidirect
29. C2×C4×C5×D4C22semidirect
34. C2×#4084C22semidirect
40. C2×C4×C22⋊D5C22semidirect
41. C2×C4×C22⋊D5C22semidirect
42. C2×C4×C22⋊D5C22semidirect
47. C2×#4042C22semidirect
50. C2×#4040C22semidirect
51. C2×#4034C22semidirect
52. C2×#4031C22semidirect
53. C2×#4030C22semidirect
54. C2×#4030C22semidirect
55. C2×#4029C22semidirect
65. C2×C4×D20C22semidirect
66. C2×#4018C22semidirect
67. C2×C42×D5C22semidirect
68. C5×#390C22semidirect
69. C5×#389C22semidirect
70. C5×#388C22semidirect
73. C4×C5×C4⋊C4C22semidirect
74. C4×C5×C22⋊C4C22semidirect
75. #65510C22semidirect
80. #65278C22semidirect
81. #65278C22semidirect
86. #65276C22semidirect
87. #65274C22semidirect
88. #65265C22semidirect
89. #65262C22semidirect
90. #65262C22semidirect
91. #65250C22semidirect
92. #65250C22semidirect
95. #65249C22semidirect
96. #65248C22semidirect
97. #65248C22semidirect
98. #65246C22semidirect
99. #65246C22semidirect
100. #65245C22semidirect
101. #65245C22semidirect
103. #65237C22semidirect
105. C4×#685C22semidirect
106. C4×#685C22semidirect
107. C4×#685C22semidirect
108. C4×#685C22semidirect
109. C4×#685C22semidirect
110. C4×#683C22semidirect
111. C4×#683C22semidirect
112. C4×#683C22semidirect
113. C42×Dic5C22semidirect
114. #64965C22semidirect
115. #64964C22semidirect
116. #64962C22semidirect
118. #64961C22semidirect
120. #64959C22semidirect
121. #64958C22semidirect
122. #64958C22semidirect
123. #64954C22semidirect
124. #64946C22semidirect
125. #64945C22semidirect
198. C4×C22⋊D5D4semidirect
257. C4×D20D4semidirect
292. C4×#121D5semidirect
325. C22×C4×C5#41semidirect
381. C2×D20#41semidirect
403. C2×C4×D5C2×D4semidirect
426. C22⋊Dic5#41semidirect
444. #685C2×D4semidirect
456. #683C2×D4semidirect
465. C4×Dic5C2×D4semidirect
504. C2×C4×D4C2×D5semidirect
533. #390C2×D5semidirect
537. #389C2×D5semidirect
541. #388C2×D5semidirect
557. C4×C4⋊C4C2×D5semidirect
566. C4×C22⋊C4C2×D5semidirect
850. C22×C5#532semidirect
887. C4×C5#525semidirect
998. C22×C4#709semidirect
1203. C5#34681semidirect
1239. C22#65882semidirect
1263. C4#65881semidirect

Maximal subgroups

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

subgroupindex
C2×#658822
C2×#658812
C22×C4×D202
C4×C5×#1212
#106144362
#106143842
C4×#40832
C4×#40862
C42×C22⋊D52
#106081752
#106080472
#106079462
#106077412
#106075882
#106072432
#106066242
#106064582
#106057472
#106056302
C4×#40412
#106053482
#106053122
#106053112
#346815