Finite Group Databasebeta

← #12267223

Subgroups — #12267223

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×#66050C211yesmaximal, characteristic, complemented
3C2×#65920C212yesmaximal, complemented
4C5×#2433C211yesmaximal, characteristic, complemented
5#10615784C211yesmaximal, characteristic, complemented
6#10614917C211yesmaximal, characteristic, complemented
7#10614907C211yesmaximal, characteristic, complemented
8Dic5×#127C211yesmaximal, characteristic, complemented
9#10614436C211yesmaximal, characteristic, complemented
10Dic5×#121C211yesmaximal, characteristic, complemented
11#10614320C212yesmaximal, complemented
12#10614317C212yesmaximal, complemented
13Dic5×#120C212yesmaximal, complemented
14#10608414C212yesmaximal, complemented
15#10608411C212yesmaximal, complemented
16#10608397C212yesmaximal, complemented
17#10608396C212yesmaximal, complemented
18#10608172C211yesmaximal, characteristic, complemented
19#10608053C211yesmaximal, characteristic, complemented
20#10608022C211yesmaximal, characteristic, complemented
21#10608020C211yesmaximal, characteristic, complemented
22#10605224C211yesmaximal, characteristic, complemented
23C4×#4027C211yesmaximal, characteristic, complemented
24C23×C5×D4C2211yescharacteristic
25C24×Dic5C2212yes—
26C22×#711C2212yescomplemented
27C2×C5×#127C2211yescharacteristic
28C2×C5×#127C2211yescharacteristic
29C2×C5×#121C2211yescharacteristic
30C2×C5×#120C2212yes—
31C2×C5×#120C2212yes—
32C2×#4099C2212yes—
33C22×C22⋊Dic5C2212yes—
34C2×#4085C2212yes—
35C2×#4085C2212yescomplemented
36C2×#4084C2211yescharacteristic
37C2×#4084C2211yescharacteristic
38C2×#4084C2212yescomplemented
39C2×#4084C2211yescharacteristic, complemented
40C2×#4082C2212yescomplemented
41C2×#4081C2212yescomplemented
42C2×D4×Dic5—28no—
43C2×D4×Dic5C2212yes—
44C2×D4×Dic5C2212yes—
45C2×D4×Dic5C2212yes—
46C2×D4×Dic5C2211yescharacteristic
47C2×D4×Dic5C2211yescharacteristic
48C2×D4×Dic5C2211yescharacteristic
49C2×D4×Dic5C2211yescharacteristic
50C2×D4×Dic5C2212yescomplemented
51C2×D4×Dic5C2212yescomplemented
52C2×D4×Dic5C2211yescharacteristic, complemented
53C2×D4×Dic5C2212yescomplemented
54C2×C4×C22⋊D5C2211yescharacteristic
55C22×C4⋊Dic5C2211yescharacteristic
56C22×C4×Dic5C2211yescharacteristic
57#66050—28no—
58#65920—216no—
59C2×#4032C2212yescomplemented
60C2×#4027C2211yescharacteristic
61C2×#4027C2211yescharacteristic
62C2×#4027C2212yescomplemented
63C2×#4024C2212yes—
64C2×#4024C2212yescomplemented
65C2×#4023C2212yescomplemented
66C2×C42×D5C2211yescharacteristic, complemented
67C2×#4015C2211yescharacteristic, complemented
68C5×#392C2212yes—
69C5×#392C2212yes—
70C5×#390C2211yescharacteristic
71C5×#390C2211yescharacteristic
72C4×C5×C22⋊C4C2211yescharacteristic
73#65536C2212yes—
74#65512C2212yes—
75#65512C2212yescomplemented
76#65511C2212yes—
77#65511C2212yescomplemented
78#65511C2212yescomplemented
79#65511C2212yescomplemented
80#65510C2211yescharacteristic
81#65510C2211yescharacteristic
82#65510C2212yescomplemented
83#65510C2212yescomplemented
84#65510C2211yescharacteristic, complemented
85#65510C2211yescharacteristic, complemented
86#65509C2212yes—
87#65509C2212yes—
88#65509C2212yescomplemented
89#65509C2212yescomplemented
90#65501C2211yescharacteristic
91#65276C2211yescharacteristic, complemented
92#65274C2211yescharacteristic, complemented
93C4⋊C4×Dic5C2211yescharacteristic, complemented
94#65262C2211yescharacteristic, complemented
95#65250C2212yescomplemented
96#65250C2212yescomplemented
97#65245C2212yescomplemented
98#65242C2212yescomplemented
99#65240C2212yescomplemented
100#65239C2212yes—
101#65239C2212yescomplemented
102#65239C2212yescomplemented
103#65237C2212yescomplemented
104#65237C2212yescomplemented
105#65236C2212yescomplemented
106#65234C2212yescomplemented
107#65234C2212yescomplemented
108#65233C2212yescomplemented
109C22⋊C4×Dic5C2211yescharacteristic
110C22⋊C4×Dic5C2211yescharacteristic
111C22⋊C4×Dic5C2212yescomplemented
112C22⋊C4×Dic5C2212yescomplemented
113C22⋊C4×Dic5C2212yescomplemented
114C4×#685C2211yescharacteristic, complemented
115#65224C2211yescharacteristic, complemented
116C4×#683C2211yescharacteristic, complemented
117C42×Dic5C2211yescharacteristic, complemented
118#65217C2211yescharacteristic, complemented
119#65217C2211yescharacteristic, complemented
120#64955C2211yescharacteristic, complemented
121#64955C2211yescharacteristic, complemented
122#64950C2212yescomplemented
123#64945C2212yescomplemented
124#64938C2211yescharacteristic, complemented
125#64938C2211yescharacteristic, complemented
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×D4C2311yescharacteristic
134C22×C5×D4C2312yes—
135C22×C5×D4C2312yes—
136C22×C5×D4C2312yes—
137C22×C5×D4C2312yes—
138C22×C5×D4C2311yescharacteristic
139C22×C5×D4C2311yescharacteristic
140C23×C4×C5C2311yescharacteristic
141C22×C22⋊D5C2312yes—
142C22×C22⋊D5C2312yes—
143C22×C22⋊D5C2312yes—
144C22×C22⋊D5C2311yescharacteristic
145C23×Dic5—28no—
146C23×Dic5—28no—
147C23×Dic5—44no—
148C23×Dic5C2312yes—
149C23×Dic5C2312yes—
150C23×Dic5C2312yes—
151C23×Dic5C2312yes—
152C23×Dic5C2311yescharacteristic
153C23×Dic5C2312yes—
154C23×Dic5C2312yes—
155C23×Dic5C2311yescharacteristic
156C2×#711—28no—
157C2×#711—28no—
158C2×#711—44no—
159C22×C4×D5C2311yescharacteristic
160C22×C4×D5C2311yescharacteristic
161C22×C4×D5C2311yescharacteristic
162C22×Dic10C2312yes—
163C5×#127—24no—
164C5×#127—24no—
165C5×#121—24no—
166C5×#120—28no—
167C5×#120—28no—
168C2×C5×C4⋊C4C2311yescharacteristic
169C2×C5×C22⋊C4C2312yes—
170C2×C5×C22⋊C4C2312yes—
171C2×C5×C22⋊C4C2312yes—
172C2×C5×C22⋊C4C2312yes—
173C2×C5×C22⋊C4C2312yes—
174C2×C5×C22⋊C4C2311yescharacteristic
175C2×C5×C22⋊C4C2311yescharacteristic
176C2×C42×C5C2311yescharacteristic
177C2×C42×C5C2311yescharacteristic
178#4099—28no—
179C2×C22⋊Dic5—28no—
180C2×C22⋊Dic5C2311yescharacteristic
181C2×C22⋊Dic5C2312yes—
182C2×C22⋊Dic5C2312yes—
183C2×C22⋊Dic5C2312yes—
184C2×C22⋊Dic5C2312yes—
185C2×C22⋊Dic5C2312yes—
186C2×C22⋊Dic5C2312yes—
187C2×C22⋊Dic5C2312yes—
188C2×C22⋊Dic5C2312yes—
189C2×C22⋊Dic5C2312yes—
190C2×C22⋊Dic5C2312yes—
191C2×C22⋊Dic5C2312yes—
192C2×C22⋊Dic5C2312yes—
193C2×C22⋊Dic5C2312yes—
194C2×C22⋊Dic5C2312yes—
195C2×C22⋊Dic5C2312yes—
196C2×C22⋊Dic5C2312yes—
197C2×C22⋊Dic5C2312yes—
198#4085—28no—
199#4085—28no—
200#4084—24no—
201#4084—24no—
202#4084—28no—
203#4084—24no—
204#4082—28no—
205#4081—28no—
206D4×Dic5—24no—
207D4×Dic5—28no—
208D4×Dic5—28no—
209D4×Dic5—28no—
210D4×Dic5—28no—
211D4×Dic5—24no—
212D4×Dic5—24no—
213D4×Dic5—24no—
214D4×Dic5—28no—
215D4×Dic5—44no—
216D4×Dic5D418yescomplemented
217C4×C22⋊D5—24no—
218C2×#685C2311yescharacteristic
219C2×#685C2312yes—
220C2×#685C2311yescharacteristic
221C2×#685C2311yescharacteristic
222C2×C4⋊Dic5—24no—
223C2×C4⋊Dic5C2311yescharacteristic
224C2×C4⋊Dic5C2312yes—
225C2×C4⋊Dic5C2312yes—
226C2×C4⋊Dic5C2312yes—
227C2×C4⋊Dic5C2312yes—
228C2×C4⋊Dic5C2311yescharacteristic
229C2×C4⋊Dic5C2311yescharacteristic
230C2×C4⋊Dic5C2312yes—
231C2×C4⋊Dic5C2311yescharacteristic
232C2×#683C2312yes—
233C2×#683C2312yes—
234C2×#683C2312yes—
235C2×#683C2311yescharacteristic
236C2×#683C2311yescharacteristic
237C2×#683C2311yescharacteristic
238C2×C4×Dic5—24no—
239C2×C4×Dic5C2311yescharacteristic
240C2×C4×Dic5C2311yescharacteristic
241C2×C4×Dic5C2312yes—
242C2×C4×Dic5C2311yescharacteristic
243C2×C4×Dic5C2311yescharacteristic
244C2×C4×Dic5C2311yescharacteristic
245C2×C4×Dic5C2311yescharacteristic
246C2×C4×Dic5C2311yescharacteristic
247C2×C4×Dic5C2311yescharacteristic
248C2×C4×Dic5C2311yescharacteristic
249C2×C4×Dic5C2311yescharacteristic
250C2×C4×Dic5C2311yescharacteristic
251#4032—28no—
252#4027—28no—
253#4027—24no—
254#4027D418yescomplemented
255#4024—28no—
256#4024—28no—
257#4023—28no—
258C42×D5—24no—
259#4015—24no—
260C5×#95C2311yescharacteristic
261C5×#95C2311yescharacteristic
262#3963C2311yescharacteristic
263#3963C2311yescharacteristic
264#3963C2312yes—
265#3963C2312yes—
266#3963C2312yes—
267#3963C2311yescharacteristic
268#3963C2311yescharacteristic
269#3963C2312yes—
270#3963C2312yes—
271#3963C2312yes—
272#3963C2312yes—
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#2433D511yescharacteristic, complemented
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×#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×C5C2412yes—
305C24×C5C2412yes—
306C24×C5C2411yescharacteristic
307C23×D5C2411yescharacteristic
308C2×C5×D4—232no—
309C2×C5×D4—24no—
310C2×C5×D4—24no—
311C2×C5×D4—24no—
312C2×C5×D4—24no—
313C2×C5×D4—24no—
314C2×C5×D4—24no—
315C2×C5×D4—24no—
316C2×C5×D4—24no—
317C2×C5×D4—24no—
318C2×C5×D4—22no—
319C2×C5×D4—24no—
320C2×C5×D4—24no—
321C2×C5×D4—22no—
322C2×C5×D4—24no—
323C2×C5×D4—22no—
324C2×C5×D4—22no—
325C2×C5×D4—22no—
326C2×C5×D4—24no—
327C2×C5×D4—24no—
328C2×C5×D4—22no—
329C2×C5×D4—22no—
330C2×C5×D4—42no—
331C2×C5×D4—42no—
332C2×C5×D4—42no—
333C2×C5×D4—42no—
334C2×C5×D4C2×D414yes—
335C2×C5×D4#4114yescomplemented
336C22×C4×C5—22no—
337C22×C4×C5—22no—
338C22×C4×C5#4114yescomplemented
339C22×C4×C5C2412yes—
340C22×C4×C5C2411yescharacteristic
341C22×C4×C5C2411yescharacteristic
342C22×C4×C5C2411yescharacteristic
343C22×C4×C5C2411yescharacteristic
344C22×C4×C5C2411yescharacteristic
345C22×C4×C5C2411yescharacteristic
346C2×C22⋊D5—22no—
347C2×C22⋊D5—22no—
348C2×C22⋊D5—24no—
349C2×C22⋊D5—24no—
350C2×C22⋊D5—24no—
351C2×C22⋊D5—24no—
352C2×C22⋊D5—24no—
353C2×C22⋊D5—24no—
354C2×C22⋊D5—42no—
355C2×C22⋊D5—42no—
356C2×C22⋊D5—42no—
357C2×C22⋊D5C2×D414yes—
358C22×Dic5—24no—
359C22×Dic5—22no—
360C22×Dic5—24no—
361C22×Dic5—22no—
362C22×Dic5—24no—
363C22×Dic5—24no—
364C22×Dic5—22no—
365C22×Dic5—22no—
366C22×Dic5—24no—
367C22×Dic5—24no—
368C22×Dic5—24no—
369C22×Dic5—24no—
370C22×Dic5—24no—
371C22×Dic5—24no—
372C22×Dic5—24no—
373C22×Dic5—24no—
374C22×Dic5—24no—
375C22×Dic5—24no—
376C22×Dic5—42no—
377C22×Dic5—42no—
378C22×Dic5—42no—
379C22×Dic5—41no—
380C22×Dic5—432no—
381C22×Dic5C2×D418yes—
382C22×Dic5C2×D414yes—
383C22×Dic5C2411yescharacteristic
384C22×Dic5C2411yescharacteristic
385C22×Dic5C2411yescharacteristic
386C22×Dic5C2412yes—
387C22×Dic5C2412yes—
388C22×Dic5C2412yes—
389C22×Dic5C2411yescharacteristic
390C22×Dic5C2411yescharacteristic
391C22×Dic5C2412yes—
392C22×Dic5C2411yescharacteristic
393C22×Dic5C2411yescharacteristic
394#711—432no—
395C2×C4×D5—22no—
396C2×C4×D5—22no—
397C2×C4×D5—22no—
398C2×C4×D5—22no—
399C2×C4×D5—22no—
400C2×C4×D5—22no—
401C2×C4×D5—22no—
402C2×C4×D5—41no—
403C2×C4×D5C2×D414yescomplemented
404C2×Dic10—24no—
405C2×Dic10—24no—
406C2×Dic10—42no—
407C5×C4⋊C4—22no—
408C5×C22⋊C4—24no—
409C5×C22⋊C4—24no—
410C5×C22⋊C4—24no—
411C5×C22⋊C4—24no—
412C5×C22⋊C4—24no—
413C5×C22⋊C4C2×D414yes—
414C5×C22⋊C4#4114yescomplemented
415C42×C5—22no—
416C42×C5—22no—
417C22⋊Dic5—24no—
418C22⋊Dic5—24no—
419C22⋊Dic5—24no—
420C22⋊Dic5—22no—
421C22⋊Dic5—24no—
422C22⋊Dic5—24no—
423C22⋊Dic5—24no—
424C22⋊Dic5—24no—
425C22⋊Dic5—24no—
426C22⋊Dic5—24no—
427C22⋊Dic5—24no—
428C22⋊Dic5—24no—
429C22⋊Dic5—24no—
430C22⋊Dic5—42no—
431C22⋊Dic5—42no—
432C22⋊Dic5—42no—
433C22⋊Dic5—42no—
434C22⋊Dic5C2×D418yes—
435#685—24no—
436#685—22no—
437#685—22no—
438#685C2×D414yescomplemented
439C4⋊Dic5—22no—
440C4⋊Dic5—24no—
441C4⋊Dic5—22no—
442C4⋊Dic5—22no—
443C4⋊Dic5—24no—
444C4⋊Dic5—24no—
445C4⋊Dic5—24no—
446C4⋊Dic5—42no—
447C4⋊Dic5C2×D414yes—
448#683—24no—
449#683—24no—
450#683—22no—
451#683—22no—
452#683—24no—
453#683C2×D414yescomplemented
454C4×Dic5—22no—
455C4×Dic5—22no—
456C4×Dic5—22no—
457C4×Dic5—22no—
458C4×Dic5—22no—
459C4×Dic5—24no—
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×#127C2×D511yescharacteristic
472C2×#127C2×D511yescharacteristic
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—51no—
481C2×#121—51no—
482C2×#121—52no—
483C2×#121—52no—
484C2×#121—52no—
485C2×#121C2×D511yescharacteristic
486C2×#120—52no—
487C2×#120C2×D512yes—
488C2×#120C2×D512yes—
489C2×C4×D4—51no—
490C2×C4×D4—51no—
491C2×C4×D4—52no—
492C2×C4×D4—51no—
493C2×C4×D4—52no—
494C2×C4×D4—51no—
495C2×C4×D4—51no—
496C2×C4×D4—52no—
497C2×C4×D4—52no—
498C2×C4×D4—52no—
499C2×C4×D4—51no—
500C2×C4×D4—52no—
501C2×C4×D4—51no—
502C2×C4×D4—51no—
503C2×C4×D4—52no—
504C2×C4×D4—108no—
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#394—52no—
521#393—52no—
522#392—52no—
523#392—52no—
524#392C2×D512yes—
525#392C2×D512yes—
526#390—51no—
527#390—51no—
528#390—52no—
529#390—52no—
530#390—51no—
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#380—51no—
553#379—52no—
554C4×C4⋊C4—51no—
555C4×C4⋊C4—51no—
556C4×C4⋊C4—51no—
557C4×C4⋊C4—51no—
558C4×C22⋊C4—52no—
559C4×C22⋊C4—52no—
560C4×C22⋊C4—52no—
561C4×C22⋊C4—51no—
562C4×C22⋊C4—51no—
563C4×C22⋊C4—51no—
564C4×C22⋊C4—51no—
565C4×C22⋊C4—51no—
566C4×C22⋊C4C2×D511yescharacteristic
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—22no—
577C23×C5—22no—
578C23×C5—22no—
579C23×C5—22no—
580C23×C5—22no—
581C23×C5—22no—
582C23×C5—22no—
583C23×C5—22no—
584C23×C5—22no—
585C23×C5—22no—
586C23×C5—22no—
587C23×C5—22no—
588C23×C5—22no—
589C23×C5—22no—
590C23×C5—22no—
591C23×C5—22no—
592C23×C5—48no—
593C23×C5—48no—
594C23×C5—48no—
595C23×C5—48no—
596C23×C5—48no—
597C23×C5—48no—
598C23×C5C22×D414yes—
599C23×C5C22×D412yes—
600C23×C5C2×#4114yes—
601C23×C5C2×#4112yes—
602C23×C5C2×#4112yes—
603C23×C5C2511yescharacteristic
604C22×D5—21no—
605C22×D5—21no—
606C22×D5—21no—
607C22×D5—21no—
608C22×D5—21no—
609C22×D5—21no—
610C22×D5C22×D412yes—
611C5×D4—216no—
612C5×D4—28no—
613C5×D4—28no—
614C5×D4—48no—
615C5×D4—48no—
616C5×D4—48no—
617C5×D4—48no—
618C5×D4—48no—
619C5×D4—44no—
620C2×C4×C5—21no—
621C2×C4×C5—21no—
622C2×C4×C5—21no—
623C2×C4×C5—21no—
624C2×C4×C5—21no—
625C2×C4×C5—21no—
626C2×C4×C5—21no—
627C2×C4×C5—21no—
628C2×C4×C5—21no—
629C2×C4×C5—21no—
630C2×C4×C5—28no—
631C2×C4×C5—22no—
632C2×C4×C5—22no—
633C2×C4×C5—22no—
634C2×C4×C5C22×D412yes—
635C2×C4×C5C22×D412yes—
636C2×C4×C5C22×D412yes—
637C2×C4×C5C2×#4112yes—
638C2×C4×C5C2×#4112yes—
639C2×C4×C5C2×#4112yes—
640C2×C4×C5C2×#4112yes—
641C2×C4×C5C2×#4112yes—
642C22⋊D5—28no—
643C22⋊D5—48no—
644C22⋊D5—48no—
645C22⋊D5—48no—
646C2×Dic5—21no—
647C2×Dic5—22no—
648C2×Dic5—21no—
649C2×Dic5—21no—
650C2×Dic5—21no—
651C2×Dic5—22no—
652C2×Dic5—21no—
653C2×Dic5—21no—
654C2×Dic5—216no—
655C2×Dic5—28no—
656C2×Dic5—21no—
657C2×Dic5—21no—
658C2×Dic5—22no—
659C2×Dic5—22no—
660C2×Dic5—22no—
661C2×Dic5—22no—
662C2×Dic5—22no—
663C2×Dic5—21no—
664C2×Dic5—21no—
665C2×Dic5—21no—
666C2×Dic5—22no—
667C2×Dic5—21no—
668C2×Dic5—21no—
669C2×Dic5—22no—
670C2×Dic5—22no—
671C2×Dic5—21no—
672C2×Dic5—21no—
673C2×Dic5—22no—
674C2×Dic5—48no—
675C2×Dic5—44no—
676C2×Dic5—48no—
677C2×Dic5—48no—
678C2×Dic5—48no—
679C2×Dic5—48no—
680C2×Dic5C22×D412yes—
681C2×Dic5C22×D412yes—
682C2×Dic5C22×D412yes—
683C2×Dic5C22×D414yes—
684C2×Dic5C22×D412yes—
685C2×Dic5C22×D412yes—
686C2×Dic5H(5,𝔽2)12yes—
687C4×D5—28no—
688C4×D5—44no—
689C4×D5—44no—
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—51no—
700C22×D4—52no—
701C22×D4—52no—
702C22×D4—52no—
703C22×D4C22×D512yes—
704C22×D4C22×D512yes—
705C22×D4C22×D511yescharacteristic
706C22×D4C22×D512yes—
707C22×D4C22×D512yes—
708C22×D4C22×D512yes—
709C22×D4C22×D512yes—
710C22×D4C22×D511yescharacteristic
711C22×D4C22×D511yescharacteristic
712C23×C4—52no—
713C23×C4—51no—
714C23×C4—51no—
715C23×C4—52no—
716C23×C4—52no—
717C23×C4—51no—
718C23×C4—52no—
719C23×C4—52no—
720C23×C4—52no—
721C23×C4—51no—
722C23×C4—51no—
723C23×C4—108no—
724C23×C4—108no—
725C23×C4—204no—
726C23×C4C22×D511yescharacteristic
727C4⋊Q8—104no—
728#127—24no—
729#127—24no—
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—108no—
740#121—104no—
741#121—104no—
742#120—28no—
743#120—28no—
744#120—108no—
745C4×D4—58no—
746C4×D4—58no—
747C4×D4—104no—
748C4×D4—108no—
749C4×D4—104no—
750C4×D4—108no—
751C4×D4—108no—
752C4×D4—104no—
753C4×D4—108no—
754C4×D4—108no—
755C4×D4—108no—
756C4×D4—104no—
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—51no—
768C2×C4⋊C4—52no—
769C2×C4⋊C4—52no—
770C2×C4⋊C4—52no—
771C2×C4⋊C4—52no—
772C2×C4⋊C4—51no—
773C2×C4⋊C4—51no—
774C2×C4⋊C4—51no—
775C2×C4⋊C4—52no—
776C2×C4⋊C4—104no—
777C2×C4⋊C4C22×D511yescharacteristic
778C2×C22⋊C4—52no—
779C2×C22⋊C4—51no—
780C2×C22⋊C4—52no—
781C2×C22⋊C4—52no—
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—51no—
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—108no—
801C2×C22⋊C4C22×D512yes—
802C2×C22⋊C4C22×D512yes—
803C2×C22⋊C4C22×D512yes—
804C2×C22⋊C4C22×D512yes—
805C2×C22⋊C4C22×D512yes—
806C2×C22⋊C4C22×D511yescharacteristic
807C2×C22⋊C4C22×D511yescharacteristic
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—104no—
821C2×C42—104no—
822C2×C42C22×D511yescharacteristic
823C2×C42C22×D511yescharacteristic
824#95—51no—
825#95—51no—
826#95—51no—
827#95—51no—
828#95—52no—
829#95—52no—
830#95—52no—
831#95—52no—
832#95—52no—
833#95—52no—
834#95—52no—
835#95C22×D511yescharacteristic
836#95C22×D511yescharacteristic
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—24no—
846C22×C5—24no—
847C22×C5—24no—
848C22×C5—24no—
849C22×C5—432no—
850C22×C5—42no—
851C22×C5—42no—
852C22×C5—42no—
853C22×C5—42no—
854C22×C5—42no—
855C22×C5—42no—
856C22×C5—42no—
857C22×C5—42no—
858C22×C5—42no—
859C22×C5—42no—
860C22×C5—42no—
861C22×C5—42no—
862C22×C5—42no—
863C22×C5—42no—
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—22no—
874C2×D5—22no—
875C2×D5—22no—
876C2×D5—41no—
877C2×D5—41no—
878C2×D5—41no—
879C2×D5—41no—
880C4×C5—22no—
881C4×C5—22no—
882C4×C5—22no—
883C4×C5—22no—
884C4×C5—22no—
885C4×C5—42no—
886C4×C5#52514yescomplemented
887Dic5—22no—
888Dic5—24no—
889Dic5—22no—
890Dic5—22no—
891Dic5—41no—
892Dic5—41no—
893Dic5—42no—
894Dic5—42no—
895Dic5—41no—
896Dic5—42no—
897Dic5D4214yes—
898C24—24no—
899C24—24no—
900C24—24no—
901C24—24no—
902C24—24no—
903C24—42no—
904C24—42no—
905C24—51no—
906C24C23×D512yes—
907C24C23×D512yes—
908C24C23×D512yes—
909C24C23×D511yescharacteristic
910#41—2032no—
911C2×Q8—104no—
912C2×Q8—104no—
913C2×Q8—202no—
914C2×D4—232no—
915C2×D4—24no—
916C2×D4—24no—
917C2×D4—24no—
918C2×D4—24no—
919C2×D4—24no—
920C2×D4—24no—
921C2×D4—24no—
922C2×D4—24no—
923C2×D4—24no—
924C2×D4—22no—
925C2×D4—24no—
926C2×D4—22no—
927C2×D4—24no—
928C2×D4—24no—
929C2×D4—22no—
930C2×D4—22no—
931C2×D4—22no—
932C2×D4—24no—
933C2×D4—24no—
934C2×D4—22no—
935C2×D4—22no—
936C2×D4—42no—
937C2×D4—42no—
938C2×D4—42no—
939C2×D4—42no—
940C2×D4—54no—
941C2×D4—104no—
942C2×D4—102no—
943C2×D4—102no—
944C2×D4—104no—
945C2×D4—104no—
946C2×D4—104no—
947C2×D4—104no—
948C2×D4—104no—
949C2×D4—202no—
950C2×D4—202no—
951C2×D4—202no—
952C2×D4D4×D514yes—
953C2×D4#71114yescomplemented
954C22×C4—22no—
955C22×C4—22no—
956C22×C4—51no—
957C22×C4—54no—
958C22×C4—58no—
959C22×C4—51no—
960C22×C4—51no—
961C22×C4—52no—
962C22×C4—51no—
963C22×C4—54no—
964C22×C4—51no—
965C22×C4—51no—
966C22×C4—51no—
967C22×C4—52no—
968C22×C4—52no—
969C22×C4—52no—
970C22×C4—102no—
971C22×C4—102no—
972C22×C4—102no—
973C22×C4—102no—
974C22×C4—104no—
975C22×C4—102no—
976C22×C4—104no—
977C22×C4—102no—
978C22×C4—104no—
979C22×C4—104no—
980C22×C4—104no—
981C22×C4—104no—
982C22×C4—104no—
983C22×C4—104no—
984C22×C4—104no—
985C22×C4—104no—
986C22×C4—104no—
987C22×C4—104no—
988C22×C4—104no—
989C22×C4—104no—
990C22×C4—102no—
991C22×C4—102no—
992C22×C4—102no—
993C22×C4—102no—
994C22×C4—102no—
995C22×C4—201no—
996C22×C4—202no—
997C22×C4—202no—
998C22×C4—202no—
999C22×C4—201no—
1000C22×C4—2032no—
1001C22×C4#71114yescomplemented
1002C22×C4C23×D512yes—
1003C22×C4C23×D511yescharacteristic
1004C22×C4C23×D511yescharacteristic
1005C22×C4C23×D511yescharacteristic
1006C22×C4C23×D511yescharacteristic
1007C22×C4C23×D511yescharacteristic
1008C22×C4C23×D511yescharacteristic
1009C4⋊C4—22no—
1010C4⋊C4—54no—
1011C4⋊C4—54no—
1012C4⋊C4—104no—
1013C4⋊C4—104no—
1014C4⋊C4—104no—
1015C4⋊C4—104no—
1016C4⋊C4—102no—
1017C4⋊C4—104no—
1018C4⋊C4—102no—
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—24no—
1030C22⋊C4—58no—
1031C22⋊C4—54no—
1032C22⋊C4—104no—
1033C22⋊C4—104no—
1034C22⋊C4—104no—
1035C22⋊C4—104no—
1036C22⋊C4—104no—
1037C22⋊C4—104no—
1038C22⋊C4—104no—
1039C22⋊C4—104no—
1040C22⋊C4—104no—
1041C22⋊C4—104no—
1042C22⋊C4—104no—
1043C22⋊C4—104no—
1044C22⋊C4—102no—
1045C22⋊C4—104no—
1046C22⋊C4—102no—
1047C22⋊C4—102no—
1048C22⋊C4—202no—
1049C22⋊C4—202no—
1050C22⋊C4—202no—
1051C22⋊C4—202no—
1052C22⋊C4D4×D514yes—
1053C22⋊C4#71114yescomplemented
1054C42—22no—
1055C42—22no—
1056C42—54no—
1057C42—54no—
1058C42—102no—
1059C42—102no—
1060C42—102no—
1061C42—102no—
1062C42—104no—
1063C42—102no—
1064C42—102no—
1065C42—102no—
1066C42—102no—
1067C42—201no—
1068C2×C5—24no—
1069C2×C5—44no—
1070C2×C5—44no—
1071C2×C5—82no—
1072C2×C5C2×#52511yescharacteristic
1073C2×C5C2×#53211yescharacteristic
1074C2×C5#346011yescharacteristic
1075C2×C5C2×D4211yescharacteristic
1076C2×C5D4×#4111yescharacteristic
1077C2×C5D4×#4111yescharacteristic
1078C2×C5#348111yescharacteristic
1079D5—42no—
1080C23—21no—
1081C23—21no—
1082C23—21no—
1083C23—21no—
1084C23—216no—
1085C23—22no—
1086C23—22no—
1087C23—22no—
1088C23—22no—
1089C23—22no—
1090C23—22no—
1091C23—22no—
1092C23—22no—
1093C23—22no—
1094C23—22no—
1095C23—22no—
1096C23—22no—
1097C23—22no—
1098C23—22no—
1099C23—22no—
1100C23—22no—
1101C23—22no—
1102C23—22no—
1103C23—22no—
1104C23—48no—
1105C23—48no—
1106C23—48no—
1107C23—48no—
1108C23—48no—
1109C23—48no—
1110C23—52no—
1111C23—101no—
1112C23—101no—
1113C23—101no—
1114C23—101no—
1115C23—101no—
1116C23—101no—
1117C23C2×D4×D514yes—
1118C23C2×D4×D512yes—
1119C23C2×#71114yes—
1120C23C2×#71112yes—
1121C23C2×#71112yes—
1122C23C24×D511yescharacteristic
1123Q8—208no—
1124D4—216no—
1125D4—28no—
1126D4—28no—
1127D4—48no—
1128D4—48no—
1129D4—48no—
1130D4—48no—
1131D4—48no—
1132D4—44no—
1133D4—108no—
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—21no—
1144C2×C4—21no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—28no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—52no—
1152C2×C4—52no—
1153C2×C4—52no—
1154C2×C4—52no—
1155C2×C4—52no—
1156C2×C4—52no—
1157C2×C4—54no—
1158C2×C4—108no—
1159C2×C4—108no—
1160C2×C4—1016no—
1161C2×C4—101no—
1162C2×C4—102no—
1163C2×C4—101no—
1164C2×C4—101no—
1165C2×C4—101no—
1166C2×C4—101no—
1167C2×C4—102no—
1168C2×C4—101no—
1169C2×C4—101no—
1170C2×C4—101no—
1171C2×C4—102no—
1172C2×C4—102no—
1173C2×C4—102no—
1174C2×C4—102no—
1175C2×C4—102no—
1176C2×C4—101no—
1177C2×C4—101no—
1178C2×C4—101no—
1179C2×C4—101no—
1180C2×C4—102no—
1181C2×C4—101no—
1182C2×C4—102no—
1183C2×C4—102no—
1184C2×C4—101no—
1185C2×C4—101no—
1186C2×C4—102no—
1187C2×C4—204no—
1188C2×C4—208no—
1189C2×C4—208no—
1190C2×C4—208no—
1191C2×C4—208no—
1192C2×C4—208no—
1193C2×C4—204no—
1194C2×C4—204no—
1195C2×C4C2×D4×D512yes—
1196C2×C4C2×D4×D512yes—
1197C2×C4C2×D4×D512yes—
1198C2×C4C2×#71112yes—
1199C2×C4C2×#71112yes—
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—24no—
1211C22—24no—
1212C22—24no—
1213C22—24no—
1214C22—24no—
1215C22—24no—
1216C22—432no—
1217C22—42no—
1218C22—42no—
1219C22—42no—
1220C22—42no—
1221C22—42no—
1222C22—42no—
1223C22—42no—
1224C22—42no—
1225C22—42no—
1226C22—42no—
1227C22—42no—
1228C22—42no—
1229C22—42no—
1230C22—42no—
1231C22—42no—
1232C22—102no—
1233C22—102no—
1234C22—102no—
1235C22—201no—
1236C22—201no—
1237C22—201no—
1238C22—201no—
1239C22#6605014yescomplemented
1240C22C22×D4×D511yescharacteristic
1241C22C22×D4×D511yescharacteristic
1242C22C22×#71111yescharacteristic
1243C22C22×#71111yescharacteristic
1244C22C22×#71111yescharacteristic
1245C22D5×H(5,𝔽2)11yescharacteristic
1246C22#6628511yescharacteristic
1247C4—22no—
1248C4—22no—
1249C4—22no—
1250C4—22no—
1251C4—22no—
1252C4—42no—
1253C4—54no—
1254C4—102no—
1255C4—102no—
1256C4—104no—
1257C4—102no—
1258C4—201no—
1259C4—201no—
1260C4—202no—
1261C4—202no—
1262C4—202no—
1263C4—201no—
1264C4#6592014yescomplemented
1265C2—24no—
1266C2—44no—
1267C2—44no—
1268C2—82no—
1269C2—202no—
1270C2C2×#6592011yescharacteristic
1271C2C2×#6605011yescharacteristic
1272C2#1061821511yescharacteristic
1273C2D4×#71111yescharacteristic
1274C2D4×#71111yescharacteristic
1275C2#1061850711yescharacteristic
1276C2D42×D511yescharacteristic
subgroupG/H
center, FrattiniC23C24×D5
commutator, socle, cosocleC23×C5C25
FittingC5×#2433C2
hypercenter#2433D5
hypocenterC5#34681
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C23 ◁ #2433

Complements

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

NH ≅ G/Ntype
1. C22×D4×Dic5C2semidirect
2. C2×#66050C2semidirect
3. C2×#65920C2semidirect
4. C5×#2433C2semidirect
5. #10615784C2semidirect
6. #10614917C2semidirect
7. #10614907C2semidirect
8. Dic5×#127C2semidirect
9. #10614436C2semidirect
10. Dic5×#121C2semidirect
11. #10614320C2semidirect
12. #10614317C2semidirect
13. Dic5×#120C2semidirect
14. #10608414C2semidirect
15. #10608411C2semidirect
16. #10608397C2semidirect
17. #10608396C2semidirect
18. #10608172C2semidirect
19. #10608053C2semidirect
20. #10608022C2semidirect
21. #10608020C2semidirect
22. #10605224C2semidirect
23. C4×#4027C2semidirect
26. C22×#711C22semidirect
35. C2×#4085C22semidirect
38. C2×#4084C22semidirect
39. C2×#4084C22semidirect
40. C2×#4082C22semidirect
41. C2×#4081C22semidirect
50. C2×D4×Dic5C22semidirect
51. C2×D4×Dic5C22semidirect
52. C2×D4×Dic5C22semidirect
53. C2×D4×Dic5C22semidirect
59. C2×#4032C22semidirect
62. C2×#4027C22semidirect
64. C2×#4024C22semidirect
65. C2×#4023C22semidirect
66. C2×C42×D5C22semidirect
67. C2×#4015C22semidirect
75. #65512C22semidirect
77. #65511C22semidirect
78. #65511C22semidirect
79. #65511C22semidirect
82. #65510C22semidirect
83. #65510C22semidirect
84. #65510C22semidirect
85. #65510C22semidirect
88. #65509C22semidirect
89. #65509C22semidirect
91. #65276C22semidirect
92. #65274C22semidirect
93. C4⋊C4×Dic5C22semidirect
94. #65262C22semidirect
95. #65250C22semidirect
96. #65250C22semidirect
97. #65245C22semidirect
98. #65242C22semidirect
99. #65240C22semidirect
101. #65239C22semidirect
102. #65239C22semidirect
103. #65237C22semidirect
104. #65237C22semidirect
105. #65236C22semidirect
106. #65234C22semidirect
107. #65234C22semidirect
108. #65233C22semidirect
111. C22⋊C4×Dic5C22semidirect
112. C22⋊C4×Dic5C22semidirect
113. C22⋊C4×Dic5C22semidirect
114. C4×#685C22semidirect
115. #65224C22semidirect
116. C4×#683C22semidirect
117. C42×Dic5C22semidirect
118. #65217C22semidirect
119. #65217C22semidirect
120. #64955C22semidirect
121. #64955C22semidirect
122. #64950C22semidirect
123. #64945C22semidirect
124. #64938C22semidirect
125. #64938C22semidirect
216. D4×Dic5D4semidirect
254. #4027D4semidirect
282. #2433D5semidirect
335. C2×C5×D4#41semidirect
338. C22×C4×C5#41semidirect
403. C2×C4×D5C2×D4semidirect
414. C5×C22⋊C4#41semidirect
438. #685C2×D4semidirect
453. #683C2×D4semidirect
465. C4×Dic5C2×D4semidirect
865. C22×C5#532semidirect
886. C4×C5#525semidirect
953. C2×D4#711semidirect
1001. C22×C4#711semidirect
1053. C22⋊C4#711semidirect
1203. C5#34681semidirect
1239. C22#66050semidirect
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×#660502
C2×#659202
C5×#24332
#106157842
#106149172
#106149072
Dic5×#1272
#106144362
Dic5×#1212
#106143202
#106143172
Dic5×#1202
#106084142
#106084112
#106083972
#106083962
#106081722
#106080532
#106080222
#106080202
#106052242
C4×#40272
#346815