Finite Group Databasebeta

← D5×#2485 #12268809

Subgroups — D5×#2485 #12268809

Order 1280.

3070 conjugacy classes of subgroups.

The subgroup lattice has 1242 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D4×D5C211yesmaximal, characteristic
2C2×D5×#117C211yesmaximal, characteristic, complemented
3C5×#2485C211yesmaximal, characteristic, complemented
4#10614103C211yesmaximal, characteristic, complemented
5#10614014C211yesmaximal, characteristic, complemented
6D5×#397C212yesmaximal, complemented
7#10609215C212yesmaximal, complemented
8D5×#394C212yesmaximal
9#10608664C212yesmaximal, complemented
10#10607961C211yesmaximal, characteristic, complemented
11#10607960C211yesmaximal, characteristic, complemented
12D5×#389C211yesmaximal, characteristic, complemented
13D5×#389C211yesmaximal, characteristic, complemented
14D5×#388C212yesmaximal, complemented
15#10607274C212yesmaximal, complemented
16D5×#387C212yesmaximal, complemented
17#10606752C212yesmaximal, complemented
18#10605757C211yesmaximal, characteristic, complemented
19#10605756C211yesmaximal, characteristic, complemented
20#10605755C211yesmaximal, characteristic, complemented
21D5×#380C211yesmaximal, characteristic, complemented
22D5×#380C211yesmaximal, characteristic, complemented
23D5×#380C211yesmaximal, characteristic, complemented
24C22×D4×D5C2211yescharacteristic
25C23×C4×D5C2211yescharacteristic
26C23×C4×D5C2211yescharacteristic
27C2×C4×C5×D4C2211yescharacteristic
28C2×C5×#117C2211yescharacteristic, complemented
29C2×D4×Dic5C2211yescharacteristic
30C2×C4×C22⋊D5C2211yescharacteristic
31C2×C4×C22⋊D5C2211yescharacteristic
32C2×#4072C2211yescharacteristic, complemented
33C4×D4×D5—28no—
34D5×#117—28no—
35C2×#4039C2211yescharacteristic
36C2×#4038C2211yescharacteristic, complemented
37C2×#4038C2211yescharacteristic, complemented
38C2×D5×C4⋊C4C2211yescharacteristic
39C2×D5×C4⋊C4C2211yescharacteristic
40C2×D5×C4⋊C4C2211yescharacteristic
41C2×D5×C4⋊C4C2211yescharacteristic
42C2×D5×C4⋊C4C2212yes—
43C2×D5×C4⋊C4C2211yescharacteristic
44C2×D5×C4⋊C4C2212yes—
45C2×#4027C2211yescharacteristic
46C2×#4027C2211yescharacteristic
47C2×D5×C22⋊C4C2212yes—
48C2×D5×C22⋊C4C2211yescharacteristic
49C2×D5×C22⋊C4C2211yescharacteristic
50C2×D5×C22⋊C4C2212yes—
51C2×D5×C22⋊C4C2212yes—
52C2×D5×C22⋊C4C2212yes—
53C2×#4023C2212yescomplemented
54C2×C4×D20C2211yescharacteristic
55C2×#4018C2212yescomplemented
56C2×C42×D5C2212yes—
57C2×C42×D5C2211yescharacteristic
58C5×#397C2212yescomplemented
59C5×#394C2212yes—
60C5×#389C2211yescharacteristic, complemented
61C5×#389C2211yescharacteristic, complemented
62C5×#388C2212yescomplemented
63C5×#387C2212yescomplemented
64C5×#380C2211yescharacteristic, complemented
65C5×#380C2211yescharacteristic, complemented
66C5×#380C2211yescharacteristic, complemented
67#65511C2212yes—
68#65501C2211yescharacteristic, complemented
69#65501C2211yescharacteristic, complemented
70#65501C2211yescharacteristic, complemented
71#65282C2212yescomplemented
72#65280C2212yes—
73#65279C2212yescomplemented
74#65276C2211yescharacteristic, complemented
75#65276C2211yescharacteristic, complemented
76#65276C2211yescharacteristic, complemented
77#65276C2211yescharacteristic, complemented
78#65276C2211yescharacteristic, complemented
79#65276C2211yescharacteristic, complemented
80#65274C2211yescharacteristic, complemented
81#65274C2211yescharacteristic, complemented
82#65270C2212yescomplemented
83#65267C2212yescomplemented
84#65262C2211yescharacteristic, complemented
85#65262C2211yescharacteristic, complemented
86#65261C2212yescomplemented
87#65261C2212yescomplemented
88#65250C2212yes—
89#65250C2212yes—
90#65248C2212yes—
91#65248C2212yes—
92#65242C2212yescomplemented
93#65241C2212yescomplemented
94#65241C2212yescomplemented
95#65240C2212yescomplemented
96#65234C2212yescomplemented
97#65233C2212yescomplemented
98#65231C2212yescomplemented
99#65231C2212yescomplemented
100#65231C2212yescomplemented
101#65229C2212yescomplemented
102#65222C2212yescomplemented
103#65217C2211yescharacteristic, complemented
104#65217C2211yescharacteristic, complemented
105#64964C2212yescomplemented
106#64964C2212yescomplemented
107#64963C2212yescomplemented
108#64961C2212yes—
109#64959C2212yescomplemented
110#64958C2212yescomplemented
111#64956C2212yescomplemented
112#64956C2212yescomplemented
113#64956C2212yescomplemented
114D5×#95C2212yes—
115D5×#95C2212yes—
116D5×#95C2212yes—
117D5×#95C2212yes—
118D5×#95C2212yes—
119#64944C2212yescomplemented
120#64943C2212yescomplemented
121#64942C2212yescomplemented
122#64941C2212yescomplemented
123#64936C2212yescomplemented
124#64936C2212yescomplemented
125C2×#2485—51nomaximal, Sylow
126C24×D5C2311yescharacteristic
127C24×D5C2311yescharacteristic
128C22×C5×D4C2311yescharacteristic
129C23×C4×C5C2311yescharacteristic
130C23×C4×C5C2311yescharacteristic
131C22×C22⋊D5C2311yescharacteristic
132C22×C22⋊D5C2311yescharacteristic
133C23×Dic5C2311yescharacteristic
134C23×Dic5C2311yescharacteristic
135C2×D4×D5—24no—
136C2×D4×D5—24no—
137C2×D4×D5—24no—
138C22×D20C2311yescharacteristic
139C22×C4×D5—24no—
140C22×C4×D5—24no—
141C22×C4×D5—24no—
142C22×C4×D5—24no—
143C22×C4×D5—24no—
144C22×C4×D5D418yes—
145C22×C4×D5C2311yescharacteristic
146C22×C4×D5C2312yes—
147C22×C4×D5C2312yes—
148C22×C4×D5C2311yescharacteristic
149C22×C4×D5C2312yes—
150C22×C4×D5C2312yes—
151C22×C4×D5C2311yescharacteristic
152C22×C4×D5C2311yescharacteristic
153C22×C4×D5C2311yescharacteristic
154C22×C4×D5C2311yescharacteristic
155C22×C4×D5C2311yescharacteristic
156C22×C4×D5C2311yescharacteristic
157C22×C4×D5C2311yescharacteristic
158C4×C5×D4—24no—
159C5×#117—24no—
160C2×C5×C4⋊C4C2312yes—
161C2×C5×C4⋊C4C2311yescharacteristic
162C2×C5×C4⋊C4C2311yescharacteristic
163C2×C5×C4⋊C4C2311yescharacteristic
164C2×C5×C4⋊C4C2311yescharacteristic
165C2×C5×C4⋊C4C2311yescharacteristic
166C2×C5×C4⋊C4C2312yes—
167C2×C5×C22⋊C4C2312yes—
168C2×C5×C22⋊C4C2311yescharacteristic
169C2×C5×C22⋊C4C2312yes—
170C2×C5×C22⋊C4C2311yescharacteristic
171C2×C5×C22⋊C4C2312yes—
172C2×C5×C22⋊C4C2312yes—
173C2×C42×C5C2312yes—
174C2×C42×C5C2311yescharacteristic
175C2×C22⋊Dic5C2312yes—
176C2×C22⋊Dic5C2311yescharacteristic
177C2×C22⋊Dic5C2311yescharacteristic
178C2×C22⋊Dic5C2312yes—
179C2×C22⋊Dic5C2312yes—
180C2×C22⋊Dic5C2312yes—
181D4×Dic5—24no—
182C4×C22⋊D5—24no—
183C4×C22⋊D5—24no—
184C2×#685C2312yes—
185C2×#685C2312yes—
186C2×#685C2311yescharacteristic
187C2×#685C2312yes—
188C2×#685C2311yescharacteristic
189C2×#685C2311yescharacteristic
190C2×#685C2311yescharacteristic
191C2×#685C2312yes—
192C2×#685C2312yes—
193C2×#685C2312yes—
194C2×#685C2312yes—
195C2×#685C2312yes—
196#4072—24no—
197C2×C4⋊Dic5C2311yescharacteristic
198C2×C4⋊Dic5C2311yescharacteristic
199C2×C4⋊Dic5C2311yescharacteristic
200C2×C4⋊Dic5C2312yes—
201C2×C4⋊Dic5C2311yescharacteristic
202C2×C4⋊Dic5C2311yescharacteristic
203C2×C4⋊Dic5C2312yes—
204C2×#683C2312yes—
205C2×#683C2312yes—
206C2×#683C2311yescharacteristic
207C2×#683C2311yescharacteristic
208C2×#683C2312yes—
209C2×#683C2312yes—
210C2×#683C2312yes—
211C2×#683C2312yes—
212C2×#683C2312yes—
213C2×#683C2312yes—
214C2×C4×Dic5C2312yes—
215C2×C4×Dic5C2312yes—
216C2×C4×Dic5C2312yes—
217C2×C4×Dic5C2311yescharacteristic
218C2×C4×Dic5C2311yescharacteristic
219C2×C4×Dic5C2311yescharacteristic
220#4039—24no—
221#4038—24no—
222#4038—24no—
223D5×C4⋊C4—24no—
224D5×C4⋊C4—24no—
225D5×C4⋊C4—24no—
226D5×C4⋊C4—28no—
227D5×C4⋊C4—24no—
228D5×C4⋊C4—24no—
229D5×C4⋊C4—44no—
230#4027—24no—
231#4027—24no—
232D5×C22⋊C4—28no—
233D5×C22⋊C4—24no—
234D5×C22⋊C4—28no—
235D5×C22⋊C4—24no—
236D5×C22⋊C4—44no—
237D5×C22⋊C4—44no—
238#4023—28no—
239C4×D20—24no—
240#4018—28no—
241C42×D5—28no—
242C42×D5—24no—
243C5×#95C2312yes—
244C5×#95C2312yes—
245C5×#95C2312yes—
246C5×#95C2312yes—
247C5×#95C2312yes—
248#3963C2312yes—
249#3963C2312yes—
250#3963C2312yes—
251#3963C2312yes—
252#3963C2312yes—
253#3963C2312yes—
254#3963C2312yes—
255#3963C2312yes—
256#3963C2312yes—
257#3963C2312yes—
258#3963C2312yes—
259#3963C2312yes—
260#3963C2312yes—
261#3963C2312yes—
262#3963C2312yes—
263C22×C4×D4—51no—
264C22×#117—51no—
265#2485—52no—
266#2485—52no—
267#2485—51no—
268#2485—51no—
269#2485—52no—
270#2485—52no—
271#2485—51no—
272#2485—51no—
273#2485—51no—
274#2485—51no—
275#2485—51no—
276#2485D511yescharacteristic, direct product factor
277C2×#397—52no—
278C2×#394—52no—
279C2×#389—51no—
280C2×#389—51no—
281C2×#388—52no—
282C2×#387—52no—
283C2×#380—51no—
284C2×#380—51no—
285C2×#380—51no—
286C24×C5C2411yescharacteristic
287C24×C5C2411yescharacteristic
288C23×D5—22no—
289C23×D5—22no—
290C23×D5—22no—
291C23×D5—22no—
292C23×D5—22no—
293C23×D5—22no—
294C23×D5—22no—
295C23×D5—22no—
296C23×D5—22no—
297C23×D5—22no—
298C23×D5—22no—
299C23×D5—22no—
300C23×D5C2×D414yes—
301C23×D5#4114yes—
302C23×D5C2411yescharacteristic
303C23×D5C2411yescharacteristic
304C23×D5C2411yescharacteristic
305C2×C5×D4—22no—
306C2×C5×D4—22no—
307C2×C5×D4—22no—
308C22×C4×C5—22no—
309C22×C4×C5—22no—
310C22×C4×C5—22no—
311C22×C4×C5—22no—
312C22×C4×C5—22no—
313C22×C4×C5C2×D414yes—
314C22×C4×C5C2412yes—
315C22×C4×C5C2412yes—
316C22×C4×C5C2411yescharacteristic
317C22×C4×C5C2412yes—
318C22×C4×C5C2412yes—
319C22×C4×C5C2411yescharacteristic
320C22×C4×C5C2411yescharacteristic
321C22×C4×C5C2411yescharacteristic
322C22×C4×C5C2411yescharacteristic
323C2×C22⋊D5—22no—
324C2×C22⋊D5—22no—
325C2×C22⋊D5—22no—
326C2×C22⋊D5—22no—
327C2×C22⋊D5—22no—
328C2×C22⋊D5—22no—
329C22×Dic5—22no—
330C22×Dic5—22no—
331C22×Dic5—22no—
332C22×Dic5—22no—
333C22×Dic5—22no—
334C22×Dic5C2×D414yes—
335C22×Dic5C2412yes—
336C22×Dic5C2412yes—
337C22×Dic5C2412yes—
338C22×Dic5C2412yes—
339C22×Dic5C2411yescharacteristic
340C22×Dic5C2411yescharacteristic
341C22×Dic5C2411yescharacteristic
342C22×Dic5C2411yescharacteristic
343C22×Dic5C2411yescharacteristic
344D4×D5—232no—
345C2×D20—22no—
346C2×D20—22no—
347C2×D20—22no—
348C2×C4×D5—22no—
349C2×C4×D5—22no—
350C2×C4×D5—22no—
351C2×C4×D5—22no—
352C2×C4×D5—22no—
353C2×C4×D5—22no—
354C2×C4×D5—22no—
355C2×C4×D5—22no—
356C2×C4×D5—232no—
357C2×C4×D5—22no—
358C2×C4×D5—22no—
359C2×C4×D5—24no—
360C2×C4×D5—24no—
361C2×C4×D5—22no—
362C2×C4×D5—22no—
363C2×C4×D5—24no—
364C2×C4×D5—24no—
365C2×C4×D5—24no—
366C2×C4×D5—24no—
367C2×C4×D5—24no—
368C2×C4×D5—24no—
369C2×C4×D5—24no—
370C2×C4×D5—24no—
371C2×C4×D5—24no—
372C2×C4×D5—22no—
373C2×C4×D5—22no—
374C2×C4×D5—24no—
375C2×C4×D5—22no—
376C2×C4×D5—22no—
377C2×C4×D5—22no—
378C2×C4×D5—22no—
379C2×C4×D5—22no—
380C2×C4×D5—22no—
381C2×C4×D5—416no—
382C2×C4×D5C2×D414yes—
383C2×C4×D5C2×D414yes—
384C2×C4×D5C2×D414yes—
385C2×C4×D5C2×D414yes—
386C2×C4×D5#4114yes—
387C2×C4×D5#4114yes—
388C2×C4×D5#4114yes—
389C5×C4⋊C4—22no—
390C5×C4⋊C4—22no—
391C5×C4⋊C4—22no—
392C5×C4⋊C4—22no—
393C5×C4⋊C4—22no—
394C5×C4⋊C4—24no—
395C5×C4⋊C4—42no—
396C5×C22⋊C4—24no—
397C5×C22⋊C4—22no—
398C5×C22⋊C4—24no—
399C5×C22⋊C4—22no—
400C5×C22⋊C4—42no—
401C5×C22⋊C4—42no—
402C42×C5—24no—
403C42×C5—22no—
404C22⋊Dic5—24no—
405C22⋊Dic5—22no—
406C22⋊Dic5—24no—
407C22⋊Dic5—22no—
408C22⋊Dic5—42no—
409C22⋊Dic5—42no—
410#685—24no—
411#685—24no—
412#685—22no—
413#685—22no—
414#685—24no—
415#685—24no—
416#685—22no—
417#685—22no—
418#685—42no—
419#685—42no—
420#685—42no—
421#685—42no—
422C4⋊Dic5—22no—
423C4⋊Dic5—22no—
424C4⋊Dic5—22no—
425C4⋊Dic5—22no—
426C4⋊Dic5—22no—
427C4⋊Dic5—24no—
428C4⋊Dic5—42no—
429#683—22no—
430#683—24no—
431#683—24no—
432#683—24no—
433#683—22no—
434#683—24no—
435#683—24no—
436#683—24no—
437#683—42no—
438#683—42no—
439C4×Dic5—24no—
440C4×Dic5—22no—
441C4×Dic5—24no—
442C4×Dic5—24no—
443C4×Dic5—22no—
444C4×Dic5—22no—
445C23×D4—51no—
446C24×C4—51no—
447C24×C4—51no—
448C2×C4×D4—51no—
449C2×C4×D4—51no—
450C2×C4×D4—51no—
451C2×C4×D4—51no—
452C2×C4×D4—51no—
453C2×C4×D4—51no—
454C2×C4×D4—51no—
455C2×C4×D4—108no—
456C2×C4×D4C2×D511yescharacteristic
457C2×#117—51no—
458C2×#117—51no—
459C2×#117—51no—
460C2×#117—52no—
461C2×#117—52no—
462C2×#117—108no—
463C2×#117C2×D511yescharacteristic, complemented
464C22×C4⋊C4—52no—
465C22×C4⋊C4—51no—
466C22×C4⋊C4—51no—
467C22×C4⋊C4—51no—
468C22×C4⋊C4—51no—
469C22×C4⋊C4—51no—
470C22×C4⋊C4—52no—
471C22×C22⋊C4—52no—
472C22×C22⋊C4—52no—
473C22×C22⋊C4—51no—
474C22×C22⋊C4—51no—
475C22×C22⋊C4—52no—
476C22×C22⋊C4—52no—
477C22×C42—52no—
478C22×C42—51no—
479#397—52no—
480#397—52no—
481#397—52no—
482#397—52no—
483#397—52no—
484#397—52no—
485#397—52no—
486#397C2×D512yescomplemented
487#394—52no—
488#394—52no—
489#394—52no—
490#394—52no—
491#394—52no—
492#394—52no—
493#394—52no—
494#394C2×D512yes—
495#389—52no—
496#389—52no—
497#389—51no—
498#389—51no—
499#389—51no—
500#389—51no—
501#389—51no—
502#389—51no—
503#389—52no—
504#389—52no—
505#389C2×D511yescharacteristic, complemented
506#389C2×D511yescharacteristic, complemented
507#388—52no—
508#388—52no—
509#388—52no—
510#388—52no—
511#388—52no—
512#388—52no—
513#388—52no—
514#388C2×D512yescomplemented
515#387—52no—
516#387—52no—
517#387—52no—
518#387—52no—
519#387—52no—
520#387—52no—
521#387—52no—
522#387C2×D512yescomplemented
523#380—51no—
524#380—51no—
525#380—51no—
526#380—51no—
527#380—51no—
528#380—51no—
529#380—51no—
530#380—51no—
531#380—51no—
532#380—52no—
533#380—52no—
534#380—52no—
535#380—52no—
536#380—52no—
537#380—52no—
538#380C2×D511yescharacteristic, complemented
539#380C2×D511yescharacteristic, complemented
540#380C2×D511yescharacteristic, complemented
541C2×#95—52no—
542C2×#95—52no—
543C2×#95—52no—
544C2×#95—52no—
545C2×#95—52no—
546C23×C5—21no—
547C23×C5—21no—
548C23×C5—21no—
549C23×C5—21no—
550C23×C5—21no—
551C23×C5—21no—
552C23×C5—21no—
553C23×C5—21no—
554C23×C5—21no—
555C23×C5—21no—
556C23×C5—21no—
557C23×C5—21no—
558C23×C5C22×D412yes—
559C23×C5C2×#4112yes—
560C23×C5C2511yescharacteristic
561C22×D5—21no—
562C22×D5—21no—
563C22×D5—21no—
564C22×D5—21no—
565C22×D5—21no—
566C22×D5—21no—
567C22×D5—21no—
568C22×D5—21no—
569C22×D5—21no—
570C22×D5—21no—
571C22×D5—21no—
572C22×D5—21no—
573C22×D5—28no—
574C22×D5—28no—
575C22×D5—28no—
576C22×D5—28no—
577C22×D5—28no—
578C22×D5—28no—
579C22×D5—44no—
580C22×D5—44no—
581C22×D5—44no—
582C22×D5—44no—
583C22×D5—44no—
584C22×D5—44no—
585C22×D5—44no—
586C22×D5—44no—
587C22×D5C22×D412yes—
588C22×D5C22×D412yes—
589C22×D5C2×#4112yes—
590C22×D5C2×#4112yes—
591C22×D5C2×#4112yes—
592C22×D5C2×#4112yes—
593C22×D5C2×#4112yes—
594C22×D5H(5,𝔽2)12yes—
595C22×D52−1+412yes—
596C5×D4—28no—
597C2×C4×C5—21no—
598C2×C4×C5—21no—
599C2×C4×C5—21no—
600C2×C4×C5—21no—
601C2×C4×C5—28no—
602C2×C4×C5—22no—
603C2×C4×C5—22no—
604C2×C4×C5—21no—
605C2×C4×C5—21no—
606C2×C4×C5—22no—
607C2×C4×C5—22no—
608C2×C4×C5—22no—
609C2×C4×C5—22no—
610C2×C4×C5—22no—
611C2×C4×C5—22no—
612C2×C4×C5—21no—
613C2×C4×C5—21no—
614C2×C4×C5—21no—
615C2×C4×C5—22no—
616C2×C4×C5—22no—
617C2×C4×C5—22no—
618C2×C4×C5—22no—
619C2×C4×C5—21no—
620C2×C4×C5—44no—
621C2×C4×C5C22×D412yes—
622C2×C4×C5C22×D412yes—
623C2×C4×C5C2×#4112yes—
624C2×C4×C5C2×#4112yes—
625C2×C4×C5C2×#4112yes—
626C22⋊D5—28no—
627C22⋊D5—28no—
628C2×Dic5—21no—
629C2×Dic5—21no—
630C2×Dic5—21no—
631C2×Dic5—21no—
632C2×Dic5—28no—
633C2×Dic5—22no—
634C2×Dic5—22no—
635C2×Dic5—21no—
636C2×Dic5—21no—
637C2×Dic5—22no—
638C2×Dic5—22no—
639C2×Dic5—22no—
640C2×Dic5—22no—
641C2×Dic5—22no—
642C2×Dic5—22no—
643C2×Dic5—21no—
644C2×Dic5—21no—
645C2×Dic5—21no—
646C2×Dic5—22no—
647C2×Dic5—22no—
648C2×Dic5—22no—
649C2×Dic5—22no—
650C2×Dic5—21no—
651C2×Dic5—44no—
652C2×Dic5C22×D412yes—
653C2×Dic5C22×D412yes—
654C2×Dic5C2×#4112yes—
655C2×Dic5C2×#4112yes—
656C2×Dic5C2×#4112yes—
657D20—28no—
658C4×D5—28no—
659C4×D5—28no—
660C4×D5—28no—
661C4×D5—28no—
662C4×D5—44no—
663C4×D5—48no—
664C4×D5—44no—
665C4×D5—48no—
666C4×D5—48no—
667C4×D5—48no—
668C4×D5—44no—
669C4×D5—44no—
670C4×D5#123116yes—
671C25—51no—
672C25—51no—
673C22×D4—51no—
674C22×D4—51no—
675C22×D4—51no—
676C22×D4—104no—
677C22×D4—104no—
678C22×D4—104no—
679C22×D4C22×D511yescharacteristic
680C23×C4—51no—
681C23×C4—51no—
682C23×C4—58no—
683C23×C4—51no—
684C23×C4—51no—
685C23×C4—51no—
686C23×C4—51no—
687C23×C4—51no—
688C23×C4—52no—
689C23×C4—52no—
690C23×C4—51no—
691C23×C4—52no—
692C23×C4—52no—
693C23×C4—51no—
694C23×C4—51no—
695C23×C4—51no—
696C23×C4—104no—
697C23×C4—104no—
698C23×C4—104no—
699C23×C4—104no—
700C23×C4—104no—
701C23×C4C22×D511yescharacteristic
702C23×C4C22×D511yescharacteristic
703C4×D4—24no—
704C4×D4—104no—
705C4×D4—104no—
706C4×D4—104no—
707C4×D4—104no—
708C4×D4—104no—
709C4×D4—104no—
710C4×D4—104no—
711#117—24no—
712#117—108no—
713#117—108no—
714#117—104no—
715#117—104no—
716#117—104no—
717C2×C4⋊C4—52no—
718C2×C4⋊C4—52no—
719C2×C4⋊C4—51no—
720C2×C4⋊C4—51no—
721C2×C4⋊C4—51no—
722C2×C4⋊C4—51no—
723C2×C4⋊C4—51no—
724C2×C4⋊C4—52no—
725C2×C4⋊C4—52no—
726C2×C4⋊C4—51no—
727C2×C4⋊C4—51no—
728C2×C4⋊C4—52no—
729C2×C4⋊C4—52no—
730C2×C4⋊C4—52no—
731C2×C4⋊C4—52no—
732C2×C4⋊C4—52no—
733C2×C4⋊C4—52no—
734C2×C4⋊C4—104no—
735C2×C4⋊C4—104no—
736C2×C4⋊C4—104no—
737C2×C4⋊C4—104no—
738C2×C4⋊C4—104no—
739C2×C4⋊C4—108no—
740C2×C4⋊C4—204no—
741C2×C4⋊C4C22×D511yescharacteristic
742C2×C4⋊C4C22×D511yescharacteristic
743C2×C4⋊C4C22×D511yescharacteristic
744C2×C4⋊C4C22×D511yescharacteristic
745C2×C4⋊C4C22×D511yescharacteristic
746C2×C4⋊C4C22×D512yes—
747C2×C4⋊C4C22×D512yes—
748C2×C22⋊C4—52no—
749C2×C22⋊C4—51no—
750C2×C22⋊C4—51no—
751C2×C22⋊C4—52no—
752C2×C22⋊C4—52no—
753C2×C22⋊C4—52no—
754C2×C22⋊C4—51no—
755C2×C22⋊C4—51no—
756C2×C22⋊C4—51no—
757C2×C22⋊C4—51no—
758C2×C22⋊C4—52no—
759C2×C22⋊C4—52no—
760C2×C22⋊C4—52no—
761C2×C22⋊C4—52no—
762C2×C22⋊C4—52no—
763C2×C22⋊C4—52no—
764C2×C22⋊C4—52no—
765C2×C22⋊C4—52no—
766C2×C22⋊C4—104no—
767C2×C22⋊C4—108no—
768C2×C22⋊C4—104no—
769C2×C22⋊C4—108no—
770C2×C22⋊C4—204no—
771C2×C22⋊C4—204no—
772C2×C22⋊C4C22×D512yes—
773C2×C22⋊C4C22×D511yescharacteristic
774C2×C22⋊C4C22×D511yescharacteristic
775C2×C22⋊C4C22×D512yes—
776C2×C22⋊C4C22×D512yes—
777C2×C22⋊C4C22×D512yes—
778C2×C42—52no—
779C2×C42—52no—
780C2×C42—52no—
781C2×C42—51no—
782C2×C42—51no—
783C2×C42—51no—
784C2×C42—108no—
785C2×C42—104no—
786C2×C42C22×D512yes—
787C2×C42C22×D511yescharacteristic
788#95—52no—
789#95—52no—
790#95—52no—
791#95—52no—
792#95—52no—
793#95—52no—
794#95—52no—
795#95—52no—
796#95—52no—
797#95—52no—
798#95—52no—
799#95—52no—
800#95—52no—
801#95—52no—
802#95—52no—
803#95C22×D512yes—
804#95C22×D512yes—
805#95C22×D512yes—
806#95C22×D512yes—
807#95C22×D512yes—
808C22×C5—22no—
809C22×C5—22no—
810C22×C5—22no—
811C22×C5—22no—
812C22×C5—22no—
813C22×C5—22no—
814C22×C5—41no—
815C22×C5—41no—
816C22×C5—41no—
817C22×C5—41no—
818C22×C5—41no—
819C22×C5—41no—
820C22×C5—41no—
821C22×C5—41no—
822C22×C5C23×D411yescharacteristic
823C22×C5C22×#4111yescharacteristic
824C22×C5C22×#4111yescharacteristic
825C22×C5C22×#4111yescharacteristic
826C22×C5C22×#4111yescharacteristic
827C22×C5C2×H(5,𝔽2)11yescharacteristic
828C22×C5C2×2−1+411yescharacteristic
829C2×D5—22no—
830C2×D5—22no—
831C2×D5—22no—
832C2×D5—22no—
833C2×D5—22no—
834C2×D5—22no—
835C2×D5—41no—
836C2×D5—41no—
837C2×D5—41no—
838C2×D5—41no—
839C2×D5—41no—
840C2×D5—41no—
841C2×D5—41no—
842C2×D5—41no—
843C2×D5—416no—
844C2×D5—416no—
845C2×D5C2×#12314yes—
846C2×D5#52514yes—
847C2×D5#53714yes—
848C2×D5#55214yes—
849C2×D5#55314yes—
850C2×D5#55514yes—
851C2×D5#55614yes—
852C4×C5—22no—
853C4×C5—22no—
854C4×C5—41no—
855C4×C5—42no—
856C4×C5—42no—
857C4×C5—41no—
858C4×C5—42no—
859C4×C5—42no—
860C4×C5C2×#12314yes—
861Dic5—22no—
862Dic5—22no—
863Dic5—41no—
864Dic5—42no—
865Dic5—42no—
866Dic5—41no—
867Dic5—42no—
868Dic5—42no—
869Dic5C2×#12314yes—
870C24—51no—
871C24—54no—
872C24—54no—
873C24—51no—
874C24—51no—
875C24—102no—
876C24—102no—
877C24—102no—
878C24—102no—
879C24—102no—
880C24—102no—
881C24—102no—
882C24—102no—
883C24—102no—
884C24—102no—
885C24—102no—
886C24—102no—
887C24C23×D511yescharacteristic
888C24C23×D511yescharacteristic
889C2×D4—22no—
890C2×D4—22no—
891C2×D4—22no—
892C2×D4—102no—
893C2×D4—102no—
894C2×D4—102no—
895C2×D4—102no—
896C2×D4—1032no—
897C2×D4—102no—
898C2×D4—102no—
899C2×D4—102no—
900C2×D4—102no—
901C2×D4—102no—
902C22×C4—22no—
903C22×C4—22no—
904C22×C4—22no—
905C22×C4—22no—
906C22×C4—22no—
907C22×C4—51no—
908C22×C4—54no—
909C22×C4—54no—
910C22×C4—54no—
911C22×C4—54no—
912C22×C4—51no—
913C22×C4—51no—
914C22×C4—54no—
915C22×C4—54no—
916C22×C4—54no—
917C22×C4—54no—
918C22×C4—51no—
919C22×C4—52no—
920C22×C4—52no—
921C22×C4—51no—
922C22×C4—52no—
923C22×C4—52no—
924C22×C4—102no—
925C22×C4—102no—
926C22×C4—1032no—
927C22×C4—102no—
928C22×C4—102no—
929C22×C4—102no—
930C22×C4—102no—
931C22×C4—102no—
932C22×C4—102no—
933C22×C4—102no—
934C22×C4—102no—
935C22×C4—104no—
936C22×C4—104no—
937C22×C4—102no—
938C22×C4—104no—
939C22×C4—104no—
940C22×C4—104no—
941C22×C4—104no—
942C22×C4—104no—
943C22×C4—104no—
944C22×C4—104no—
945C22×C4—104no—
946C22×C4—104no—
947C22×C4—102no—
948C22×C4—102no—
949C22×C4—102no—
950C22×C4—102no—
951C22×C4—104no—
952C22×C4—102no—
953C22×C4—102no—
954C22×C4—102no—
955C22×C4—102no—
956C22×C4—102no—
957C22×C4—102no—
958C22×C4—102no—
959C22×C4—102no—
960C22×C4—102no—
961C22×C4—102no—
962C22×C4—2016no—
963C22×C4D4×D514yes—
964C22×C4C23×D511yescharacteristic
965C22×C4C23×D512yes—
966C22×C4C23×D512yes—
967C22×C4C23×D511yescharacteristic
968C22×C4C23×D512yes—
969C22×C4C23×D512yes—
970C22×C4C23×D511yescharacteristic
971C22×C4C23×D511yescharacteristic
972C22×C4C23×D511yescharacteristic
973C4⋊C4—22no—
974C4⋊C4—22no—
975C4⋊C4—22no—
976C4⋊C4—24no—
977C4⋊C4—22no—
978C4⋊C4—22no—
979C4⋊C4—42no—
980C4⋊C4—104no—
981C4⋊C4—104no—
982C4⋊C4—102no—
983C4⋊C4—102no—
984C4⋊C4—104no—
985C4⋊C4—104no—
986C4⋊C4—104no—
987C4⋊C4—104no—
988C4⋊C4—102no—
989C4⋊C4—102no—
990C4⋊C4—102no—
991C4⋊C4—104no—
992C4⋊C4—102no—
993C4⋊C4—102no—
994C4⋊C4—202no—
995C4⋊C4—202no—
996C4⋊C4—202no—
997C22⋊C4—24no—
998C22⋊C4—22no—
999C22⋊C4—24no—
1000C22⋊C4—22no—
1001C22⋊C4—42no—
1002C22⋊C4—42no—
1003C22⋊C4—102no—
1004C22⋊C4—104no—
1005C22⋊C4—104no—
1006C22⋊C4—102no—
1007C22⋊C4—102no—
1008C22⋊C4—104no—
1009C22⋊C4—104no—
1010C22⋊C4—102no—
1011C22⋊C4—104no—
1012C22⋊C4—102no—
1013C22⋊C4—104no—
1014C22⋊C4—102no—
1015C22⋊C4—202no—
1016C22⋊C4—202no—
1017C22⋊C4—202no—
1018C22⋊C4—202no—
1019C22⋊C4—202no—
1020C22⋊C4—202no—
1021C42—24no—
1022C42—22no—
1023C42—104no—
1024C42—104no—
1025C42—102no—
1026C42—102no—
1027C42—104no—
1028C42—102no—
1029C2×C5—42no—
1030C2×C5—42no—
1031C2×C5C22×#12311yescharacteristic
1032C2×C5C2×#52511yescharacteristic
1033C2×C5C2×#53711yescharacteristic
1034C2×C5C2×#55211yescharacteristic
1035C2×C5C2×#55311yescharacteristic
1036C2×C5C2×#55511yescharacteristic
1037C2×C5C2×#55611yescharacteristic
1038D5—42no—
1039D5—42no—
1040D5#248518yesdirect product factor
1041C23—21no—
1042C23—21no—
1043C23—21no—
1044C23—21no—
1045C23—21no—
1046C23—21no—
1047C23—21no—
1048C23—21no—
1049C23—21no—
1050C23—21no—
1051C23—21no—
1052C23—21no—
1053C23—52no—
1054C23—52no—
1055C23—52no—
1056C23—52no—
1057C23—52no—
1058C23—52no—
1059C23—52no—
1060C23—52no—
1061C23—52no—
1062C23—108no—
1063C23—108no—
1064C23—108no—
1065C23—108no—
1066C23—108no—
1067C23—108no—
1068C23—101no—
1069C23—101no—
1070C23—101no—
1071C23—101no—
1072C23—101no—
1073C23—101no—
1074C23—101no—
1075C23—101no—
1076C23—101no—
1077C23—101no—
1078C23—101no—
1079C23—101no—
1080C23—204no—
1081C23—204no—
1082C23—204no—
1083C23—204no—
1084C23—204no—
1085C23—204no—
1086C23—204no—
1087C23—204no—
1088C23C2×D4×D512yes—
1089C23D5×#4112yes—
1090C23C24×D511yescharacteristic
1091D4—28no—
1092D4—108no—
1093D4—108no—
1094D4—108no—
1095C2×C4—21no—
1096C2×C4—21no—
1097C2×C4—21no—
1098C2×C4—21no—
1099C2×C4—28no—
1100C2×C4—21no—
1101C2×C4—22no—
1102C2×C4—22no—
1103C2×C4—21no—
1104C2×C4—22no—
1105C2×C4—22no—
1106C2×C4—22no—
1107C2×C4—22no—
1108C2×C4—22no—
1109C2×C4—22no—
1110C2×C4—21no—
1111C2×C4—21no—
1112C2×C4—22no—
1113C2×C4—22no—
1114C2×C4—22no—
1115C2×C4—21no—
1116C2×C4—21no—
1117C2×C4—22no—
1118C2×C4—44no—
1119C2×C4—52no—
1120C2×C4—52no—
1121C2×C4—52no—
1122C2×C4—516no—
1123C2×C4—52no—
1124C2×C4—52no—
1125C2×C4—108no—
1126C2×C4—108no—
1127C2×C4—108no—
1128C2×C4—108no—
1129C2×C4—101no—
1130C2×C4—101no—
1131C2×C4—101no—
1132C2×C4—101no—
1133C2×C4—108no—
1134C2×C4—101no—
1135C2×C4—102no—
1136C2×C4—102no—
1137C2×C4—101no—
1138C2×C4—102no—
1139C2×C4—102no—
1140C2×C4—102no—
1141C2×C4—102no—
1142C2×C4—102no—
1143C2×C4—102no—
1144C2×C4—101no—
1145C2×C4—101no—
1146C2×C4—102no—
1147C2×C4—102no—
1148C2×C4—102no—
1149C2×C4—101no—
1150C2×C4—101no—
1151C2×C4—102no—
1152C2×C4—204no—
1153C2×C4—204no—
1154C2×C4—208no—
1155C2×C4—204no—
1156C2×C4—208no—
1157C2×C4—208no—
1158C2×C4—208no—
1159C2×C4—204no—
1160C2×C4—204no—
1161C2×C4C2×D4×D512yes—
1162C2×C4C2×D4×D512yes—
1163C2×C4D5×#4112yes—
1164C2×C4D5×#4112yes—
1165C2×C4D5×#4112yes—
1166C5C2×#248511yescharacteristic, complemented, Sylow
1167C22—22no—
1168C22—22no—
1169C22—22no—
1170C22—22no—
1171C22—22no—
1172C22—22no—
1173C22—41no—
1174C22—41no—
1175C22—41no—
1176C22—41no—
1177C22—41no—
1178C22—41no—
1179C22—41no—
1180C22—41no—
1181C22—54no—
1182C22—54no—
1183C22—54no—
1184C22—54no—
1185C22—54no—
1186C22—54no—
1187C22—54no—
1188C22—102no—
1189C22—102no—
1190C22—102no—
1191C22—102no—
1192C22—102no—
1193C22—102no—
1194C22—2016no—
1195C22—2016no—
1196C22—201no—
1197C22—201no—
1198C22—201no—
1199C22—201no—
1200C22—201no—
1201C22—201no—
1202C22—201no—
1203C22—201no—
1204C22C22×D4×D511yescharacteristic
1205C22C2×D5×#4111yescharacteristic
1206C22C2×D5×#4111yescharacteristic
1207C22C2×D5×#4111yescharacteristic
1208C22C2×D5×#4111yescharacteristic
1209C22D5×H(5,𝔽2)11yescharacteristic
1210C22D5×2−1+411yescharacteristic
1211C4—22no—
1212C4—22no—
1213C4—41no—
1214C4—42no—
1215C4—41no—
1216C4—42no—
1217C4—42no—
1218C4—42no—
1219C4—54no—
1220C4—102no—
1221C4—102no—
1222C4—201no—
1223C4—202no—
1224C4—201no—
1225C4—202no—
1226C4—202no—
1227C4—202no—
1228C4D5×#12314yes—
1229C2—42no—
1230C2—42no—
1231C2—58no—
1232C2—202no—
1233C2—202no—
1234C2C2×D5×#12311yescharacteristic
1235C2D5×#52511yescharacteristic
1236C2D5×#53711yescharacteristic
1237C2D5×#55211yescharacteristic
1238C2D5×#55311yescharacteristic
1239C2D5×#55511yescharacteristic
1240C2D5×#55611yescharacteristic
subgroupG/H
center, FrattiniC23C24×D5
commutator, socle, cosocleC23×C5C25
FittingC5×#2485C2
prime radicalC22×D4×D5C22
hypercenter#2485D5
hypocenterC5C2×#2485
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C23 ◁ #2485

Complements

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

NH ≅ G/Ntype
2. C2×D5×#117C2semidirect
3. C5×#2485C2semidirect
4. #10614103C2semidirect
5. #10614014C2semidirect
6. D5×#397C2semidirect
7. #10609215C2semidirect
9. #10608664C2semidirect
10. #10607961C2semidirect
11. #10607960C2semidirect
12. D5×#389C2semidirect
13. D5×#389C2semidirect
14. D5×#388C2semidirect
15. #10607274C2semidirect
16. D5×#387C2semidirect
17. #10606752C2semidirect
18. #10605757C2semidirect
19. #10605756C2semidirect
20. #10605755C2semidirect
21. D5×#380C2semidirect
22. D5×#380C2semidirect
23. D5×#380C2semidirect
28. C2×C5×#117C22semidirect
32. C2×#4072C22semidirect
36. C2×#4038C22semidirect
37. C2×#4038C22semidirect
53. C2×#4023C22semidirect
55. C2×#4018C22semidirect
58. C5×#397C22semidirect
60. C5×#389C22semidirect
61. C5×#389C22semidirect
62. C5×#388C22semidirect
63. C5×#387C22semidirect
64. C5×#380C22semidirect
65. C5×#380C22semidirect
66. C5×#380C22semidirect
68. #65501C22semidirect
69. #65501C22semidirect
70. #65501C22semidirect
71. #65282C22semidirect
73. #65279C22semidirect
74. #65276C22semidirect
75. #65276C22semidirect
76. #65276C22semidirect
77. #65276C22semidirect
78. #65276C22semidirect
79. #65276C22semidirect
80. #65274C22semidirect
81. #65274C22semidirect
82. #65270C22semidirect
83. #65267C22semidirect
84. #65262C22semidirect
85. #65262C22semidirect
86. #65261C22semidirect
87. #65261C22semidirect
92. #65242C22semidirect
93. #65241C22semidirect
94. #65241C22semidirect
95. #65240C22semidirect
96. #65234C22semidirect
97. #65233C22semidirect
98. #65231C22semidirect
99. #65231C22semidirect
100. #65231C22semidirect
101. #65229C22semidirect
102. #65222C22semidirect
103. #65217C22semidirect
104. #65217C22semidirect
105. #64964C22semidirect
106. #64964C22semidirect
107. #64963C22semidirect
109. #64959C22semidirect
110. #64958C22semidirect
111. #64956C22semidirect
112. #64956C22semidirect
113. #64956C22semidirect
119. #64944C22semidirect
120. #64943C22semidirect
121. #64942C22semidirect
122. #64941C22semidirect
123. #64936C22semidirect
124. #64936C22semidirect
276. #2485D5direct (N × H)
463. C2×#117C2×D5semidirect
486. #397C2×D5semidirect
505. #389C2×D5semidirect
506. #389C2×D5semidirect
514. #388C2×D5semidirect
522. #387C2×D5semidirect
538. #380C2×D5semidirect
539. #380C2×D5semidirect
540. #380C2×D5semidirect
1040. D5#2485direct (N × H)
1166. C5C2×#2485semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D4×D52
C2×D5×#1172
C5×#24852
#106141032
#106140142
D5×#3972
#106092152
D5×#3942
#106086642
#106079612
#106079602
D5×#3892
D5×#3882
#106072742
D5×#3872
#106067522
#106057572
#106057562
#106057552
D5×#3802
C2×#24855