Finite Group Databasebeta

← #12262264

Subgroups — #12262264

Order 1280.

3082 conjugacy classes of subgroups.

The subgroup lattice has 1222 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D5×#121C211yesmaximal, characteristic
2C5×#2324C211yesmaximal, characteristic, complemented
3#10614364C211yesmaximal, characteristic, complemented
4#10614130C211yesmaximal, characteristic, complemented
5D4×#685C211yesmaximal, characteristic, complemented
6#10613998C211yesmaximal, characteristic, complemented
7#10613967C211yesmaximal, characteristic, complemented
8#10608164C211yesmaximal, characteristic, complemented
9#10608162C211yesmaximal, characteristic, complemented
10#10608162C212yesmaximal, complemented
11#10608041C212yesmaximal, complemented
12#10607937C211yesmaximal, characteristic, complemented
13#10607932C211yesmaximal, characteristic, complemented
14#10607560C212yesmaximal, complemented
15#10607556C212yesmaximal, complemented
16#10606609C212yesmaximal, complemented
17#10606414C212yesmaximal, complemented
18#10606325C212yesmaximal, complemented
19#10606322C212yesmaximal, complemented
20D5×#380C211yesmaximal, characteristic, complemented
21#10605603C211yesmaximal, characteristic, complemented
22#10605505C211yesmaximal, characteristic, complemented
23#10605499C211yesmaximal, characteristic, complemented
24C22×D4×D5C2212yes—
25C22×D4×D5C2211yescharacteristic
26C23×C4×D5C2211yescharacteristic
27C2×C5×#121C2211yescharacteristic
28C2×C4×C5×D4C2211yescharacteristic, complemented
29C2×C5×#117C2211yescharacteristic, complemented
30C2×#4085C2212yes—
31C2×#4084C2211yescharacteristic
32C2×D4×Dic5C2211yescharacteristic, complemented
33C2×#4076C2211yescharacteristic
34C2×C4×C22⋊D5C2212yescomplemented
35C22×#685C2212yes—
36C2×#4072C2211yescharacteristic, complemented
37D5×#121C4116yescomplemented
38C2×#4041C2211yescharacteristic
39C2×#4039C2211yescharacteristic, complemented
40C2×#4039C2212yescomplemented
41C2×D5×C4⋊C4C2211yescharacteristic
42C2×D5×C4⋊C4C2211yescharacteristic, complemented
43C2×D5×C4⋊C4C2211yescharacteristic, complemented
44C2×#4030C2212yes—
45C2×#4027C2212yescomplemented
46C2×D5×C22⋊C4C2212yes—
47C2×D5×C22⋊C4C2212yes—
48C2×D5×C22⋊C4C2212yes—
49C2×C4×D20C2211yescharacteristic, complemented
50C2×C4×D20C2212yescomplemented
51C5×#390C2211yescharacteristic, complemented
52C5×#390C2212yescomplemented
53C5×#389C2211yescharacteristic, complemented
54C5×#388C2212yescomplemented
55C5×#386C2212yescomplemented
56C5×#385C2212yescomplemented
57C5×#380C2211yescharacteristic, complemented
58C4×C5×C4⋊C4C2211yescharacteristic, complemented
59#65510C2212yescomplemented
60#65510C2211yescharacteristic, complemented
61#65509C2212yescomplemented
62#65502C2212yescomplemented
63#65501C2211yescharacteristic, complemented
64#65499C2212yescomplemented
65#65279C2212yescomplemented
66#65278C2212yescomplemented
67#65278C2212yescomplemented
68#65277C2211yescharacteristic, complemented
69#65276C2212yes—
70#65276C2211yescharacteristic
71#65276C2211yescharacteristic
72#65276C2211yescharacteristic
73#65276C2211yescharacteristic
74#65276C2211yescharacteristic, complemented
75#65276C2211yescharacteristic, complemented
76#65274C2211yescharacteristic, complemented
77#65267C2212yescomplemented
78C4⋊C4×Dic5C2211yescharacteristic, complemented
79C4⋊C4×Dic5C2211yescharacteristic, complemented
80#65262C2211yescharacteristic, complemented
81#65247C2212yescomplemented
82#65246C2212yescomplemented
83#65246C2212yescomplemented
84#65245C2212yescomplemented
85#65245C2212yescomplemented
86#65245C2212yescomplemented
87#65245C2212yescomplemented
88#65245C2212yescomplemented
89#65245C2212yescomplemented
90#65244C2211yescharacteristic
91#65244C2212yes—
92#65244C2211yescharacteristic
93#65244C2212yes—
94#65240C2212yescomplemented
95#65239C2212yescomplemented
96#65235C2212yescomplemented
97#65234C2212yescomplemented
98#65233C2212yescomplemented
99#65232C2211yescharacteristic, complemented
100#65232C2211yescharacteristic, complemented
101#65231C2212yescomplemented
102#65229C2212yescomplemented
103#65228C2211yescharacteristic, complemented
104C4×#685C2211yescharacteristic
105C4×#685C2212yes—
106C4×#685C2211yescharacteristic
107C4×#685C2211yescharacteristic, complemented
108C4×#685C2211yescharacteristic, complemented
109C4×C4⋊Dic5C2211yescharacteristic, complemented
110#65222C2212yescomplemented
111#65217C2211yescharacteristic, complemented
112#64959C2212yescomplemented
113#64958C2212yescomplemented
114#64957C2212yescomplemented
115#64957C2212yescomplemented
116#64956C2212yes—
117#64956C2212yes—
118#64955C2212yes—
119#64954C2212yescomplemented
120#64954C2212yescomplemented
121D5×#95C2212yescomplemented
122#64944C2212yescomplemented
123#64941C2212yescomplemented
124#34379—51nomaximal, Sylow
125C24×D5C2311yescharacteristic
126C24×D5C2312yes—
127C22×C5×D4C2311yescharacteristic
128C22×C5×D4C2312yes—
129C23×C4×C5C2311yescharacteristic
130C23×C4×C5C2312yes—
131C22×C22⋊D5C2312yes—
132C22×C22⋊D5C2312yes—
133C22×C22⋊D5C2312yes—
134C23×Dic5C2312yes—
135C23×Dic5C2311yescharacteristic
136C2×D4×D5—42no—
137C2×D4×D5—42no—
138C2×D4×D5—44no—
139C2×D4×D5—44no—
140C2×D4×D5C2×C418yescomplemented
141C2×D4×D5C2×C4116yescomplemented
142C22×D20C2312yes—
143C22×D20C2311yescharacteristic
144C22×C4×D5—42no—
145C22×C4×D5—42no—
146C22×C4×D5C2×C418yescomplemented
147C22×C4×D5C2311yescharacteristic
148C22×C4×D5C2311yescharacteristic
149C22×C4×D5C2312yes—
150C22×C4×D5C2312yes—
151C22×C4×D5C2312yes—
152C22×C4×D5C2312yes—
153C22×C4×D5C2311yescharacteristic
154C22×C4×D5C2312yes—
155C22×C4×D5C2311yescharacteristic
156C5×#121C2×C418yescomplemented
157C4×C5×D4—42no—
158C5×#117—42no—
159C2×C5×C4⋊C4C2311yescharacteristic
160C2×C5×C4⋊C4C2311yescharacteristic
161C2×C5×C4⋊C4C2311yescharacteristic
162C2×C5×C4⋊C4C2312yes—
163C2×C5×C4⋊C4C2311yescharacteristic
164C2×C5×C4⋊C4C2311yescharacteristic
165C2×C5×C22⋊C4C2312yes—
166C2×C5×C22⋊C4C2312yes—
167C2×C5×C22⋊C4C2311yescharacteristic
168C2×C5×C22⋊C4C2312yes—
169C2×C5×C22⋊C4C2312yes—
170C2×C5×C22⋊C4C2311yescharacteristic
171C2×C5×C22⋊C4C2312yes—
172C2×C42×C5C2311yescharacteristic
173C2×C42×C5C2311yescharacteristic
174C2×C42×C5C2312yes—
175C2×C22⋊Dic5C2312yes—
176C2×C22⋊Dic5C2312yes—
177C2×C22⋊Dic5C2311yescharacteristic
178C2×C22⋊Dic5C2311yescharacteristic
179C2×C22⋊Dic5C2312yes—
180C2×C22⋊Dic5C2312yes—
181C2×C22⋊Dic5C2312yes—
182#4085C2×C4116yescomplemented
183#4084C2×C418yescomplemented
184D4×Dic5—42no—
185#4076C2×C418yescomplemented
186C4×C22⋊D5—44no—
187C2×#685—44no—
188C2×#685C2311yescharacteristic
189C2×#685C2312yes—
190C2×#685C2311yescharacteristic
191C2×#685C2312yes—
192C2×#685C2311yescharacteristic
193C2×#685C2311yescharacteristic
194C2×#685C2311yescharacteristic
195C2×#685C2311yescharacteristic
196C2×#685C2311yescharacteristic
197C2×#685C2311yescharacteristic
198C2×#685C2312yes—
199C2×#685C2312yes—
200C2×#685C2312yes—
201C2×#685C2312yes—
202C2×#685C2312yes—
203C2×#685C2312yes—
204C2×#685C2312yes—
205C2×#685C2312yes—
206#4072—42no—
207C2×C4⋊Dic5C2311yescharacteristic
208C2×C4⋊Dic5C2311yescharacteristic
209C2×C4⋊Dic5C2312yes—
210C2×C4⋊Dic5C2311yescharacteristic
211C2×C4⋊Dic5C2311yescharacteristic
212C2×C4⋊Dic5C2311yescharacteristic
213C2×#683C2312yes—
214C2×#683C2312yes—
215C2×#683C2312yes—
216C2×#683C2312yes—
217C2×#683C2312yes—
218C2×C4×Dic5C2311yescharacteristic
219C2×C4×Dic5C2311yescharacteristic
220C2×C4×Dic5C2312yes—
221C2×C4×Dic5C2312yes—
222C2×C4×Dic5C2312yes—
223#4041C2×C418yescomplemented
224#4039—42no—
225#4039—44no—
226D5×C4⋊C4—42no—
227D5×C4⋊C4—42no—
228D5×C4⋊C4C2×C418yescomplemented
229#4030C2×C4116yescomplemented
230#4027—44no—
231D5×C22⋊C4—44no—
232D5×C22⋊C4—44no—
233D5×C22⋊C4C2×C4116yescomplemented
234C4×D20—42no—
235C4×D20—44no—
236C5×#95C2312yes—
237C5×#95C2312yes—
238C5×#95C2312yes—
239#3963C2311yescharacteristic
240#3963C2312yes—
241#3963C2312yes—
242#3963C2311yescharacteristic
243#3963C2312yes—
244#3963C2312yes—
245#3963C2312yes—
246#3963C2312yes—
247#3963C2312yes—
248#3963C2311yescharacteristic
249#3963C2311yescharacteristic
250#3963C2312yes—
251#3963C2311yescharacteristic
252#3963C2312yes—
253#3963C2311yescharacteristic
254#3963C2311yescharacteristic
255#3963C2311yescharacteristic
256C22×#121—51no—
257#2377—52no—
258#2377—52no—
259#2361—51no—
260#2361—51no—
261#2361—51no—
262#2361—51no—
263#2345—51no—
264#2345—51no—
265D4×C22⋊C4—51no—
266D4×C22⋊C4—52no—
267D4×C22⋊C4—52no—
268D4×C22⋊C4—51no—
269#2325—52no—
270#2325—52no—
271#2324—51no—
272#2324—51no—
273#2324—51no—
274#2324D511yescharacteristic, complemented
275#2315—52no—
276#2312—52no—
277#2280—51no—
278C2×#380—51no—
279C24×C5C2411yescharacteristic
280C24×C5C2412yes—
281C23×D5—22no—
282C23×D5—22no—
283C23×D5—22no—
284C23×D5—22no—
285C23×D5—24no—
286C23×D5—24no—
287C23×D5—41no—
288C23×D5—41no—
289C23×D5—42no—
290C23×D5—42no—
291C23×D5—42no—
292C23×D5—42no—
293C23×D5C22×C414yes—
294C23×D5C22×C418yes—
295C23×D5C2412yes—
296C23×D5C2411yescharacteristic
297C23×D5C2411yescharacteristic
298C2×C5×D4—22no—
299C2×C5×D4—22no—
300C2×C5×D4—42no—
301C2×C5×D4—42no—
302C2×C5×D4C22×C414yes—
303C2×C5×D4C22×C418yes—
304C22×C4×C5—22no—
305C22×C4×C5—22no—
306C22×C4×C5—42no—
307C22×C4×C5—42no—
308C22×C4×C5—42no—
309C22×C4×C5C22×C414yes—
310C22×C4×C5C2411yescharacteristic
311C22×C4×C5C2411yescharacteristic
312C22×C4×C5C2412yes—
313C22×C4×C5C2411yescharacteristic
314C22×C4×C5C2411yescharacteristic
315C22×C4×C5C2412yes—
316C22×C4×C5C2412yes—
317C22×C4×C5C2411yescharacteristic
318C22×C4×C5C2411yescharacteristic
319C2×C22⋊D5—24no—
320C2×C22⋊D5—24no—
321C2×C22⋊D5—42no—
322C2×C22⋊D5—42no—
323C2×C22⋊D5—42no—
324C2×C22⋊D5—42no—
325C2×C22⋊D5C22×C418yes—
326C2×C22⋊D5C22×C418yes—
327C2×C22⋊D5C22×C418yes—
328C22×Dic5—41no—
329C22×Dic5—41no—
330C22×Dic5—42no—
331C22×Dic5—42no—
332C22×Dic5—42no—
333C22×Dic5C22×C414yes—
334C22×Dic5C2412yes—
335C22×Dic5C2411yescharacteristic
336C22×Dic5C2411yescharacteristic
337C22×Dic5C2411yescharacteristic
338C22×Dic5C2412yes—
339C22×Dic5C2411yescharacteristic
340C22×Dic5C2411yescharacteristic
341C22×Dic5C2412yes—
342C22×Dic5C2411yescharacteristic
343D4×D5—416no—
344D4×D5—432no—
345C2×D20—24no—
346C2×D20—24no—
347C2×D20—22no—
348C2×D20—22no—
349C2×D20C22×C418yes—
350C2×D20C22×C414yes—
351C2×C4×D5—22no—
352C2×C4×D5—22no—
353C2×C4×D5—22no—
354C2×C4×D5—22no—
355C2×C4×D5—24no—
356C2×C4×D5—24no—
357C2×C4×D5—416no—
358C2×C4×D5—41no—
359C2×C4×D5—41no—
360C2×C4×D5—41no—
361C2×C4×D5—41no—
362C2×C4×D5—42no—
363C2×C4×D5—42no—
364C2×C4×D5—42no—
365C2×C4×D5—42no—
366C2×C4×D5—42no—
367C2×C4×D5—42no—
368C2×C4×D5—42no—
369C2×C4×D5—42no—
370C2×C4×D5—42no—
371C2×C4×D5—42no—
372C2×C4×D5—42no—
373C2×C4×D5—42no—
374C2×C4×D5C22×C414yes—
375C2×C4×D5C22×C414yes—
376C2×C4×D5C22×C414yes—
377C2×C4×D5C22×C414yes—
378C2×C4×D5C22×C418yes—
379C5×C4⋊C4—22no—
380C5×C4⋊C4—22no—
381C5×C4⋊C4—41no—
382C5×C4⋊C4—41no—
383C5×C4⋊C4—42no—
384C5×C4⋊C4C22×C414yes—
385C5×C22⋊C4—41no—
386C5×C22⋊C4—41no—
387C5×C22⋊C4—42no—
388C5×C22⋊C4—42no—
389C5×C22⋊C4—42no—
390C5×C22⋊C4—42no—
391C5×C22⋊C4C22×C418yes—
392C42×C5—22no—
393C42×C5—22no—
394C42×C5—42no—
395C22⋊Dic5—42no—
396C22⋊Dic5—42no—
397C22⋊Dic5—41no—
398C22⋊Dic5—41no—
399C22⋊Dic5—42no—
400C22⋊Dic5—42no—
401C22⋊Dic5C22×C418yes—
402#685—22no—
403#685—24no—
404#685—22no—
405#685—24no—
406#685—22no—
407#685—22no—
408#685—22no—
409#685—22no—
410#685—22no—
411#685—22no—
412#685—42no—
413#685—42no—
414#685—42no—
415#685—42no—
416#685—42no—
417#685—42no—
418#685C22×C418yes—
419#685C22×C418yes—
420C4⋊Dic5—22no—
421C4⋊Dic5—22no—
422C4⋊Dic5—42no—
423C4⋊Dic5—41no—
424C4⋊Dic5—41no—
425C4⋊Dic5C22×C414yes—
426#683—42no—
427#683—42no—
428#683—42no—
429#683—42no—
430#683C22×C418yes—
431C4×Dic5—22no—
432C4×Dic5—22no—
433C4×Dic5—42no—
434C4×Dic5—42no—
435C4×Dic5—42no—
436C23×D4—51no—
437C23×D4—52no—
438C24×C4—51no—
439C2×#121—51no—
440C2×#121—52no—
441C2×#121—51no—
442C2×#121—516no—
443C2×#121—51no—
444C2×#121—52no—
445C2×#121C2×D511yescharacteristic
446C2×C4×D4—51no—
447C2×C4×D4—52no—
448C2×C4×D4—51no—
449C2×C4×D4—52no—
450C2×C4×D4—52no—
451C2×C4×D4—51no—
452C2×C4×D4—52no—
453C2×C4×D4C2×D511yescharacteristic, complemented
454C2×#117—51no—
455C2×#117C2×D511yescharacteristic, complemented
456C22×C4⋊C4—51no—
457C22×C4⋊C4—51no—
458C22×C4⋊C4—51no—
459C22×C22⋊C4—52no—
460C22×C22⋊C4—52no—
461C22×C22⋊C4—52no—
462C22×C22⋊C4—52no—
463#390—51no—
464#390—52no—
465#390—51no—
466#390—52no—
467#390—52no—
468#390—51no—
469#390C2×D511yescharacteristic, complemented
470#390C2×D512yescomplemented
471#389—51no—
472#389—51no—
473#389—51no—
474#389C2×D511yescharacteristic, complemented
475#388—52no—
476#388—52no—
477#388—52no—
478#388—52no—
479#388—52no—
480#388—52no—
481#388—52no—
482#388C2×D512yescomplemented
483#387—52no—
484#387—52no—
485#387—52no—
486#387—52no—
487#386—52no—
488#386—52no—
489#386—52no—
490#386—52no—
491#386—52no—
492#386—52no—
493#386—52no—
494#386—52no—
495#386—52no—
496#386—52no—
497#386—52no—
498#386C2×D512yescomplemented
499#385—52no—
500#385—52no—
501#385—52no—
502#385—52no—
503#385—52no—
504#385—52no—
505#385—52no—
506#385C2×D512yescomplemented
507#381—51no—
508#381—51no—
509#380—51no—
510#380—51no—
511#380—51no—
512#380—52no—
513#380—51no—
514#380—51no—
515#380—51no—
516#380—51no—
517#380—52no—
518#380—52no—
519#380—52no—
520#380C2×D511yescharacteristic, complemented
521#379—52no—
522#379—52no—
523#379—51no—
524#379—51no—
525C4×C4⋊C4—51no—
526C4×C4⋊C4—51no—
527C4×C4⋊C4—51no—
528C4×C4⋊C4C2×D511yescharacteristic, complemented
529C4×C22⋊C4—52no—
530C4×C22⋊C4—51no—
531C4×C22⋊C4—51no—
532C4×C22⋊C4—51no—
533C4×C22⋊C4—51no—
534C4×C22⋊C4—52no—
535C2×#95—52no—
536C23×C5—21no—
537C23×C5—21no—
538C23×C5—22no—
539C23×C5—22no—
540C23×C5—22no—
541C23×C5—21no—
542C23×C5—22no—
543C23×C5—22no—
544C23×C5—21no—
545C23×C5—21no—
546C23×C5—21no—
547C23×C5—22no—
548C23×C5C23×C414yes—
549C23×C5C23×C412yes—
550C23×C5C2511yescharacteristic
551C22×D5—21no—
552C22×D5—21no—
553C22×D5—21no—
554C22×D5—21no—
555C22×D5—21no—
556C22×D5—21no—
557C22×D5—21no—
558C22×D5—21no—
559C22×D5—22no—
560C22×D5—22no—
561C22×D5—22no—
562C22×D5—22no—
563C22×D5—22no—
564C22×D5—22no—
565C22×D5—28no—
566C22×D5—28no—
567C22×D5—216no—
568C22×D5—44no—
569C22×D5—44no—
570C22×D5—44no—
571C22×D5—44no—
572C22×D5—44no—
573C22×D5—48no—
574C22×D5—48no—
575C22×D5—84no—
576C22×D5—84no—
577C22×D5—84no—
578C22×D5—84no—
579C22×D5C23×C414yes—
580C22×D5C23×C412yes—
581C22×D5C23×C412yes—
582C22×D5H(5,𝔽2)12yes—
583C22×D5H(5,𝔽2)12yes—
584C22×D5H(5,𝔽2)12yes—
585C22×D52−1+412yes—
586C5×D4—28no—
587C5×D4—48no—
588C2×C4×C5—22no—
589C2×C4×C5—21no—
590C2×C4×C5—22no—
591C2×C4×C5—21no—
592C2×C4×C5—28no—
593C2×C4×C5—21no—
594C2×C4×C5—22no—
595C2×C4×C5—21no—
596C2×C4×C5—22no—
597C2×C4×C5—22no—
598C2×C4×C5—22no—
599C2×C4×C5—21no—
600C2×C4×C5—21no—
601C2×C4×C5—22no—
602C2×C4×C5—21no—
603C2×C4×C5—22no—
604C2×C4×C5—21no—
605C2×C4×C5—21no—
606C2×C4×C5—21no—
607C2×C4×C5—21no—
608C2×C4×C5—21no—
609C2×C4×C5—21no—
610C2×C4×C5—21no—
611C2×C4×C5—84no—
612C2×C4×C5C23×C414yes—
613C2×C4×C5C23×C412yes—
614C2×C4×C5C23×C412yes—
615C2×C4×C5H(5,𝔽2)12yes—
616C2×C4×C5H(5,𝔽2)12yes—
617C22⋊D5—216no—
618C22⋊D5—48no—
619C22⋊D5—48no—
620C2×Dic5—22no—
621C2×Dic5—22no—
622C2×Dic5—21no—
623C2×Dic5—21no—
624C2×Dic5—21no—
625C2×Dic5—21no—
626C2×Dic5—21no—
627C2×Dic5—21no—
628C2×Dic5—21no—
629C2×Dic5—21no—
630C2×Dic5—21no—
631C2×Dic5—21no—
632C2×Dic5—22no—
633C2×Dic5—22no—
634C2×Dic5—21no—
635C2×Dic5—22no—
636C2×Dic5—22no—
637C2×Dic5—21no—
638C2×Dic5—21no—
639C2×Dic5—22no—
640C2×Dic5—22no—
641C2×Dic5—21no—
642C2×Dic5—21no—
643C2×Dic5—21no—
644C2×Dic5—44no—
645C2×Dic5—84no—
646C2×Dic5C23×C412yes—
647C2×Dic5C23×C414yes—
648C2×Dic5C23×C412yes—
649D20—216no—
650D20—28no—
651C4×D5—28no—
652C4×D5—28no—
653C4×D5—44no—
654C4×D5—44no—
655C4×D5—48no—
656C4×D5—84no—
657C4×D5—84no—
658C4×D5—84no—
659C4×D5—84no—
660C25—51no—
661C25—52no—
662C22×D4—52no—
663C22×D4—52no—
664C22×D4—52no—
665C22×D4—58no—
666C22×D4—516no—
667C22×D4—52no—
668C22×D4—51no—
669C22×D4—202no—
670C22×D4—202no—
671C22×D4—204no—
672C22×D4—204no—
673C22×D4C22×D511yescharacteristic
674C22×D4C22×D512yes—
675C23×C4—51no—
676C23×C4—51no—
677C23×C4—51no—
678C23×C4—58no—
679C23×C4—51no—
680C23×C4—52no—
681C23×C4—51no—
682C23×C4—52no—
683C23×C4—52no—
684C23×C4—52no—
685C23×C4—52no—
686C23×C4—52no—
687C23×C4—202no—
688C23×C4—202no—
689C23×C4C22×D511yescharacteristic
690C23×C4C22×D512yes—
691#121—58no—
692#121—516no—
693#121—58no—
694#121—58no—
695#121—516no—
696#121C4×D518yescomplemented
697C4×D4—42no—
698C4×D4—202no—
699C4×D4—204no—
700C4×D4—202no—
701C4×D4—202no—
702C4×D4—204no—
703C4×D4—204no—
704C4×D4—204no—
705#117—42no—
706#117—202no—
707C2×C4⋊C4—51no—
708C2×C4⋊C4—52no—
709C2×C4⋊C4—58no—
710C2×C4⋊C4—51no—
711C2×C4⋊C4—51no—
712C2×C4⋊C4—52no—
713C2×C4⋊C4—52no—
714C2×C4⋊C4—51no—
715C2×C4⋊C4—51no—
716C2×C4⋊C4—52no—
717C2×C4⋊C4—52no—
718C2×C4⋊C4—52no—
719C2×C4⋊C4—202no—
720C2×C4⋊C4—202no—
721C2×C4⋊C4C22×D511yescharacteristic
722C2×C4⋊C4C22×D511yescharacteristic
723C2×C4⋊C4C22×D511yescharacteristic
724C2×C4⋊C4C22×D511yescharacteristic
725C2×C4⋊C4C22×D512yes—
726C2×C4⋊C4C22×D511yescharacteristic
727C2×C22⋊C4—52no—
728C2×C22⋊C4—52no—
729C2×C22⋊C4—52no—
730C2×C22⋊C4—516no—
731C2×C22⋊C4—51no—
732C2×C22⋊C4—52no—
733C2×C22⋊C4—51no—
734C2×C22⋊C4—52no—
735C2×C22⋊C4—51no—
736C2×C22⋊C4—51no—
737C2×C22⋊C4—51no—
738C2×C22⋊C4—51no—
739C2×C22⋊C4—51no—
740C2×C22⋊C4—51no—
741C2×C22⋊C4—52no—
742C2×C22⋊C4—52no—
743C2×C22⋊C4—51no—
744C2×C22⋊C4—51no—
745C2×C22⋊C4—52no—
746C2×C22⋊C4—52no—
747C2×C22⋊C4—52no—
748C2×C22⋊C4—52no—
749C2×C22⋊C4—52no—
750C2×C22⋊C4—52no—
751C2×C22⋊C4—52no—
752C2×C22⋊C4—52no—
753C2×C22⋊C4—204no—
754C2×C22⋊C4—204no—
755C2×C22⋊C4—204no—
756C2×C22⋊C4C22×D512yes—
757C2×C22⋊C4C22×D512yes—
758C2×C22⋊C4C22×D511yescharacteristic
759C2×C22⋊C4C22×D511yescharacteristic
760C2×C22⋊C4C22×D512yes—
761C2×C22⋊C4C22×D512yes—
762C2×C22⋊C4C22×D512yes—
763C2×C42—51no—
764C2×C42—51no—
765C2×C42—52no—
766C2×C42—52no—
767C2×C42—52no—
768C2×C42C22×D511yescharacteristic
769C2×C42C22×D511yescharacteristic
770C2×C42C22×D512yes—
771#95—52no—
772#95—52no—
773#95—52no—
774#95—51no—
775#95—51no—
776#95—51no—
777#95—51no—
778#95—51no—
779#95—51no—
780#95—51no—
781#95—51no—
782#95—52no—
783#95—52no—
784#95—52no—
785#95—52no—
786#95—52no—
787#95—52no—
788#95C22×D512yes—
789#95C22×D512yes—
790#95C22×D512yes—
791C22×C5—22no—
792C22×C5—24no—
793C22×C5—22no—
794C22×C5—24no—
795C22×C5—22no—
796C22×C5—24no—
797C22×C5—41no—
798C22×C5—41no—
799C22×C5—42no—
800C22×C5—42no—
801C22×C5—42no—
802C22×C5—42no—
803C22×C5—41no—
804C22×C5—41no—
805C22×C5C24×C411yescharacteristic
806C22×C5C2×H(5,𝔽2)11yescharacteristic
807C22×C5C2×H(5,𝔽2)11yescharacteristic
808C22×C5C2×H(5,𝔽2)11yescharacteristic
809C22×C5C2×H(5,𝔽2)11yescharacteristic
810C22×C5C2×H(5,𝔽2)11yescharacteristic
811C22×C5C2×2−1+411yescharacteristic
812C2×D5—22no—
813C2×D5—22no—
814C2×D5—22no—
815C2×D5—22no—
816C2×D5—22no—
817C2×D5—22no—
818C2×D5—22no—
819C2×D5—22no—
820C2×D5—22no—
821C2×D5—22no—
822C2×D5—22no—
823C2×D5—22no—
824C2×D5—24no—
825C2×D5—24no—
826C2×D5—24no—
827C2×D5—416no—
828C2×D5—42no—
829C2×D5—42no—
830C2×D5—42no—
831C2×D5—42no—
832C2×D5—816no—
833C2×D5#51814yes—
834C2×D5#52014yes—
835C4×C5—22no—
836C4×C5—24no—
837C4×C5—41no—
838C4×C5—41no—
839C4×C5—42no—
840C4×C5—41no—
841C4×C5—42no—
842C4×C5—41no—
843C4×C5#51814yes—
844Dic5—22no—
845Dic5—22no—
846Dic5—24no—
847Dic5—41no—
848Dic5—41no—
849Dic5—41no—
850Dic5—42no—
851Dic5—42no—
852Dic5—41no—
853C24—51no—
854C24—51no—
855C24—52no—
856C24—54no—
857C24—58no—
858C24—102no—
859C24—102no—
860C24—102no—
861C24—102no—
862C24—104no—
863C24—104no—
864C24—201no—
865C24—201no—
866C24—202no—
867C24—202no—
868C24—202no—
869C24—202no—
870C24C23×D511yescharacteristic
871C24C23×D512yes—
872C2×D4—22no—
873C2×D4—22no—
874C2×D4—42no—
875C2×D4—42no—
876C2×D4—58no—
877C2×D4—58no—
878C2×D4—58no—
879C2×D4—58no—
880C2×D4—54no—
881C2×D4—104no—
882C2×D4—104no—
883C2×D4—104no—
884C2×D4—104no—
885C2×D4—102no—
886C2×D4—102no—
887C2×D4—2016no—
888C2×D4—202no—
889C2×D4—202no—
890C2×D4—202no—
891C2×D4—202no—
892C2×D4—2032no—
893C2×D4C2×C4×D514yes—
894C2×D4C2×C4×D518yes—
895C22×C4—22no—
896C22×C4—22no—
897C22×C4—42no—
898C22×C4—42no—
899C22×C4—42no—
900C22×C4—51no—
901C22×C4—52no—
902C22×C4—51no—
903C22×C4—54no—
904C22×C4—54no—
905C22×C4—54no—
906C22×C4—54no—
907C22×C4—58no—
908C22×C4—54no—
909C22×C4—51no—
910C22×C4—51no—
911C22×C4—52no—
912C22×C4—51no—
913C22×C4—51no—
914C22×C4—52no—
915C22×C4—104no—
916C22×C4—104no—
917C22×C4—102no—
918C22×C4—102no—
919C22×C4—102no—
920C22×C4—102no—
921C22×C4—2016no—
922C22×C4—201no—
923C22×C4—201no—
924C22×C4—201no—
925C22×C4—201no—
926C22×C4—202no—
927C22×C4—202no—
928C22×C4—202no—
929C22×C4—202no—
930C22×C4—202no—
931C22×C4—202no—
932C22×C4—202no—
933C22×C4—202no—
934C22×C4—202no—
935C22×C4—202no—
936C22×C4—202no—
937C22×C4—202no—
938C22×C4—201no—
939C22×C4—201no—
940C22×C4—202no—
941C22×C4—202no—
942C22×C4—202no—
943C22×C4C2×C4×D514yes—
944C22×C4C23×D511yescharacteristic
945C22×C4C23×D511yescharacteristic
946C22×C4C23×D511yescharacteristic
947C22×C4C23×D512yes—
948C22×C4C23×D511yescharacteristic
949C22×C4C23×D512yes—
950C22×C4C23×D512yes—
951C22×C4C23×D511yescharacteristic
952C22×C4C23×D511yescharacteristic
953C4⋊C4—22no—
954C4⋊C4—22no—
955C4⋊C4—41no—
956C4⋊C4—41no—
957C4⋊C4—42no—
958C4⋊C4—58no—
959C4⋊C4—54no—
960C4⋊C4—102no—
961C4⋊C4—102no—
962C4⋊C4—202no—
963C4⋊C4—202no—
964C4⋊C4—201no—
965C4⋊C4—201no—
966C4⋊C4—202no—
967C4⋊C4—202no—
968C4⋊C4—202no—
969C4⋊C4C2×C4×D514yes—
970C22⋊C4—42no—
971C22⋊C4—42no—
972C22⋊C4—41no—
973C22⋊C4—41no—
974C22⋊C4—42no—
975C22⋊C4—42no—
976C22⋊C4—58no—
977C22⋊C4—58no—
978C22⋊C4—58no—
979C22⋊C4—104no—
980C22⋊C4—102no—
981C22⋊C4—104no—
982C22⋊C4—102no—
983C22⋊C4—102no—
984C22⋊C4—102no—
985C22⋊C4—102no—
986C22⋊C4—102no—
987C22⋊C4—102no—
988C22⋊C4—102no—
989C22⋊C4—202no—
990C22⋊C4—202no—
991C22⋊C4—202no—
992C22⋊C4—202no—
993C22⋊C4—202no—
994C22⋊C4—202no—
995C22⋊C4—202no—
996C22⋊C4—202no—
997C22⋊C4—201no—
998C22⋊C4—201no—
999C22⋊C4—202no—
1000C22⋊C4—202no—
1001C22⋊C4C2×C4×D518yes—
1002C42—22no—
1003C42—22no—
1004C42—42no—
1005C42—102no—
1006C42—102no—
1007C42—202no—
1008C42—202no—
1009C42—202no—
1010C2×C5—42no—
1011C2×C5—44no—
1012C2×C5C2×#51811yescharacteristic
1013C2×C5C2×#51811yescharacteristic
1014C2×C5C2×#52011yescharacteristic
1015C2×C5#353611yescharacteristic
1016C2×C5#353611yescharacteristic
1017C2×C5#353711yescharacteristic
1018C2×C5#353711yescharacteristic
1019D5—24no—
1020D5—24no—
1021D5—44no—
1022C23—21no—
1023C23—22no—
1024C23—21no—
1025C23—22no—
1026C23—21no—
1027C23—22no—
1028C23—22no—
1029C23—22no—
1030C23—21no—
1031C23—21no—
1032C23—21no—
1033C23—22no—
1034C23—52no—
1035C23—52no—
1036C23—52no—
1037C23—52no—
1038C23—52no—
1039C23—52no—
1040C23—54no—
1041C23—108no—
1042C23—108no—
1043C23—1016no—
1044C23—101no—
1045C23—101no—
1046C23—101no—
1047C23—101no—
1048C23—101no—
1049C23—101no—
1050C23—101no—
1051C23—101no—
1052C23—102no—
1053C23—102no—
1054C23—102no—
1055C23—102no—
1056C23—102no—
1057C23—102no—
1058C23—204no—
1059C23—208no—
1060C23—208no—
1061C23—204no—
1062C23—204no—
1063C23—204no—
1064C23—204no—
1065C23—404no—
1066C23—404no—
1067C23—404no—
1068C23—404no—
1069C23C22×C4×D514yes—
1070C23C22×C4×D512yes—
1071C23C24×D511yescharacteristic
1072D4—28no—
1073D4—48no—
1074D4—1016no—
1075D4—1016no—
1076D4—108no—
1077D4—208no—
1078D4—208no—
1079C2×C4—21no—
1080C2×C4—21no—
1081C2×C4—22no—
1082C2×C4—22no—
1083C2×C4—28no—
1084C2×C4—21no—
1085C2×C4—21no—
1086C2×C4—21no—
1087C2×C4—21no—
1088C2×C4—22no—
1089C2×C4—22no—
1090C2×C4—21no—
1091C2×C4—22no—
1092C2×C4—21no—
1093C2×C4—22no—
1094C2×C4—22no—
1095C2×C4—21no—
1096C2×C4—22no—
1097C2×C4—21no—
1098C2×C4—21no—
1099C2×C4—21no—
1100C2×C4—21no—
1101C2×C4—21no—
1102C2×C4—52no—
1103C2×C4—54no—
1104C2×C4—52no—
1105C2×C4—84no—
1106C2×C4—101no—
1107C2×C4—101no—
1108C2×C4—101no—
1109C2×C4—101no—
1110C2×C4—102no—
1111C2×C4—102no—
1112C2×C4—108no—
1113C2×C4—108no—
1114C2×C4—102no—
1115C2×C4—101no—
1116C2×C4—101no—
1117C2×C4—101no—
1118C2×C4—101no—
1119C2×C4—102no—
1120C2×C4—101no—
1121C2×C4—101no—
1122C2×C4—102no—
1123C2×C4—102no—
1124C2×C4—101no—
1125C2×C4—102no—
1126C2×C4—101no—
1127C2×C4—102no—
1128C2×C4—101no—
1129C2×C4—101no—
1130C2×C4—101no—
1131C2×C4—101no—
1132C2×C4—204no—
1133C2×C4—204no—
1134C2×C4—208no—
1135C2×C4—204no—
1136C2×C4—404no—
1137C2×C4—404no—
1138C2×C4—404no—
1139C2×C4—404no—
1140C2×C4—404no—
1141C2×C4C22×C4×D512yes—
1142C2×C4C22×C4×D514yes—
1143C2×C4C22×C4×D512yes—
1144C2×C4#414412yes—
1145C2×C4#414912yes—
1146C5#3437911yescharacteristic, complemented, Sylow
1147C22—22no—
1148C22—24no—
1149C22—22no—
1150C22—24no—
1151C22—22no—
1152C22—24no—
1153C22—42no—
1154C22—41no—
1155C22—41no—
1156C22—42no—
1157C22—42no—
1158C22—41no—
1159C22—41no—
1160C22—42no—
1161C22—54no—
1162C22—54no—
1163C22—102no—
1164C22—102no—
1165C22—102no—
1166C22—102no—
1167C22—102no—
1168C22—102no—
1169C22—102no—
1170C22—102no—
1171C22—102no—
1172C22—102no—
1173C22—102no—
1174C22—102no—
1175C22—104no—
1176C22—104no—
1177C22—104no—
1178C22—2016no—
1179C22—202no—
1180C22—202no—
1181C22—202no—
1182C22—202no—
1183C22—4016no—
1184C22C23×C4×D511yescharacteristic
1185C22C2×#414411yescharacteristic
1186C22C2×#414911yescharacteristic
1187C22D5×H(5,𝔽2)11yescharacteristic
1188C22D5×H(5,𝔽2)11yescharacteristic
1189C22D5×H(5,𝔽2)11yescharacteristic
1190C22D5×2−1+411yescharacteristic
1191C4—22no—
1192C4—24no—
1193C4—42no—
1194C4—41no—
1195C4—42no—
1196C4—41no—
1197C4—41no—
1198C4—41no—
1199C4—102no—
1200C4—102no—
1201C4—104no—
1202C4—201no—
1203C4—201no—
1204C4—202no—
1205C4—201no—
1206C4—201no—
1207C4—202no—
1208C4#6587914yes—
1209C2—42no—
1210C2—44no—
1211C2—104no—
1212C2—104no—
1213C2—204no—
1214C2C2×#6587911yescharacteristic
1215C2D5×#51811yescharacteristic
1216C2D5×#52011yescharacteristic
1217C2#1061823511yescharacteristic
1218C2#1061828511yescharacteristic
1219C2#1061839211yescharacteristic
1220C2#1061846211yescharacteristic
subgroupG/H
center, FrattiniC23C24×D5
commutatorC22×C5C24×C4
FittingC5×#2324C2
socle, cosocleC23×C5C25
prime radicalC2×D5×#121C2
hypercenter#2324D5
hypocenterC5#34379
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ #2324

Complements

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

NH ≅ G/Ntype
2. C5×#2324C2semidirect
3. #10614364C2semidirect
4. #10614130C2semidirect
5. D4×#685C2semidirect
6. #10613998C2semidirect
7. #10613967C2semidirect
8. #10608164C2semidirect
9. #10608162C2semidirect
10. #10608162C2semidirect
11. #10608041C2semidirect
12. #10607937C2semidirect
13. #10607932C2semidirect
14. #10607560C2semidirect
15. #10607556C2semidirect
16. #10606609C2semidirect
17. #10606414C2semidirect
18. #10606325C2semidirect
19. #10606322C2semidirect
20. D5×#380C2semidirect
21. #10605603C2semidirect
22. #10605505C2semidirect
23. #10605499C2semidirect
28. C2×C4×C5×D4C22semidirect
29. C2×C5×#117C22semidirect
32. C2×D4×Dic5C22semidirect
34. C2×C4×C22⋊D5C22semidirect
36. C2×#4072C22semidirect
37. D5×#121C4semidirect
39. C2×#4039C22semidirect
40. C2×#4039C22semidirect
42. C2×D5×C4⋊C4C22semidirect
43. C2×D5×C4⋊C4C22semidirect
45. C2×#4027C22semidirect
49. C2×C4×D20C22semidirect
50. C2×C4×D20C22semidirect
51. C5×#390C22semidirect
52. C5×#390C22semidirect
53. C5×#389C22semidirect
54. C5×#388C22semidirect
55. C5×#386C22semidirect
56. C5×#385C22semidirect
57. C5×#380C22semidirect
58. C4×C5×C4⋊C4C22semidirect
59. #65510C22semidirect
60. #65510C22semidirect
61. #65509C22semidirect
62. #65502C22semidirect
63. #65501C22semidirect
64. #65499C22semidirect
65. #65279C22semidirect
66. #65278C22semidirect
67. #65278C22semidirect
68. #65277C22semidirect
74. #65276C22semidirect
75. #65276C22semidirect
76. #65274C22semidirect
77. #65267C22semidirect
78. C4⋊C4×Dic5C22semidirect
79. C4⋊C4×Dic5C22semidirect
80. #65262C22semidirect
81. #65247C22semidirect
82. #65246C22semidirect
83. #65246C22semidirect
84. #65245C22semidirect
85. #65245C22semidirect
86. #65245C22semidirect
87. #65245C22semidirect
88. #65245C22semidirect
89. #65245C22semidirect
94. #65240C22semidirect
95. #65239C22semidirect
96. #65235C22semidirect
97. #65234C22semidirect
98. #65233C22semidirect
99. #65232C22semidirect
100. #65232C22semidirect
101. #65231C22semidirect
102. #65229C22semidirect
103. #65228C22semidirect
107. C4×#685C22semidirect
108. C4×#685C22semidirect
109. C4×C4⋊Dic5C22semidirect
110. #65222C22semidirect
111. #65217C22semidirect
112. #64959C22semidirect
113. #64958C22semidirect
114. #64957C22semidirect
115. #64957C22semidirect
119. #64954C22semidirect
120. #64954C22semidirect
121. D5×#95C22semidirect
122. #64944C22semidirect
123. #64941C22semidirect
140. C2×D4×D5C2×C4semidirect
141. C2×D4×D5C2×C4semidirect
146. C22×C4×D5C2×C4semidirect
156. C5×#121C2×C4semidirect
182. #4085C2×C4semidirect
183. #4084C2×C4semidirect
185. #4076C2×C4semidirect
223. #4041C2×C4semidirect
228. D5×C4⋊C4C2×C4semidirect
229. #4030C2×C4semidirect
233. D5×C22⋊C4C2×C4semidirect
274. #2324D5semidirect
453. C2×C4×D4C2×D5semidirect
455. C2×#117C2×D5semidirect
469. #390C2×D5semidirect
470. #390C2×D5semidirect
474. #389C2×D5semidirect
482. #388C2×D5semidirect
498. #386C2×D5semidirect
506. #385C2×D5semidirect
520. #380C2×D5semidirect
528. C4×C4⋊C4C2×D5semidirect
696. #121C4×D5semidirect
1146. C5#34379semidirect

Maximal subgroups

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

subgroupindex
C2×D5×#1212
C5×#23242
#106143642
#106141302
D4×#6852
#106139982
#106139672
#106081642
#106081622
#106080412
#106079372
#106079322
#106075602
#106075562
#106066092
#106064142
#106063252
#106063222
D5×#3802
#106056032
#106055052
#106054992
#343795