Finite Group Databasebeta

← #12307585

Subgroups — #12307585

Order 1280.

1574 conjugacy classes of subgroups.

The subgroup lattice has 1414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2635C211yesmaximal, characteristic
2#10614429C211yesmaximal, characteristic, complemented
3#10614366C211yesmaximal, characteristic, complemented
4#10614123C211yesmaximal, characteristic, complemented
5#10614049C211yesmaximal, characteristic, complemented
6#10610000C211yesmaximal, characteristic, complemented
7#10609988C211yesmaximal, characteristic, complemented
8#10609810C211yesmaximal, characteristic, complemented
9#10609810C211yesmaximal, characteristic, complemented
10#10608805C211yesmaximal, characteristic, complemented
11#10608802C211yesmaximal, characteristic, complemented
12#10608802C211yesmaximal, characteristic, complemented
13#10608800C211yesmaximal, characteristic, complemented
14#10608774C211yesmaximal, characteristic, complemented
15#10608750C211yesmaximal, characteristic, complemented
16#10608470C211yesmaximal, characteristic, complemented
17#10608467C211yesmaximal, characteristic, complemented
18#10608466C211yesmaximal, characteristic, complemented
19#10608464C211yesmaximal, characteristic, complemented
20#10608457C211yesmaximal, characteristic, complemented
21#10608450C211yesmaximal, characteristic, complemented
22#10607343C211yesmaximal, characteristic, complemented
23#10607340C211yesmaximal, characteristic, complemented
24#10607322C211yesmaximal, characteristic, complemented
25#10607313C211yesmaximal, characteristic, complemented
26#10606505C211yesmaximal, characteristic, complemented
27#10606504C211yesmaximal, characteristic, complemented
28#10606464C211yesmaximal, characteristic, complemented
29#10606454C211yesmaximal, characteristic, complemented
30#10605848C211yesmaximal, characteristic, complemented
31#10605788C211yesmaximal, characteristic, complemented
32C2×C5×#121C2211yescharacteristic
33C2×C4×C5×D4C2211yescharacteristic
34C2×#4082C2211yescharacteristic
35C2×#4081C2211yescharacteristic
36C2×#4072C2211yescharacteristic
37C2×#4070C2211yescharacteristic
38C22×C4×Dic5C2211yescharacteristic
39C2×#4024C2211yescharacteristic
40C2×#4024C2211yescharacteristic
41C5×#400C2211yescharacteristic
42C5×#399C2211yescharacteristic
43C5×#394C2211yescharacteristic
44C5×#394C2211yescharacteristic
45C5×#394C2211yescharacteristic
46C5×#392C2211yescharacteristic
47C5×#392C2211yescharacteristic
48C5×#392C2211yescharacteristic
49C5×#388C2211yescharacteristic
50C5×#388C2211yescharacteristic
51C5×#386C2211yescharacteristic
52C5×#386C2211yescharacteristic
53C5×#381C2211yescharacteristic
54#65511C2211yescharacteristic
55#65511C2211yescharacteristic
56#65511C2211yescharacteristic
57#65511C2211yescharacteristic
58#65511C2211yescharacteristic
59#65511C2211yescharacteristic
60#65510C2211yescharacteristic
61#65510C2211yescharacteristic
62#65510C2211yescharacteristic
63#65510C2211yescharacteristic
64#65510C2211yescharacteristic
65#65509C2211yescharacteristic
66#65509C2211yescharacteristic
67#65509C2211yescharacteristic
68#65509C2211yescharacteristic
69#65509C2211yescharacteristic
70#65509C2211yescharacteristic
71#65509C2211yescharacteristic
72#65509C2211yescharacteristic
73#65509C2211yescharacteristic
74#65509C2211yescharacteristic
75#65509C2211yescharacteristic
76#65500C2211yescharacteristic
77#65499C2211yescharacteristic
78#65499C2211yescharacteristic
79C4×C22⋊Dic5C2211yescharacteristic
80C4×C22⋊Dic5C2211yescharacteristic
81#65275C2211yescharacteristic
82#65275C2211yescharacteristic
83#65272C2211yescharacteristic
84#65272C2211yescharacteristic
85#65272C2211yescharacteristic
86#65270C2211yescharacteristic
87#65270C2211yescharacteristic
88#65270C2211yescharacteristic
89#65270C2211yescharacteristic
90#65270C2211yescharacteristic
91#65270C2211yescharacteristic
92#65268C2211yescharacteristic
93#65266C2211yescharacteristic
94#65266C2211yescharacteristic
95#65263C2211yescharacteristic
96#65263C2211yescharacteristic
97#65242C2211yescharacteristic
98#65242C2211yescharacteristic
99#65242C2211yescharacteristic
100#65242C2211yescharacteristic
101#65241C2211yescharacteristic
102#65241C2211yescharacteristic
103#65241C2211yescharacteristic
104#65241C2211yescharacteristic
105#65241C2211yescharacteristic
106#65241C2211yescharacteristic
107#65241C2211yescharacteristic
108#65241C2211yescharacteristic
109#65241C2211yescharacteristic
110#65241C2211yescharacteristic
111#65240C2211yescharacteristic
112#65240C2211yescharacteristic
113#65240C2211yescharacteristic
114#65240C2211yescharacteristic
115#65240C2211yescharacteristic
116#65240C2211yescharacteristic
117#65239C2211yescharacteristic
118#65239C2211yescharacteristic
119#65239C2211yescharacteristic
120#65239C2211yescharacteristic
121#65239C2211yescharacteristic
122#65239C2211yescharacteristic
123#65238C2211yescharacteristic
124#65237C2211yescharacteristic
125#65237C2211yescharacteristic
126#65236C2211yescharacteristic
127#65236C2211yescharacteristic
128#65236C2211yescharacteristic
129#65235C2211yescharacteristic
130#65234C2211yescharacteristic
131#65234C2211yescharacteristic
132#65234C2211yescharacteristic
133#65234C2211yescharacteristic
134#65234C2211yescharacteristic
135#65234C2211yescharacteristic
136#65234C2211yescharacteristic
137#65234C2211yescharacteristic
138#65234C2211yescharacteristic
139#65234C2211yescharacteristic
140#65233C2211yescharacteristic
141#65233C2211yescharacteristic
142#65233C2211yescharacteristic
143#65233C2211yescharacteristic
144#65233C2211yescharacteristic
145#65233C2211yescharacteristic
146#65232C2211yescharacteristic
147#65231C2211yescharacteristic
148#65231C2211yescharacteristic
149C22⋊C4×Dic5C2211yescharacteristic
150C22⋊C4×Dic5C2211yescharacteristic
151C4×C4⋊Dic5C2211yescharacteristic
152#65222C2211yescharacteristic
153#65222C2211yescharacteristic
154#65221C2211yescharacteristic
155#64949C2211yescharacteristic
156#64949C2211yescharacteristic
157#64949C2211yescharacteristic
158#64949C2211yescharacteristic
159#64948C2211yescharacteristic
160#64948C2211yescharacteristic
161#64948C2211yescharacteristic
162#64946C2211yescharacteristic
163#64944C2211yescharacteristic
164#64944C2211yescharacteristic
165#64943C2211yescharacteristic
166#64943C2211yescharacteristic
167#64943C2211yescharacteristic
168#64943C2211yescharacteristic
169#64943C2211yescharacteristic
170#64943C2211yescharacteristic
171#64942C2211yescharacteristic
172#64941C2211yescharacteristic
173#64941C2211yescharacteristic
174#64941C2211yescharacteristic
175#64940C2211yescharacteristic
176#64940C2211yescharacteristic
177#64939C2211yescharacteristic
178#64938C2211yescharacteristic
179#64938C2211yescharacteristic
180#64936C2211yescharacteristic
181#64936C2211yescharacteristic
182#64936C2211yescharacteristic
183#64935C2211yescharacteristic
184#64935C2211yescharacteristic
185#64935C2211yescharacteristic
186#64935C2211yescharacteristic
187#36774—51nomaximal, Sylow
188C22×C5×D4C2311yescharacteristic
189C22×C5×D4C2311yescharacteristic
190C22×C5×D4C2311yescharacteristic
191C22×C5×D4C2311yescharacteristic
192C22×C5×D4C2311yescharacteristic
193C22×C5×D4C2311yescharacteristic
194C23×C4×C5C2311yescharacteristic
195C23×C4×C5C2311yescharacteristic
196C23×Dic5C2311yescharacteristic
197C23×Dic5C2311yescharacteristic
198C23×Dic5C2311yescharacteristic
199C23×Dic5C2311yescharacteristic
200C22×Dic10C2311yescharacteristic
201C22×Dic10C2311yescharacteristic
202C5×#121—24no—
203C4×C5×D4—24no—
204C2×C5×C4⋊C4C2311yescharacteristic
205C2×C5×C4⋊C4C2311yescharacteristic
206C2×C5×C4⋊C4C2311yescharacteristic
207C2×C5×C4⋊C4C2311yescharacteristic
208C2×C5×C22⋊C4C2311yescharacteristic
209C2×C5×C22⋊C4C2311yescharacteristic
210C2×C5×C22⋊C4C2311yescharacteristic
211C2×C5×C22⋊C4C2311yescharacteristic
212C2×C5×C22⋊C4C2311yescharacteristic
213C2×C5×C22⋊C4C2311yescharacteristic
214C2×C5×C22⋊C4C2311yescharacteristic
215C2×C5×C22⋊C4C2311yescharacteristic
216C2×C5×C22⋊C4C2311yescharacteristic
217C2×C5×C22⋊C4C2311yescharacteristic
218C2×C5×C22⋊C4C2311yescharacteristic
219C2×C5×C22⋊C4C2311yescharacteristic
220C2×C5×C22⋊C4C2311yescharacteristic
221C2×C5×C22⋊C4C2311yescharacteristic
222C2×C42×C5C2311yescharacteristic
223C2×C22⋊Dic5C2311yescharacteristic
224C2×C22⋊Dic5C2311yescharacteristic
225C2×C22⋊Dic5C2311yescharacteristic
226C2×C22⋊Dic5C2311yescharacteristic
227C2×C22⋊Dic5C2311yescharacteristic
228C2×C22⋊Dic5C2311yescharacteristic
229C2×C22⋊Dic5C2311yescharacteristic
230C2×C22⋊Dic5C2311yescharacteristic
231C2×C22⋊Dic5C2311yescharacteristic
232C2×C22⋊Dic5C2311yescharacteristic
233C2×C22⋊Dic5C2311yescharacteristic
234C2×C22⋊Dic5C2311yescharacteristic
235C2×C22⋊Dic5C2311yescharacteristic
236C2×C22⋊Dic5C2311yescharacteristic
237C2×C22⋊Dic5C2311yescharacteristic
238C2×C22⋊Dic5C2311yescharacteristic
239C2×C22⋊Dic5C2311yescharacteristic
240C2×C22⋊Dic5C2311yescharacteristic
241C2×C22⋊Dic5C2311yescharacteristic
242C2×C22⋊Dic5C2311yescharacteristic
243C2×C22⋊Dic5C2311yescharacteristic
244C2×C22⋊Dic5C2311yescharacteristic
245C2×C22⋊Dic5C2311yescharacteristic
246C2×C22⋊Dic5C2311yescharacteristic
247C2×C22⋊Dic5C2311yescharacteristic
248C2×C22⋊Dic5C2311yescharacteristic
249C2×C22⋊Dic5C2311yescharacteristic
250C2×C22⋊Dic5C2311yescharacteristic
251#4082—42no—
252#4081—42no—
253#4072—42no—
254C2×C4⋊Dic5C2311yescharacteristic
255C2×C4⋊Dic5C2311yescharacteristic
256C2×C4⋊Dic5C2311yescharacteristic
257C2×C4⋊Dic5C2311yescharacteristic
258C2×C4⋊Dic5C2311yescharacteristic
259C2×C4⋊Dic5C2311yescharacteristic
260C2×C4⋊Dic5C2311yescharacteristic
261C2×C4⋊Dic5C2311yescharacteristic
262C2×C4⋊Dic5C2311yescharacteristic
263C2×C4⋊Dic5C2311yescharacteristic
264#4070—24no—
265C2×#683C2311yescharacteristic
266C2×#683C2311yescharacteristic
267C2×#683C2311yescharacteristic
268C2×#683C2311yescharacteristic
269C2×#683C2311yescharacteristic
270C2×#683C2311yescharacteristic
271C2×#683C2311yescharacteristic
272C2×#683C2311yescharacteristic
273C2×#683C2311yescharacteristic
274C2×#683C2311yescharacteristic
275C2×#683C2311yescharacteristic
276C2×#683C2311yescharacteristic
277C2×#683C2311yescharacteristic
278C2×#683C2311yescharacteristic
279C2×#683C2311yescharacteristic
280C2×#683C2311yescharacteristic
281C2×C4×Dic5—42no—
282C2×C4×Dic5C2311yescharacteristic
283C2×C4×Dic5C2311yescharacteristic
284C2×C4×Dic5C2311yescharacteristic
285C2×C4×Dic5C2311yescharacteristic
286C2×C4×Dic5C2311yescharacteristic
287C2×C4×Dic5C2311yescharacteristic
288C2×C4×Dic5C2311yescharacteristic
289C2×C4×Dic5C2311yescharacteristic
290C2×C4×Dic5C2311yescharacteristic
291C2×C4×Dic5C2311yescharacteristic
292C2×C4×Dic5C2311yescharacteristic
293C2×C4×Dic5C2311yescharacteristic
294#4024—42no—
295#4024—42no—
296C5×#95C2311yescharacteristic
297C5×#95C2311yescharacteristic
298C5×#95C2311yescharacteristic
299C5×#95C2311yescharacteristic
300C5×#95C2311yescharacteristic
301C5×#95C2311yescharacteristic
302C5×#95C2311yescharacteristic
303C5×#95C2311yescharacteristic
304#3963C2311yescharacteristic
305#3963C2311yescharacteristic
306#3963C2311yescharacteristic
307#3963C2311yescharacteristic
308#3963C2311yescharacteristic
309#3963C2311yescharacteristic
310#3963C2311yescharacteristic
311#3963C2311yescharacteristic
312#3963C2311yescharacteristic
313#3963C2311yescharacteristic
314#3963C2311yescharacteristic
315#3963C2311yescharacteristic
316#3963C2311yescharacteristic
317#3963C2311yescharacteristic
318#3963C2311yescharacteristic
319#3963C2311yescharacteristic
320#3963C2311yescharacteristic
321#3963C2311yescharacteristic
322#3963C2311yescharacteristic
323#3963C2311yescharacteristic
324#3963C2311yescharacteristic
325#3963C2311yescharacteristic
326#3963C2311yescharacteristic
327#3963C2311yescharacteristic
328#3963C2311yescharacteristic
329#3963C2311yescharacteristic
330#3963C2311yescharacteristic
331#3963C2311yescharacteristic
332#3963C2311yescharacteristic
333#3963C2311yescharacteristic
334#3963C2311yescharacteristic
335#3963C2311yescharacteristic
336#3963C2311yescharacteristic
337#3963C2311yescharacteristic
338#3963C2311yescharacteristic
339#3963C2311yescharacteristic
340#3963C2311yescharacteristic
341#3963C2311yescharacteristic
342#3963C2311yescharacteristic
343#3963C2311yescharacteristic
344#3963C2311yescharacteristic
345#3963C2311yescharacteristic
346#3963C2311yescharacteristic
347#3963C2311yescharacteristic
348#3963C2311yescharacteristic
349#3963C2311yescharacteristic
350#3963C2311yescharacteristic
351#3963C2311yescharacteristic
352#2855—51no—
353#2850—51no—
354#2797—51no—
355#2796—51no—
356#2786—51no—
357#2786—51no—
358#2782—51no—
359#2767—51no—
360#2758—51no—
361#2756—51no—
362#2754—51no—
363#2754—51no—
364#2753—51no—
365#2749—51no—
366#2728—51no—
367#2710—51no—
368#2700—51no—
369#2696—51no—
370#2638—51no—
371#2635D511yescharacteristic
372#2597—51no—
373#2595—51no—
374#2577—51no—
375#2575—51no—
376#2532—51no—
377#2529—51no—
378#2477—51no—
379#2470—51no—
380#2333—51no—
381#2332—51no—
382#2290—51no—
383C24×C5C2411yescharacteristic
384C24×C5C2411yescharacteristic
385C24×C5C2411yescharacteristic
386C24×C5C2411yescharacteristic
387C2×C5×D4—22no—
388C2×C5×D4—22no—
389C2×C5×D4—22no—
390C2×C5×D4—22no—
391C2×C5×D4—41no—
392C2×C5×D4—41no—
393C2×C5×D4—41no—
394C2×C5×D4—41no—
395C2×C5×D4—41no—
396C2×C5×D4—41no—
397C2×C5×D4—41no—
398C2×C5×D4—41no—
399C2×C5×D4—41no—
400C2×C5×D4—41no—
401C2×C5×D4—41no—
402C2×C5×D4—41no—
403C2×C5×D4—41no—
404C2×C5×D4—41no—
405C22×C4×C5—22no—
406C22×C4×C5—41no—
407C22×C4×C5—41no—
408C22×C4×C5—41no—
409C22×C4×C5—41no—
410C22×C4×C5#4114yes—
411C22×C4×C5C2411yescharacteristic
412C22×C4×C5C2411yescharacteristic
413C22×C4×C5C2411yescharacteristic
414C22×C4×C5C2411yescharacteristic
415C22×C4×C5C2411yescharacteristic
416C22×C4×C5C2411yescharacteristic
417C22×C4×C5C2411yescharacteristic
418C22×C4×C5C2411yescharacteristic
419C22×C4×C5C2411yescharacteristic
420C22×C4×C5C2411yescharacteristic
421C22×C4×C5C2411yescharacteristic
422C22×Dic5—22no—
423C22×Dic5—41no—
424C22×Dic5—41no—
425C22×Dic5—41no—
426C22×Dic5—41no—
427C22×Dic5—41no—
428C22×Dic5—41no—
429C22×Dic5—41no—
430C22×Dic5—41no—
431C22×Dic5—41no—
432C22×Dic5—41no—
433C22×Dic5—41no—
434C22×Dic5C2411yescharacteristic
435C22×Dic5C2411yescharacteristic
436C22×Dic5C2411yescharacteristic
437C22×Dic5C2411yescharacteristic
438C22×Dic5C2411yescharacteristic
439C22×Dic5C2411yescharacteristic
440C22×Dic5C2411yescharacteristic
441C22×Dic5C2411yescharacteristic
442C22×Dic5C2411yescharacteristic
443C22×Dic5C2411yescharacteristic
444C22×Dic5C2411yescharacteristic
445C22×Dic5C2411yescharacteristic
446C22×Dic5C2411yescharacteristic
447C22×Dic5C2411yescharacteristic
448C22×Dic5C2411yescharacteristic
449C22×Dic5C2411yescharacteristic
450C2×Dic10—22no—
451C2×Dic10—22no—
452C2×Dic10—41no—
453C2×Dic10—41no—
454C2×Dic10—41no—
455C2×Dic10—41no—
456C5×C4⋊C4—22no—
457C5×C4⋊C4—22no—
458C5×C4⋊C4—41no—
459C5×C4⋊C4—41no—
460C5×C22⋊C4—22no—
461C5×C22⋊C4—22no—
462C5×C22⋊C4—22no—
463C5×C22⋊C4—22no—
464C5×C22⋊C4—41no—
465C5×C22⋊C4—41no—
466C5×C22⋊C4—41no—
467C5×C22⋊C4—41no—
468C5×C22⋊C4—41no—
469C5×C22⋊C4—41no—
470C5×C22⋊C4—41no—
471C5×C22⋊C4—41no—
472C5×C22⋊C4—41no—
473C5×C22⋊C4—41no—
474C42×C5—22no—
475C22⋊Dic5—22no—
476C22⋊Dic5—22no—
477C22⋊Dic5—22no—
478C22⋊Dic5—22no—
479C22⋊Dic5—22no—
480C22⋊Dic5—41no—
481C22⋊Dic5—41no—
482C22⋊Dic5—41no—
483C22⋊Dic5—41no—
484C22⋊Dic5—41no—
485C22⋊Dic5—41no—
486C22⋊Dic5—41no—
487C22⋊Dic5—41no—
488C22⋊Dic5—41no—
489C22⋊Dic5—41no—
490C22⋊Dic5—41no—
491C22⋊Dic5—41no—
492C22⋊Dic5—41no—
493C22⋊Dic5—41no—
494C22⋊Dic5—41no—
495C22⋊Dic5—41no—
496C22⋊Dic5—41no—
497C22⋊Dic5—41no—
498C22⋊Dic5—41no—
499C22⋊Dic5—41no—
500C22⋊Dic5—41no—
501C22⋊Dic5—41no—
502C22⋊Dic5—41no—
503C4⋊Dic5—22no—
504C4⋊Dic5—22no—
505C4⋊Dic5—41no—
506C4⋊Dic5—41no—
507C4⋊Dic5—41no—
508C4⋊Dic5—41no—
509C4⋊Dic5—41no—
510C4⋊Dic5—41no—
511C4⋊Dic5—41no—
512C4⋊Dic5—41no—
513#683—22no—
514#683—22no—
515#683—22no—
516#683—41no—
517#683—41no—
518#683—41no—
519#683—41no—
520#683—41no—
521#683—41no—
522#683—41no—
523#683—41no—
524#683—41no—
525#683—41no—
526#683—41no—
527#683—41no—
528#683—41no—
529C4×Dic5—22no—
530C4×Dic5—22no—
531C4×Dic5—41no—
532C4×Dic5—41no—
533C4×Dic5—41no—
534C4×Dic5—41no—
535C4×Dic5—41no—
536C4×Dic5—41no—
537C4×Dic5—41no—
538C4×Dic5—41no—
539C4×Dic5—41no—
540C4×Dic5—41no—
541C2×#124—51no—
542C2×#123—51no—
543C2×C22⋊Q8—51no—
544C2×C22⋊Q8—51no—
545C2×C22⋊Q8—51no—
546C2×#121C2×D511yescharacteristic
547C2×C4×D4C2×D511yescharacteristic
548C2×#117—51no—
549C22×C42—51no—
550#400—51no—
551#400—51no—
552#400—51no—
553#400—51no—
554#400—51no—
555#400—51no—
556#400—51no—
557#400—51no—
558#400—51no—
559#400C2×D511yescharacteristic
560#399—51no—
561#399C2×D511yescharacteristic
562#398—51no—
563#398—51no—
564#398—51no—
565#398—51no—
566#397—51no—
567#397—51no—
568#397—51no—
569#397—51no—
570#397—51no—
571#397—51no—
572#397—51no—
573#397—51no—
574#397—51no—
575#397—51no—
576#397—51no—
577#397—51no—
578#397—51no—
579#397—51no—
580#396—51no—
581#396—51no—
582#395—51no—
583#394—51no—
584#394—51no—
585#394—51no—
586#394—51no—
587#394—51no—
588#394—51no—
589#394C2×D511yescharacteristic
590#394C2×D511yescharacteristic
591#394C2×D511yescharacteristic
592#393—51no—
593#393—51no—
594#393—51no—
595#392C2×D511yescharacteristic
596#392C2×D511yescharacteristic
597#392C2×D511yescharacteristic
598#391—51no—
599#391—51no—
600#391—51no—
601#391—51no—
602#391—51no—
603#391—51no—
604#390—51no—
605#390—51no—
606#390—51no—
607#390—51no—
608#390—51no—
609#389—51no—
610#389—51no—
611#389—51no—
612#388—51no—
613#388—51no—
614#388—51no—
615#388—51no—
616#388—51no—
617#388—51no—
618#388—51no—
619#388—51no—
620#388—51no—
621#388—51no—
622#388—51no—
623#388—51no—
624#388—51no—
625#388—51no—
626#388—51no—
627#388—51no—
628#388—51no—
629#388—51no—
630#388—51no—
631#388—51no—
632#388—51no—
633#388—51no—
634#388C2×D511yescharacteristic
635#388C2×D511yescharacteristic
636#387—51no—
637#387—51no—
638#387—51no—
639#387—51no—
640#387—51no—
641#387—51no—
642#387—51no—
643#387—51no—
644#387—51no—
645#387—51no—
646#387—51no—
647#387—51no—
648#387—51no—
649#387—51no—
650#387—51no—
651#387—51no—
652#387—51no—
653#387—51no—
654#387—51no—
655#387—51no—
656#386—51no—
657#386—51no—
658#386—51no—
659#386—51no—
660#386—51no—
661#386—51no—
662#386—51no—
663#386—51no—
664#386—51no—
665#386—51no—
666#386—51no—
667#386C2×D511yescharacteristic
668#386C2×D511yescharacteristic
669#385—51no—
670#385—51no—
671#385—51no—
672#385—51no—
673#385—51no—
674#385—51no—
675#385—51no—
676#385—51no—
677#385—51no—
678#383—51no—
679#383—51no—
680#382—51no—
681#382—51no—
682#382—51no—
683#381—51no—
684#381—51no—
685#381C2×D511yescharacteristic
686#380—51no—
687#380—51no—
688C4×C4⋊C4—51no—
689C4×C4⋊C4—51no—
690C4×C4⋊C4—51no—
691C4×C22⋊C4—51no—
692C4×C22⋊C4—51no—
693C4×C22⋊C4—51no—
694C4×C22⋊C4—51no—
695#376—51no—
696C23×C5—21no—
697C23×C5—21no—
698C23×C5—21no—
699C23×C5—21no—
700C23×C5—21no—
701C23×C5—21no—
702C23×C5—21no—
703C23×C5—21no—
704C23×C5—21no—
705C23×C5—21no—
706C23×C5—21no—
707C23×C5—21no—
708C23×C5—21no—
709C23×C5—21no—
710C23×C5—21no—
711C23×C5—21no—
712C23×C5—21no—
713C23×C5—21no—
714C23×C5—21no—
715C23×C5—21no—
716C23×C5—21no—
717C23×C5—21no—
718C23×C5—21no—
719C23×C5—21no—
720C23×C5—21no—
721C23×C5—21no—
722C23×C5—21no—
723C23×C5C2×#4112yes—
724C23×C5C2511yescharacteristic
725C5×D4—44no—
726C5×D4—82no—
727C5×D4—82no—
728C5×D4—82no—
729C5×D4—82no—
730C5×D4—82no—
731C2×C4×C5—21no—
732C2×C4×C5—21no—
733C2×C4×C5—21no—
734C2×C4×C5—21no—
735C2×C4×C5—21no—
736C2×C4×C5—21no—
737C2×C4×C5—21no—
738C2×C4×C5—21no—
739C2×C4×C5—21no—
740C2×C4×C5—21no—
741C2×C4×C5—21no—
742C2×C4×C5—21no—
743C2×C4×C5—21no—
744C2×C4×C5—21no—
745C2×C4×C5—21no—
746C2×C4×C5—21no—
747C2×C4×C5—21no—
748C2×C4×C5—21no—
749C2×C4×C5—21no—
750C2×C4×C5—21no—
751C2×C4×C5—21no—
752C2×C4×C5—21no—
753C2×C4×C5—21no—
754C2×C4×C5—21no—
755C2×C4×C5—21no—
756C2×C4×C5—21no—
757C2×C4×C5—21no—
758C2×C4×C5—21no—
759C2×C4×C5—21no—
760C2×C4×C5—21no—
761C2×C4×C5—21no—
762C2×C4×C5—44no—
763C2×C4×C5—44no—
764C2×C4×C5C2×#4112yes—
765C2×C4×C5C2×#4112yes—
766C2×Dic5—21no—
767C2×Dic5—21no—
768C2×Dic5—21no—
769C2×Dic5—21no—
770C2×Dic5—21no—
771C2×Dic5—21no—
772C2×Dic5—21no—
773C2×Dic5—21no—
774C2×Dic5—21no—
775C2×Dic5—21no—
776C2×Dic5—21no—
777C2×Dic5—21no—
778C2×Dic5—21no—
779C2×Dic5—21no—
780C2×Dic5—21no—
781C2×Dic5—21no—
782C2×Dic5—21no—
783C2×Dic5—21no—
784C2×Dic5—21no—
785C2×Dic5—21no—
786C2×Dic5—21no—
787C2×Dic5—21no—
788C2×Dic5—21no—
789C2×Dic5—21no—
790C2×Dic5—21no—
791C2×Dic5—21no—
792C2×Dic5—21no—
793C2×Dic5—21no—
794C2×Dic5—21no—
795C2×Dic5—21no—
796C2×Dic5—21no—
797C2×Dic5—21no—
798C2×Dic5—21no—
799C2×Dic5—21no—
800C2×Dic5—21no—
801C2×Dic5—21no—
802C2×Dic5—21no—
803C2×Dic5—21no—
804C2×Dic5—21no—
805C2×Dic5—21no—
806C2×Dic5—21no—
807C2×Dic5—21no—
808C2×Dic5—21no—
809C2×Dic5—21no—
810C2×Dic5—21no—
811C2×Dic5—21no—
812C2×Dic5—21no—
813C2×Dic5—44no—
814C2×Dic5—44no—
815C2×Dic5—82no—
816C2×Dic5—82no—
817C2×Dic5H(5,𝔽2)12yes—
818Dic10—82no—
819Dic10—82no—
820C22×Q8—51no—
821C22×Q8—51no—
822C22×D4C22×D511yescharacteristic
823C22×D4C22×D511yescharacteristic
824C22×D4C22×D511yescharacteristic
825C22×D4C22×D511yescharacteristic
826C22×D4C22×D511yescharacteristic
827C22×D4C22×D511yescharacteristic
828C23×C4—51no—
829C23×C4—51no—
830C23×C4—51no—
831C23×C4—51no—
832C23×C4C22×D511yescharacteristic
833C23×C4C22×D511yescharacteristic
834#124—202no—
835#123—202no—
836C22⋊Q8—104no—
837C22⋊Q8—202no—
838C22⋊Q8—202no—
839#121—24no—
840C4×D4—24no—
841#117—202no—
842C2×C4⋊C4—51no—
843C2×C4⋊C4—51no—
844C2×C4⋊C4—51no—
845C2×C4⋊C4—51no—
846C2×C4⋊C4—51no—
847C2×C4⋊C4—51no—
848C2×C4⋊C4—51no—
849C2×C4⋊C4—51no—
850C2×C4⋊C4—51no—
851C2×C4⋊C4—51no—
852C2×C4⋊C4—51no—
853C2×C4⋊C4—51no—
854C2×C4⋊C4—51no—
855C2×C4⋊C4—51no—
856C2×C4⋊C4—51no—
857C2×C4⋊C4—51no—
858C2×C4⋊C4—51no—
859C2×C4⋊C4—51no—
860C2×C4⋊C4—51no—
861C2×C4⋊C4—51no—
862C2×C4⋊C4—51no—
863C2×C4⋊C4—51no—
864C2×C4⋊C4—51no—
865C2×C4⋊C4—51no—
866C2×C4⋊C4—51no—
867C2×C4⋊C4—51no—
868C2×C4⋊C4C22×D511yescharacteristic
869C2×C4⋊C4C22×D511yescharacteristic
870C2×C4⋊C4C22×D511yescharacteristic
871C2×C4⋊C4C22×D511yescharacteristic
872C2×C22⋊C4—51no—
873C2×C22⋊C4—51no—
874C2×C22⋊C4—51no—
875C2×C22⋊C4—51no—
876C2×C22⋊C4—51no—
877C2×C22⋊C4—51no—
878C2×C22⋊C4—51no—
879C2×C22⋊C4—51no—
880C2×C22⋊C4—51no—
881C2×C22⋊C4—51no—
882C2×C22⋊C4—51no—
883C2×C22⋊C4—51no—
884C2×C22⋊C4—51no—
885C2×C22⋊C4—51no—
886C2×C22⋊C4—51no—
887C2×C22⋊C4—51no—
888C2×C22⋊C4—51no—
889C2×C22⋊C4—51no—
890C2×C22⋊C4—51no—
891C2×C22⋊C4—51no—
892C2×C22⋊C4—51no—
893C2×C22⋊C4—51no—
894C2×C22⋊C4—51no—
895C2×C22⋊C4—51no—
896C2×C22⋊C4—51no—
897C2×C22⋊C4—51no—
898C2×C22⋊C4—51no—
899C2×C22⋊C4—51no—
900C2×C22⋊C4C22×D511yescharacteristic
901C2×C22⋊C4C22×D511yescharacteristic
902C2×C22⋊C4C22×D511yescharacteristic
903C2×C22⋊C4C22×D511yescharacteristic
904C2×C22⋊C4C22×D511yescharacteristic
905C2×C22⋊C4C22×D511yescharacteristic
906C2×C22⋊C4C22×D511yescharacteristic
907C2×C22⋊C4C22×D511yescharacteristic
908C2×C22⋊C4C22×D511yescharacteristic
909C2×C22⋊C4C22×D511yescharacteristic
910C2×C22⋊C4C22×D511yescharacteristic
911C2×C22⋊C4C22×D511yescharacteristic
912C2×C22⋊C4C22×D511yescharacteristic
913C2×C22⋊C4C22×D511yescharacteristic
914C2×C42—51no—
915C2×C42—51no—
916C2×C42—51no—
917C2×C42—51no—
918C2×C42—51no—
919C2×C42—51no—
920C2×C42—51no—
921C2×C42—51no—
922C2×C42—51no—
923C2×C42—51no—
924C2×C42—51no—
925C2×C42—51no—
926C2×C42—202no—
927C2×C42C22×D511yescharacteristic
928#95—51no—
929#95—51no—
930#95—51no—
931#95—51no—
932#95—51no—
933#95—51no—
934#95—51no—
935#95—51no—
936#95—51no—
937#95—51no—
938#95—51no—
939#95—51no—
940#95—51no—
941#95—51no—
942#95—51no—
943#95—51no—
944#95—51no—
945#95—51no—
946#95—51no—
947#95—51no—
948#95—51no—
949#95—51no—
950#95—51no—
951#95—51no—
952#95—51no—
953#95—51no—
954#95—51no—
955#95—51no—
956#95—51no—
957#95—51no—
958#95—51no—
959#95—51no—
960#95—51no—
961#95—51no—
962#95—51no—
963#95—51no—
964#95—51no—
965#95—51no—
966#95—51no—
967#95—51no—
968#95—51no—
969#95—51no—
970#95—51no—
971#95—51no—
972#95—51no—
973#95—51no—
974#95—51no—
975#95—51no—
976#95C22×D511yescharacteristic
977#95C22×D511yescharacteristic
978#95C22×D511yescharacteristic
979#95C22×D511yescharacteristic
980#95C22×D511yescharacteristic
981#95C22×D511yescharacteristic
982#95C22×D511yescharacteristic
983#95C22×D511yescharacteristic
984C22×C5—22no—
985C22×C5—22no—
986C22×C5—22no—
987C22×C5—41no—
988C22×C5—41no—
989C22×C5—41no—
990C22×C5—41no—
991C22×C5—41no—
992C22×C5—41no—
993C22×C5—41no—
994C22×C5—41no—
995C22×C5—41no—
996C22×C5—41no—
997C22×C5—41no—
998C22×C5—41no—
999C22×C5—41no—
1000C22×C5—41no—
1001C22×C5—41no—
1002C22×C5—41no—
1003C22×C5—41no—
1004C22×C5—41no—
1005C22×C5—41no—
1006C22×C5—41no—
1007C22×C5—41no—
1008C22×C5—41no—
1009C22×C5—41no—
1010C22×C5—41no—
1011C22×C5—41no—
1012C22×C5C22×#4111yescharacteristic
1013C22×C5C2×H(5,𝔽2)11yescharacteristic
1014C22×C5#58511yescharacteristic
1015C22×C5#58511yescharacteristic
1016C22×C5#58511yescharacteristic
1017C22×C5#58511yescharacteristic
1018C22×C5#58511yescharacteristic
1019C4×C5—22no—
1020C4×C5—22no—
1021C4×C5—41no—
1022C4×C5—41no—
1023C4×C5—41no—
1024C4×C5—41no—
1025C4×C5—41no—
1026C4×C5—41no—
1027C4×C5—41no—
1028C4×C5—41no—
1029C4×C5—41no—
1030Dic5—22no—
1031Dic5—41no—
1032Dic5—41no—
1033Dic5—41no—
1034Dic5—41no—
1035Dic5—41no—
1036Dic5—41no—
1037Dic5—41no—
1038Dic5—41no—
1039Dic5—41no—
1040Dic5—41no—
1041Dic5—41no—
1042Dic5—41no—
1043Dic5—41no—
1044Dic5—41no—
1045Dic5—41no—
1046C24C23×D511yescharacteristic
1047C24C23×D511yescharacteristic
1048C24C23×D511yescharacteristic
1049C24C23×D511yescharacteristic
1050C2×Q8—102no—
1051C2×Q8—102no—
1052C2×Q8—201no—
1053C2×Q8—201no—
1054C2×Q8—201no—
1055C2×Q8—201no—
1056C2×D4—22no—
1057C2×D4—22no—
1058C2×D4—22no—
1059C2×D4—22no—
1060C2×D4—41no—
1061C2×D4—41no—
1062C2×D4—41no—
1063C2×D4—41no—
1064C2×D4—41no—
1065C2×D4—41no—
1066C2×D4—41no—
1067C2×D4—41no—
1068C2×D4—41no—
1069C2×D4—41no—
1070C2×D4—41no—
1071C2×D4—41no—
1072C2×D4—41no—
1073C2×D4—41no—
1074C22×C4—22no—
1075C22×C4—41no—
1076C22×C4—41no—
1077C22×C4—41no—
1078C22×C4—41no—
1079C22×C4—51no—
1080C22×C4—51no—
1081C22×C4—51no—
1082C22×C4—51no—
1083C22×C4—51no—
1084C22×C4—51no—
1085C22×C4—51no—
1086C22×C4—51no—
1087C22×C4—51no—
1088C22×C4—51no—
1089C22×C4—51no—
1090C22×C4—51no—
1091C22×C4—51no—
1092C22×C4—51no—
1093C22×C4—51no—
1094C22×C4—51no—
1095C22×C4—102no—
1096C22×C4—201no—
1097C22×C4—201no—
1098C22×C4—201no—
1099C22×C4—201no—
1100C22×C4—201no—
1101C22×C4—201no—
1102C22×C4—201no—
1103C22×C4—201no—
1104C22×C4—201no—
1105C22×C4—201no—
1106C22×C4—201no—
1107C22×C4#71114yes—
1108C22×C4C23×D511yescharacteristic
1109C22×C4C23×D511yescharacteristic
1110C22×C4C23×D511yescharacteristic
1111C22×C4C23×D511yescharacteristic
1112C22×C4C23×D511yescharacteristic
1113C22×C4C23×D511yescharacteristic
1114C22×C4C23×D511yescharacteristic
1115C22×C4C23×D511yescharacteristic
1116C22×C4C23×D511yescharacteristic
1117C22×C4C23×D511yescharacteristic
1118C22×C4C23×D511yescharacteristic
1119C4⋊C4—22no—
1120C4⋊C4—22no—
1121C4⋊C4—41no—
1122C4⋊C4—41no—
1123C4⋊C4—102no—
1124C4⋊C4—102no—
1125C4⋊C4—102no—
1126C4⋊C4—102no—
1127C4⋊C4—102no—
1128C4⋊C4—201no—
1129C4⋊C4—201no—
1130C4⋊C4—201no—
1131C4⋊C4—201no—
1132C4⋊C4—201no—
1133C4⋊C4—201no—
1134C4⋊C4—201no—
1135C4⋊C4—201no—
1136C4⋊C4—201no—
1137C4⋊C4—201no—
1138C4⋊C4—201no—
1139C4⋊C4—201no—
1140C4⋊C4—201no—
1141C4⋊C4—201no—
1142C4⋊C4—201no—
1143C4⋊C4—201no—
1144C4⋊C4—201no—
1145C4⋊C4—201no—
1146C4⋊C4—201no—
1147C4⋊C4—201no—
1148C4⋊C4—201no—
1149C22⋊C4—22no—
1150C22⋊C4—22no—
1151C22⋊C4—22no—
1152C22⋊C4—22no—
1153C22⋊C4—41no—
1154C22⋊C4—41no—
1155C22⋊C4—41no—
1156C22⋊C4—41no—
1157C22⋊C4—41no—
1158C22⋊C4—41no—
1159C22⋊C4—41no—
1160C22⋊C4—41no—
1161C22⋊C4—41no—
1162C22⋊C4—41no—
1163C22⋊C4—102no—
1164C22⋊C4—102no—
1165C22⋊C4—102no—
1166C22⋊C4—102no—
1167C22⋊C4—102no—
1168C22⋊C4—201no—
1169C22⋊C4—201no—
1170C22⋊C4—201no—
1171C22⋊C4—201no—
1172C22⋊C4—201no—
1173C22⋊C4—201no—
1174C22⋊C4—201no—
1175C22⋊C4—201no—
1176C22⋊C4—201no—
1177C22⋊C4—201no—
1178C22⋊C4—201no—
1179C22⋊C4—201no—
1180C22⋊C4—201no—
1181C22⋊C4—201no—
1182C22⋊C4—201no—
1183C22⋊C4—201no—
1184C22⋊C4—201no—
1185C22⋊C4—201no—
1186C22⋊C4—201no—
1187C22⋊C4—201no—
1188C22⋊C4—201no—
1189C22⋊C4—201no—
1190C22⋊C4—201no—
1191C42—22no—
1192C42—102no—
1193C42—102no—
1194C42—201no—
1195C42—201no—
1196C42—201no—
1197C42—201no—
1198C42—201no—
1199C42—201no—
1200C42—201no—
1201C42—201no—
1202C42—201no—
1203C42—201no—
1204C2×C5—42no—
1205C2×C5—81no—
1206C2×C5—81no—
1207C2×C5—81no—
1208C2×C5#345511yescharacteristic
1209C2×C5#350511yescharacteristic
1210C2×C5#351011yescharacteristic
1211C2×C5#353311yescharacteristic
1212C2×C5#354011yescharacteristic
1213C2×C5#356611yescharacteristic
1214C2×C5#356711yescharacteristic
1215C23—21no—
1216C23—21no—
1217C23—21no—
1218C23—21no—
1219C23—21no—
1220C23—21no—
1221C23—21no—
1222C23—21no—
1223C23—21no—
1224C23—21no—
1225C23—21no—
1226C23—21no—
1227C23—21no—
1228C23—21no—
1229C23—21no—
1230C23—21no—
1231C23—21no—
1232C23—21no—
1233C23—21no—
1234C23—21no—
1235C23—21no—
1236C23—21no—
1237C23—21no—
1238C23—21no—
1239C23—21no—
1240C23—21no—
1241C23—21no—
1242C23C2×#71112yes—
1243C23C24×D511yescharacteristic
1244Q8—402no—
1245Q8—402no—
1246D4—44no—
1247D4—82no—
1248D4—82no—
1249D4—82no—
1250D4—82no—
1251D4—82no—
1252C2×C4—21no—
1253C2×C4—21no—
1254C2×C4—21no—
1255C2×C4—21no—
1256C2×C4—21no—
1257C2×C4—21no—
1258C2×C4—21no—
1259C2×C4—21no—
1260C2×C4—21no—
1261C2×C4—21no—
1262C2×C4—21no—
1263C2×C4—21no—
1264C2×C4—21no—
1265C2×C4—21no—
1266C2×C4—21no—
1267C2×C4—21no—
1268C2×C4—21no—
1269C2×C4—21no—
1270C2×C4—21no—
1271C2×C4—21no—
1272C2×C4—21no—
1273C2×C4—21no—
1274C2×C4—21no—
1275C2×C4—21no—
1276C2×C4—21no—
1277C2×C4—21no—
1278C2×C4—21no—
1279C2×C4—21no—
1280C2×C4—21no—
1281C2×C4—21no—
1282C2×C4—21no—
1283C2×C4—44no—
1284C2×C4—44no—
1285C2×C4—52no—
1286C2×C4—101no—
1287C2×C4—101no—
1288C2×C4—101no—
1289C2×C4—101no—
1290C2×C4—101no—
1291C2×C4—101no—
1292C2×C4—101no—
1293C2×C4—101no—
1294C2×C4—101no—
1295C2×C4—101no—
1296C2×C4—101no—
1297C2×C4—101no—
1298C2×C4—101no—
1299C2×C4—101no—
1300C2×C4—101no—
1301C2×C4—101no—
1302C2×C4—101no—
1303C2×C4—101no—
1304C2×C4—101no—
1305C2×C4—101no—
1306C2×C4—101no—
1307C2×C4—101no—
1308C2×C4—101no—
1309C2×C4—101no—
1310C2×C4—101no—
1311C2×C4—101no—
1312C2×C4—101no—
1313C2×C4—101no—
1314C2×C4—101no—
1315C2×C4—101no—
1316C2×C4—101no—
1317C2×C4—101no—
1318C2×C4—101no—
1319C2×C4—101no—
1320C2×C4—101no—
1321C2×C4—101no—
1322C2×C4—101no—
1323C2×C4—101no—
1324C2×C4—101no—
1325C2×C4—101no—
1326C2×C4—101no—
1327C2×C4—101no—
1328C2×C4—101no—
1329C2×C4—101no—
1330C2×C4—101no—
1331C2×C4—101no—
1332C2×C4—101no—
1333C2×C4—204no—
1334C2×C4—204no—
1335C2×C4—402no—
1336C2×C4—402no—
1337C2×C4C2×#71112yes—
1338C2×C4C2×#71112yes—
1339C5#3677411yescharacteristic, complemented, Sylow
1340C22—22no—
1341C22—22no—
1342C22—22no—
1343C22—41no—
1344C22—41no—
1345C22—41no—
1346C22—41no—
1347C22—41no—
1348C22—41no—
1349C22—41no—
1350C22—41no—
1351C22—41no—
1352C22—41no—
1353C22—41no—
1354C22—41no—
1355C22—41no—
1356C22—41no—
1357C22—41no—
1358C22—41no—
1359C22—41no—
1360C22—41no—
1361C22—41no—
1362C22—41no—
1363C22—41no—
1364C22—41no—
1365C22—41no—
1366C22—41no—
1367C22—41no—
1368C22C22×#71111yescharacteristic
1369C22#6628311yescharacteristic
1370C22#6628311yescharacteristic
1371C22D5×H(5,𝔽2)11yescharacteristic
1372C22#6628511yescharacteristic
1373C22#6628511yescharacteristic
1374C22#6628511yescharacteristic
1375C4—22no—
1376C4—22no—
1377C4—41no—
1378C4—41no—
1379C4—41no—
1380C4—41no—
1381C4—41no—
1382C4—41no—
1383C4—41no—
1384C4—41no—
1385C4—41no—
1386C4—102no—
1387C4—201no—
1388C4—201no—
1389C4—201no—
1390C4—201no—
1391C4—201no—
1392C4—201no—
1393C4—201no—
1394C4—201no—
1395C4—201no—
1396C4—201no—
1397C4—201no—
1398C4—201no—
1399C4—201no—
1400C4—201no—
1401C4—201no—
1402C2—42no—
1403C2—81no—
1404C2—81no—
1405C2—81no—
1406C2#1061792011yescharacteristic
1407C2#1061820011yescharacteristic
1408C2#1061822111yescharacteristic
1409C2#1061829811yescharacteristic
1410C2#1061831011yescharacteristic
1411C2#1061838411yescharacteristic
1412C2#1061839011yescharacteristic
subgroupG/H
center, FrattiniC23C24×D5
commutator, socle, cosocleC23×C5C25
Fitting, prime radicalC5×#2635C2
hypercenter#2635D5
hypocenterC5#36774
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C23 ◁ #2635

Complements

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

NH ≅ G/Ntype
2. #10614429C2semidirect
3. #10614366C2semidirect
4. #10614123C2semidirect
5. #10614049C2semidirect
6. #10610000C2semidirect
7. #10609988C2semidirect
8. #10609810C2semidirect
9. #10609810C2semidirect
10. #10608805C2semidirect
11. #10608802C2semidirect
12. #10608802C2semidirect
13. #10608800C2semidirect
14. #10608774C2semidirect
15. #10608750C2semidirect
16. #10608470C2semidirect
17. #10608467C2semidirect
18. #10608466C2semidirect
19. #10608464C2semidirect
20. #10608457C2semidirect
21. #10608450C2semidirect
22. #10607343C2semidirect
23. #10607340C2semidirect
24. #10607322C2semidirect
25. #10607313C2semidirect
26. #10606505C2semidirect
27. #10606504C2semidirect
28. #10606464C2semidirect
29. #10606454C2semidirect
30. #10605848C2semidirect
31. #10605788C2semidirect
1339. C5#36774semidirect

Maximal subgroups

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

subgroupindex
C5×#26352
#106144292
#106143662
#106141232
#106140492
#106100002
#106099882
#106098102
#106088052
#106088022
#106088002
#106087742
#106087502
#106084702
#106084672
#106084662
#106084642
#106084572
#106084502
#106073432
#106073402
#106073222
#106073132
#106065052
#106065042
#106064642
#106064542
#106058482
#106057882
#367745