Finite Group Databasebeta

← #12307115

Subgroups — #12307115

Order 1280.

1496 conjugacy classes of subgroups.

The subgroup lattice has 1330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2318C211yesmaximal, characteristic
2#10614056C211yesmaximal, characteristic
3#10614049C211yesmaximal, characteristic
4#10607542C211yesmaximal, characteristic, complemented
5#10607518C211yesmaximal, characteristic, complemented
6#10607484C211yesmaximal, characteristic, complemented
7#10607428C211yesmaximal, characteristic, complemented
8#10607005C211yesmaximal, characteristic, complemented
9#10606980C211yesmaximal, characteristic, complemented
10#10606918C211yesmaximal, characteristic, complemented
11#10606907C211yesmaximal, characteristic, complemented
12#10606589C211yesmaximal, characteristic
13#10606588C211yesmaximal, characteristic
14#10606569C211yesmaximal, characteristic
15#10606561C211yesmaximal, characteristic
16#10606308C211yesmaximal, characteristic, complemented
17#10606290C211yesmaximal, characteristic, complemented
18#10606290C211yesmaximal, characteristic, complemented
19#10606254C211yesmaximal, characteristic, complemented
20#10606007C211yesmaximal, characteristic, complemented
21#10606007C211yesmaximal, characteristic, complemented
22#10605923C211yesmaximal, characteristic, complemented
23#10605917C211yesmaximal, characteristic, complemented
24#10605848C211yesmaximal, characteristic, complemented
25#10605824C211yesmaximal, characteristic, complemented
26#10605729C211yesmaximal, characteristic, complemented
27#10605690C211yesmaximal, characteristic, complemented
28#10605285C211yesmaximal, characteristic, complemented
29#10605225C211yesmaximal, characteristic, complemented
30#10605090C211yesmaximal, characteristic, complemented
31#10605081C211yesmaximal, characteristic, complemented
32C2×C4×C5×D4C2211yescharacteristic
33C2×#4072C2211yescharacteristic
34C2×#4070C2211yescharacteristic
35C22×C4×Dic5C2211yescharacteristic
36C2×#4036C2211yescharacteristic
37C2×#4024C2211yescharacteristic
38C2×#4016C2211yescharacteristic
39C5×#388C2211yescharacteristic
40C5×#388C2211yescharacteristic
41C5×#387C2211yescharacteristic
42C5×#387C2211yescharacteristic
43C5×#386C2211yescharacteristic
44C5×#386C2211yescharacteristic
45C5×#385C2211yescharacteristic
46C5×#385C2211yescharacteristic
47C5×#383C2211yescharacteristic
48C5×#382C2211yescharacteristic
49C5×#381C2211yescharacteristic
50C5×#380C2211yescharacteristic
51C4×C5×C22⋊C4C2211yescharacteristic
52C2×C5×#95C2211yescharacteristic
53#65510C2211yescharacteristic
54#65510C2211yescharacteristic
55#65509C2211yescharacteristic
56#65509C2211yescharacteristic
57#65501C2211yescharacteristic
58#65501C2211yescharacteristic
59#65501C2211yescharacteristic
60#65501C2211yescharacteristic
61#65501C2211yescharacteristic
62#65500C2211yescharacteristic
63#65500C2211yescharacteristic
64#65499C2211yescharacteristic
65#65499C2211yescharacteristic
66#65499C2211yescharacteristic
67#65499C2211yescharacteristic
68C4×C22⋊Dic5C2211yescharacteristic
69C4×C22⋊Dic5C2211yescharacteristic
70#65275C2211yescharacteristic
71#65274C2211yescharacteristic
72#65274C2211yescharacteristic
73#65274C2211yescharacteristic
74#65274C2211yescharacteristic
75#65274C2211yescharacteristic
76#65273C2211yescharacteristic
77#65273C2211yescharacteristic
78#65273C2211yescharacteristic
79#65273C2211yescharacteristic
80#65273C2211yescharacteristic
81#65273C2211yescharacteristic
82#65270C2211yescharacteristic
83#65270C2211yescharacteristic
84#65268C2211yescharacteristic
85#65266C2211yescharacteristic
86#65266C2211yescharacteristic
87#65265C2211yescharacteristic
88#65262C2211yescharacteristic
89#65240C2211yescharacteristic
90#65240C2211yescharacteristic
91#65240C2211yescharacteristic
92#65240C2211yescharacteristic
93#65240C2211yescharacteristic
94#65240C2211yescharacteristic
95#65239C2211yescharacteristic
96#65239C2211yescharacteristic
97#65239C2211yescharacteristic
98#65239C2211yescharacteristic
99#65239C2211yescharacteristic
100#65238C2211yescharacteristic
101#65238C2211yescharacteristic
102#65238C2211yescharacteristic
103#65238C2211yescharacteristic
104#65238C2211yescharacteristic
105#65238C2211yescharacteristic
106#65237C2211yescharacteristic
107#65237C2211yescharacteristic
108#65237C2211yescharacteristic
109#65237C2211yescharacteristic
110#65237C2211yescharacteristic
111#65237C2211yescharacteristic
112#65237C2211yescharacteristic
113#65237C2211yescharacteristic
114#65237C2211yescharacteristic
115#65237C2211yescharacteristic
116#65235C2211yescharacteristic
117#65235C2211yescharacteristic
118#65235C2211yescharacteristic
119#65231C2211yescharacteristic
120#65224C2211yescharacteristic
121C4×C4⋊Dic5C2211yescharacteristic
122C4×C4⋊Dic5C2211yescharacteristic
123#65222C2211yescharacteristic
124#65222C2211yescharacteristic
125#65221C2211yescharacteristic
126#65221C2211yescharacteristic
127#65217C2211yescharacteristic
128#65217C2211yescharacteristic
129#65217C2211yescharacteristic
130#65217C2211yescharacteristic
131#64950C2211yescharacteristic
132#64950C2211yescharacteristic
133#64950C2211yescharacteristic
134#64950C2211yescharacteristic
135#64950C2211yescharacteristic
136#64950C2211yescharacteristic
137#64950C2211yescharacteristic
138#64950C2211yescharacteristic
139#64950C2211yescharacteristic
140#64950C2211yescharacteristic
141#64950C2211yescharacteristic
142#64949C2211yescharacteristic
143#64949C2211yescharacteristic
144#64949C2211yescharacteristic
145#64949C2211yescharacteristic
146#64949C2211yescharacteristic
147#64946C2211yescharacteristic
148#64946C2211yescharacteristic
149#64946C2211yescharacteristic
150#64946C2211yescharacteristic
151#64946C2211yescharacteristic
152#64946C2211yescharacteristic
153#64946C2211yescharacteristic
154#64945C2211yescharacteristic
155#64944C2211yescharacteristic
156#64944C2211yescharacteristic
157#64944C2211yescharacteristic
158#64944C2211yescharacteristic
159#64944C2211yescharacteristic
160#64944C2211yescharacteristic
161#64944C2211yescharacteristic
162#64944C2211yescharacteristic
163#64944C2211yescharacteristic
164#64943C2211yescharacteristic
165#64943C2211yescharacteristic
166#64943C2211yescharacteristic
167#64943C2211yescharacteristic
168#64943C2211yescharacteristic
169#64943C2211yescharacteristic
170#64943C2211yescharacteristic
171#64943C2211yescharacteristic
172#64943C2211yescharacteristic
173#64936C2211yescharacteristic
174#64936C2211yescharacteristic
175#64936C2211yescharacteristic
176#64936C2211yescharacteristic
177#64936C2211yescharacteristic
178#64936C2211yescharacteristic
179#64936C2211yescharacteristic
180#64936C2211yescharacteristic
181#64936C2211yescharacteristic
182#64936C2211yescharacteristic
183#64936C2211yescharacteristic
184#64935C2211yescharacteristic
185#64935C2211yescharacteristic
186#64935C2211yescharacteristic
187#36756—51nomaximal, Sylow
188C22×C5×D4C2311yescharacteristic
189C23×C4×C5C2311yescharacteristic
190C23×C4×C5C2311yescharacteristic
191C23×C4×C5C2311yescharacteristic
192C23×C4×C5C2311yescharacteristic
193C23×Dic5C2311yescharacteristic
194C23×Dic5C2311yescharacteristic
195C22×Dic10C2311yescharacteristic
196C4×C5×D4Q818yescomplemented
197C2×C5×C4⋊C4C2311yescharacteristic
198C2×C5×C4⋊C4C2311yescharacteristic
199C2×C5×C4⋊C4C2311yescharacteristic
200C2×C5×C4⋊C4C2311yescharacteristic
201C2×C5×C4⋊C4C2311yescharacteristic
202C2×C5×C22⋊C4C2311yescharacteristic
203C2×C5×C22⋊C4C2311yescharacteristic
204C2×C5×C22⋊C4C2311yescharacteristic
205C2×C5×C22⋊C4C2311yescharacteristic
206C2×C5×C22⋊C4C2311yescharacteristic
207C2×C5×C22⋊C4C2311yescharacteristic
208C2×C5×C22⋊C4C2311yescharacteristic
209C2×C5×C22⋊C4C2311yescharacteristic
210C2×C42×C5C2311yescharacteristic
211C2×C42×C5C2311yescharacteristic
212C2×C42×C5C2311yescharacteristic
213C2×C22⋊Dic5C2311yescharacteristic
214C2×C22⋊Dic5C2311yescharacteristic
215C2×C22⋊Dic5C2311yescharacteristic
216C2×C22⋊Dic5C2311yescharacteristic
217C2×C22⋊Dic5C2311yescharacteristic
218C2×C22⋊Dic5C2311yescharacteristic
219C2×C22⋊Dic5C2311yescharacteristic
220C2×C22⋊Dic5C2311yescharacteristic
221C2×C22⋊Dic5C2311yescharacteristic
222C2×C22⋊Dic5C2311yescharacteristic
223C2×C22⋊Dic5C2311yescharacteristic
224C2×C22⋊Dic5C2311yescharacteristic
225C2×C22⋊Dic5C2311yescharacteristic
226C2×C22⋊Dic5C2311yescharacteristic
227#4072—42no—
228C2×C4⋊Dic5C2311yescharacteristic
229C2×C4⋊Dic5C2311yescharacteristic
230C2×C4⋊Dic5C2311yescharacteristic
231C2×C4⋊Dic5C2311yescharacteristic
232C2×C4⋊Dic5C2311yescharacteristic
233C2×C4⋊Dic5C2311yescharacteristic
234C2×C4⋊Dic5C2311yescharacteristic
235C2×C4⋊Dic5C2311yescharacteristic
236C2×C4⋊Dic5C2311yescharacteristic
237C2×C4⋊Dic5C2311yescharacteristic
238C2×C4⋊Dic5C2311yescharacteristic
239C2×C4⋊Dic5C2311yescharacteristic
240C2×C4⋊Dic5C2311yescharacteristic
241C2×C4⋊Dic5C2311yescharacteristic
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
251C2×C4⋊Dic5C2311yescharacteristic
252C2×C4⋊Dic5C2311yescharacteristic
253#4070—42no—
254C2×#683C2311yescharacteristic
255C2×#683C2311yescharacteristic
256C2×#683C2311yescharacteristic
257C2×#683C2311yescharacteristic
258C2×#683C2311yescharacteristic
259C2×#683C2311yescharacteristic
260C2×#683C2311yescharacteristic
261C2×#683C2311yescharacteristic
262C2×#683C2311yescharacteristic
263C2×#683C2311yescharacteristic
264C2×#683C2311yescharacteristic
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×C4×Dic5—42no—
281C2×C4×Dic5C2311yescharacteristic
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
291#4036—42no—
292#4024—42no—
293#4016—42no—
294C5×#95C2311yescharacteristic
295C5×#95C2311yescharacteristic
296C5×#95C2311yescharacteristic
297C5×#95C2311yescharacteristic
298C5×#95C2311yescharacteristic
299C5×#95C2311yescharacteristic
300C5×#95C2311yescharacteristic
301C5×#95C2311yescharacteristic
302C5×#95C2311yescharacteristic
303C5×#95C2311yescharacteristic
304C5×#95C2311yescharacteristic
305C5×#95C2311yescharacteristic
306C5×#95C2311yescharacteristic
307C5×#95C2311yescharacteristic
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#2855—51no—
351#2851—51no—
352#2807—51no—
353#2802—51no—
354#2791—51no—
355#2790—51no—
356#2790—51no—
357#2780—51no—
358#2780—51no—
359#2768—51no—
360#2768—51no—
361#2768—51no—
362#2755—51no—
363#2748—51no—
364#2732—51no—
365#2726—51no—
366#2720—51no—
367#2704—51no—
368#2667—51no—
369#2667—51no—
370#2612—51no—
371#2608—51no—
372#2606—51no—
373#2606—51no—
374#2570—51no—
375#2569—51no—
376#2441—51no—
377#2438—51no—
378#2319—51no—
379#2318D511yescharacteristic
380#2290—51no—
381C24×C5C2411yescharacteristic
382C24×C5C2411yescharacteristic
383C2×C5×D4—41no—
384C2×C5×D4—41no—
385C2×C5×D4C2×Q814yes—
386C22×C4×C5—41no—
387C22×C4×C5—41no—
388C22×C4×C5—41no—
389C22×C4×C5—41no—
390C22×C4×C5—41no—
391C22×C4×C5—41no—
392C22×C4×C5—41no—
393C22×C4×C5—41no—
394C22×C4×C5—41no—
395C22×C4×C5—41no—
396C22×C4×C5C2×Q814yes—
397C22×C4×C5C2×Q814yes—
398C22×C4×C5C2411yescharacteristic
399C22×C4×C5C2411yescharacteristic
400C22×C4×C5C2411yescharacteristic
401C22×C4×C5C2411yescharacteristic
402C22×C4×C5C2411yescharacteristic
403C22×C4×C5C2411yescharacteristic
404C22×C4×C5C2411yescharacteristic
405C22×C4×C5C2411yescharacteristic
406C22×C4×C5C2411yescharacteristic
407C22×C4×C5C2411yescharacteristic
408C22×C4×C5C2411yescharacteristic
409C22×C4×C5C2411yescharacteristic
410C22×C4×C5C2411yescharacteristic
411C22×Dic5—22no—
412C22×Dic5—41no—
413C22×Dic5—41no—
414C22×Dic5—41no—
415C22×Dic5—41no—
416C22×Dic5—41no—
417C22×Dic5C2411yescharacteristic
418C22×Dic5C2411yescharacteristic
419C22×Dic5C2411yescharacteristic
420C22×Dic5C2411yescharacteristic
421C22×Dic5C2411yescharacteristic
422C22×Dic5C2411yescharacteristic
423C22×Dic5C2411yescharacteristic
424C22×Dic5C2411yescharacteristic
425C22×Dic5C2411yescharacteristic
426C22×Dic5C2411yescharacteristic
427C22×Dic5C2411yescharacteristic
428C22×Dic5C2411yescharacteristic
429C22×Dic5C2411yescharacteristic
430C22×Dic5C2411yescharacteristic
431C22×Dic5C2411yescharacteristic
432C22×Dic5C2411yescharacteristic
433C2×Dic10—22no—
434C2×Dic10—41no—
435C2×Dic10—41no—
436C5×C4⋊C4—41no—
437C5×C4⋊C4—41no—
438C5×C4⋊C4—41no—
439C5×C4⋊C4—41no—
440C5×C4⋊C4C2×Q814yes—
441C5×C22⋊C4—41no—
442C5×C22⋊C4—41no—
443C5×C22⋊C4—41no—
444C5×C22⋊C4—41no—
445C5×C22⋊C4—41no—
446C5×C22⋊C4—41no—
447C5×C22⋊C4C2×Q814yes—
448C5×C22⋊C4C2×Q814yes—
449C42×C5—41no—
450C42×C5—41no—
451C42×C5C2×Q814yes—
452C22⋊Dic5—22no—
453C22⋊Dic5—41no—
454C22⋊Dic5—41no—
455C22⋊Dic5—41no—
456C22⋊Dic5—41no—
457C22⋊Dic5—41no—
458C22⋊Dic5—41no—
459C22⋊Dic5—41no—
460C22⋊Dic5—41no—
461C22⋊Dic5—41no—
462C22⋊Dic5—41no—
463C22⋊Dic5—41no—
464C22⋊Dic5—41no—
465C22⋊Dic5—41no—
466C4⋊Dic5—22no—
467C4⋊Dic5—41no—
468C4⋊Dic5—41no—
469C4⋊Dic5—41no—
470C4⋊Dic5—41no—
471C4⋊Dic5—41no—
472C4⋊Dic5—41no—
473C4⋊Dic5—41no—
474C4⋊Dic5—41no—
475C4⋊Dic5—41no—
476C4⋊Dic5—41no—
477C4⋊Dic5—41no—
478C4⋊Dic5—41no—
479C4⋊Dic5—41no—
480C4⋊Dic5—41no—
481C4⋊Dic5—41no—
482C4⋊Dic5—41no—
483C4⋊Dic5—41no—
484C4⋊Dic5—41no—
485C4⋊Dic5—41no—
486C4⋊Dic5—41no—
487C4⋊Dic5—41no—
488C4⋊Dic5—41no—
489C4⋊Dic5—41no—
490C4⋊Dic5—41no—
491#683—22no—
492#683—22no—
493#683—22no—
494#683—41no—
495#683—41no—
496#683—41no—
497#683—41no—
498#683—41no—
499#683—41no—
500#683—41no—
501#683—41no—
502#683—41no—
503#683—41no—
504#683—41no—
505#683—41no—
506#683—41no—
507#683—41no—
508#683—41no—
509#683—41no—
510#683—41no—
511#683—41no—
512#683—41no—
513#683—41no—
514#683—41no—
515#683—41no—
516#683—41no—
517C4×Dic5—22no—
518C4×Dic5—22no—
519C4×Dic5—41no—
520C4×Dic5—41no—
521C4×Dic5—41no—
522C4×Dic5—41no—
523C4×Dic5—41no—
524C4×Dic5—41no—
525C4×Dic5—41no—
526C4×Dic5—41no—
527C2×#125—51no—
528C2×#125—51no—
529C2×C22⋊Q8—51no—
530C2×C22⋊Q8—51no—
531C2×C4×D4C2×D511yescharacteristic
532C2×#117—51no—
533C22×C42—51no—
534#400—51no—
535#400—51no—
536#400—51no—
537#400—51no—
538#400—51no—
539#400—51no—
540#399—51no—
541#399—51no—
542#399—51no—
543#399—51no—
544#399—51no—
545#399—51no—
546#398—51no—
547#398—51no—
548#398—51no—
549#398—51no—
550#398—51no—
551#398—51no—
552#398—51no—
553#398—51no—
554#398—51no—
555#398—51no—
556#398—51no—
557#398—51no—
558#398—51no—
559#398—51no—
560#398—51no—
561#398—51no—
562#398—51no—
563#398—51no—
564#398—51no—
565#398—51no—
566#398—51no—
567#398—51no—
568#398—51no—
569#398—51no—
570#396—51no—
571#396—51no—
572#396—51no—
573#396—51no—
574#396—51no—
575#396—51no—
576#396—51no—
577#396—51no—
578#396—51no—
579#396—51no—
580#395—51no—
581#395—51no—
582#391—51no—
583#391—51no—
584#391—51no—
585#390—51no—
586#390—51no—
587#389—51no—
588#389—51no—
589#389—51no—
590#389—51no—
591#389—51no—
592#389—51no—
593#389—51no—
594#389—51no—
595#389—51no—
596#389—51no—
597#389—51no—
598#389—51no—
599#389—51no—
600#389—51no—
601#389—51no—
602#389—51no—
603#389—51no—
604#389—51no—
605#389—51no—
606#389—51no—
607#389—51no—
608#388—51no—
609#388—51no—
610#388—51no—
611#388—51no—
612#388—51no—
613#388—51no—
614#388C2×D511yescharacteristic
615#388C2×D511yescharacteristic
616#387—51no—
617#387—51no—
618#387—51no—
619#387—51no—
620#387—51no—
621#387—51no—
622#387—51no—
623#387—51no—
624#387—51no—
625#387—51no—
626#387—51no—
627#387—51no—
628#387—51no—
629#387—51no—
630#387—51no—
631#387—51no—
632#387—51no—
633#387—51no—
634#387—51no—
635#387—51no—
636#387—51no—
637#387—51no—
638#387C2×D511yescharacteristic
639#387C2×D511yescharacteristic
640#386—51no—
641#386—51no—
642#386C2×D511yescharacteristic
643#386C2×D511yescharacteristic
644#385—51no—
645#385—51no—
646#385—51no—
647#385—51no—
648#385—51no—
649#385—51no—
650#385—51no—
651#385—51no—
652#385—51no—
653#385—51no—
654#385—51no—
655#385—51no—
656#385C2×D511yescharacteristic
657#385C2×D511yescharacteristic
658#384—51no—
659#384—51no—
660#383C2×D511yescharacteristic
661#382—51no—
662#382—51no—
663#382C2×D511yescharacteristic
664#381—51no—
665#381—51no—
666#381C2×D511yescharacteristic
667#380—51no—
668#380—51no—
669#380—51no—
670#380—51no—
671#380—51no—
672#380—51no—
673#380C2×D511yescharacteristic
674C4×C4⋊C4—51no—
675C4×C4⋊C4—51no—
676C4×C22⋊C4—51no—
677C4×C22⋊C4—51no—
678C4×C22⋊C4C2×D511yescharacteristic
679#376—51no—
680#376—51no—
681C2×#95C2×D511yescharacteristic
682C23×C5—21no—
683C23×C5—21no—
684C23×C5—21no—
685C23×C5—21no—
686C23×C5—21no—
687C23×C5—21no—
688C23×C5—21no—
689C23×C5—21no—
690C23×C5—21no—
691C23×C5—21no—
692C23×C5—21no—
693C23×C5—21no—
694C23×C5C22×Q812yes—
695C23×C5C22×Q812yes—
696C23×C5C2511yescharacteristic
697C5×D4—44no—
698C2×C4×C5—21no—
699C2×C4×C5—21no—
700C2×C4×C5—21no—
701C2×C4×C5—21no—
702C2×C4×C5—21no—
703C2×C4×C5—21no—
704C2×C4×C5—21no—
705C2×C4×C5—21no—
706C2×C4×C5—21no—
707C2×C4×C5—21no—
708C2×C4×C5—21no—
709C2×C4×C5—21no—
710C2×C4×C5—21no—
711C2×C4×C5—21no—
712C2×C4×C5—21no—
713C2×C4×C5—21no—
714C2×C4×C5—21no—
715C2×C4×C5—21no—
716C2×C4×C5—21no—
717C2×C4×C5—21no—
718C2×C4×C5—21no—
719C2×C4×C5—21no—
720C2×C4×C5—21no—
721C2×C4×C5—21no—
722C2×C4×C5—21no—
723C2×C4×C5—21no—
724C2×C4×C5—21no—
725C2×C4×C5—21no—
726C2×C4×C5—21no—
727C2×C4×C5—21no—
728C2×C4×C5—21no—
729C2×C4×C5—21no—
730C2×C4×C5—21no—
731C2×C4×C5—21no—
732C2×C4×C5—44no—
733C2×C4×C5—44no—
734C2×C4×C5—82no—
735C2×C4×C5—82no—
736C2×C4×C5C22×Q812yes—
737C2×C4×C5C22×Q812yes—
738C2×C4×C5C22×Q812yes—
739C2×C4×C5C22×Q812yes—
740C2×C4×C5C22×Q812yes—
741C2×Dic5—21no—
742C2×Dic5—21no—
743C2×Dic5—21no—
744C2×Dic5—21no—
745C2×Dic5—21no—
746C2×Dic5—21no—
747C2×Dic5—21no—
748C2×Dic5—21no—
749C2×Dic5—21no—
750C2×Dic5—21no—
751C2×Dic5—21no—
752C2×Dic5—21no—
753C2×Dic5—21no—
754C2×Dic5—21no—
755C2×Dic5—21no—
756C2×Dic5—21no—
757C2×Dic5—21no—
758C2×Dic5—21no—
759C2×Dic5—21no—
760C2×Dic5—21no—
761C2×Dic5—21no—
762C2×Dic5—21no—
763C2×Dic5—21no—
764C2×Dic5—21no—
765C2×Dic5—21no—
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—44no—
789C2×Dic5—44no—
790C2×Dic5H(5,𝔽2)12yes—
791Dic10—82no—
792C22×Q8—51no—
793C22×D4C22×D511yescharacteristic
794C23×C4—51no—
795C23×C4—51no—
796C23×C4C22×D511yescharacteristic
797C23×C4C22×D511yescharacteristic
798C23×C4C22×D511yescharacteristic
799C23×C4C22×D511yescharacteristic
800#125—202no—
801#125—202no—
802C22⋊Q8—202no—
803C22⋊Q8—202no—
804C4×D4Dic1018yescomplemented
805#117—202no—
806C2×C4⋊C4—51no—
807C2×C4⋊C4—51no—
808C2×C4⋊C4—51no—
809C2×C4⋊C4—51no—
810C2×C4⋊C4—51no—
811C2×C4⋊C4—51no—
812C2×C4⋊C4—51no—
813C2×C4⋊C4—51no—
814C2×C4⋊C4—51no—
815C2×C4⋊C4—51no—
816C2×C4⋊C4—51no—
817C2×C4⋊C4—51no—
818C2×C4⋊C4—51no—
819C2×C4⋊C4—51no—
820C2×C4⋊C4—51no—
821C2×C4⋊C4—51no—
822C2×C4⋊C4—51no—
823C2×C4⋊C4—51no—
824C2×C4⋊C4—51no—
825C2×C4⋊C4—51no—
826C2×C4⋊C4—51no—
827C2×C4⋊C4—51no—
828C2×C4⋊C4—51no—
829C2×C4⋊C4—51no—
830C2×C4⋊C4—51no—
831C2×C4⋊C4—51no—
832C2×C4⋊C4—51no—
833C2×C4⋊C4—51no—
834C2×C4⋊C4—51no—
835C2×C4⋊C4—51no—
836C2×C4⋊C4—51no—
837C2×C4⋊C4—51no—
838C2×C4⋊C4—51no—
839C2×C4⋊C4—51no—
840C2×C4⋊C4—51no—
841C2×C4⋊C4—51no—
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⋊C4C22×D511yescharacteristic
858C2×C4⋊C4C22×D511yescharacteristic
859C2×C4⋊C4C22×D511yescharacteristic
860C2×C4⋊C4C22×D511yescharacteristic
861C2×C4⋊C4C22×D511yescharacteristic
862C2×C22⋊C4—51no—
863C2×C22⋊C4—51no—
864C2×C22⋊C4—51no—
865C2×C22⋊C4—51no—
866C2×C22⋊C4—51no—
867C2×C22⋊C4—51no—
868C2×C22⋊C4—51no—
869C2×C22⋊C4—51no—
870C2×C22⋊C4—51no—
871C2×C22⋊C4—51no—
872C2×C22⋊C4—51no—
873C2×C22⋊C4—51no—
874C2×C22⋊C4—51no—
875C2×C22⋊C4—51no—
876C2×C22⋊C4C22×D511yescharacteristic
877C2×C22⋊C4C22×D511yescharacteristic
878C2×C22⋊C4C22×D511yescharacteristic
879C2×C22⋊C4C22×D511yescharacteristic
880C2×C22⋊C4C22×D511yescharacteristic
881C2×C22⋊C4C22×D511yescharacteristic
882C2×C22⋊C4C22×D511yescharacteristic
883C2×C22⋊C4C22×D511yescharacteristic
884C2×C42—51no—
885C2×C42—51no—
886C2×C42—51no—
887C2×C42—51no—
888C2×C42—51no—
889C2×C42—51no—
890C2×C42—51no—
891C2×C42—51no—
892C2×C42—51no—
893C2×C42—51no—
894C2×C42—202no—
895C2×C42C22×D511yescharacteristic
896C2×C42C22×D511yescharacteristic
897C2×C42C22×D511yescharacteristic
898#95—51no—
899#95—51no—
900#95—51no—
901#95—51no—
902#95—51no—
903#95—51no—
904#95—51no—
905#95—51no—
906#95—51no—
907#95—51no—
908#95—51no—
909#95—51no—
910#95—51no—
911#95—51no—
912#95—51no—
913#95—51no—
914#95—51no—
915#95—51no—
916#95—51no—
917#95—51no—
918#95—51no—
919#95—51no—
920#95—51no—
921#95—51no—
922#95—51no—
923#95—51no—
924#95—51no—
925#95—51no—
926#95—51no—
927#95—51no—
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#95C22×D511yescharacteristic
941#95C22×D511yescharacteristic
942#95C22×D511yescharacteristic
943#95C22×D511yescharacteristic
944#95C22×D511yescharacteristic
945#95C22×D511yescharacteristic
946#95C22×D511yescharacteristic
947#95C22×D511yescharacteristic
948#95C22×D511yescharacteristic
949#95C22×D511yescharacteristic
950#95C22×D511yescharacteristic
951#95C22×D511yescharacteristic
952#95C22×D511yescharacteristic
953#95C22×D511yescharacteristic
954C22×C5—22no—
955C22×C5—22no—
956C22×C5—22no—
957C22×C5—22no—
958C22×C5—22no—
959C22×C5—22no—
960C22×C5—41no—
961C22×C5—41no—
962C22×C5—41no—
963C22×C5—41no—
964C22×C5—41no—
965C22×C5—41no—
966C22×C5—41no—
967C22×C5—41no—
968C22×C5C23×Q811yescharacteristic
969C22×C5C2×H(5,𝔽2)11yescharacteristic
970C22×C5#58511yescharacteristic
971C22×C5#58511yescharacteristic
972C22×C5#58511yescharacteristic
973C22×C5#58511yescharacteristic
974C22×C5#58511yescharacteristic
975C4×C5—22no—
976C4×C5—22no—
977C4×C5—22no—
978C4×C5—22no—
979C4×C5—22no—
980C4×C5—41no—
981C4×C5—41no—
982C4×C5—41no—
983C4×C5—41no—
984C4×C5—41no—
985C4×C5—41no—
986C4×C5—41no—
987C4×C5—41no—
988Dic5—22no—
989Dic5—41no—
990Dic5—41no—
991Dic5—41no—
992Dic5—41no—
993Dic5—41no—
994Dic5—41no—
995Dic5—41no—
996Dic5—41no—
997Dic5—41no—
998Dic5—41no—
999Dic5—41no—
1000Dic5—41no—
1001Dic5—41no—
1002Dic5—41no—
1003Dic5—41no—
1004C24C23×D511yescharacteristic
1005C24C23×D511yescharacteristic
1006C2×Q8—102no—
1007C2×Q8—201no—
1008C2×Q8—201no—
1009C2×D4—41no—
1010C2×D4—41no—
1011C2×D4C2×Dic1014yes—
1012C22×C4—41no—
1013C22×C4—41no—
1014C22×C4—41no—
1015C22×C4—41no—
1016C22×C4—41no—
1017C22×C4—41no—
1018C22×C4—41no—
1019C22×C4—41no—
1020C22×C4—41no—
1021C22×C4—41no—
1022C22×C4—51no—
1023C22×C4—51no—
1024C22×C4—51no—
1025C22×C4—51no—
1026C22×C4—51no—
1027C22×C4—51no—
1028C22×C4—51no—
1029C22×C4—51no—
1030C22×C4—51no—
1031C22×C4—51no—
1032C22×C4—51no—
1033C22×C4—51no—
1034C22×C4—51no—
1035C22×C4—51no—
1036C22×C4—51no—
1037C22×C4—51no—
1038C22×C4—102no—
1039C22×C4—201no—
1040C22×C4—201no—
1041C22×C4—201no—
1042C22×C4—201no—
1043C22×C4—201no—
1044C22×C4C2×Dic1014yes—
1045C22×C4C2×Dic1014yes—
1046C22×C4C23×D511yescharacteristic
1047C22×C4C23×D511yescharacteristic
1048C22×C4C23×D511yescharacteristic
1049C22×C4C23×D511yescharacteristic
1050C22×C4C23×D511yescharacteristic
1051C22×C4C23×D511yescharacteristic
1052C22×C4C23×D511yescharacteristic
1053C22×C4C23×D511yescharacteristic
1054C22×C4C23×D511yescharacteristic
1055C22×C4C23×D511yescharacteristic
1056C22×C4C23×D511yescharacteristic
1057C22×C4C23×D511yescharacteristic
1058C22×C4C23×D511yescharacteristic
1059C4⋊C4—41no—
1060C4⋊C4—41no—
1061C4⋊C4—41no—
1062C4⋊C4—41no—
1063C4⋊C4—102no—
1064C4⋊C4—102no—
1065C4⋊C4—102no—
1066C4⋊C4—102no—
1067C4⋊C4—201no—
1068C4⋊C4—201no—
1069C4⋊C4—201no—
1070C4⋊C4—201no—
1071C4⋊C4—201no—
1072C4⋊C4—201no—
1073C4⋊C4—201no—
1074C4⋊C4—201no—
1075C4⋊C4—201no—
1076C4⋊C4—201no—
1077C4⋊C4—201no—
1078C4⋊C4—201no—
1079C4⋊C4—201no—
1080C4⋊C4—201no—
1081C4⋊C4—201no—
1082C4⋊C4—201no—
1083C4⋊C4—201no—
1084C4⋊C4—201no—
1085C4⋊C4—201no—
1086C4⋊C4—201no—
1087C4⋊C4—201no—
1088C4⋊C4—201no—
1089C4⋊C4—201no—
1090C4⋊C4—201no—
1091C4⋊C4—201no—
1092C4⋊C4—201no—
1093C4⋊C4—201no—
1094C4⋊C4—201no—
1095C4⋊C4—201no—
1096C4⋊C4—201no—
1097C4⋊C4—201no—
1098C4⋊C4—201no—
1099C4⋊C4—201no—
1100C4⋊C4—201no—
1101C4⋊C4—201no—
1102C4⋊C4—201no—
1103C4⋊C4—201no—
1104C4⋊C4—201no—
1105C4⋊C4—201no—
1106C4⋊C4—201no—
1107C4⋊C4—201no—
1108C4⋊C4—201no—
1109C4⋊C4—201no—
1110C4⋊C4—201no—
1111C4⋊C4—201no—
1112C4⋊C4—201no—
1113C4⋊C4—201no—
1114C4⋊C4C2×Dic1014yes—
1115C22⋊C4—41no—
1116C22⋊C4—41no—
1117C22⋊C4—41no—
1118C22⋊C4—41no—
1119C22⋊C4—41no—
1120C22⋊C4—41no—
1121C22⋊C4—102no—
1122C22⋊C4—201no—
1123C22⋊C4—201no—
1124C22⋊C4—201no—
1125C22⋊C4—201no—
1126C22⋊C4—201no—
1127C22⋊C4—201no—
1128C22⋊C4—201no—
1129C22⋊C4—201no—
1130C22⋊C4—201no—
1131C22⋊C4—201no—
1132C22⋊C4—201no—
1133C22⋊C4—201no—
1134C22⋊C4—201no—
1135C22⋊C4C2×Dic1014yes—
1136C22⋊C4C2×Dic1014yes—
1137C42—41no—
1138C42—41no—
1139C42—102no—
1140C42—102no—
1141C42—201no—
1142C42—201no—
1143C42—201no—
1144C42—201no—
1145C42—201no—
1146C42—201no—
1147C42—201no—
1148C42—201no—
1149C42C2×Dic1014yes—
1150C2×C5—42no—
1151C2×C5—42no—
1152C2×C5#345811yescharacteristic
1153C2×C5#350111yescharacteristic
1154C2×C5#350411yescharacteristic
1155C2×C5#353311yescharacteristic
1156C2×C5#353911yescharacteristic
1157C2×C5#356611yescharacteristic
1158C2×C5#356711yescharacteristic
1159C23—21no—
1160C23—21no—
1161C23—21no—
1162C23—21no—
1163C23—21no—
1164C23—21no—
1165C23—21no—
1166C23—21no—
1167C23—21no—
1168C23—21no—
1169C23—21no—
1170C23—21no—
1171C23C22×Dic1012yes—
1172C23C22×Dic1012yes—
1173C23C24×D511yescharacteristic
1174Q8—402no—
1175D4—44no—
1176C2×C4—21no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—21no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—21no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—21no—
1206C2×C4—21no—
1207C2×C4—21no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—44no—
1211C2×C4—44no—
1212C2×C4—52no—
1213C2×C4—82no—
1214C2×C4—82no—
1215C2×C4—101no—
1216C2×C4—101no—
1217C2×C4—101no—
1218C2×C4—101no—
1219C2×C4—101no—
1220C2×C4—101no—
1221C2×C4—101no—
1222C2×C4—101no—
1223C2×C4—101no—
1224C2×C4—101no—
1225C2×C4—101no—
1226C2×C4—101no—
1227C2×C4—101no—
1228C2×C4—101no—
1229C2×C4—101no—
1230C2×C4—101no—
1231C2×C4—101no—
1232C2×C4—101no—
1233C2×C4—101no—
1234C2×C4—101no—
1235C2×C4—101no—
1236C2×C4—101no—
1237C2×C4—101no—
1238C2×C4—101no—
1239C2×C4—101no—
1240C2×C4—101no—
1241C2×C4—101no—
1242C2×C4—101no—
1243C2×C4—101no—
1244C2×C4—101no—
1245C2×C4—101no—
1246C2×C4—101no—
1247C2×C4—101no—
1248C2×C4—101no—
1249C2×C4—101no—
1250C2×C4—101no—
1251C2×C4—101no—
1252C2×C4—101no—
1253C2×C4—101no—
1254C2×C4—101no—
1255C2×C4—101no—
1256C2×C4—101no—
1257C2×C4—101no—
1258C2×C4—101no—
1259C2×C4—101no—
1260C2×C4—101no—
1261C2×C4—101no—
1262C2×C4—204no—
1263C2×C4—204no—
1264C2×C4C22×Dic1012yes—
1265C2×C4C22×Dic1012yes—
1266C2×C4C22×Dic1012yes—
1267C2×C4C22×Dic1012yes—
1268C2×C4C22×Dic1012yes—
1269C5#3675611yescharacteristic, complemented, Sylow
1270C22—22no—
1271C22—22no—
1272C22—22no—
1273C22—22no—
1274C22—22no—
1275C22—22no—
1276C22—41no—
1277C22—41no—
1278C22—41no—
1279C22—41no—
1280C22—41no—
1281C22—41no—
1282C22—41no—
1283C22—41no—
1284C22C23×Dic1011yescharacteristic
1285C22#6628311yescharacteristic
1286C22#6628311yescharacteristic
1287C22D5×H(5,𝔽2)11yescharacteristic
1288C22#6628511yescharacteristic
1289C22#6628511yescharacteristic
1290C22#6628711yescharacteristic
1291C4—22no—
1292C4—22no—
1293C4—22no—
1294C4—22no—
1295C4—22no—
1296C4—41no—
1297C4—41no—
1298C4—41no—
1299C4—41no—
1300C4—41no—
1301C4—41no—
1302C4—41no—
1303C4—41no—
1304C4—102no—
1305C4—201no—
1306C4—201no—
1307C4—201no—
1308C4—201no—
1309C4—201no—
1310C4—201no—
1311C4—201no—
1312C4—201no—
1313C4—201no—
1314C4—201no—
1315C4—201no—
1316C4—201no—
1317C4—201no—
1318C4—201no—
1319C4—201no—
1320C2—42no—
1321C2—42no—
1322C2#1061762611yescharacteristic
1323C2#1061776111yescharacteristic
1324C2#1061779111yescharacteristic
1325C2#1061831011yescharacteristic
1326C2#1061832011yescharacteristic
1327C2#1061833711yescharacteristic
1328C2#1061835211yescharacteristic
subgroupG/H
center, FrattiniC23C24×D5
commutator, socle, cosocleC23×C5C25
FittingC5×#2318C2
prime radicalC22×C5×D4C23
hypercenter#2318D5
hypocenterC5#36756
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C23 ◁ #2318

Complements

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

NH ≅ G/Ntype
4. #10607542C2semidirect
5. #10607518C2semidirect
6. #10607484C2semidirect
7. #10607428C2semidirect
8. #10607005C2semidirect
9. #10606980C2semidirect
10. #10606918C2semidirect
11. #10606907C2semidirect
16. #10606308C2semidirect
17. #10606290C2semidirect
18. #10606290C2semidirect
19. #10606254C2semidirect
20. #10606007C2semidirect
21. #10606007C2semidirect
22. #10605923C2semidirect
23. #10605917C2semidirect
24. #10605848C2semidirect
25. #10605824C2semidirect
26. #10605729C2semidirect
27. #10605690C2semidirect
28. #10605285C2semidirect
29. #10605225C2semidirect
30. #10605090C2semidirect
31. #10605081C2semidirect
196. C4×C5×D4Q8semidirect
804. C4×D4Dic10semidirect
1269. C5#36756semidirect

Maximal subgroups

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

subgroupindex
C5×#23182
#106140562
#106140492
#106075422
#106075182
#106074842
#106074282
#106070052
#106069802
#106069182
#106069072
#106065892
#106065882
#106065692
#106065612
#106063082
#106062902
#106062542
#106060072
#106059232
#106059172
#106058482
#106058242
#106057292
#106056902
#106052852
#106052252
#106050902
#106050812
#367565