Finite Group Databasebeta

← #12305968

Subgroups — #12305968

Order 1280.

1484 conjugacy classes of subgroups.

The subgroup lattice has 1314 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2821C211yesmaximal, characteristic, complemented
2#10614999C211yesmaximal, characteristic, complemented
3Dic5×C4⋊Q8C211yesmaximal, characteristic, complemented
4#10614850C211yesmaximal, characteristic
5Dic5×#126C211yesmaximal, characteristic, complemented
6#10610062C211yesmaximal, characteristic, complemented
7#10610060C211yesmaximal, characteristic, complemented
8#10609864C211yesmaximal, characteristic, complemented
9#10609863C211yesmaximal, characteristic, complemented
10#10609827C211yesmaximal, characteristic
11#10609826C211yesmaximal, characteristic, complemented
12#10609749C211yesmaximal, characteristic, complemented
13#10609748C211yesmaximal, characteristic
14#10609745C211yesmaximal, characteristic, complemented
15#10609669C211yesmaximal, characteristic, complemented
16#10609472C211yesmaximal, characteristic, complemented
17#10609470C211yesmaximal, characteristic, complemented
18#10609467C211yesmaximal, characteristic
19#10609395C211yesmaximal, characteristic, complemented
20#10609192C211yesmaximal, characteristic, complemented
21#10609190C211yesmaximal, characteristic
22#10609009C211yesmaximal, characteristic, complemented
23#10608974C211yesmaximal, characteristic, complemented
24#10608902C211yesmaximal, characteristic, complemented
25#10608901C211yesmaximal, characteristic, complemented
26#10608588C211yesmaximal, characteristic
27#10608587C211yesmaximal, characteristic, complemented
28#10608510C211yesmaximal, characteristic
29#10608509C211yesmaximal, characteristic, complemented
30#10606023C211yesmaximal, characteristic, complemented
31#10605990C211yesmaximal, characteristic, complemented
32C2×C5×C4⋊Q8C2211yescharacteristic
33C2×C5×#126C2211yescharacteristic
34C2×Q8×Dic5C2211yescharacteristic
35C2×Q8×Dic5C2211yescharacteristic
36C2×#4038C2211yescharacteristic
37C2×#4033C2211yescharacteristic
38C2×#4027C2211yescharacteristic
39C2×#4023C2211yescharacteristic
40C2×#4022C2211yescharacteristic
41C5×#400C2211yescharacteristic
42C5×#400C2211yescharacteristic
43C5×#399C2211yescharacteristic
44C5×#399C2211yescharacteristic
45C5×#398C2211yescharacteristic
46C5×#398C2211yescharacteristic
47C5×#397C2211yescharacteristic
48C5×#397C2211yescharacteristic
49C5×#395C2211yescharacteristic
50C5×#395C2211yescharacteristic
51C5×#393C2211yescharacteristic
52C5×#393C2211yescharacteristic
53C5×#383C2211yescharacteristic
54#65520C2211yescharacteristic
55#65520C2211yescharacteristic
56#65519C2211yescharacteristic
57#65519C2211yescharacteristic
58#65518C2211yescharacteristic
59#65518C2211yescharacteristic
60#65283C2211yescharacteristic
61#65283C2211yescharacteristic
62#65283C2211yescharacteristic
63#65283C2211yescharacteristic
64#65283C2211yescharacteristic
65#65282C2211yescharacteristic
66#65282C2211yescharacteristic
67#65282C2211yescharacteristic
68#65281C2211yescharacteristic
69#65281C2211yescharacteristic
70#65275C2211yescharacteristic
71#65275C2211yescharacteristic
72#65274C2211yescharacteristic
73#65274C2211yescharacteristic
74#65274C2211yescharacteristic
75#65274C2211yescharacteristic
76#65273C2211yescharacteristic
77#65273C2211yescharacteristic
78#65273C2211yescharacteristic
79#65273C2211yescharacteristic
80#65273C2211yescharacteristic
81#65272C2211yescharacteristic
82#65272C2211yescharacteristic
83#65271C2211yescharacteristic
84#65271C2211yescharacteristic
85#65271C2211yescharacteristic
86#65271C2211yescharacteristic
87#65270C2211yescharacteristic
88#65270C2211yescharacteristic
89#65270C2211yescharacteristic
90#65269C2211yescharacteristic
91#65269C2211yescharacteristic
92#65269C2211yescharacteristic
93C4⋊C4×Dic5C2211yescharacteristic
94C4⋊C4×Dic5C2211yescharacteristic
95C4⋊C4×Dic5C2211yescharacteristic
96C4⋊C4×Dic5C2211yescharacteristic
97C4⋊C4×Dic5C2211yescharacteristic
98C4⋊C4×Dic5C2211yescharacteristic
99C4⋊C4×Dic5C2211yescharacteristic
100C4⋊C4×Dic5C2211yescharacteristic
101C4⋊C4×Dic5C2211yescharacteristic
102#65250C2211yescharacteristic
103#65250C2211yescharacteristic
104#65250C2211yescharacteristic
105#65250C2211yescharacteristic
106#65250C2211yescharacteristic
107#65248C2211yescharacteristic
108#65242C2211yescharacteristic
109#65242C2211yescharacteristic
110#65241C2211yescharacteristic
111#65241C2211yescharacteristic
112#65241C2211yescharacteristic
113#65240C2211yescharacteristic
114#65240C2211yescharacteristic
115#65240C2211yescharacteristic
116#65238C2211yescharacteristic
117#65237C2211yescharacteristic
118#65237C2211yescharacteristic
119#65237C2211yescharacteristic
120#65237C2211yescharacteristic
121#65237C2211yescharacteristic
122#65236C2211yescharacteristic
123C22⋊C4×Dic5C2211yescharacteristic
124C22⋊C4×Dic5C2211yescharacteristic
125C22⋊C4×Dic5C2211yescharacteristic
126C22⋊C4×Dic5C2211yescharacteristic
127C22⋊C4×Dic5C2211yescharacteristic
128#65226C2211yescharacteristic
129#65224C2211yescharacteristic
130C42×Dic5C2211yescharacteristic
131#64966C2211yescharacteristic
132#64964C2211yescharacteristic
133#64964C2211yescharacteristic
134#64963C2211yescharacteristic
135#64963C2211yescharacteristic
136#64962C2211yescharacteristic
137#64958C2211yescharacteristic
138#64958C2211yescharacteristic
139#64958C2211yescharacteristic
140#64955C2211yescharacteristic
141#64955C2211yescharacteristic
142#64955C2211yescharacteristic
143#64955C2211yescharacteristic
144#64955C2211yescharacteristic
145C5⋊#401C2211yescharacteristic
146C5⋊#401C2211yescharacteristic
147#64950C2211yescharacteristic
148#64950C2211yescharacteristic
149#64950C2211yescharacteristic
150#64950C2211yescharacteristic
151#64950C2211yescharacteristic
152#64949C2211yescharacteristic
153#64949C2211yescharacteristic
154#64949C2211yescharacteristic
155#64949C2211yescharacteristic
156#64949C2211yescharacteristic
157#64949C2211yescharacteristic
158#64949C2211yescharacteristic
159#64948C2211yescharacteristic
160#64948C2211yescharacteristic
161#64948C2211yescharacteristic
162#64947C2211yescharacteristic
163#64947C2211yescharacteristic
164#64947C2211yescharacteristic
165#64947C2211yescharacteristic
166#64946C2211yescharacteristic
167#64946C2211yescharacteristic
168#64946C2211yescharacteristic
169#64946C2211yescharacteristic
170#64946C2211yescharacteristic
171#64945C2211yescharacteristic
172#64945C2211yescharacteristic
173#64945C2211yescharacteristic
174#64945C2211yescharacteristic
175#64941C2211yescharacteristic
176#64941C2211yescharacteristic
177#64941C2211yescharacteristic
178#64938C2211yescharacteristic
179#64938C2211yescharacteristic
180#64938C2211yescharacteristic
181#64938C2211yescharacteristic
182#64938C2211yescharacteristic
183#64938C2211yescharacteristic
184#64938C2211yescharacteristic
185#64937C2211yescharacteristic
186#64937C2211yescharacteristic
187#36697—51nomaximal, Sylow
188C22×C5×Q8C2311yescharacteristic
189C22×C5×Q8C2311yescharacteristic
190C22×C22⋊D5C2311yescharacteristic
191C23×Dic5C2311yescharacteristic
192C22×C4×D5C2311yescharacteristic
193C22×Dic10C2311yescharacteristic
194C5×C4⋊Q8—24no—
195C5×#126—24no—
196C2×C5×C4⋊C4C2311yescharacteristic
197C2×C5×C4⋊C4C2311yescharacteristic
198C2×C5×C4⋊C4C2311yescharacteristic
199C2×C5×C4⋊C4C2311yescharacteristic
200C2×C5×C4⋊C4C2311yescharacteristic
201C2×C5×C4⋊C4C2311yescharacteristic
202C2×C5×C4⋊C4C2311yescharacteristic
203C2×C5×C4⋊C4C2311yescharacteristic
204C2×C5×C4⋊C4C2311yescharacteristic
205C2×C5×C4⋊C4C2311yescharacteristic
206C2×C5×C4⋊C4C2311yescharacteristic
207C2×C5×C22⋊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×C42×C5C2311yescharacteristic
215C2×C22⋊Dic5C2311yescharacteristic
216C2×C22⋊Dic5C2311yescharacteristic
217C2×C22⋊Dic5C2311yescharacteristic
218C2×C22⋊Dic5C2311yescharacteristic
219C2×C22⋊Dic5C2311yescharacteristic
220C2×C22⋊Dic5C2311yescharacteristic
221Q8×Dic5—42no—
222Q8×Dic5—42no—
223C2×#685C2311yescharacteristic
224C2×#685C2311yescharacteristic
225C2×#685C2311yescharacteristic
226C2×#685C2311yescharacteristic
227C2×#685C2311yescharacteristic
228C2×#685C2311yescharacteristic
229C2×#685C2311yescharacteristic
230C2×#685C2311yescharacteristic
231C2×#685C2311yescharacteristic
232C2×#685C2311yescharacteristic
233C2×#685C2311yescharacteristic
234C2×#685C2311yescharacteristic
235C2×#685C2311yescharacteristic
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×#683C2311yescharacteristic
253C2×#683C2311yescharacteristic
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×C4×Dic5C2311yescharacteristic
272C2×C4×Dic5C2311yescharacteristic
273C2×C4×Dic5C2311yescharacteristic
274C2×C4×Dic5C2311yescharacteristic
275C2×C4×Dic5C2311yescharacteristic
276C2×C4×Dic5C2311yescharacteristic
277C2×C4×Dic5C2311yescharacteristic
278C2×C4×Dic5C2311yescharacteristic
279C2×C4×Dic5C2311yescharacteristic
280C2×C4×Dic5C2311yescharacteristic
281C2×C4×Dic5C2311yescharacteristic
282C2×C4×Dic5C2311yescharacteristic
283C2×C4×Dic5C2311yescharacteristic
284C2×C4×Dic5C2311yescharacteristic
285C2×C4×Dic5C2311yescharacteristic
286C2×C4×Dic5C2311yescharacteristic
287#4038—42no—
288#4033—42no—
289#4027—42no—
290#4023—42no—
291#4022—24no—
292C5×#95C2311yescharacteristic
293C5×#95C2311yescharacteristic
294C5×#95C2311yescharacteristic
295C5×#95C2311yescharacteristic
296C5×#95C2311yescharacteristic
297C5×#95C2311yescharacteristic
298C5×#95C2311yescharacteristic
299C5×#95C2311yescharacteristic
300C5×#95C2311yescharacteristic
301C5×#95C2311yescharacteristic
302C5×#95C2311yescharacteristic
303C5×#95C2311yescharacteristic
304C5×#95C2311yescharacteristic
305C5×#95C2311yescharacteristic
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#2843—51no—
353#2839—51no—
354#2839—51no—
355#2838—51no—
356#2838—51no—
357#2837—51no—
358#2837—51no—
359#2836—51no—
360#2836—51no—
361#2833—51no—
362#2832—51no—
363#2831—51no—
364#2831—51no—
365#2823—51no—
366#2821—51no—
367#2821D511yescharacteristic, complemented
368#2402—51no—
369#2402—51no—
370#2401—51no—
371#2401—51no—
372#2399—51no—
373#2398—51no—
374#2396—51no—
375#2396—51no—
376#2396—51no—
377#2396—51no—
378#2395—51no—
379#2395—51no—
380C4×C4⋊Q8—51no—
381C4×#126—51no—
382C4×#126—51no—
383C24×C5C2411yescharacteristic
384C23×D5C2411yescharacteristic
385C2×C5×Q8—22no—
386C2×C5×Q8—22no—
387C2×C5×Q8—41no—
388C2×C5×Q8—41no—
389C2×C5×Q8—41no—
390C2×C5×Q8—41no—
391C22×C4×C5C2411yescharacteristic
392C22×C4×C5C2411yescharacteristic
393C22×C4×C5C2411yescharacteristic
394C22×C4×C5C2411yescharacteristic
395C22×C4×C5C2411yescharacteristic
396C22×C4×C5C2411yescharacteristic
397C22×C4×C5C2411yescharacteristic
398C22×C4×C5C2411yescharacteristic
399C22×C4×C5C2411yescharacteristic
400C22×C4×C5C2411yescharacteristic
401C22×C4×C5C2411yescharacteristic
402C22×C4×C5C2411yescharacteristic
403C22×C4×C5C2411yescharacteristic
404C22×C4×C5C2411yescharacteristic
405C2×C22⋊D5—41no—
406C2×C22⋊D5—41no—
407C2×C22⋊D5—41no—
408C22×Dic5—22no—
409C22×Dic5—22no—
410C22×Dic5—22no—
411C22×Dic5C2411yescharacteristic
412C22×Dic5C2411yescharacteristic
413C22×Dic5C2411yescharacteristic
414C22×Dic5C2411yescharacteristic
415C22×Dic5C2411yescharacteristic
416C22×Dic5C2411yescharacteristic
417C22×Dic5C2411yescharacteristic
418C22×Dic5C2411yescharacteristic
419C22×Dic5C2411yescharacteristic
420C22×Dic5C2411yescharacteristic
421C22×Dic5C2411yescharacteristic
422C22×Dic5C2411yescharacteristic
423C22×Dic5C2411yescharacteristic
424C22×Dic5C2411yescharacteristic
425C22×Dic5C2411yescharacteristic
426C2×C4×D5—22no—
427C2×C4×D5—22no—
428C2×C4×D5—22no—
429C2×Dic10—41no—
430C2×Dic10—41no—
431C2×Dic10—41no—
432C5×C4⋊C4—22no—
433C5×C4⋊C4—22no—
434C5×C4⋊C4—22no—
435C5×C4⋊C4—22no—
436C5×C4⋊C4—22no—
437C5×C4⋊C4—22no—
438C5×C4⋊C4—22no—
439C5×C4⋊C4—41no—
440C5×C4⋊C4—41no—
441C5×C4⋊C4—41no—
442C5×C4⋊C4—41no—
443C5×C22⋊C4—22no—
444C5×C22⋊C4—22no—
445C5×C22⋊C4—22no—
446C5×C22⋊C4—41no—
447C5×C22⋊C4—41no—
448C5×C22⋊C4—41no—
449C5×C22⋊C4—41no—
450C42×C5#4114yes—
451C22⋊Dic5—41no—
452C22⋊Dic5—41no—
453C22⋊Dic5—41no—
454C22⋊Dic5—41no—
455C22⋊Dic5—41no—
456C22⋊Dic5—41no—
457#685—22no—
458#685—22no—
459#685—22no—
460#685—41no—
461#685—41no—
462#685—41no—
463#685—41no—
464#685—41no—
465#685—41no—
466#685—41no—
467#685—41no—
468#685—41no—
469#685—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—
486#683—22no—
487#683—22no—
488#683—22no—
489#683—41no—
490#683—41no—
491#683—41no—
492#683—41no—
493#683—41no—
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—
505C4×Dic5—22no—
506C4×Dic5—22no—
507C4×Dic5—22no—
508C4×Dic5—22no—
509C4×Dic5—22no—
510C4×Dic5—22no—
511C4×Dic5—22no—
512C4×Dic5—22no—
513C4×Dic5—22no—
514C4×Dic5—22no—
515C4×Dic5—22no—
516C4×Dic5—22no—
517C4×Dic5—22no—
518C4×Dic5—41no—
519C4×Dic5—41no—
520C4×Dic5—41no—
521C2×C4⋊Q8C2×D511yescharacteristic
522C2×#126—51no—
523C2×#126C2×D511yescharacteristic
524C2×C4×Q8—51no—
525C2×C4×Q8—51no—
526C2×C4×Q8—51no—
527C2×C4×D4—51no—
528C2×#117—51no—
529C2×#117—51no—
530#401—51no—
531#401—51no—
532#400—51no—
533#400—51no—
534#400—51no—
535#400—51no—
536#400—51no—
537#400—51no—
538#400—51no—
539#400—51no—
540#400—51no—
541#400—51no—
542#400—51no—
543#400—51no—
544#400—51no—
545#400—51no—
546#400—51no—
547#400—51no—
548#400—51no—
549#400—51no—
550#400—51no—
551#400—51no—
552#400C2×D511yescharacteristic
553#400C2×D511yescharacteristic
554#399—51no—
555#399—51no—
556#399—51no—
557#399—51no—
558#399C2×D511yescharacteristic
559#399C2×D511yescharacteristic
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#398—51no—
571#398—51no—
572#398—51no—
573#398—51no—
574#398—51no—
575#398—51no—
576#398—51no—
577#398—51no—
578#398—51no—
579#398—51no—
580#398C2×D511yescharacteristic
581#398C2×D511yescharacteristic
582#397—51no—
583#397—51no—
584#397—51no—
585#397—51no—
586#397—51no—
587#397—51no—
588#397—51no—
589#397—51no—
590#397—51no—
591#397—51no—
592#397—51no—
593#397—51no—
594#397C2×D511yescharacteristic
595#397C2×D511yescharacteristic
596#396—51no—
597#396—51no—
598#396—51no—
599#396—51no—
600#396—51no—
601#396—51no—
602#396—51no—
603#396—51no—
604#396—51no—
605#396—51no—
606#395—51no—
607#395—51no—
608#395—51no—
609#395—51no—
610#395—51no—
611#395—51no—
612#395C2×D511yescharacteristic
613#395C2×D511yescharacteristic
614#394—51no—
615#394—51no—
616#394—51no—
617#394—51no—
618#394—51no—
619#394—51no—
620#393—51no—
621#393—51no—
622#393—51no—
623#393—51no—
624#393C2×D511yescharacteristic
625#393C2×D511yescharacteristic
626#391—51no—
627#391—51no—
628#389—51no—
629#389—51no—
630#389—51no—
631#389—51no—
632#388—51no—
633#388—51no—
634#388—51no—
635#388—51no—
636#388—51no—
637#388—51no—
638#387—51no—
639#387—51no—
640#387—51no—
641#387—51no—
642#387—51no—
643#387—51no—
644#384—51no—
645#383—51no—
646#383C2×D511yescharacteristic
647C4×C4⋊C4—51no—
648C4×C4⋊C4—51no—
649C4×C4⋊C4—51no—
650C4×C4⋊C4—51no—
651C4×C4⋊C4—51no—
652C4×C4⋊C4—51no—
653C4×C4⋊C4—51no—
654C4×C4⋊C4—51no—
655C4×C4⋊C4—51no—
656C4×C4⋊C4—51no—
657C4×C4⋊C4—51no—
658C4×C4⋊C4—51no—
659C4×C4⋊C4—51no—
660C4×C4⋊C4—51no—
661C4×C4⋊C4—51no—
662C4×C4⋊C4—51no—
663C4×C22⋊C4—51no—
664C4×C22⋊C4—51no—
665C4×C22⋊C4—51no—
666C4×C22⋊C4—51no—
667C4×C22⋊C4—51no—
668C4×C22⋊C4—51no—
669C4×C22⋊C4—51no—
670C4×C22⋊C4—51no—
671C4×C22⋊C4—51no—
672C4×C22⋊C4—51no—
673#376—51no—
674#376—51no—
675C43—51no—
676C23×C5—21no—
677C23×C5—21no—
678C23×C5—21no—
679C23×C5—21no—
680C23×C5—21no—
681C23×C5—21no—
682C23×C5—21no—
683C23×C5C2511yescharacteristic
684C22×D5—21no—
685C22×D5—21no—
686C22×D5—21no—
687C22×D5—21no—
688C22×D5—21no—
689C22×D5—21no—
690C22×D5—21no—
691C5×Q8—44no—
692C5×Q8—44no—
693C2×C4×C5—21no—
694C2×C4×C5—21no—
695C2×C4×C5—21no—
696C2×C4×C5—21no—
697C2×C4×C5—21no—
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×C5C2×#4112yes—
733C2×C4×C5C2×#4112yes—
734C2×C4×C5C2×#4112yes—
735C22⋊D5—44no—
736C2×Dic5—21no—
737C2×Dic5—21no—
738C2×Dic5—21no—
739C2×Dic5—21no—
740C2×Dic5—21no—
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—44no—
779C2×Dic5H(5,𝔽2)12yes—
780C2×Dic52−1+412yes—
781C2×Dic52−1+412yes—
782C4×D5—44no—
783Dic10—44no—
784C22×Q8—51no—
785C22×Q8C22×D511yescharacteristic
786C22×Q8C22×D511yescharacteristic
787C22×D4—51no—
788C23×C4—51no—
789C23×C4—51no—
790C4⋊Q8—24no—
791#126—24no—
792#126—104no—
793C4×Q8—202no—
794C4×Q8—202no—
795C4×Q8—202no—
796C4×D4—202no—
797#117—202no—
798#117—202no—
799C2×C4⋊C4—51no—
800C2×C4⋊C4—51no—
801C2×C4⋊C4—51no—
802C2×C4⋊C4—51no—
803C2×C4⋊C4—51no—
804C2×C4⋊C4—51no—
805C2×C4⋊C4—51no—
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⋊C4C22×D511yescharacteristic
835C2×C4⋊C4C22×D511yescharacteristic
836C2×C4⋊C4C22×D511yescharacteristic
837C2×C4⋊C4C22×D511yescharacteristic
838C2×C4⋊C4C22×D511yescharacteristic
839C2×C4⋊C4C22×D511yescharacteristic
840C2×C4⋊C4C22×D511yescharacteristic
841C2×C4⋊C4C22×D511yescharacteristic
842C2×C4⋊C4C22×D511yescharacteristic
843C2×C4⋊C4C22×D511yescharacteristic
844C2×C4⋊C4C22×D511yescharacteristic
845C2×C22⋊C4—51no—
846C2×C22⋊C4—51no—
847C2×C22⋊C4—51no—
848C2×C22⋊C4—51no—
849C2×C22⋊C4—51no—
850C2×C22⋊C4—51no—
851C2×C22⋊C4—51no—
852C2×C22⋊C4—51no—
853C2×C22⋊C4—51no—
854C2×C22⋊C4—51no—
855C2×C22⋊C4—51no—
856C2×C22⋊C4—51no—
857C2×C22⋊C4—51no—
858C2×C22⋊C4—51no—
859C2×C22⋊C4—51no—
860C2×C22⋊C4—51no—
861C2×C22⋊C4—51no—
862C2×C22⋊C4—51no—
863C2×C22⋊C4—51no—
864C2×C22⋊C4C22×D511yescharacteristic
865C2×C22⋊C4C22×D511yescharacteristic
866C2×C22⋊C4C22×D511yescharacteristic
867C2×C22⋊C4C22×D511yescharacteristic
868C2×C22⋊C4C22×D511yescharacteristic
869C2×C22⋊C4C22×D511yescharacteristic
870C2×C22⋊C4C22×D511yescharacteristic
871C2×C42—51no—
872C2×C42—51no—
873C2×C42—51no—
874C2×C42—51no—
875C2×C42—51no—
876C2×C42—51no—
877C2×C42—51no—
878C2×C42—51no—
879C2×C42—51no—
880C2×C42—51no—
881C2×C42—51no—
882C2×C42—51no—
883C2×C42—51no—
884C2×C42—51no—
885C2×C42—51no—
886C2×C42—51no—
887C2×C42C22×D511yescharacteristic
888#95—51no—
889#95—51no—
890#95—51no—
891#95—51no—
892#95—51no—
893#95—51no—
894#95—51no—
895#95—51no—
896#95—51no—
897#95—51no—
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#95C22×D511yescharacteristic
935#95C22×D511yescharacteristic
936#95C22×D511yescharacteristic
937#95C22×D511yescharacteristic
938#95C22×D511yescharacteristic
939#95C22×D511yescharacteristic
940#95C22×D511yescharacteristic
941#95C22×D511yescharacteristic
942#95C22×D511yescharacteristic
943#95C22×D511yescharacteristic
944#95C22×D511yescharacteristic
945#95C22×D511yescharacteristic
946#95C22×D511yescharacteristic
947#95C22×D511yescharacteristic
948C22×C5—41no—
949C22×C5—41no—
950C22×C5—41no—
951C22×C5—41no—
952C22×C5—41no—
953C22×C5—41no—
954C22×C5—41no—
955C22×C5C22×#4111yescharacteristic
956C22×C5C2×H(5,𝔽2)11yescharacteristic
957C22×C5C2×2−1+411yescharacteristic
958C22×C5C2×2−1+411yescharacteristic
959C22×C5#58511yescharacteristic
960C22×C5#58511yescharacteristic
961C22×C5#58511yescharacteristic
962C2×D5—41no—
963C2×D5—41no—
964C2×D5—41no—
965C2×D5—41no—
966C2×D5—41no—
967C2×D5—41no—
968C2×D5—41no—
969C4×C5—22no—
970C4×C5—22no—
971C4×C5—22no—
972C4×C5—41no—
973C4×C5—41no—
974C4×C5—41no—
975C4×C5—41no—
976C4×C5—41no—
977C4×C5—41no—
978C4×C5—41no—
979C4×C5—41no—
980C4×C5—41no—
981C4×C5—41no—
982C4×C5—41no—
983Dic5—41no—
984Dic5—41no—
985Dic5—41no—
986Dic5—41no—
987Dic5—41no—
988Dic5—41no—
989Dic5—41no—
990Dic5—41no—
991Dic5—41no—
992Dic5—41no—
993Dic5—41no—
994Dic5—41no—
995Dic5—41no—
996Dic5—41no—
997Dic5#56314yes—
998C24—51no—
999C24C23×D511yescharacteristic
1000C2×Q8—22no—
1001C2×Q8—22no—
1002C2×Q8—41no—
1003C2×Q8—41no—
1004C2×Q8—41no—
1005C2×Q8—41no—
1006C2×Q8—201no—
1007C2×Q8—201no—
1008C2×Q8—201no—
1009C2×D4—201no—
1010C2×D4—201no—
1011C2×D4—201no—
1012C22×C4—51no—
1013C22×C4—51no—
1014C22×C4—51no—
1015C22×C4—51no—
1016C22×C4—51no—
1017C22×C4—51no—
1018C22×C4—51no—
1019C22×C4—51no—
1020C22×C4—51no—
1021C22×C4—51no—
1022C22×C4—51no—
1023C22×C4—51no—
1024C22×C4—51no—
1025C22×C4—51no—
1026C22×C4—51no—
1027C22×C4—102no—
1028C22×C4—102no—
1029C22×C4—102no—
1030C22×C4—102no—
1031C22×C4—102no—
1032C22×C4—102no—
1033C22×C4C23×D511yescharacteristic
1034C22×C4C23×D511yescharacteristic
1035C22×C4C23×D511yescharacteristic
1036C22×C4C23×D511yescharacteristic
1037C22×C4C23×D511yescharacteristic
1038C22×C4C23×D511yescharacteristic
1039C22×C4C23×D511yescharacteristic
1040C22×C4C23×D511yescharacteristic
1041C22×C4C23×D511yescharacteristic
1042C22×C4C23×D511yescharacteristic
1043C22×C4C23×D511yescharacteristic
1044C22×C4C23×D511yescharacteristic
1045C22×C4C23×D511yescharacteristic
1046C22×C4C23×D511yescharacteristic
1047C4⋊C4—22no—
1048C4⋊C4—22no—
1049C4⋊C4—22no—
1050C4⋊C4—22no—
1051C4⋊C4—22no—
1052C4⋊C4—22no—
1053C4⋊C4—22no—
1054C4⋊C4—41no—
1055C4⋊C4—41no—
1056C4⋊C4—41no—
1057C4⋊C4—41no—
1058C4⋊C4—102no—
1059C4⋊C4—102no—
1060C4⋊C4—102no—
1061C4⋊C4—201no—
1062C4⋊C4—201no—
1063C4⋊C4—201no—
1064C4⋊C4—201no—
1065C4⋊C4—201no—
1066C4⋊C4—201no—
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—
1093C22⋊C4—22no—
1094C22⋊C4—22no—
1095C22⋊C4—22no—
1096C22⋊C4—41no—
1097C22⋊C4—41no—
1098C22⋊C4—41no—
1099C22⋊C4—41no—
1100C22⋊C4—102no—
1101C22⋊C4—102no—
1102C22⋊C4—102no—
1103C22⋊C4—201no—
1104C22⋊C4—201no—
1105C22⋊C4—201no—
1106C22⋊C4—201no—
1107C22⋊C4—201no—
1108C22⋊C4—201no—
1109C22⋊C4—201no—
1110C22⋊C4—201no—
1111C22⋊C4—201no—
1112C22⋊C4—201no—
1113C22⋊C4—201no—
1114C22⋊C4—201no—
1115C22⋊C4—201no—
1116C22⋊C4—201no—
1117C22⋊C4—201no—
1118C22⋊C4—201no—
1119C42—102no—
1120C42—102no—
1121C42—102no—
1122C42—102no—
1123C42—102no—
1124C42—102no—
1125C42—102no—
1126C42—102no—
1127C42—102no—
1128C42—102no—
1129C42—102no—
1130C42—102no—
1131C42—102no—
1132C42—201no—
1133C42—201no—
1134C42—201no—
1135C42#71114yes—
1136C2×C5—81no—
1137C2×C5#346011yescharacteristic
1138C2×C5#346111yescharacteristic
1139C2×C5#346111yescharacteristic
1140C2×C5C2×#56311yescharacteristic
1141C2×C5#352911yescharacteristic
1142C2×C5#353111yescharacteristic
1143C2×C5#353111yescharacteristic
1144D5—81no—
1145C23—21no—
1146C23—21no—
1147C23—21no—
1148C23—21no—
1149C23—21no—
1150C23—21no—
1151C23—21no—
1152C23—101no—
1153C23—101no—
1154C23—101no—
1155C23—101no—
1156C23—101no—
1157C23—101no—
1158C23—101no—
1159C23C24×D511yescharacteristic
1160Q8—44no—
1161Q8—44no—
1162Q8—204no—
1163D4—204no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—21no—
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—52no—
1204C2×C4—52no—
1205C2×C4—52no—
1206C2×C4—101no—
1207C2×C4—101no—
1208C2×C4—101no—
1209C2×C4—101no—
1210C2×C4—101no—
1211C2×C4—101no—
1212C2×C4—101no—
1213C2×C4—101no—
1214C2×C4—101no—
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—204no—
1249C2×C4—204no—
1250C2×C4C2×#71112yes—
1251C2×C4C2×#71112yes—
1252C2×C4C2×#71112yes—
1253C5#3669711yescharacteristic, complemented, Sylow
1254C22—41no—
1255C22—41no—
1256C22—41no—
1257C22—41no—
1258C22—41no—
1259C22—41no—
1260C22—41no—
1261C22—201no—
1262C22—201no—
1263C22—201no—
1264C22—201no—
1265C22—201no—
1266C22—201no—
1267C22—201no—
1268C22C22×#71111yescharacteristic
1269C22D5×H(5,𝔽2)11yescharacteristic
1270C22#6628511yescharacteristic
1271C22D5×2−1+411yescharacteristic
1272C22D5×2−1+411yescharacteristic
1273C22#6628711yescharacteristic
1274C22#6628711yescharacteristic
1275C4—22no—
1276C4—22no—
1277C4—22no—
1278C4—41no—
1279C4—41no—
1280C4—41no—
1281C4—41no—
1282C4—41no—
1283C4—41no—
1284C4—41no—
1285C4—41no—
1286C4—41no—
1287C4—41no—
1288C4—41no—
1289C4—54no—
1290C4—201no—
1291C4—201no—
1292C4—201no—
1293C4—201no—
1294C4—201no—
1295C4—201no—
1296C4—201no—
1297C4—201no—
1298C4—201no—
1299C4—201no—
1300C4—201no—
1301C4—201no—
1302C4—201no—
1303C4—201no—
1304C2—81no—
1305C2—401no—
1306C2#1061821511yescharacteristic
1307C2#1061824011yescharacteristic
1308C2#1061824011yescharacteristic
1309C2#1061901611yescharacteristic
1310C2#1061901711yescharacteristic
1311C2#1061901711yescharacteristic
1312C2D5×#56311yescharacteristic
subgroupG/H
center, FrattiniC23C24×D5
commutator, socle, cosocleC23×C5C25
FittingC5×#2821C2
prime radicalC22×C22⋊D5C23
hypercenter#2821D5
hypocenterC5#36697
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C23 ◁ #2821

Complements

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

NH ≅ G/Ntype
1. C5×#2821C2semidirect
2. #10614999C2semidirect
3. Dic5×C4⋊Q8C2semidirect
5. Dic5×#126C2semidirect
6. #10610062C2semidirect
7. #10610060C2semidirect
8. #10609864C2semidirect
9. #10609863C2semidirect
11. #10609826C2semidirect
12. #10609749C2semidirect
14. #10609745C2semidirect
15. #10609669C2semidirect
16. #10609472C2semidirect
17. #10609470C2semidirect
19. #10609395C2semidirect
20. #10609192C2semidirect
22. #10609009C2semidirect
23. #10608974C2semidirect
24. #10608902C2semidirect
25. #10608901C2semidirect
27. #10608587C2semidirect
29. #10608509C2semidirect
30. #10606023C2semidirect
31. #10605990C2semidirect
367. #2821D5semidirect
1253. C5#36697semidirect

Maximal subgroups

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

subgroupindex
C5×#28212
#106149992
Dic5×C4⋊Q82
#106148502
Dic5×#1262
#106100622
#106100602
#106098642
#106098632
#106098272
#106098262
#106097492
#106097482
#106097452
#106096692
#106094722
#106094702
#106094672
#106093952
#106091922
#106091902
#106090092
#106089742
#106089022
#106089012
#106085882
#106085872
#106085102
#106085092
#106060232
#106059902
#366975