Finite Group Databasebeta

← #12104203

Subgroups — #12104203

Order 1280.

826 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2314C211yesmaximal, characteristic
2#10613954C211yesmaximal, characteristic
3C2×#65289C211yesmaximal, characteristic
4#10600361C211yesmaximal, characteristic, complemented
5#10600360C211yesmaximal, characteristic, complemented
6#10600333C211yesmaximal, characteristic, complemented
7#10600333C211yesmaximal, characteristic, complemented
8#10600299C211yesmaximal, characteristic
9#10600299C211yesmaximal, characteristic
10#10600298C211yesmaximal, characteristic
11#10600297C211yesmaximal, characteristic
12#10600274C211yesmaximal, characteristic, complemented
13#10600274C211yesmaximal, characteristic, complemented
14C4×#3939C211yesmaximal, characteristic, complemented
15C4×#3940C211yesmaximal, characteristic, complemented
16C2×C5×#117C2211yescharacteristic
17C2×#4072C2211yescharacteristic
18C22×C4⋊Dic5C2211yescharacteristic
19C5×#388—21no—
20C5×#388—21no—
21C5×#387—21no—
22C5×#387—21no—
23C5×#384C2211yescharacteristic
24C5×#382C2211yescharacteristic
25C5×#380C2211yescharacteristic
26C5×#380C2211yescharacteristic
27C4×C5×C4⋊C4C2211yescharacteristic
28C4×C5×C4⋊C4C2211yescharacteristic
29C2×C22⋊#168C2211yescharacteristic
30C2×C22⋊#168C2211yescharacteristic
31#65289C418yescomplemented
32C4⋊C4×Dic5—21no—
33C4⋊C4×Dic5—21no—
34C2×#3940C2211yescharacteristic
35C2×#3940C2211yescharacteristic
36C2×#3940C2211yescharacteristic
37C2×#3940C2211yescharacteristic
38C2×#3939C2211yescharacteristic
39C2×#3939C2211yescharacteristic
40C2×#3939C2211yescharacteristic
41C2×#3939C2211yescharacteristic
42C22⋊C4×Dic5—21no—
43C22⋊C4×Dic5—21no—
44C4×C4⋊Dic5C2211yescharacteristic
45C4×C4⋊Dic5C2211yescharacteristic
46C4×C4⋊Dic5C2211yescharacteristic
47C4×C4⋊Dic5C2211yescharacteristic
48C2×C4⋊#168C2211yescharacteristic
49C2×C4⋊#168C2211yescharacteristic
50C2×#3935C2211yescharacteristic
51C2×C4×#168C2211yescharacteristic
52#64749C2211yescharacteristic
53#64749C2211yescharacteristic
54#64749C2211yescharacteristic
55#64749C2211yescharacteristic
56#64749C2211yescharacteristic
57#64749C2211yescharacteristic
58#64749C2211yescharacteristic
59#64749C2211yescharacteristic
60#21367—51nomaximal, Sylow
61C23×C4×C5C2311yescharacteristic
62C23×Dic5—21no—
63C5×#117C2×C414yes—
64C5×#117Q814yes—
65C2×C5×C4⋊C4—21no—
66C2×C5×C4⋊C4—21no—
67C2×C5×C4⋊C4D411yescharacteristic
68C2×C5×C4⋊C4D411yescharacteristic
69C2×C5×C4⋊C4C2311yescharacteristic
70C2×C5×C4⋊C4C2311yescharacteristic
71C2×C5×C4⋊C4C2311yescharacteristic
72C2×C5×C4⋊C4C2311yescharacteristic
73C2×C5×C22⋊C4—21no—
74C2×C5×C22⋊C4—21no—
75C2×C5×C22⋊C4D411yescharacteristic
76C2×C5×C22⋊C4D411yescharacteristic
77C2×C42×C5—21no—
78C2×C42×C5—21no—
79C2×C42×C5C2311yescharacteristic
80C2×C42×C5C2311yescharacteristic
81C2×C22⋊Dic5—21no—
82#4072—22no—
83#4072—22no—
84C2×C4⋊Dic5—21no—
85C2×C4⋊Dic5—22no—
86C2×C4⋊Dic5—22no—
87C2×C4⋊Dic5C2311yescharacteristic
88C2×C4⋊Dic5C2311yescharacteristic
89C2×C4⋊Dic5C2311yescharacteristic
90C2×C4⋊Dic5C2311yescharacteristic
91C2×C4×Dic5—21no—
92C2×C4×Dic5—21no—
93C2×C4×Dic5—21no—
94C2×C4×Dic5—21no—
95C2×C4×Dic5—21no—
96C22×#168C2311yescharacteristic
97C22×#168C2311yescharacteristic
98C22×#168C2311yescharacteristic
99C22×#168C2311yescharacteristic
100C5×#95—21no—
101C5×#95—21no—
102C5×#95—21no—
103C5×#95—21no—
104C5×#95—21no—
105C5×#95—21no—
106#3963—21no—
107#3963—21no—
108#3963—21no—
109#3963—21no—
110C22⋊#168C2×C414yes—
111C22⋊#168C2×C414yes—
112#3940—22no—
113#3940—22no—
114#3940—22no—
115#3940—22no—
116#3939—22no—
117#3939—22no—
118#3939—22no—
119#3939—22no—
120C4⋊#168C2×C414yescomplemented
121C4⋊#168C2×C414yescomplemented
122#3935C2×C414yescomplemented
123C4×#168C2×C414yescomplemented
124C2×#433—51no—
125#2314D511yescharacteristic
126#2274—51no—
127#1949—51no—
128#1949—51no—
129#1948—51no—
130#1947—51no—
131#1854—51no—
132#1854—51no—
133#1853—51no—
134#1852—51no—
135#1776—51no—
136#1776—51no—
137C4×#107—51no—
138C4×#106—51no—
139C24×C5C2×D411yescharacteristic
140C22×C4×C5—21no—
141C22×C4×C5—21no—
142C22×C4×C5—21no—
143C22×C4×C5—21no—
144C22×C4×C5—21no—
145C22×C4×C5—21no—
146C22×C4×C5—21no—
147C22×C4×C5—21no—
148C22×C4×C5C22×C412yes—
149C22×C4×C5C2×D411yescharacteristic
150C22×C4×C5C2×D411yescharacteristic
151C22×C4×C5C2×D411yescharacteristic
152C22×C4×C5C2×D411yescharacteristic
153C22×C4×C5C2×D411yescharacteristic
154C22×C4×C5C2×Q812yes—
155C22×C4×C5C2411yescharacteristic
156C22×Dic5—21no—
157C22×Dic5—21no—
158C22×Dic5—21no—
159C22×Dic5—21no—
160C22×Dic5—24no—
161C22×Dic5—81no—
162C22×Dic5—81no—
163C5×C4⋊C4—21no—
164C5×C4⋊C4—21no—
165C5×C4⋊C4—21no—
166C5×C4⋊C4—21no—
167C5×C4⋊C4—21no—
168C5×C4⋊C4—21no—
169C5×C4⋊C4—21no—
170C5×C4⋊C4—21no—
171C5×C4⋊C4—81no—
172C5×C4⋊C4—81no—
173C5×C4⋊C4C4⋊C414yes—
174C5×C4⋊C4C4⋊C414yes—
175C5×C22⋊C4—81no—
176C5×C22⋊C4—81no—
177C5×C22⋊C4C4⋊C414yes—
178C5×C22⋊C4C4⋊C414yes—
179C42×C5—81no—
180C42×C5—81no—
181C42×C5C22×C412yes—
182C42×C5C22×C412yes—
183C42×C5C2×Q812yes—
184C42×C5C2×Q812yes—
185C22⋊Dic5—24no—
186C4⋊Dic5—24no—
187C4⋊Dic5—21no—
188C4⋊Dic5—21no—
189C4⋊Dic5—21no—
190C4⋊Dic5—21no—
191C4⋊Dic5#4112yes—
192C4⋊Dic5#4112yes—
193C4⋊Dic5#4112yes—
194C4⋊Dic5#4112yes—
195C4×Dic5—24no—
196C4×Dic5—81no—
197C4×Dic5—81no—
198C4×Dic5—81no—
199C4×Dic5—81no—
200C2×#168—21no—
201C2×#168—21no—
202C2×#168—21no—
203C2×#168—21no—
204C2×#168—21no—
205C2×#168—21no—
206C2×#168—21no—
207C2×#168—21no—
208C2×#168C22×C412yes—
209C2×#168C22×C412yes—
210C2×#168C22×C412yes—
211C2×#168C22×C412yes—
212C2×#117—51no—
213C2×#117C2×D511yescharacteristic
214C22×C4⋊C4—51no—
215#433—58no—
216C2×#107—51no—
217C2×#107—51no—
218C2×#107—51no—
219C2×#107—51no—
220C2×#106—51no—
221C2×#106—51no—
222C2×#106—51no—
223C2×#106—51no—
224C2×C4⋊C8—51no—
225C2×C4⋊C8—51no—
226C2×C22⋊C8—51no—
227C2×C22⋊C8—51no—
228C2×#97—51no—
229C2×C4×C8—51no—
230#388—21no—
231#388—21no—
232#387—21no—
233#387—21no—
234#384C2×D511yescharacteristic
235#382C2×D511yescharacteristic
236#380C2×D511yescharacteristic
237#380C2×D511yescharacteristic
238C4×C4⋊C4—51no—
239C4×C4⋊C4—51no—
240C4×C4⋊C4—51no—
241C4×C4⋊C4—51no—
242C4×C4⋊C4—101no—
243C4×C4⋊C4—101no—
244C4×C4⋊C4C2×D511yescharacteristic
245C4×C4⋊C4C2×D511yescharacteristic
246C4×C22⋊C4—101no—
247C4×C22⋊C4—101no—
248#340—51no—
249#340—51no—
250#340—51no—
251#340—51no—
252#340—51no—
253#340—51no—
254#340—51no—
255#340—51no—
256C23×C5—21no—
257C23×C5—21no—
258C23×C5—21no—
259C23×C5—21no—
260C23×C5—21no—
261C23×C5—21no—
262C23×C5C2×C4⋊C412yes—
263C23×C5C22×D411yescharacteristic
264C2×C4×C5—21no—
265C2×C4×C5—21no—
266C2×C4×C5—21no—
267C2×C4×C5—21no—
268C2×C4×C5—21no—
269C2×C4×C5—21no—
270C2×C4×C5—21no—
271C2×C4×C5—21no—
272C2×C4×C5—21no—
273C2×C4×C5—21no—
274C2×C4×C5—22no—
275C2×C4×C5—22no—
276C2×C4×C5—22no—
277C2×C4×C5—22no—
278C2×C4×C5—41no—
279C2×C4×C5—41no—
280C2×C4×C5—41no—
281C2×C4×C5—41no—
282C2×C4×C5—41no—
283C2×C4×C5—41no—
284C2×C4×C5—41no—
285C2×C4×C5—41no—
286C2×C4×C5—41no—
287C2×C4×C5—41no—
288C2×C4×C5—41no—
289C2×C4×C5—41no—
290C2×C4×C5C2×C4⋊C412yes—
291C2×C4×C5C2×C4⋊C412yes—
292C2×C4×C5C2×C4⋊C412yes—
293C2×C4×C5C2×C4⋊C412yes—
294C2×C4×C5C2×C4⋊C412yes—
295C2×C4×C5C23×C411yescharacteristic
296C2×C4×C5C22×Q811yescharacteristic
297C2×C4×C5C2×#4111yescharacteristic
298C2×C4×C5C2×#4111yescharacteristic
299C2×C4×C5C2×#4111yescharacteristic
300C2×C4×C5C2×#4111yescharacteristic
301C2×Dic5—22no—
302C2×Dic5—22no—
303C2×Dic5—22no—
304C2×Dic5—22no—
305C2×Dic5—41no—
306C2×Dic5—41no—
307C2×Dic5—41no—
308C2×Dic5—41no—
309C2×Dic5—41no—
310C2×Dic5—41no—
311C2×Dic5—41no—
312C2×Dic5—41no—
313C2×Dic5—84no—
314#168—22no—
315#168—22no—
316#168—22no—
317#168—22no—
318C23×C4—101no—
319C23×C4C22×D511yescharacteristic
320C22×C8—51no—
321C22×C8—51no—
322C22×C8—51no—
323C22×C8—51no—
324#117—102no—
325#117—102no—
326#117Dic1014yes—
327#117C4×D514yes—
328C2×C4⋊C4—21no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4—51no—
331C2×C4⋊C4—51no—
332C2×C4⋊C4—51no—
333C2×C4⋊C4—51no—
334C2×C4⋊C4—102no—
335C2×C4⋊C4—102no—
336C2×C4⋊C4—101no—
337C2×C4⋊C4C22⋊D511yescharacteristic
338C2×C4⋊C4C22⋊D511yescharacteristic
339C2×C4⋊C4C22×D511yescharacteristic
340C2×C4⋊C4C22×D511yescharacteristic
341C2×C4⋊C4C22×D511yescharacteristic
342C2×C4⋊C4C22×D511yescharacteristic
343C2×C22⋊C4—21no—
344C2×C22⋊C4—21no—
345C2×C22⋊C4—101no—
346C2×C22⋊C4C22⋊D511yescharacteristic
347C2×C22⋊C4C22⋊D511yescharacteristic
348C2×C42—21no—
349C2×C42—21no—
350C2×C42—101no—
351C2×C42—101no—
352C2×C42—101no—
353C2×C42—101no—
354C2×C42—101no—
355C2×C42C22×D511yescharacteristic
356C2×C42C22×D511yescharacteristic
357#107—102no—
358#107—102no—
359#107—102no—
360#107—102no—
361#106—102no—
362#106—102no—
363#106—102no—
364#106—102no—
365C4⋊C8—54no—
366C4⋊C8—54no—
367C22⋊C8—54no—
368C22⋊C8—54no—
369#97—54no—
370C4×C8—54no—
371#95—21no—
372#95—21no—
373#95—21no—
374#95—21no—
375#95—21no—
376#95—21no—
377#95—101no—
378#95—101no—
379#95—101no—
380#95—101no—
381C22×C5—22no—
382C22×C5—22no—
383C22×C5—22no—
384C22×C5—41no—
385C22×C5—41no—
386C22×C5—41no—
387C22×C5—41no—
388C22×C5C22×C4⋊C411yescharacteristic
389C22×C5#52511yescharacteristic
390C22×C5#52511yescharacteristic
391C22×C5#57611yescharacteristic
392C22×C5#57711yescharacteristic
393C22×C5#57711yescharacteristic
394C22×C5#57811yescharacteristic
395C4×C5—22no—
396C4×C5—22no—
397C4×C5—22no—
398C4×C5—22no—
399C4×C5—22no—
400C4×C5—81no—
401C4×C5—81no—
402C4×C5—81no—
403C4×C5—81no—
404C4×C5C4×#4111yescharacteristic
405C4×C5C4×#4111yescharacteristic
406C4×C5#53311yescharacteristic
407C4×C5#53311yescharacteristic
408Dic5—42no—
409Dic5—42no—
410Dic5—42no—
411Dic5—42no—
412C24C2×C22⋊D511yescharacteristic
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—101no—
422C22×C4—101no—
423C22×C4—101no—
424C22×C4—101no—
425C22×C4—104no—
426C22×C4—401no—
427C22×C4—401no—
428C22×C4C2×Dic1012yes—
429C22×C4C2×C4×D512yes—
430C22×C4C2×C22⋊D511yescharacteristic
431C22×C4C2×C22⋊D511yescharacteristic
432C22×C4C2×C22⋊D511yescharacteristic
433C22×C4C2×C22⋊D511yescharacteristic
434C22×C4C2×C22⋊D511yescharacteristic
435C22×C4C23×D511yescharacteristic
436C2×C8—52no—
437C2×C8—52no—
438C2×C8—52no—
439C2×C8—52no—
440C2×C8—101no—
441C2×C8—101no—
442C2×C8—101no—
443C2×C8—101no—
444C2×C8—101no—
445C2×C8—101no—
446C2×C8—101no—
447C2×C8—101no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—52no—
457C4⋊C4—52no—
458C4⋊C4—52no—
459C4⋊C4—52no—
460C4⋊C4—81no—
461C4⋊C4—81no—
462C4⋊C4—104no—
463C4⋊C4—101no—
464C4⋊C4—101no—
465C4⋊C4—101no—
466C4⋊C4—101no—
467C4⋊C4#68314yes—
468C4⋊C4#68314yes—
469C22⋊C4—81no—
470C22⋊C4—81no—
471C22⋊C4—104no—
472C22⋊C4#68314yes—
473C22⋊C4#68314yes—
474C42—81no—
475C42—81no—
476C42—104no—
477C42—401no—
478C42—401no—
479C42—401no—
480C42—401no—
481C42C2×Dic1012yes—
482C42C2×Dic1012yes—
483C42C2×C4×D512yes—
484C42C2×C4×D512yes—
485C2×C5—42no—
486C2×C5#229611yescharacteristic
487C2×C5#291211yescharacteristic
488C2×C5#291311yescharacteristic
489C2×C5#311811yescharacteristic
490C2×C5#311911yescharacteristic
491C2×C5#312011yescharacteristic
492C2×C5#312111yescharacteristic
493C23—21no—
494C23—21no—
495C23—21no—
496C23—21no—
497C23—21no—
498C23—21no—
499C23C2×#68312yes—
500C23C22×C22⋊D511yescharacteristic
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—102no—
528C2×C4—102no—
529C2×C4—102no—
530C2×C4—102no—
531C2×C4—201no—
532C2×C4—201no—
533C2×C4—201no—
534C2×C4—201no—
535C2×C4—201no—
536C2×C4—201no—
537C2×C4—201no—
538C2×C4—201no—
539C2×C4—404no—
540C2×C4C2×#68312yes—
541C2×C4C2×#68312yes—
542C2×C4C2×#68312yes—
543C2×C4C2×#68312yes—
544C2×C4C2×#68312yes—
545C2×C4C22×Dic1011yescharacteristic
546C2×C4C22×C4×D511yescharacteristic
547C2×C4D5×#4111yescharacteristic
548C2×C4D5×#4111yescharacteristic
549C2×C4D5×#4111yescharacteristic
550C2×C4D5×#4111yescharacteristic
551C8—102no—
552C8—102no—
553C8—102no—
554C8—102no—
555C5#2136711yescharacteristic, complemented, Sylow
556C22—22no—
557C22—22no—
558C22—22no—
559C22—41no—
560C22—41no—
561C22—41no—
562C22—41no—
563C22C22×#68311yescharacteristic
564C22#6616211yescharacteristic
565C22#6616211yescharacteristic
566C22#6616911yescharacteristic
567C22#6617011yescharacteristic
568C22#6617111yescharacteristic
569C22#6617211yescharacteristic
570C4—22no—
571C4—22no—
572C4—22no—
573C4—22no—
574C4—22no—
575C4—81no—
576C4—81no—
577C4—81no—
578C4—81no—
579C4—202no—
580C4—202no—
581C4—202no—
582C4—202no—
583C4#6585111yescharacteristic
584C4#6585111yescharacteristic
585C4#6585611yescharacteristic
586C4#6585611yescharacteristic
587C2—42no—
588C2#1061395711yescharacteristic
589C2#1061429211yescharacteristic
590C2#1061429311yescharacteristic
591C2#1061516511yescharacteristic
592C2#1061517711yescharacteristic
593C2#1061519111yescharacteristic
594C2#1061519811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D5
commutatorC2×C4×C5C23×C4
FrattiniC22×C4C23×D5
FittingC5×#2314C2
socleC23×C5C22×D4
prime radicalC24×C5C2×D4
cosocleC22×C4×C5C24
hypercenter#2314D5
hypocenterC5#21367
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2314

Complements

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

NH ≅ G/Ntype
4. #10600361C2semidirect
5. #10600360C2semidirect
6. #10600333C2semidirect
7. #10600333C2semidirect
12. #10600274C2semidirect
13. #10600274C2semidirect
14. C4×#3939C2semidirect
15. C4×#3940C2semidirect
31. #65289C4semidirect
120. C4⋊#168C2×C4semidirect
121. C4⋊#168C2×C4semidirect
122. #3935C2×C4semidirect
123. C4×#168C2×C4semidirect
555. C5#21367semidirect

Maximal subgroups

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

subgroupindex
C5×#23142
#106139542
C2×#652892
#106003612
#106003602
#106003332
#106002992
#106002982
#106002972
#106002742
C4×#39392
C4×#39402
#213675