Finite Group Databasebeta

← #12104174

Subgroups — #12104174

Order 1280.

938 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65124C211yesmaximal, characteristic
2#10605878C211yesmaximal, characteristic
3C4×D5×C4⋊C4C211yesmaximal, characteristic
4C5×#1949C211yesmaximal, characteristic, complemented
5#10601425C211yesmaximal, characteristic
6#10601398C211yesmaximal, characteristic, complemented
7#10601372C211yesmaximal, characteristic
8#10601346C211yesmaximal, characteristic, complemented
9#10601248C211yesmaximal, characteristic, complemented
10#10600333C211yesmaximal, characteristic, complemented
11#10600261C211yesmaximal, characteristic, complemented
12#10599668C211yesmaximal, characteristic
13#10599667C211yesmaximal, characteristic
14#10599579C211yesmaximal, characteristic, complemented
15#10599579C211yesmaximal, characteristic, complemented
16C2×D5×C4⋊C4C2211yescharacteristic
17C2×D5×C4⋊C4C2211yescharacteristic
18C2×C42×D5—21no—
19C2×C42×D5C2211yescharacteristic
20C2×C5×#107C2211yescharacteristic
21C2×C5×#106C2211yescharacteristic
22C2×C5×C4⋊C8C2211yescharacteristic
23C5×#382C2211yescharacteristic
24C4×C5×C4⋊C4C2211yescharacteristic
25C2×#3952C2211yescharacteristic
26C2×#3952C2211yescharacteristic
27C2×#3950C2211yescharacteristic
28C2×#3949C2211yescharacteristic
29C2×#3947C2211yescharacteristic
30C2×#3947C2211yescharacteristic
31#65276C2211yescharacteristic
32#65276C2211yescharacteristic
33C4⋊C4×Dic5C2211yescharacteristic
34C4⋊C4×Dic5C2211yescharacteristic
35C4⋊C4×Dic5C2211yescharacteristic
36C4⋊C4×Dic5C2211yescharacteristic
37C2×#3940C2211yescharacteristic
38C2×#3940C2211yescharacteristic
39C2×#3939C2211yescharacteristic
40C2×#3939C2211yescharacteristic
41#65225C2211yescharacteristic
42C4×C4⋊Dic5C2211yescharacteristic
43C4×#683—21no—
44C2×C4⋊#168C2211yescharacteristic
45#65124C418yescomplemented
46#64955—21no—
47#64953—21no—
48D5×#95—21no—
49#64940—21no—
50#64938—21no—
51#64937—21no—
52C5×#340C2211yescharacteristic
53C5×#340C2211yescharacteristic
54#64771C2211yescharacteristic
55#64771C2211yescharacteristic
56#64749C2211yescharacteristic
57#64749C2211yescharacteristic
58#64749C2211yescharacteristic
59#64749C2211yescharacteristic
60#21363—51nomaximal, Sylow
61C22×C4×D5—21no—
62C22×C4×D5—21no—
63C22×C4×D5D411yescharacteristic
64C22×C4×D5D411yescharacteristic
65C22×C4×D5C2311yescharacteristic
66C22×C5×C8C2311yescharacteristic
67C22×C5×C8C2311yescharacteristic
68C2×C5×C4⋊C4C2311yescharacteristic
69C2×C5×C4⋊C4C2311yescharacteristic
70C2×C5×C4⋊C4C2311yescharacteristic
71C2×C5×C4⋊C4C2311yescharacteristic
72C2×C42×C5—21no—
73C2×C42×C5C2311yescharacteristic
74C2×#685—21no—
75C2×#685—21no—
76C2×C4⋊Dic5C2311yescharacteristic
77C2×C4⋊Dic5C2311yescharacteristic
78C2×C4⋊Dic5C2311yescharacteristic
79C2×C4⋊Dic5C2311yescharacteristic
80C2×#683—21no—
81C2×#683—21no—
82C2×C4×Dic5—21no—
83C2×C4×Dic5—21no—
84C2×C4×Dic5—21no—
85C2×C4×Dic5—21no—
86C2×C4×Dic5—21no—
87C2×C4×Dic5D411yescharacteristic
88C2×C4×Dic5D411yescharacteristic
89C2×C4×Dic5C2311yescharacteristic
90C22×#168C2311yescharacteristic
91C22×#168C2311yescharacteristic
92D5×C4⋊C4—22no—
93D5×C4⋊C4—22no—
94D5×C4⋊C4—22no—
95D5×C4⋊C4—22no—
96C42×D5—44no—
97C42×D5C2×C414yes—
98C42×D5Q814yes—
99C5×#107—22no—
100C5×#106—22no—
101C5×C4⋊C8C2×C414yescomplemented
102C5×#95—21no—
103C5×#95—21no—
104C5×#95—21no—
105#3963—21no—
106#3963—21no—
107#3963—21no—
108#3963—21no—
109#3963—21no—
110#3963—21no—
111#3963—21no—
112#3963—21no—
113#3963—21no—
114#3952C2×C414yes—
115#3952C2×C414yes—
116#3950—22no—
117#3949—22no—
118#3947C2×C414yescomplemented
119#3947C2×C414yescomplemented
120#3940—22no—
121#3940—22no—
122#3939—22no—
123#3939—22no—
124C4⋊#168C2×C414yescomplemented
125C2×#432—51no—
126#2283—51no—
127C2×C4×C4⋊C4—51no—
128#1949—51no—
129#1949—51no—
130#1949—51no—
131#1949D511yescharacteristic, complemented
132#1853—51no—
133#1853—51no—
134#1852—51no—
135#1852—51no—
136#1776—51no—
137#1776—51no—
138#1776—51no—
139#1776—51no—
140C23×D5C2×D411yescharacteristic
141C22×C4×C5—21no—
142C22×C4×C5—21no—
143C22×C4×C5—21no—
144C22×C4×C5—21no—
145C22×C4×C5C2×D411yescharacteristic
146C22×C4×C5C2×D411yescharacteristic
147C22×C4×C5C2411yescharacteristic
148C22×Dic5—21no—
149C22×Dic5—21no—
150C22×Dic5—21no—
151C22×Dic5—21no—
152C22×Dic5C2×D411yescharacteristic
153C22×Dic5C2×D411yescharacteristic
154C22×Dic5C2×D411yescharacteristic
155C2×C4×D5—22no—
156C2×C4×D5—22no—
157C2×C4×D5—21no—
158C2×C4×D5—21no—
159C2×C4×D5—21no—
160C2×C4×D5—21no—
161C2×C4×D5—24no—
162C2×C4×D5—24no—
163C2×C4×D5—41no—
164C2×C4×D5—41no—
165C2×C4×D5—42no—
166C2×C4×D5—42no—
167C2×C4×D5—42no—
168C2×C4×D5—42no—
169C2×C4×D5C4⋊C414yes—
170C2×C4×D5C4⋊C414yes—
171C2×C4×D5C22×C412yes—
172C2×C4×D5C2×Q812yes—
173C2×C5×C8—21no—
174C2×C5×C8—21no—
175C2×C5×C8—21no—
176C2×C5×C8—21no—
177C2×C5×C8C22×C412yes—
178C2×C5×C8C22×C412yes—
179C5×C4⋊C4—21no—
180C5×C4⋊C4—21no—
181C5×C4⋊C4—21no—
182C5×C4⋊C4—21no—
183C5×C4⋊C4—21no—
184C5×C4⋊C4—21no—
185C5×C4⋊C4#4112yes—
186C5×C4⋊C4#4112yes—
187C42×C5—42no—
188C42×C5C22×C412yes—
189C42×C5C2×Q812yes—
190#685—42no—
191#685—42no—
192C4⋊Dic5—21no—
193C4⋊Dic5—21no—
194C4⋊Dic5—21no—
195C4⋊Dic5—21no—
196C4⋊Dic5—21no—
197C4⋊Dic5—21no—
198C4⋊Dic5#4112yes—
199C4⋊Dic5#4112yes—
200#683—24no—
201#683—24no—
202C4×Dic5—42no—
203C4×Dic5—42no—
204C4×Dic5—42no—
205C4×Dic5—42no—
206C4×Dic5—42no—
207C4×Dic5C4⋊C414yes—
208C4×Dic5C4⋊C414yes—
209C4×Dic5C22×C412yes—
210C4×Dic5C2×Q812yes—
211C2×#168—21no—
212C2×#168—21no—
213C2×#168—21no—
214C2×#168—21no—
215C2×#168C22×C412yes—
216C2×#168C22×C412yes—
217C22×C4⋊C4—51no—
218C22×C4⋊C4—51no—
219C22×C42—51no—
220C22×C42—101no—
221#432—58no—
222C2×#107—51no—
223C2×#107—51no—
224C2×#107—51no—
225C2×#107C2×D511yescharacteristic
226C2×#106—51no—
227C2×#106—51no—
228C2×#106—51no—
229C2×#106C2×D511yescharacteristic
230C2×C4⋊C8—51no—
231C2×C4⋊C8C2×D511yescharacteristic
232C2×C22⋊C8—51no—
233C2×C22⋊C8—51no—
234C2×#97—51no—
235C2×#97—51no—
236#383—101no—
237#382—51no—
238#382C2×D511yescharacteristic
239#381—101no—
240#380—51no—
241#380—51no—
242C4×C4⋊C4—51no—
243C4×C4⋊C4—51no—
244C4×C4⋊C4—51no—
245C4×C4⋊C4—51no—
246C4×C4⋊C4—51no—
247C4×C4⋊C4—101no—
248C4×C4⋊C4—101no—
249C4×C4⋊C4C2×D511yescharacteristic
250C4×C22⋊C4—101no—
251#376—101no—
252C2×#95—101no—
253#340—51no—
254#340—51no—
255#340—51no—
256#340—51no—
257#340—51no—
258#340—51no—
259#340C2×D511yescharacteristic
260#340C2×D511yescharacteristic
261C23×C5C22×D411yescharacteristic
262C22×D5—21no—
263C22×D5—21no—
264C22×D5—21no—
265C22×D5—21no—
266C22×D5C2×C4⋊C412yes—
267C22×D5AGL(1,ℤ/8)12yes—
268C22×D5#13712yes—
269C2×C4×C5—21no—
270C2×C4×C5—21no—
271C2×C4×C5—21no—
272C2×C4×C5—21no—
273C2×C4×C5—22no—
274C2×C4×C5—22no—
275C2×C4×C5—41no—
276C2×C4×C5—41no—
277C2×C4×C5—41no—
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×C5C2×C4⋊C412yes—
286C2×C4×C5C2×C4⋊C412yes—
287C2×C4×C5C23×C411yescharacteristic
288C2×C4×C5C22×Q811yescharacteristic
289C2×C4×C5C2×#4111yescharacteristic
290C2×C4×C5C2×#4111yescharacteristic
291C2×C4×C5C2×#4111yescharacteristic
292C2×C4×C5C2×#4111yescharacteristic
293C2×Dic5—21no—
294C2×Dic5—21no—
295C2×Dic5—21no—
296C2×Dic5—21no—
297C2×Dic5—21no—
298C2×Dic5—21no—
299C2×Dic5—22no—
300C2×Dic5—22no—
301C2×Dic5—41no—
302C2×Dic5—41no—
303C2×Dic5—41no—
304C2×Dic5—41no—
305C2×Dic5—41no—
306C2×Dic5—41no—
307C2×Dic5—41no—
308C2×Dic5—41no—
309C2×Dic5—41no—
310C2×Dic5—41no—
311C2×Dic5C2×C4⋊C412yes—
312C2×Dic5C2×C4⋊C412yes—
313C2×Dic5C2×C4⋊C412yes—
314C4×D5—28no—
315C4×D5—22no—
316C4×D5—22no—
317C4×D5—22no—
318C4×D5—22no—
319C4×D5—44no—
320C4×D5—48no—
321C4×D5—48no—
322C5×C8—22no—
323C5×C8—22no—
324#168—22no—
325#168—22no—
326C23×C4—51no—
327C23×C4—51no—
328C23×C4—51no—
329C23×C4—101no—
330C23×C4—101no—
331C22×C8—51no—
332C22×C8—51no—
333C22×C8C22×D511yescharacteristic
334C22×C8C22×D511yescharacteristic
335C2×C4⋊C4—51no—
336C2×C4⋊C4—51no—
337C2×C4⋊C4—51no—
338C2×C4⋊C4—51no—
339C2×C4⋊C4—102no—
340C2×C4⋊C4—102no—
341C2×C4⋊C4—101no—
342C2×C4⋊C4—101no—
343C2×C4⋊C4—102no—
344C2×C4⋊C4—102no—
345C2×C4⋊C4C22×D511yescharacteristic
346C2×C4⋊C4C22×D511yescharacteristic
347C2×C4⋊C4C22×D511yescharacteristic
348C2×C4⋊C4C22×D511yescharacteristic
349C2×C22⋊C4—101no—
350C2×C22⋊C4—101no—
351C2×C42—21no—
352C2×C42—51no—
353C2×C42—51no—
354C2×C42—51no—
355C2×C42—54no—
356C2×C42—54no—
357C2×C42—101no—
358C2×C42—101no—
359C2×C42—101no—
360C2×C42—101no—
361C2×C42—101no—
362C2×C42—204no—
363C2×C42C22×D511yescharacteristic
364#107—22no—
365#107—102no—
366#107—102no—
367#107—102no—
368#106—22no—
369#106—102no—
370#106—102no—
371#106—102no—
372C4⋊C8—54no—
373C4⋊C8C4×D514yescomplemented
374C22⋊C8—54no—
375C22⋊C8—54no—
376#97—54no—
377#97—54no—
378#95—21no—
379#95—21no—
380#95—21no—
381#95—101no—
382#95—101no—
383#95—101no—
384#95—101no—
385#95—101no—
386#95—101no—
387#95—101no—
388#95—101no—
389#95—101no—
390C22×C5C22×C4⋊C411yescharacteristic
391C22×C5#52511yescharacteristic
392C22×C5#52511yescharacteristic
393C22×C5C2×AGL(1,ℤ/8)11yescharacteristic
394C22×C5C2×#13711yescharacteristic
395C22×C5#57511yescharacteristic
396C22×C5#57511yescharacteristic
397C2×D5—22no—
398C2×D5—22no—
399C2×D5—22no—
400C2×D5—22no—
401C2×D5—22no—
402C2×D5—22no—
403C2×D5#42814yes—
404C4×C5—22no—
405C4×C5—22no—
406C4×C5—42no—
407C4×C5—42no—
408C4×C5—81no—
409C4×C5—81no—
410C4×C5C4×#4111yescharacteristic
411C4×C5C4×#4111yescharacteristic
412C4×C5#53311yescharacteristic
413C4×C5#53311yescharacteristic
414Dic5—22no—
415Dic5—22no—
416Dic5—22no—
417Dic5—42no—
418Dic5—42no—
419Dic5—81no—
420Dic5—81no—
421C24—51no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—51no—
427C22×C4—51no—
428C22×C4—51no—
429C22×C4—52no—
430C22×C4—52no—
431C22×C4—54no—
432C22×C4—54no—
433C22×C4—102no—
434C22×C4—102no—
435C22×C4—104no—
436C22×C4—104no—
437C22×C4—101no—
438C22×C4—101no—
439C22×C4—101no—
440C22×C4—101no—
441C22×C4—101no—
442C22×C4—101no—
443C22×C4—101no—
444C22×C4—101no—
445C22×C4—201no—
446C22×C4—201no—
447C22×C4—202no—
448C22×C4—202no—
449C22×C4—202no—
450C22×C4—202no—
451C22×C4D4×D511yescharacteristic
452C22×C4D4×D511yescharacteristic
453C22×C4C23×D511yescharacteristic
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—52no—
459C2×C8—52no—
460C2×C8—101no—
461C2×C8—101no—
462C2×C8—101no—
463C2×C8—101no—
464C2×C8C2×C4×D512yes—
465C2×C8C2×C4×D512yes—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—52no—
473C4⋊C4—52no—
474C4⋊C4—104no—
475C4⋊C4—104no—
476C4⋊C4—101no—
477C4⋊C4—101no—
478C4⋊C4—101no—
479C4⋊C4—101no—
480C4⋊C4—101no—
481C4⋊C4—101no—
482C4⋊C4#71112yes—
483C4⋊C4#71312yes—
484C22⋊C4—202no—
485C22⋊C4—202no—
486C42—42no—
487C42—52no—
488C42—52no—
489C42—54no—
490C42—54no—
491C42—202no—
492C42—202no—
493C42—202no—
494C42—202no—
495C42—202no—
496C42C2×C4×D512yes—
497C42Q8×D512yes—
498C2×C5#229611yescharacteristic
499C2×C5C2×#42811yescharacteristic
500C2×C5#291111yescharacteristic
501C2×C5#311411yescharacteristic
502C2×C5#311411yescharacteristic
503C2×C5#311711yescharacteristic
504C2×C5#311711yescharacteristic
505D5—24no—
506C23—52no—
507C23—52no—
508C23—52no—
509C23—101no—
510C23—101no—
511C23—101no—
512C23—101no—
513C23C2×D4×D511yescharacteristic
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—52no—
531C2×C4—52no—
532C2×C4—52no—
533C2×C4—108no—
534C2×C4—101no—
535C2×C4—101no—
536C2×C4—101no—
537C2×C4—101no—
538C2×C4—101no—
539C2×C4—101no—
540C2×C4—102no—
541C2×C4—102no—
542C2×C4—102no—
543C2×C4—102no—
544C2×C4—102no—
545C2×C4—102no—
546C2×C4—204no—
547C2×C4—208no—
548C2×C4—208no—
549C2×C4—201no—
550C2×C4—201no—
551C2×C4—201no—
552C2×C4—201no—
553C2×C4—201no—
554C2×C4—201no—
555C2×C4—201no—
556C2×C4—201no—
557C2×C4—201no—
558C2×C4—201no—
559C2×C4D5×C4⋊C412yes—
560C2×C4D5×C4⋊C412yes—
561C2×C4C22×C4×D511yescharacteristic
562C2×C4C2×#71111yescharacteristic
563C2×C4C2×Q8×D511yescharacteristic
564C2×C4C2×#71311yescharacteristic
565C2×C4D5×#4111yescharacteristic
566C2×C4D5×#4111yescharacteristic
567C8—22no—
568C8—22no—
569C8—102no—
570C8—102no—
571C5#2136311yescharacteristic, complemented, Sylow
572C22—54no—
573C22—102no—
574C22—102no—
575C22—102no—
576C22—102no—
577C22—102no—
578C22—102no—
579C22C2×D5×C4⋊C411yescharacteristic
580C22#6594011yescharacteristic
581C22#6596111yescharacteristic
582C22#6610211yescharacteristic
583C22#6610211yescharacteristic
584C22D5×AGL(1,ℤ/8)11yescharacteristic
585C22D5×#13711yescharacteristic
586C4—22no—
587C4—22no—
588C4—42no—
589C4—42no—
590C4—81no—
591C4—81no—
592C4—102no—
593C4—102no—
594C4—102no—
595C4—202no—
596C4—202no—
597C4—401no—
598C4—401no—
599C4C4×#71111yescharacteristic
600C4C4×#71311yescharacteristic
601C4#6602211yescharacteristic
602C4#6606211yescharacteristic
603C2—104no—
604C2#1060769411yescharacteristic
605C2#1061090811yescharacteristic
606C2D5×#42811yescharacteristic
607C2#1061223811yescharacteristic
608C2#1061230211yescharacteristic
609C2#1061287411yescharacteristic
610C2#1061293811yescharacteristic
subgroupG/H
centerC23C2×D4×D5
commutatorC2×C4×C5C23×C4
FrattiniC22×C4C23×D5
FittingC5×#1949C2
socleC23×C5C22×D4
prime radicalC23×D5C2×D4
cosocleC22×C4×C5C24
hypercenter#1949D5
hypocenterC5#21363
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1949

Complements

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

NH ≅ G/Ntype
4. C5×#1949C2semidirect
6. #10601398C2semidirect
8. #10601346C2semidirect
9. #10601248C2semidirect
10. #10600333C2semidirect
11. #10600261C2semidirect
14. #10599579C2semidirect
15. #10599579C2semidirect
45. #65124C4semidirect
101. C5×C4⋊C8C2×C4semidirect
118. #3947C2×C4semidirect
119. #3947C2×C4semidirect
124. C4⋊#168C2×C4semidirect
131. #1949D5semidirect
373. C4⋊C8C4×D5semidirect
571. C5#21363semidirect

Maximal subgroups

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

subgroupindex
C2×#651242
#106058782
C4×D5×C4⋊C42
C5×#19492
#106014252
#106013982
#106013722
#106013462
#106012482
#106003332
#106002612
#105996682
#105996672
#105995792
#213635