Finite Group Databasebeta

← #12107026

Subgroups — #12107026

Order 1280.

868 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#478C211yesmaximal, characteristic
2#10614754C211yesmaximal, characteristic, complemented
3#10614048C211yesmaximal, characteristic
4#10602531C211yesmaximal, characteristic, complemented
5#10602397C211yesmaximal, characteristic
6#10601403C211yesmaximal, characteristic, complemented
7Dic5×#107C211yesmaximal, characteristic, complemented
8#10601351C211yesmaximal, characteristic, complemented
9#10601346C211yesmaximal, characteristic, complemented
10#10601246C211yesmaximal, characteristic, complemented
11#10601235C211yesmaximal, characteristic, complemented
12#10600961C211yesmaximal, characteristic
13#10600961C211yesmaximal, characteristic
14#10600945C211yesmaximal, characteristic
15Dic5×#102C211yesmaximal, characteristic
16C2×C5×#125C2211yescharacteristic
17C2×C4×C5×D4C2211yescharacteristic
18C2×D4×Dic5C2211yescharacteristic
19C2×D4×Dic5C2211yescharacteristic
20C5×#478C418yescomplemented
21C2×C5×#107C2211yescharacteristic
22C2×C5×#106C2211yescharacteristic
23C2×C5×C4⋊C8C2211yescharacteristic
24C2×C5×#102C2211yescharacteristic
25C2×C5×#102C2211yescharacteristic
26C2×#3964C2211yescharacteristic
27C2×#3964C2211yescharacteristic
28C4×C22⋊Dic5—21no—
29C2×#3963—21no—
30C2×#3950C2211yescharacteristic
31C2×#3950C2211yescharacteristic
32C2×#3947C2211yescharacteristic
33C2×C8×Dic5C2211yescharacteristic
34#65274—21no—
35#65274—21no—
36#65274C2211yescharacteristic
37#65274C2211yescharacteristic
38#65270—21no—
39#65270—21no—
40C4⋊C4×Dic5C2211yescharacteristic
41C4⋊C4×Dic5C2211yescharacteristic
42C4⋊C4×Dic5C2211yescharacteristic
43C4⋊C4×Dic5C2211yescharacteristic
44C22⋊C4×Dic5—21no—
45C22⋊C4×Dic5—21no—
46#65224C2211yescharacteristic
47C4×C4⋊Dic5C2211yescharacteristic
48#65221C2211yescharacteristic
49C2×C4⋊#168C2211yescharacteristic
50#64771C2211yescharacteristic
51#64771C2211yescharacteristic
52#64770C2211yescharacteristic
53#64770C2211yescharacteristic
54#64749C2211yescharacteristic
55#64749C2211yescharacteristic
56#64749C2211yescharacteristic
57#64749C2211yescharacteristic
58#64749C2211yescharacteristic
59#64749C2211yescharacteristic
60#21620—51nomaximal, Sylow
61C22×C5×D4C2311yescharacteristic
62C23×C4×C5—21no—
63C23×Dic5—21no—
64C23×Dic5—21no—
65C22×C5×C8C2311yescharacteristic
66C22×C5×C8C2311yescharacteristic
67C5×#125—22no—
68C5×#125C2×C414yescomplemented
69C4×C5×D4—22no—
70C4×C5×D4C2×C414yes—
71C2×C5×C4⋊C4—21no—
72C2×C5×C4⋊C4—21no—
73C2×C5×C4⋊C4C2311yescharacteristic
74C2×C5×C4⋊C4C2311yescharacteristic
75C2×C5×C4⋊C4C2311yescharacteristic
76C2×C5×C22⋊C4—21no—
77C2×C42×C5C2311yescharacteristic
78C2×C22⋊Dic5—21no—
79C2×C22⋊Dic5—21no—
80D4×Dic5—22no—
81D4×Dic5—22no—
82D4×Dic5—22no—
83D4×Dic5Q814yes—
84C2×C4⋊Dic5—21no—
85C2×C4⋊Dic5—21no—
86C2×C4⋊Dic5—21no—
87C2×C4⋊Dic5—21no—
88C2×C4⋊Dic5C2311yescharacteristic
89C2×C4⋊Dic5C2311yescharacteristic
90C2×C4⋊Dic5C2311yescharacteristic
91C2×C4⋊Dic5C2311yescharacteristic
92C2×C4×Dic5—21no—
93C2×C4×Dic5—21no—
94C2×C4×Dic5—21no—
95C2×C4×Dic5—21no—
96C2×C4×Dic5—21no—
97C2×C4×Dic5C2311yescharacteristic
98C2×C4×Dic5C2311yescharacteristic
99C22×#168C2311yescharacteristic
100C22×#168C2311yescharacteristic
101C5×#107C2×C414yescomplemented
102C5×#106C2×C414yescomplemented
103C5×C4⋊C8C2×C414yescomplemented
104C5×#102C2×C414yes—
105C5×#102C2×C414yes—
106#3964—22no—
107#3964—22no—
108#3963—21no—
109#3963—21no—
110#3963—21no—
111#3963—21no—
112#3963—21no—
113#3963—21no—
114#3963—21no—
115#3963D411yescharacteristic
116#3963D411yescharacteristic
117#3963D411yescharacteristic
118#3963D411yescharacteristic
119#3950—22no—
120#3950—22no—
121#3947—22no—
122C8×Dic5—22no—
123C4⋊#168—22no—
124C2×#478D511yescharacteristic
125#2330—51no—
126#2275—51no—
127#1989—51no—
128#1947—51no—
129#1921—51no—
130#1920—51no—
131#1862—51no—
132#1862—51no—
133#1802—51no—
134#1776—51no—
135C4×#107—51no—
136#1768—51no—
137#1762—51no—
138C4×#102—51no—
139C24×C5—21no—
140C2×C5×D4—21no—
141C2×C5×D4—21no—
142C2×C5×D4—21no—
143C2×C5×D4C22×C412yes—
144C2×C5×D4C2×Q812yes—
145C2×C5×D4#4112yes—
146C22×C4×C5—21no—
147C22×C4×C5—21no—
148C22×C4×C5—21no—
149C22×C4×C5—24no—
150C22×C4×C5—81no—
151C22×C4×C5—81no—
152C22×C4×C5C2×D411yescharacteristic
153C22×C4×C5C2×D411yescharacteristic
154C22×C4×C5C2411yescharacteristic
155C22×Dic5—21no—
156C22×Dic5—21no—
157C22×Dic5—24no—
158C22×Dic5—24no—
159C22×Dic5—21no—
160C22×Dic5—21no—
161C22×Dic5—81no—
162C22×Dic5—81no—
163C22×Dic5—81no—
164C22×Dic5—81no—
165C22×Dic5C2×D411yescharacteristic
166C22×Dic5C2×D411yescharacteristic
167C22×Dic5C2×D411yescharacteristic
168C22×Dic5C2×D411yescharacteristic
169C2×C5×C8—21no—
170C2×C5×C8—21no—
171C2×C5×C8—21no—
172C2×C5×C8—21no—
173C2×C5×C8C22×C412yes—
174C2×C5×C8C22×C412yes—
175C5×C4⋊C4—24no—
176C5×C4⋊C4—24no—
177C5×C4⋊C4—21no—
178C5×C4⋊C4—21no—
179C5×C4⋊C4—21no—
180C5×C4⋊C4C22×C412yes—
181C5×C4⋊C4C22×C412yes—
182C5×C4⋊C4C22×C412yes—
183C5×C22⋊C4—24no—
184C42×C5C22×C412yes—
185C42×C5#4112yes—
186C22⋊Dic5—24no—
187C22⋊Dic5—24no—
188C4⋊Dic5—21no—
189C4⋊Dic5—21no—
190C4⋊Dic5—21no—
191C4⋊Dic5—21no—
192C4⋊Dic5—21no—
193C4⋊Dic5—21no—
194C4⋊Dic5—81no—
195C4⋊Dic5—81no—
196C4⋊Dic5—81no—
197C4⋊Dic5—81no—
198C4⋊Dic5C2×Q812yes—
199C4⋊Dic5#4112yes—
200C4×Dic5—21no—
201C4×Dic5—21no—
202C4×Dic5—81no—
203C4×Dic5—81no—
204C4×Dic5—81no—
205C4×Dic5—81no—
206C4×Dic5—81no—
207C4×Dic5C2×Q812yes—
208C4×Dic5#4112yes—
209C2×#168—21no—
210C2×#168—21no—
211C2×#168—21no—
212C2×#168—21no—
213C2×#168—21no—
214C2×#168—21no—
215C2×#125C2×D511yescharacteristic
216C2×C4×D4—51no—
217C2×C4×D4—51no—
218C2×C4×D4C2×D511yescharacteristic
219#478Dic518yescomplemented
220C2×#107—51no—
221C2×#107—51no—
222C2×#107C2×D511yescharacteristic
223C2×#106C2×D511yescharacteristic
224C2×C4⋊C8—51no—
225C2×C4⋊C8C2×D511yescharacteristic
226C2×#102—51no—
227C2×#102—51no—
228C2×#102C2×D511yescharacteristic
229C2×#102C2×D511yescharacteristic
230C2×#97—51no—
231C2×C4×C8—51no—
232#389—51no—
233#389—51no—
234#389—101no—
235#389—101no—
236#387—101no—
237#387—101no—
238#384—51no—
239C4×C4⋊C4—51no—
240C4×C4⋊C4—51no—
241C4×C4⋊C4—51no—
242C4×C4⋊C4—51no—
243C4×C4⋊C4—51no—
244C4×C22⋊C4—101no—
245C4×C22⋊C4—101no—
246C4×C22⋊C4—101no—
247#376—51no—
248C2×#95—101no—
249#340—51no—
250#340—51no—
251#340—51no—
252#340—51no—
253#340—51no—
254#340—51no—
255#340—51no—
256#340—51no—
257#336—51no—
258#336—51no—
259C23×C5—22no—
260C23×C5—22no—
261C23×C5—22no—
262C23×C5—41no—
263C23×C5—41no—
264C23×C5—41no—
265C23×C5—41no—
266C23×C5C22×D411yescharacteristic
267C5×D4—22no—
268C5×D4—22no—
269C5×D4—22no—
270C5×D4C4×Q814yes—
271C2×C4×C5—21no—
272C2×C4×C5—21no—
273C2×C4×C5—21no—
274C2×C4×C5—21no—
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—84no—
285C2×C4×C5C4×D412yes—
286C2×C4×C5C4×D412yes—
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—22no—
298C2×Dic5—21no—
299C2×Dic5—21no—
300C2×Dic5—22no—
301C2×Dic5—21no—
302C2×Dic5—21no—
303C2×Dic5—21no—
304C2×Dic5—21no—
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—41no—
314C2×Dic5—41no—
315C2×Dic5—84no—
316C2×Dic5—84no—
317C2×Dic5C22⋊Q812yes—
318C2×Dic5C22⋊Q812yes—
319C5×C8—22no—
320C5×C8—22no—
321#168—41no—
322#168—41no—
323C22×D4C22×D511yescharacteristic
324C23×C4—21no—
325C23×C4—101no—
326C23×C4—101no—
327C22×C8—51no—
328C22×C8—51no—
329C22×C8C22×D511yescharacteristic
330C22×C8C22×D511yescharacteristic
331#125—22no—
332#125C2×Dic514yescomplemented
333C4×D4—22no—
334C4×D4—54no—
335C4×D4—102no—
336C4×D4—102no—
337C4×D4—102no—
338C4×D4C2×Dic514yes—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—51no—
342C2×C4⋊C4—51no—
343C2×C4⋊C4—51no—
344C2×C4⋊C4—51no—
345C2×C4⋊C4—101no—
346C2×C4⋊C4—101no—
347C2×C4⋊C4—101no—
348C2×C4⋊C4—101no—
349C2×C4⋊C4C22×D511yescharacteristic
350C2×C4⋊C4C22×D511yescharacteristic
351C2×C4⋊C4C22×D511yescharacteristic
352C2×C22⋊C4—21no—
353C2×C22⋊C4—101no—
354C2×C22⋊C4—101no—
355C2×C42—51no—
356C2×C42—51no—
357C2×C42—101no—
358C2×C42—101no—
359C2×C42—101no—
360C2×C42—101no—
361C2×C42—101no—
362C2×C42C22×D511yescharacteristic
363#107—102no—
364#107—102no—
365#107C2×Dic514yescomplemented
366#106C2×Dic514yescomplemented
367C4⋊C8—102no—
368C4⋊C8C2×Dic514yescomplemented
369#102—102no—
370#102—102no—
371#102C2×Dic514yes—
372#102C2×Dic514yes—
373#97—102no—
374C4×C8—102no—
375#95—51no—
376#95—51no—
377#95—51no—
378#95—51no—
379#95—101no—
380#95—101no—
381#95—101no—
382#95—101no—
383#95—101no—
384#95—101no—
385#95—101no—
386C22×C5—24no—
387C22×C5—42no—
388C22×C5—42no—
389C22×C5—42no—
390C22×C5—42no—
391C22×C5—42no—
392C22×C5—42no—
393C22×C5C2×C4×D411yescharacteristic
394C22×C5C2×C22⋊Q811yescharacteristic
395C22×C5#52511yescharacteristic
396C22×C5#57611yescharacteristic
397C22×C5#57611yescharacteristic
398C22×C5#57711yescharacteristic
399C22×C5#57811yescharacteristic
400C4×C5—22no—
401C4×C5—22no—
402C4×C5—42no—
403C4×C5—42no—
404C4×C5—42no—
405C4×C5C2×C4×Q811yescharacteristic
406C4×C5C4×#4111yescharacteristic
407C4×C5#52911yescharacteristic
408C4×C5#53311yescharacteristic
409Dic5—22no—
410Dic5—22no—
411Dic5—42no—
412Dic5—41no—
413Dic5—41no—
414Dic5—42no—
415Dic5—81no—
416Dic5—81no—
417C24—21no—
418C2×D4—21no—
419C2×D4—21no—
420C2×D4—21no—
421C2×D4Q8×D512yes—
422C2×D4#71312yes—
423C2×D4C22×Dic512yes—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—24no—
428C22×C4—51no—
429C22×C4—51no—
430C22×C4—51no—
431C22×C4—51no—
432C22×C4—81no—
433C22×C4—81no—
434C22×C4—104no—
435C22×C4—101no—
436C22×C4—101no—
437C22×C4—104no—
438C22×C4—101no—
439C22×C4—101no—
440C22×C4—401no—
441C22×C4—401no—
442C22×C4—401no—
443C22×C4—401no—
444C22×C4D4×D511yescharacteristic
445C22×C4D4×D511yescharacteristic
446C22×C4C23×D511yescharacteristic
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—101no—
452C2×C8—101no—
453C2×C8—101no—
454C2×C8—101no—
455C2×C8—101no—
456C2×C8—101no—
457C2×C8C22×Dic512yes—
458C2×C8C22×Dic512yes—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—24no—
463C4⋊C4—24no—
464C4⋊C4—52no—
465C4⋊C4—52no—
466C4⋊C4—101no—
467C4⋊C4—101no—
468C4⋊C4—101no—
469C4⋊C4—101no—
470C4⋊C4—101no—
471C4⋊C4—101no—
472C4⋊C4—401no—
473C4⋊C4—401no—
474C4⋊C4—401no—
475C4⋊C4—401no—
476C4⋊C4C22×Dic512yes—
477C4⋊C4C22×Dic512yes—
478C4⋊C4C22×Dic512yes—
479C22⋊C4—24no—
480C22⋊C4—104no—
481C22⋊C4—104no—
482C42—52no—
483C42—52no—
484C42—101no—
485C42—101no—
486C42—401no—
487C42—401no—
488C42—401no—
489C42—401no—
490C42—401no—
491C42#71112yes—
492C42C22×Dic512yes—
493C2×C5—44no—
494C2×C5C4×C22⋊Q811yescharacteristic
495C2×C5#294611yescharacteristic
496C2×C5#295111yescharacteristic
497C2×C5#308111yescharacteristic
498C2×C5#308311yescharacteristic
499C2×C5#312011yescharacteristic
500C2×C5#312211yescharacteristic
501C23—22no—
502C23—22no—
503C23—22no—
504C23—41no—
505C23—41no—
506C23—41no—
507C23—41no—
508C23C2×D4×D511yescharacteristic
509D4—22no—
510D4—22no—
511D4—22no—
512D4Q8×Dic514yes—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—22no—
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—52no—
527C2×C4—52no—
528C2×C4—84no—
529C2×C4—101no—
530C2×C4—101no—
531C2×C4—101no—
532C2×C4—101no—
533C2×C4—101no—
534C2×C4—101no—
535C2×C4—101no—
536C2×C4—101no—
537C2×C4—102no—
538C2×C4—101no—
539C2×C4—101no—
540C2×C4—102no—
541C2×C4—201no—
542C2×C4—201no—
543C2×C4—201no—
544C2×C4—201no—
545C2×C4—201no—
546C2×C4—201no—
547C2×C4—201no—
548C2×C4—201no—
549C2×C4—201no—
550C2×C4—201no—
551C2×C4—404no—
552C2×C4—404no—
553C2×C4D4×Dic512yes—
554C2×C4D4×Dic512yes—
555C2×C4C2×#71111yescharacteristic
556C2×C4C2×Q8×D511yescharacteristic
557C2×C4C2×#71311yescharacteristic
558C2×C4D5×#4111yescharacteristic
559C2×C4D5×#4111yescharacteristic
560C2×C4C23×Dic511yescharacteristic
561C8—22no—
562C8—22no—
563C8—201no—
564C8—201no—
565C5#2162011yescharacteristic, complemented, Sylow
566C22—24no—
567C22—42no—
568C22—42no—
569C22—42no—
570C22—42no—
571C22—42no—
572C22—42no—
573C22D5×C22⋊Q811yescharacteristic
574C22#6596111yescharacteristic
575C22#6610311yescharacteristic
576C22#6610511yescharacteristic
577C22#6610811yescharacteristic
578C22#6610911yescharacteristic
579C22C2×D4×Dic511yescharacteristic
580C4—22no—
581C4—22no—
582C4—42no—
583C4—42no—
584C4—42no—
585C4—102no—
586C4—102no—
587C4—201no—
588C4—201no—
589C4—202no—
590C4—202no—
591C4—401no—
592C4—401no—
593C4#6595611yescharacteristic
594C4#6595811yescharacteristic
595C4C2×Q8×Dic511yescharacteristic
596C4#41×Dic511yescharacteristic
597C2—44no—
598C2#1061287611yescharacteristic
599C2#1061287711yescharacteristic
600C2#1061290011yescharacteristic
601C2#1061290111yescharacteristic
602C2Dic5×C22⋊Q811yescharacteristic
603C2#1061562911yescharacteristic
604C2#1061566111yescharacteristic
subgroupG/H
centerC23C2×D4×D5
commutatorC2×C4×C5C23×C4
FrattiniC22×C4C23×D5
FittingC2×C5×#478C2
socleC23×C5C22×D4
prime radicalC22×C5×D4C23
cosocleC22×C4×C5C24
hypercenterC2×#478D5
hypocenterC5#21620
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#478

Complements

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

NH ≅ G/Ntype
2. #10614754C2semidirect
4. #10602531C2semidirect
6. #10601403C2semidirect
7. Dic5×#107C2semidirect
8. #10601351C2semidirect
9. #10601346C2semidirect
10. #10601246C2semidirect
11. #10601235C2semidirect
20. C5×#478C4semidirect
68. C5×#125C2×C4semidirect
101. C5×#107C2×C4semidirect
102. C5×#106C2×C4semidirect
103. C5×C4⋊C8C2×C4semidirect
219. #478Dic5semidirect
332. #125C2×Dic5semidirect
365. #107C2×Dic5semidirect
366. #106C2×Dic5semidirect
368. C4⋊C8C2×Dic5semidirect
565. C5#21620semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#4782
#106147542
#106140482
#106025312
#106023972
#106014032
Dic5×#1072
#106013512
#106013462
#106012462
#106012352
#106009612
#106009452
Dic5×#1022
#216205