Finite Group Databasebeta

← #12098895

Subgroups — #12098895

Order 1280.

1438 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#4047C211yesmaximal, characteristic
2C2×#65169C211yesmaximal, characteristic, complemented
3C2×D5×#107C211yesmaximal, characteristic, complemented
4#10605734C212yesmaximal
5C5×#1808C211yesmaximal, characteristic, complemented
6#10602764C211yesmaximal, characteristic, complemented
7#10601423C211yesmaximal, characteristic, complemented
8#10601423C211yesmaximal, characteristic, complemented
9#10600306C212yesmaximal, complemented
10#10599663C212yesmaximal, complemented
11#10599660C212yesmaximal, complemented
12C22×#709C2211yescharacteristic
13C23×C5×C8C2211yescharacteristic
14C22×#681C2211yescharacteristic
15C2×#4047—24no—
16C2×#4047—24no—
17C2×#4047C418yescomplemented
18C22×#676C2211yescharacteristic
19C22×#676C2211yescharacteristic
20C22×C8×D5C2211yescharacteristic
21C22×C8×D5C2211yescharacteristic
22C2×#4038C2212yes—
23C2×D5×C4⋊C4C2212yes—
24C2×C5×#107C2211yescharacteristic
25C2×C5×#107C2211yescharacteristic
26C5×#380C2212yes—
27#65501C2212yes—
28C2×#3950C2211yescharacteristic
29C2×#3950C2211yescharacteristic
30#65276C2212yes—
31#65276C2212yes—
32C2×#3940C2212yes—
33C2×#3939C2212yes—
34#65246—22no—
35#65245—22no—
36#65169—24no—
37D5×#107—24no—
38#64954—22no—
39#64935—22no—
40C5×#340C2212yes—
41#64771C2212yes—
42#64749C2212yes—
43#64749C2212yes—
44#20663—51nomaximal, Sylow
45C23×C4×C5C2311yescharacteristic
46C22×C22⋊D5D411yescharacteristic
47C22×C22⋊D5D411yescharacteristic
48C2×#709—22no—
49C2×#709—22no—
50C2×#709—22no—
51C2×#709—22no—
52C2×#709C2×C414yes—
53C2×#709Q814yes—
54C22×D20D411yescharacteristic
55C22×C4×D5—22no—
56C22×C4×D5C2311yescharacteristic
57C22×C4×D5C2311yescharacteristic
58C22×Dic10D411yescharacteristic
59C22×C5×C8—22no—
60C22×C5×C8—22no—
61C22×C5×C8C2×C414yescomplemented
62C22×C5×C8C2311yescharacteristic
63C22×C5×C8C2311yescharacteristic
64C2×C5×C4⋊C4C2312yes—
65C2×C5×C4⋊C4C2312yes—
66C2×C5×C22⋊C4—22no—
67C2×C22⋊Dic5—22no—
68C2×#685—22no—
69C2×#685—22no—
70C2×#685—22no—
71C2×C4⋊Dic5C2312yes—
72C2×C4⋊Dic5C2312yes—
73C2×#683—22no—
74C2×C4×Dic5—22no—
75C2×#681—22no—
76C2×#681—22no—
77C2×#681C2×C414yescomplemented
78C22×#168C2311yescharacteristic
79C22×#168C2311yescharacteristic
80#4047—232no—
81C2×#676—22no—
82C2×#676—22no—
83C2×#676—22no—
84C2×#676—22no—
85C2×#676C2×C414yes—
86C2×#676C2×C414yescomplemented
87C2×C8×D5—22no—
88C2×C8×D5—22no—
89C2×C8×D5C2×C414yes—
90C2×C8×D5C2×C414yescomplemented
91C2×C8×D5D414yes—
92C2×C8×D5D414yes—
93#4038—24no—
94#4038—24no—
95D5×C4⋊C4—24no—
96D5×C4⋊C4—24no—
97C5×#107—22no—
98C5×#107—22no—
99C5×#95—22no—
100#3963—22no—
101#3963—22no—
102#3963—22no—
103#3950—22no—
104#3950—22no—
105#3940—24no—
106#3939—24no—
107C22×#131—51no—
108C2×#427—51no—
109C22×#107—51no—
110#2311—52no—
111#1809—52no—
112#1809—52no—
113#1808—51no—
114#1808—51no—
115#1808—51no—
116#1808D511yescharacteristic, complemented
117#1736—52no—
118C24×C5C2×D411yescharacteristic
119C23×D5C2×D411yescharacteristic
120C23×D5C2×D411yescharacteristic
121C22×C4×C5—21no—
122C22×C4×C5—21no—
123C22×C4×C5—21no—
124C22×C4×C5—21no—
125C22×C4×C5—22no—
126C22×C4×C5—22no—
127C22×C4×C5C22×C412yes—
128C22×C4×C5C2×D411yescharacteristic
129C22×C4×C5C2×Q812yes—
130C22×C4×C5C2411yescharacteristic
131C2×C22⋊D5—22no—
132C2×C22⋊D5—22no—
133C2×C22⋊D5—22no—
134C2×C22⋊D5—22no—
135C2×C22⋊D5C4⋊C414yes—
136C2×C22⋊D5C4⋊C414yes—
137C22×Dic5—22no—
138C22×Dic5—22no—
139C22×Dic5C2×D411yescharacteristic
140C22×Dic5C2×D411yescharacteristic
141#709—28no—
142#709—28no—
143#709—28no—
144#709—28no—
145C2×D20—22no—
146C2×D20—22no—
147C2×D20C4⋊C414yes—
148C2×C4×D5—21no—
149C2×C4×D5—21no—
150C2×C4×D5—21no—
151C2×C4×D5—21no—
152C2×C4×D5—44no—
153C2×C4×D5—82no—
154C2×C4×D5—82no—
155C2×C4×D5C22×C412yes—
156C2×C4×D5C22×C412yes—
157C2×C4×D5C2×D412yes—
158C2×C4×D5C2×D412yes—
159C2×C4×D5C2×Q812yes—
160C2×C4×D5C2×Q812yes—
161C2×C4×D5#4112yes—
162C2×C4×D5#4112yes—
163C2×Dic10—22no—
164C2×Dic10—22no—
165C2×Dic10C4⋊C414yes—
166C2×C5×C8—21no—
167C2×C5×C8—21no—
168C2×C5×C8—28no—
169C2×C5×C8C22×C412yes—
170C2×C5×C8C22×C412yes—
171C2×C5×C8C2×D412yes—
172C2×C5×C8C2×D412yes—
173C5×C4⋊C4—22no—
174C5×C4⋊C4—22no—
175C5×C4⋊C4—22no—
176C5×C4⋊C4—22no—
177C5×C22⋊C4—82no—
178C22⋊Dic5—82no—
179#685—44no—
180#685—82no—
181#685—82no—
182C4⋊Dic5—22no—
183C4⋊Dic5—22no—
184C4⋊Dic5—22no—
185C4⋊Dic5—22no—
186#683—44no—
187C4×Dic5—44no—
188#681—28no—
189C2×#168—21no—
190C2×#168—21no—
191C2×#168C22×C412yes—
192C2×#168C22×C412yes—
193C2×#168C2×D412yes—
194C2×#168C2×D412yes—
195#676—28no—
196#676—28no—
197C8×D5—28no—
198C8×D5C22⋊C4116yescomplemented
199C22×#41—51no—
200C2×#131—58no—
201C2×#131—104no—
202C2×#131—104no—
203C22×M16—51no—
204C22×M16—51no—
205C22×M16—51no—
206C23×C8—51no—
207C23×C8—51no—
208C23×C8C2×D511yescharacteristic
209C2×#117—52no—
210C22×C4⋊C4—52no—
211#427—104no—
212C2×#107—51no—
213C2×#107—51no—
214C2×#107—52no—
215C2×#107—104no—
216C2×#107C2×D511yescharacteristic
217C2×#107C2×D511yescharacteristic
218C2×#106—52no—
219#391—102no—
220#390—102no—
221#386—102no—
222#386—102no—
223#380—52no—
224#380—52no—
225#380—52no—
226#380C2×D512yes—
227#340—52no—
228#340—52no—
229#340—52no—
230#340C2×D512yes—
231C23×C5—21no—
232C23×C5—21no—
233C23×C5—21no—
234C23×C5—21no—
235C23×C5—21no—
236C23×C5—21no—
237C23×C5C2×C4⋊C412yes—
238C23×C5C22×D411yescharacteristic
239C22×D5—21no—
240C22×D5—21no—
241C22×D5—21no—
242C22×D5—21no—
243C22×D5—21no—
244C22×D5—21no—
245C22×D5—21no—
246C22×D5—21no—
247C22×D5—21no—
248C22×D5—21no—
249C22×D5C2×C4⋊C412yes—
250C22×D5C2×C4⋊C412yes—
251C22×D5#12112yes—
252C22×D5#12112yes—
253C2×C4×C5—21no—
254C2×C4×C5—21no—
255C2×C4×C5—22no—
256C2×C4×C5—22no—
257C2×C4×C5—22no—
258C2×C4×C5—22no—
259C2×C4×C5—42no—
260C2×C4×C5—42no—
261C2×C4×C5—42no—
262C2×C4×C5—42no—
263C2×C4×C5—42no—
264C2×C4×C5—42no—
265C2×C4×C5C2×C4⋊C412yes—
266C2×C4×C5C23×C411yescharacteristic
267C2×C4×C5C22×D411yescharacteristic
268C2×C4×C5C22×D411yescharacteristic
269C2×C4×C5C22×Q811yescharacteristic
270C2×C4×C5C2×#4111yescharacteristic
271C2×C4×C5C2×#4111yescharacteristic
272C22⋊D5—28no—
273C22⋊D5—28no—
274C2×Dic5—21no—
275C2×Dic5—21no—
276C2×Dic5—42no—
277C2×Dic5—42no—
278C2×Dic5—42no—
279C2×Dic5—42no—
280C2×Dic5—42no—
281C2×Dic5—42no—
282C2×Dic5C2×C4⋊C412yes—
283C2×Dic5C2×C4⋊C412yes—
284C2×Dic5#12112yes—
285C2×Dic5#12112yes—
286D20—28no—
287C4×D5—22no—
288C4×D5—22no—
289C4×D5—22no—
290C4×D5—22no—
291C4×D5—88no—
292C4×D5C2×C22⋊C414yes—
293C4×D5#11714yes—
294C4×D5C22⋊Q814yes—
295C4×D5C22⋊Q814yes—
296Dic10—28no—
297C5×C8—22no—
298C5×C8C2×C22⋊C414yes—
299#168—22no—
300#168C2×C22⋊C414yes—
301C2×#41—54no—
302C2×#41—54no—
303C2×#41—102no—
304C2×#41—102no—
305C2×#41—102no—
306C2×#41—102no—
307C22×Q8—51no—
308C22×D4—51no—
309C22×D4—51no—
310C22×D4—51no—
311C23×C4—51no—
312C23×C4—51no—
313C23×C4—102no—
314C23×C4C22×D511yescharacteristic
315#131—1032no—
316C2×M16—54no—
317C2×M16—54no—
318C2×M16—54no—
319C2×M16—102no—
320C2×M16—102no—
321C2×M16—102no—
322C2×M16—102no—
323C2×M16—102no—
324C2×M16—102no—
325C22×C8—22no—
326C22×C8—22no—
327C22×C8—51no—
328C22×C8—54no—
329C22×C8—54no—
330C22×C8—54no—
331C22×C8—51no—
332C22×C8—54no—
333C22×C8—102no—
334C22×C8—102no—
335C22×C8C4×D514yescomplemented
336C22×C8C22×D511yescharacteristic
337C22×C8C22×D511yescharacteristic
338#117—104no—
339#117—104no—
340C2×C4⋊C4—52no—
341C2×C4⋊C4—52no—
342C2×C4⋊C4—104no—
343C2×C4⋊C4—104no—
344C2×C4⋊C4—102no—
345C2×C4⋊C4C22×D512yes—
346C2×C4⋊C4C22×D512yes—
347C2×C22⋊C4—22no—
348C2×C22⋊C4—102no—
349C2×C22⋊C4—102no—
350C2×C22⋊C4—102no—
351C2×C22⋊C4—102no—
352C2×C42—102no—
353#107—22no—
354#107—22no—
355#107—104no—
356#107—102no—
357#107—102no—
358#106—104no—
359#95—22no—
360#95—102no—
361#95—102no—
362#95—102no—
363C22×C5—22no—
364C22×C5—22no—
365C22×C5—22no—
366C22×C5—41no—
367C22×C5—41no—
368C22×C5—41no—
369C22×C5—41no—
370C22×C5C22×C4⋊C411yescharacteristic
371C22×C5C2×#12111yescharacteristic
372C22×C5C2×#12111yescharacteristic
373C22×C5#57611yescharacteristic
374C22×C5#57611yescharacteristic
375C22×C5#57811yescharacteristic
376C22×C5#57811yescharacteristic
377C2×D5—22no—
378C2×D5—22no—
379C2×D5—22no—
380C2×D5—22no—
381C2×D5—22no—
382C2×D5—22no—
383C2×D5—22no—
384C2×D5—22no—
385C2×D5—22no—
386C2×D5—41no—
387C2×D5—41no—
388C2×D5—41no—
389C2×D5—41no—
390C2×D5#38014yes—
391C4×C5—22no—
392C4×C5—82no—
393C4×C5—82no—
394C4×C5C22×C22⋊C411yescharacteristic
395C4×C5C2×#11711yescharacteristic
396C4×C5C2×C22⋊Q811yescharacteristic
397C4×C5C2×C22⋊Q811yescharacteristic
398Dic5—22no—
399Dic5—82no—
400Dic5—82no—
401Dic5#38014yes—
402C24—51no—
403C24—51no—
404C24D4×D511yescharacteristic
405#41—108no—
406#41—108no—
407#41—108no—
408#41—108no—
409C2×Q8—54no—
410C2×Q8—102no—
411C2×Q8—102no—
412C2×D4—54no—
413C2×D4—54no—
414C2×D4—54no—
415C2×D4—102no—
416C2×D4—102no—
417C2×D4—102no—
418C2×D4—102no—
419C2×D4—102no—
420C2×D4—102no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—51no—
428C22×C4—52no—
429C22×C4—52no—
430C22×C4—52no—
431C22×C4—52no—
432C22×C4—52no—
433C22×C4—52no—
434C22×C4—51no—
435C22×C4—52no—
436C22×C4—52no—
437C22×C4—101no—
438C22×C4—101no—
439C22×C4—101no—
440C22×C4—101no—
441C22×C4—102no—
442C22×C4—102no—
443C22×C4—204no—
444C22×C4—402no—
445C22×C4—402no—
446C22×C4C2×C4×D512yes—
447C22×C4D4×D511yescharacteristic
448C22×C4Q8×D512yes—
449C22×C4C23×D511yescharacteristic
450M16—108no—
451M16—108no—
452M16—108no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—28no—
456C2×C8—52no—
457C2×C8—52no—
458C2×C8—52no—
459C2×C8—516no—
460C2×C8—52no—
461C2×C8—101no—
462C2×C8—101no—
463C2×C8—108no—
464C2×C8C2×C4×D512yes—
465C2×C8C2×C4×D512yes—
466C2×C8D4×D512yes—
467C2×C8D4×D512yes—
468C4⋊C4—22no—
469C4⋊C4—22no—
470C4⋊C4—22no—
471C4⋊C4—22no—
472C4⋊C4—102no—
473C4⋊C4—102no—
474C4⋊C4—102no—
475C4⋊C4—102no—
476C4⋊C4—204no—
477C22⋊C4—82no—
478C22⋊C4—204no—
479C22⋊C4—402no—
480C22⋊C4—402no—
481C22⋊C4—402no—
482C42—204no—
483C2×C5—42no—
484C2×C5C2×#38011yescharacteristic
485C2×C5#291311yescharacteristic
486C2×C5#291311yescharacteristic
487C2×C5#305811yescharacteristic
488C2×C5#305911yescharacteristic
489C2×C5#306111yescharacteristic
490C2×C5#306111yescharacteristic
491D5—24no—
492D5—42no—
493C23—21no—
494C23—21no—
495C23—21no—
496C23—21no—
497C23—21no—
498C23—21no—
499C23—52no—
500C23—52no—
501C23—52no—
502C23—52no—
503C23—101no—
504C23—101no—
505C23—101no—
506C23—101no—
507C23—101no—
508C23—101no—
509C23—101no—
510C23—101no—
511C23—101no—
512C23—101no—
513C23D5×C4⋊C412yes—
514C23C2×D4×D511yescharacteristic
515Q8—108no—
516D4—108no—
517D4—108no—
518D4—108no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—22no—
522C2×C4—22no—
523C2×C4—22no—
524C2×C4—22no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—52no—
532C2×C4—52no—
533C2×C4—52no—
534C2×C4—54no—
535C2×C4—54no—
536C2×C4—54no—
537C2×C4—54no—
538C2×C4—52no—
539C2×C4—101no—
540C2×C4—101no—
541C2×C4—102no—
542C2×C4—102no—
543C2×C4—102no—
544C2×C4—102no—
545C2×C4—202no—
546C2×C4—202no—
547C2×C4—202no—
548C2×C4—202no—
549C2×C4—202no—
550C2×C4—202no—
551C2×C4—408no—
552C2×C4D5×C4⋊C412yes—
553C2×C4C22×C4×D511yescharacteristic
554C2×C4C2×D4×D511yescharacteristic
555C2×C4C2×D4×D511yescharacteristic
556C2×C4C2×Q8×D511yescharacteristic
557C2×C4D5×#4111yescharacteristic
558C2×C4D5×#4111yescharacteristic
559C8—22no—
560C8—54no—
561C8—102no—
562C8D5×C22⋊C414yes—
563C5#2066311yescharacteristic, complemented, Sylow
564C22—22no—
565C22—22no—
566C22—22no—
567C22—41no—
568C22—41no—
569C22—41no—
570C22—41no—
571C22—54no—
572C22—102no—
573C22—102no—
574C22—102no—
575C22—102no—
576C22—102no—
577C22—102no—
578C22—102no—
579C22—102no—
580C22—102no—
581C22—201no—
582C22—201no—
583C22—201no—
584C22—201no—
585C22C2×D5×C4⋊C411yescharacteristic
586C22D5×#12111yescharacteristic
587C22D5×#12111yescharacteristic
588C22#6609111yescharacteristic
589C22#6610011yescharacteristic
590C22#6610311yescharacteristic
591C22#6610511yescharacteristic
592C4—22no—
593C4—54no—
594C4—82no—
595C4—82no—
596C4—102no—
597C4—402no—
598C4—402no—
599C4C2×D5×C22⋊C411yescharacteristic
600C4D5×#11711yescharacteristic
601C4D5×C22⋊Q811yescharacteristic
602C4D5×C22⋊Q811yescharacteristic
603C2—42no—
604C2—104no—
605C2—202no—
606C2D5×#38011yescharacteristic
607C2#1061087711yescharacteristic
608C2#1061091011yescharacteristic
609C2#1061244711yescharacteristic
610C2#1061244811yescharacteristic
611C2#1061249111yescharacteristic
612C2#1061249211yescharacteristic
subgroupG/H
centerC23C2×D4×D5
commutatorC2×C4×C5C23×C4
FrattiniC22×C4C23×D5
FittingC5×#1808C2
socleC23×C5C22×D4
prime radicalC22×#709C22
cosocleC22×C4×C5C24
hypercenter#1808D5
hypocenterC5#20663
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1808

Complements

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

NH ≅ G/Ntype
2. C2×#65169C2semidirect
3. C2×D5×#107C2semidirect
5. C5×#1808C2semidirect
6. #10602764C2semidirect
7. #10601423C2semidirect
8. #10601423C2semidirect
9. #10600306C2semidirect
10. #10599663C2semidirect
11. #10599660C2semidirect
17. C2×#4047C4semidirect
61. C22×C5×C8C2×C4semidirect
77. C2×#681C2×C4semidirect
86. C2×#676C2×C4semidirect
90. C2×C8×D5C2×C4semidirect
116. #1808D5semidirect
198. C8×D5C22⋊C4semidirect
335. C22×C8C4×D5semidirect
563. C5#20663semidirect

Maximal subgroups

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

subgroupindex
C22×#40472
C2×#651692
C2×D5×#1072
#106057342
C5×#18082
#106027642
#106014232
#106003062
#105996632
#105996602
#206635