Finite Group Databasebeta

← #12069018

Subgroups — #12069018

Order 1280.

660 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10610745C211yesmaximal, characteristic, complemented
2#10610744C211yesmaximal, characteristic, complemented
3C4×#4050C211yesmaximal, characteristic
4C2×C5×#334C211yesmaximal, characteristic, complemented
5#10601218C211yesmaximal, characteristic, complemented
6#10601218C211yesmaximal, characteristic, complemented
7#10600519C211yesmaximal, characteristic, complemented
8#10599315C212yesmaximal, complemented
9#10599314C212yesmaximal, complemented
10#10599313C212yesmaximal, complemented
11#10599312C212yesmaximal, complemented
12C2×#4050C411yescharacteristic
13C4×#709C2211yescharacteristic
14C4×#709C2211yescharacteristic
15C2×C5×C4⋊C8C2211yescharacteristic
16C2×C5×C4⋊C8C2211yescharacteristic
17C2×C4×C5×C8C2211yescharacteristic
18#65402C411yescharacteristic
19#65402C411yescharacteristic
20#65400—22no—
21C8×C22⋊D5—22no—
22#65395C411yescharacteristic
23#65214C2211yescharacteristic
24#65214C2211yescharacteristic
25#65127C2212yes—
26#65126—21no—
27#65124—21no—
28#65123C2212yes—
29#65122—21no—
30D5×C4⋊C8—21no—
31#65120C2212yes—
32#65119C2212yes—
33C4×Dic20C411yescharacteristic
34C4×Dic20C2211yescharacteristic
35C4×D40C411yescharacteristic
36C4×D40C2211yescharacteristic
37C4×#677C411yescharacteristic
38C4×#677C411yescharacteristic
39C4×#677C2211yescharacteristic
40C4×#677C2211yescharacteristic
41C5×#334C2212yes—
42C5×#334C2212yes—
43#64704C2212yes—
44#64704C2212yes—
45#64703C2212yes—
46#64703C2212yes—
47#64674C2212yes—
48#64674C2212yes—
49#17882—51nomaximal, Sylow
50C2×#709C2×C411yescharacteristic
51C2×#709C2×C411yescharacteristic
52C22×C5×C8—21no—
53C22×C5×C8—21no—
54C22×C5×C8C2×C411yescharacteristic
55C22×C5×C8C2×C411yescharacteristic
56C2×C42×C5C2311yescharacteristic
57C4×C22⋊D5—21no—
58C4×C22⋊D5—21no—
59C4×C22⋊D5—21no—
60C4×C22⋊D5—21no—
61#4072C2×C411yescharacteristic
62#4072C2×C411yescharacteristic
63C2×Dic20C2×C411yescharacteristic
64#4050—24no—
65C2×D40C2×C411yescharacteristic
66C2×#677C2×C411yescharacteristic
67C2×#677C2×C411yescharacteristic
68C2×#676—22no—
69C2×C8×D5—22no—
70C4×D20C2×C411yescharacteristic
71C4×D20C2×C411yescharacteristic
72C4×D20C2311yescharacteristic
73C4×D20C2311yescharacteristic
74#4018—21no—
75#4018—21no—
76C42×D5—21no—
77C42×D5—21no—
78C4×Dic10C2×C411yescharacteristic
79C4×Dic10C2×C411yescharacteristic
80C4×Dic10C2311yescharacteristic
81C4×Dic10C2311yescharacteristic
82C5×C4⋊C8—21no—
83C5×C4⋊C8—21no—
84C5×C4⋊C8C2312yes—
85C5×C4⋊C8C2312yes—
86C4×C5×C8C2×C411yescharacteristic
87C4×C5×C8C2×C411yescharacteristic
88C4×C5×C8C2311yescharacteristic
89C4×C5×C8C2311yescharacteristic
90C22⋊#168—21no—
91C22⋊#168D412yes—
92#3953C2×C411yescharacteristic
93#3953C2×C411yescharacteristic
94#3953C2×C411yescharacteristic
95#3953C2×C411yescharacteristic
96#3952—22no—
97#3952—22no—
98#3950C2×C411yescharacteristic
99#3950C2×C411yescharacteristic
100#3949C2×C411yescharacteristic
101#3949C2×C411yescharacteristic
102#3948C2×C411yescharacteristic
103#3948C2×C411yescharacteristic
104#3948C2×C411yescharacteristic
105#3948C2×C411yescharacteristic
106#3947—22no—
107#3946—22no—
108#3946—22no—
109C8×Dic5—22no—
110C4⋊#168—21no—
111C4⋊#168D411yescharacteristic
112C4⋊#168D411yescharacteristic
113C4×#168C2312yes—
114C4×#168C2312yes—
115#2989—51no—
116#2988—51no—
117C4×#135—51no—
118#1587—52no—
119#1586—52no—
120#1583—52no—
121#1582—52no—
122C2×#334D511yescharacteristic, complemented
123#1477—51no—
124#1477—51no—
125#1452—51no—
126C22×C4×C5C22×C411yescharacteristic
127C22×C4×C5C2×D411yescharacteristic
128C22×C4×C5#4111yescharacteristic
129C2×C22⋊D5—21no—
130C2×C22⋊D5—21no—
131#709—22no—
132#709—22no—
133#709—22no—
134#709M1614yescomplemented
135C2×D20C22×C411yescharacteristic
136C2×D20C22×C411yescharacteristic
137C2×C4×D5—21no—
138C2×C4×D5—21no—
139C2×C4×D5—21no—
140C2×C4×D5—21no—
141C2×C4×D5—21no—
142C2×C4×D5—21no—
143C2×Dic10C22×C411yescharacteristic
144C2×Dic10C22×C411yescharacteristic
145C2×C5×C8—22no—
146C2×C5×C8—22no—
147C2×C5×C8—22no—
148C2×C5×C8—22no—
149C2×C5×C8—81no—
150C2×C5×C8—81no—
151C2×C5×C8C22×C411yescharacteristic
152C2×C5×C8C22×C411yescharacteristic
153C2×C5×C8C22×C411yescharacteristic
154C2×C5×C8C22×C411yescharacteristic
155C42×C5C22×C411yescharacteristic
156C42×C5C2×D411yescharacteristic
157C42×C5#4111yescharacteristic
158C42×C5C2411yescharacteristic
159C22⋊Dic5—21no—
160C22⋊Dic5—21no—
161#685—21no—
162#685—21no—
163#685—21no—
164#685—21no—
165C4⋊Dic5C22×C411yescharacteristic
166C4⋊Dic5C22×C411yescharacteristic
167C4⋊Dic5C22×C411yescharacteristic
168C4⋊Dic5C22×C411yescharacteristic
169#683—21no—
170#683—21no—
171#683—21no—
172#683—21no—
173C4×Dic5—21no—
174C4×Dic5—21no—
175C4×Dic5—21no—
176C4×Dic5—21no—
177C4×Dic5—21no—
178C4×Dic5—21no—
179C2×#168—22no—
180C2×#168C2×D412yes—
181C2×#168C2×D412yes—
182Dic20—22no—
183D40—22no—
184#677—22no—
185#677—22no—
186#676—82no—
187C8×D5—82no—
188C2×#135—51no—
189C4×#41—51no—
190C4×#41—51no—
191#446—52no—
192C8×Q8—52no—
193C4×Q16—51no—
194C4×Q16—51no—
195C4×SD16—51no—
196C4×SD16—51no—
197C4×SD16—51no—
198C4×SD16—51no—
199C4×D8—51no—
200C4×D8—51no—
201#436—52no—
202#435—102no—
203C8×D4—52no—
204C8×D4—102no—
205#432—101no—
206#431—51no—
207#431—51no—
208#431—101no—
209#427—51no—
210#423—101no—
211C2×C4⋊C8—101no—
212C2×C4⋊C8C2×D511yescharacteristic
213C2×C4⋊C8C2×D511yescharacteristic
214#416—51no—
215#416—51no—
216C2×C4×C8C2×D511yescharacteristic
217#334C2×D512yes—
218#334C2×D512yes—
219Q8⋊C8—52no—
220Q8⋊C8—52no—
221D4⋊C8—52no—
222D4⋊C8—52no—
223#322—52no—
224#322—52no—
225C23×C5C4×D411yescharacteristic
226C22×D5—21no—
227C22×D5—21no—
228C2×C4×C5—21no—
229C2×C4×C5—21no—
230C2×C4×C5—41no—
231C2×C4×C5C4×D411yescharacteristic
232C2×C4×C5C4×D411yescharacteristic
233C2×C4×C5C4×D411yescharacteristic
234C2×C4×C5C2×M1612yes—
235C2×C4×C5#13112yes—
236C2×C4×C5C23×C411yescharacteristic
237C2×C4×C5C22×D411yescharacteristic
238C2×C4×C5C2×#4111yescharacteristic
239C22⋊D5—24no—
240C22⋊D5—42no—
241C2×Dic5—21no—
242C2×Dic5—21no—
243C2×Dic5—21no—
244C2×Dic5—21no—
245C2×Dic5—21no—
246C2×Dic5—21no—
247D20—21no—
248D20—21no—
249D20—21no—
250D20C2×M1612yes—
251C4×D5—24no—
252C4×D5—41no—
253C4×D5—41no—
254C4×D5—41no—
255C4×D5—41no—
256C4×D5—42no—
257C4×D5—81no—
258C4×D5—81no—
259Dic10—21no—
260Dic10—21no—
261Dic10—21no—
262Dic10C2×M1612yes—
263C5×C8—21no—
264C5×C8—21no—
265C5×C8—21no—
266C5×C8—21no—
267C5×C8—42no—
268C5×C8—42no—
269#168—22no—
270#168—22no—
271#168—42no—
272C2×#41—51no—
273C2×#41—51no—
274#135—104no—
275C2×Q16—51no—
276C2×SD16—51no—
277C2×SD16—51no—
278C2×D8—51no—
279C2×M16—102no—
280C22×C8—21no—
281C22×C8—21no—
282C22×C8—102no—
283C22×C8C4×D511yescharacteristic
284C22×C8C4×D511yescharacteristic
285C4×Q8—51no—
286C4×Q8—51no—
287C4×Q8—51no—
288C4×Q8—51no—
289C4×D4—51no—
290C4×D4—51no—
291C4×D4—51no—
292C4×D4—51no—
293C4×D4—101no—
294C4×D4—101no—
295C4×D4—101no—
296C4×D4—101no—
297#117—51no—
298#117—51no—
299#117—101no—
300#117—101no—
301C2×C42—101no—
302C2×C42—101no—
303C2×C42C22×D511yescharacteristic
304#107—51no—
305#107—51no—
306#106—51no—
307#106—51no—
308C4⋊C8—21no—
309C4⋊C8—21no—
310C4⋊C8—51no—
311C4⋊C8—51no—
312C4⋊C8—102no—
313C4⋊C8—102no—
314C4⋊C8—101no—
315C4⋊C8C22×D512yes—
316C4⋊C8C22×D512yes—
317#103—51no—
318#103—51no—
319#103—51no—
320#103—51no—
321#102—51no—
322#102—51no—
323#102—51no—
324#102—51no—
325C22⋊C8—52no—
326C22⋊C8—102no—
327C22⋊C8—102no—
328C22⋊C8—101no—
329#97—102no—
330C4×C8—52no—
331C4×C8—52no—
332C4×C8—102no—
333C4×C8C4×D511yescharacteristic
334C4×C8C4×D511yescharacteristic
335C4×C8C22×D511yescharacteristic
336C4×C8C22×D511yescharacteristic
337C22×C5—21no—
338C22×C5—21no—
339C22×C5#43512yes—
340C22×C5C2×C4×D411yescharacteristic
341C2×D5—22no—
342C2×D5—41no—
343C2×D5—41no—
344C2×D5—41no—
345C2×D5—41no—
346C2×D5—41no—
347C4×C5—21no—
348C4×C5—21no—
349C4×C5—21no—
350C4×C5#43512yes—
351C4×C5C22×M1611yescharacteristic
352C4×C5C2×#13111yescharacteristic
353C4×C5#57711yescharacteristic
354C4×C5#57711yescharacteristic
355Dic5—22no—
356Dic5—41no—
357Dic5—41no—
358Dic5—41no—
359Dic5—41no—
360Dic5—41no—
361#41—54no—
362#41—102no—
363#41—102no—
364#41—102no—
365C2×Q8—51no—
366C2×Q8—51no—
367C2×D4—51no—
368C2×D4—51no—
369C2×D4—101no—
370C2×D4—101no—
371C22×C4—101no—
372C22×C4—101no—
373C22×C4—101no—
374C22×C4—101no—
375C22×C4—101no—
376C22×C4—101no—
377C22×C4C2×C4×D511yescharacteristic
378C22×C4D4×D511yescharacteristic
379C22×C4#71311yescharacteristic
380Q16—102no—
381SD16—102no—
382SD16—102no—
383D8—102no—
384M16—402no—
385C2×C8—22no—
386C2×C8—22no—
387C2×C8—22no—
388C2×C8—22no—
389C2×C8—52no—
390C2×C8—52no—
391C2×C8—81no—
392C2×C8—81no—
393C2×C8—102no—
394C2×C8—402no—
395C2×C8C2×C4×D511yescharacteristic
396C2×C8C2×C4×D511yescharacteristic
397C2×C8C2×C4×D511yescharacteristic
398C2×C8C2×C4×D511yescharacteristic
399C4⋊C4—51no—
400C4⋊C4—51no—
401C4⋊C4—51no—
402C4⋊C4—51no—
403C4⋊C4—101no—
404C4⋊C4—101no—
405C4⋊C4—101no—
406C4⋊C4—101no—
407C22⋊C4—101no—
408C22⋊C4—101no—
409C22⋊C4—101no—
410C22⋊C4—101no—
411C22⋊C4—101no—
412C22⋊C4—101no—
413C42—101no—
414C42—101no—
415C42—101no—
416C42—101no—
417C42—101no—
418C42—101no—
419C42C2×C4×D511yescharacteristic
420C42D4×D511yescharacteristic
421C42#71311yescharacteristic
422C42C23×D511yescharacteristic
423C2×C5—22no—
424C2×C5C2×#43511yescharacteristic
425C2×C5#295211yescharacteristic
426C2×C5#295711yescharacteristic
427D5—42no—
428D5—81no—
429C23—101no—
430C23—101no—
431C23#403911yescharacteristic
432Q8—52no—
433Q8—101no—
434Q8—101no—
435Q8—101no—
436D4—52no—
437D4—104no—
438D4—101no—
439D4—101no—
440D4—101no—
441D4—202no—
442C2×C4—21no—
443C2×C4—21no—
444C2×C4—41no—
445C2×C4—101no—
446C2×C4—104no—
447C2×C4—101no—
448C2×C4—101no—
449C2×C4—101no—
450C2×C4—101no—
451C2×C4—101no—
452C2×C4—201no—
453C2×C4—201no—
454C2×C4—201no—
455C2×C4—201no—
456C2×C4—202no—
457C2×C4—401no—
458C2×C4—401no—
459C2×C4#403911yescharacteristic
460C2×C4#403911yescharacteristic
461C2×C4#403911yescharacteristic
462C2×C4#404712yes—
463C2×C4D5×M1612yes—
464C2×C4C22×C4×D511yescharacteristic
465C2×C4C2×D4×D511yescharacteristic
466C2×C4C2×#71311yescharacteristic
467C8—21no—
468C8—21no—
469C8—21no—
470C8—21no—
471C8—42no—
472C8—42no—
473C8—102no—
474C8—102no—
475C8—202no—
476C5#1788211yescharacteristic, complemented, Sylow
477C22—21no—
478C22—21no—
479C22—102no—
480C22—201no—
481C22—201no—
482C22—201no—
483C22—201no—
484C22—201no—
485C22#6512512yes—
486C22C2×#403911yescharacteristic
487C4—21no—
488C4—21no—
489C4—21no—
490C4—102no—
491C4—201no—
492C4—201no—
493C4—201no—
494C4—201no—
495C4—201no—
496C4#6512512yes—
497C4C2×#404711yescharacteristic
498C4C2×D5×M1611yescharacteristic
499C4#6609611yescharacteristic
500C4#6609611yescharacteristic
501C2—22no—
502C2—202no—
503C2—401no—
504C2C2×#6512511yescharacteristic
505C2#1061083711yescharacteristic
506C2#1061098011yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D5
commutatorC2×C4×C5C23×C4
FrattiniC42C23×D5
FittingC2×C5×#334C2
socleC22×C5C2×C4×D4
prime radicalC2×#4050C4
cosocleC42×C5C24
hypercenterC2×#334D5
hypocenterC5#17882
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×#334

Complements

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

NH ≅ G/Ntype
1. #10610745C2semidirect
2. #10610744C2semidirect
4. C2×C5×#334C2semidirect
5. #10601218C2semidirect
6. #10601218C2semidirect
7. #10600519C2semidirect
8. #10599315C2semidirect
9. #10599314C2semidirect
10. #10599313C2semidirect
11. #10599312C2semidirect
122. C2×#334D5semidirect
134. #709M16semidirect
476. C5#17882semidirect

Maximal subgroups

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

subgroupindex
#106107452
#106107442
C4×#40502
C2×C5×#3342
#106012182
#106005192
#105993152
#105993142
#105993132
#105993122
#178825