Finite Group Databasebeta

← #12115452

Subgroups — #12115452

Order 1280.

1132 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65875C211yesmaximal, characteristic
2#10605187C212yesmaximal, complemented
3C4×C5×#99C211yesmaximal, characteristic
4#10602412C211yesmaximal, characteristic
5#10600822C214yesmaximal
6#10600250C212yesmaximal, complemented
7#10599746C212yesmaximal, complemented
8#10599744C212yesmaximal, complemented
9C2×C4×C5×D4C2211yescharacteristic
10C2×#4081C2212yes—
11C2×#4072C411yescharacteristic, complemented
12C22×C4⋊Dic5C2211yescharacteristic
13C2×#4070C411yescharacteristic, complemented
14C2×#4070C2211yescharacteristic
15#65875—24no—
16#65875—22no—
17#65875—22no—
18C2×#4035C412yescomplemented
19C2×#4025C412yescomplemented
20C2×#4023C2212yes—
21C2×#4023C2214yes—
22C2×#4016C411yescharacteristic, complemented
23C2×C4×Dic10C411yescharacteristic, complemented
24C2×C5×#99C2212yes—
25C4×C5×C22⋊C4C2212yes—
26C2×#3966C2212yes—
27#65501C2212yes—
28#65232C2214yes—
29C4×C4⋊Dic5—22no—
30#65217—22no—
31#64942—24no—
32C5×#342C2211yescharacteristic
33C5×#342C2211yescharacteristic
34#64747C2214yes—
35#64747C2214yes—
36#64746C2212yes—
37#22478—51nomaximal, Sylow
38C22×C5×D4C2311yescharacteristic
39C23×C4×C5C2×C411yescharacteristic
40C23×C4×C5C2311yescharacteristic
41C23×Dic5C2312yes—
42C22×Dic10C2×C411yescharacteristic
43C4×C5×D4—22no—
44C4×C5×D4—22no—
45C2×C5×C4⋊C4C2×C411yescharacteristic
46C2×C5×C22⋊C4C2×C411yescharacteristic
47C2×C5×C22⋊C4C2312yes—
48C2×C5×C22⋊C4C2311yescharacteristic
49C2×C5×C22⋊C4C2312yes—
50C2×C42×C5—22no—
51C2×C42×C5C2×C411yescharacteristic
52C2×C22⋊Dic5C2×C412yes—
53C2×C22⋊Dic5C2×C412yes—
54C2×C22⋊Dic5C2314yes—
55C2×C22⋊Dic5C2312yes—
56#4081—24no—
57#4081—24no—
58#4072—22no—
59#4072—21no—
60#4072—21no—
61C2×C4⋊Dic5—22no—
62C2×C4⋊Dic5C2×C411yescharacteristic
63C2×C4⋊Dic5C2×C411yescharacteristic
64C2×C4⋊Dic5C2×C411yescharacteristic
65C2×C4⋊Dic5C2×C412yes—
66C2×C4⋊Dic5D414yes—
67C2×C4⋊Dic5D412yes—
68C2×C4⋊Dic5D412yes—
69#4070—22no—
70#4070—22no—
71#4070—22no—
72#4070—22no—
73C2×#683—24no—
74C2×#683C2×C412yes—
75C2×#683C2×C412yes—
76C2×#683C2×C412yes—
77C2×#683C2×C412yes—
78C2×#683C2×C412yes—
79C2×C4×Dic5—24no—
80C2×C4×Dic5C2×C412yes—
81C2×C4×Dic5C2×C412yes—
82#4035—24no—
83#4035—24no—
84#4025—24no—
85#4025—24no—
86#4023—24no—
87#4023—24no—
88#4023—28no—
89#4023—44no—
90#4016—22no—
91#4016—22no—
92C4×Dic10—22no—
93C4×Dic10—21no—
94C4×Dic10—21no—
95C5×#99—24no—
96C5×#95—22no—
97#3966—42no—
98#3963—22no—
99#3963—24no—
100#3963—24no—
101C2×#552—51no—
102#2344—52no—
103#1996—52no—
104#1899—54no—
105#1820—52no—
106#1799—51no—
107C4×#99D511yescharacteristic
108#1740—52no—
109C24×C5C22×C411yescharacteristic
110C24×C5C2411yescharacteristic
111C2×C5×D4—22no—
112C2×C5×D4—22no—
113C2×C5×D4—21no—
114C2×C5×D4—21no—
115C22×C4×C5—22no—
116C22×C4×C5—21no—
117C22×C4×C5—21no—
118C22×C4×C5—22no—
119C22×C4×C5—42no—
120C22×C4×C5—42no—
121C22×C4×C5C22×C411yescharacteristic
122C22×C4×C5C22×C411yescharacteristic
123C22×C4×C5C22×C411yescharacteristic
124C22×C4×C5C22×C411yescharacteristic
125C22×C4×C5C22×C411yescharacteristic
126C22×C4×C5C2×D412yes—
127C22×C4×C5C2×D412yes—
128C22×Dic5—24no—
129C22×Dic5—22no—
130C22×Dic5—22no—
131C22×Dic5—24no—
132C22×Dic5C22×C412yes—
133C22×Dic5C22×C412yes—
134C22×Dic5C22×C412yes—
135C22×Dic5C22×C412yes—
136C22×Dic5C2×D414yes—
137C22×Dic5C2×D414yes—
138C2×Dic10—21no—
139C2×Dic10—21no—
140C2×Dic10—42no—
141C5×C4⋊C4—22no—
142C5×C22⋊C4—22no—
143C5×C22⋊C4—22no—
144C5×C22⋊C4—22no—
145C5×C22⋊C4—22no—
146C5×C22⋊C4—22no—
147C5×C22⋊C4#4114yes—
148C42×C5—21no—
149C42×C5—21no—
150C42×C5—44no—
151C22⋊Dic5—24no—
152C22⋊Dic5—24no—
153C22⋊Dic5—22no—
154C22⋊Dic5—22no—
155C22⋊Dic5—24no—
156C22⋊Dic5—24no—
157C4⋊Dic5—21no—
158C4⋊Dic5—21no—
159C4⋊Dic5—44no—
160C4⋊Dic5C22⋊C412yes—
161C4⋊Dic5C22⋊C411yescharacteristic
162C4⋊Dic5C22⋊C411yescharacteristic
163C4⋊Dic5C22⋊C412yes—
164C4⋊Dic5C22⋊C412yes—
165C4⋊Dic5C22⋊C414yes—
166C4⋊Dic5C22⋊C414yes—
167#683—24no—
168#683—22no—
169#683—22no—
170#683—24no—
171#683—24no—
172#683—24no—
173#683—48no—
174C4×Dic5—22no—
175C4×Dic5—22no—
176C4×Dic5—22no—
177C4×Dic5—22no—
178C4×Dic5—48no—
179#552—102no—
180#552—104no—
181#552—102no—
182C2×#126—52no—
183C2×#125—52no—
184C2×#125—51no—
185C2×#123—52no—
186C2×C22⋊Q8—51no—
187C2×C22⋊Q8—51no—
188C2×C4×Q8—51no—
189C2×C4×D4C2×D511yescharacteristic
190C2×#117—51no—
191C2×#117—52no—
192C2×#117—54no—
193C22×C4⋊C4—51no—
194C2×#99—52no—
195C2×#99C2×D512yes—
196#389—102no—
197#387—104no—
198#381—54no—
199#380—52no—
200C4×C4⋊C4—102no—
201C4×C22⋊C4C2×D512yes—
202#342—52no—
203#342—54no—
204#342—54no—
205#342C2×D511yescharacteristic
206#342C2×D511yescharacteristic
207C23×C5—21no—
208C23×C5—21no—
209C23×C5—21no—
210C23×C5—41no—
211C23×C5—41no—
212C23×C5—41no—
213C23×C5—41no—
214C23×C5C23×C411yescharacteristic
215C23×C5C22×D412yes—
216C23×C5C2×#4112yes—
217C23×C5H(5,𝔽2)11yescharacteristic
218C23×C52−1+411yescharacteristic
219C5×D4—42no—
220C5×D4—42no—
221C2×C4×C5—24no—
222C2×C4×C5—22no—
223C2×C4×C5—21no—
224C2×C4×C5—21no—
225C2×C4×C5—21no—
226C2×C4×C5—21no—
227C2×C4×C5—21no—
228C2×C4×C5—24no—
229C2×C4×C5—41no—
230C2×C4×C5—42no—
231C2×C4×C5—42no—
232C2×C4×C5—42no—
233C2×C4×C5—42no—
234C2×C4×C5—42no—
235C2×C4×C5—41no—
236C2×C4×C5—41no—
237C2×C4×C5—42no—
238C2×C4×C5—42no—
239C2×C4×C5—42no—
240C2×C4×C5C2×C22⋊C412yes—
241C2×C4×C5C2×C22⋊C411yescharacteristic
242C2×C4×C5C2×C22⋊C411yescharacteristic
243C2×Dic5—22no—
244C2×Dic5—22no—
245C2×Dic5—22no—
246C2×Dic5—22no—
247C2×Dic5—24no—
248C2×Dic5—24no—
249C2×Dic5—24no—
250C2×Dic5—24no—
251C2×Dic5—22no—
252C2×Dic5—22no—
253C2×Dic5—42no—
254C2×Dic5—42no—
255C2×Dic5—44no—
256C2×Dic5—44no—
257C2×Dic5—44no—
258C2×Dic5C2×C22⋊C412yes—
259C2×Dic5C2×C22⋊C412yes—
260C2×Dic5C2×C22⋊C414yes—
261Dic10—42no—
262Dic10—42no—
263C22×Q8—51no—
264C22×D4C22×D511yescharacteristic
265C23×C4—52no—
266C23×C4C4×D511yescharacteristic
267C23×C4C22×D511yescharacteristic
268#126—104no—
269#126—104no—
270#125—102no—
271#125—102no—
272#125—104no—
273#125—104no—
274#123—104no—
275#123—104no—
276C22⋊Q8—102no—
277C22⋊Q8—102no—
278C22⋊Q8—102no—
279C22⋊Q8—102no—
280C4×Q8—102no—
281C4×Q8—101no—
282C4×Q8—101no—
283C4×D4—22no—
284C4×D4—22no—
285#117—104no—
286#117—104no—
287#117—102no—
288#117—101no—
289#117—101no—
290#117—108no—
291#117—204no—
292C2×C4⋊C4—51no—
293C2×C4⋊C4—51no—
294C2×C4⋊C4—52no—
295C2×C4⋊C4—52no—
296C2×C4⋊C4—54no—
297C2×C4⋊C4—52no—
298C2×C4⋊C4—52no—
299C2×C4⋊C4—51no—
300C2×C4⋊C4—52no—
301C2×C4⋊C4—52no—
302C2×C4⋊C4—52no—
303C2×C4⋊C4—52no—
304C2×C4⋊C4—104no—
305C2×C4⋊C4—102no—
306C2×C4⋊C4C4×D511yescharacteristic
307C2×C22⋊C4—52no—
308C2×C22⋊C4—52no—
309C2×C22⋊C4—52no—
310C2×C22⋊C4—54no—
311C2×C22⋊C4C4×D511yescharacteristic
312C2×C22⋊C4C22×D512yes—
313C2×C22⋊C4C22×D511yescharacteristic
314C2×C22⋊C4C22×D512yes—
315C2×C42—22no—
316C2×C42—52no—
317C2×C42—52no—
318C2×C42—104no—
319C2×C42C4×D511yescharacteristic
320#99—24no—
321#99—202no—
322#95—22no—
323#95—104no—
324#95—104no—
325#95—102no—
326C22×C5—22no—
327C22×C5—21no—
328C22×C5—22no—
329C22×C5—21no—
330C22×C5—42no—
331C22×C5—41no—
332C22×C5—41no—
333C22×C5—41no—
334C22×C5—41no—
335C22×C5—41no—
336C22×C5—81no—
337C22×C5—81no—
338C22×C5C22×C22⋊C411yescharacteristic
339C22×C5C4×#4111yescharacteristic
340C22×C5#52011yescharacteristic
341C22×C5#54612yes—
342C22×C5#54712yes—
343C4×C5—21no—
344C4×C5—22no—
345C4×C5—44no—
346C4×C5—41no—
347C4×C5—41no—
348C4×C5—41no—
349C4×C5—82no—
350C4×C5#41012yes—
351Dic5—22no—
352Dic5—24no—
353Dic5—22no—
354Dic5—42no—
355Dic5—42no—
356Dic5—84no—
357C24C2×C4×D511yescharacteristic
358C24C23×D511yescharacteristic
359C2×Q8—101no—
360C2×Q8—101no—
361C2×Q8—202no—
362C2×D4—22no—
363C2×D4—22no—
364C2×D4—21no—
365C2×D4—21no—
366C22×C4—22no—
367C22×C4—21no—
368C22×C4—21no—
369C22×C4—22no—
370C22×C4—42no—
371C22×C4—42no—
372C22×C4—52no—
373C22×C4—52no—
374C22×C4—54no—
375C22×C4—54no—
376C22×C4—52no—
377C22×C4—52no—
378C22×C4—104no—
379C22×C4—102no—
380C22×C4—102no—
381C22×C4—104no—
382C22×C4C2×C4×D511yescharacteristic
383C22×C4C2×C4×D511yescharacteristic
384C22×C4C2×C4×D511yescharacteristic
385C22×C4C2×C4×D511yescharacteristic
386C22×C4C2×C4×D511yescharacteristic
387C22×C4D4×D512yes—
388C22×C4D4×D512yes—
389C4⋊C4—22no—
390C4⋊C4—52no—
391C4⋊C4—51no—
392C4⋊C4—51no—
393C4⋊C4—52no—
394C4⋊C4—52no—
395C4⋊C4—54no—
396C4⋊C4—54no—
397C4⋊C4—104no—
398C4⋊C4—104no—
399C4⋊C4—102no—
400C4⋊C4—102no—
401C4⋊C4—104no—
402C4⋊C4—101no—
403C4⋊C4—101no—
404C4⋊C4—104no—
405C4⋊C4—208no—
406C4⋊C4—204no—
407C22⋊C4—22no—
408C22⋊C4—22no—
409C22⋊C4—22no—
410C22⋊C4—22no—
411C22⋊C4—22no—
412C22⋊C4—102no—
413C22⋊C4—102no—
414C22⋊C4—104no—
415C22⋊C4—104no—
416C22⋊C4—104no—
417C22⋊C4—104no—
418C22⋊C4#70914yes—
419C42—21no—
420C42—21no—
421C42—44no—
422C42—102no—
423C42—102no—
424C42—102no—
425C42—102no—
426C42—208no—
427C2×C5—22no—
428C2×C5—22no—
429C2×C5—21no—
430C2×C5—21no—
431C2×C5—81no—
432C2×C5#233911yescharacteristic
433C2×C5C2×#41011yescharacteristic
434C2×C5#288411yescharacteristic
435C23—21no—
436C23—21no—
437C23—21no—
438C23—41no—
439C23—41no—
440C23—41no—
441C23—41no—
442C23C22×C4×D511yescharacteristic
443C23C2×#70912yes—
444C23C2×D4×D512yes—
445C23#414911yescharacteristic
446C23#415011yescharacteristic
447Q8—202no—
448Q8—202no—
449D4—42no—
450D4—42no—
451C2×C4—24no—
452C2×C4—22no—
453C2×C4—21no—
454C2×C4—21no—
455C2×C4—21no—
456C2×C4—21no—
457C2×C4—21no—
458C2×C4—24no—
459C2×C4—41no—
460C2×C4—42no—
461C2×C4—42no—
462C2×C4—42no—
463C2×C4—42no—
464C2×C4—42no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—42no—
470C2×C4—52no—
471C2×C4—52no—
472C2×C4—54no—
473C2×C4—102no—
474C2×C4—102no—
475C2×C4—102no—
476C2×C4—102no—
477C2×C4—104no—
478C2×C4—104no—
479C2×C4—104no—
480C2×C4—104no—
481C2×C4—102no—
482C2×C4—102no—
483C2×C4—202no—
484C2×C4—202no—
485C2×C4—204no—
486C2×C4—204no—
487C2×C4—204no—
488C2×C4D5×C22⋊C411yescharacteristic
489C2×C4D5×C22⋊C412yes—
490C2×C4D5×C22⋊C411yescharacteristic
491C5#2247811yescharacteristic, complemented, Sylow
492C22—22no—
493C22—21no—
494C22—22no—
495C22—21no—
496C22—42no—
497C22—41no—
498C22—41no—
499C22—41no—
500C22—41no—
501C22—41no—
502C22—81no—
503C22—81no—
504C22C4×#70911yescharacteristic
505C22C2×D5×C22⋊C411yescharacteristic
506C22#6585711yescharacteristic
507C22#6588412yes—
508C22#6588512yes—
509C4—21no—
510C4—22no—
511C4—44no—
512C4—41no—
513C4—41no—
514C4—41no—
515C4—82no—
516C4—102no—
517C4—102no—
518C4—104no—
519C4—202no—
520C4—202no—
521C4—404no—
522C4#6502912yes—
523C2—22no—
524C2—22no—
525C2—21no—
526C2—21no—
527C2—81no—
528C2#1060530411yescharacteristic
529C2C2×#6502911yescharacteristic
530C2#1061042011yescharacteristic
subgroupG/H
centerC22C2×D5×C22⋊C4
commutatorC23×C5C23×C4
FrattiniC24C23×D5
FittingC4×C5×#99C2
socleC22×C5C22×C22⋊C4
prime radicalC22×C5×D4C23
cosocleC24×C5C24
hypercenterC4×#99D5
hypocenterC5#22478
LCSG ▷ C23×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C23×C4 ◁ C4×#99

Complements

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

NH ≅ G/Ntype
2. #10605187C2semidirect
6. #10600250C2semidirect
7. #10599746C2semidirect
8. #10599744C2semidirect
11. C2×#4072C4semidirect
13. C2×#4070C4semidirect
18. C2×#4035C4semidirect
19. C2×#4025C4semidirect
22. C2×#4016C4semidirect
23. C2×C4×Dic10C4semidirect
491. C5#22478semidirect

Maximal subgroups

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

subgroupindex
C2×#658752
#106051872
C4×C5×#992
#106024122
#106008222
#106002502
#105997462
#105997442
#224785