Finite Group Databasebeta

← #12108797

Subgroups — #12108797

Order 1280.

1042 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D5×#125C211yesmaximal, characteristic
2C2×#64974C211yesmaximal, characteristic
3#10605878C211yesmaximal, characteristic
4C5×#1991C211yesmaximal, characteristic, complemented
5#10602533C211yesmaximal, characteristic, complemented
6#10600571C211yesmaximal, characteristic, complemented
7#10600347C211yesmaximal, characteristic, complemented
8#10599665C212yesmaximal
9#10599664C212yesmaximal
10#10599595C212yesmaximal, complemented
11#10599594C212yesmaximal, complemented
12C2×C5×#125C2211yescharacteristic
13D5×#125—24no—
14D5×#125C418yescomplemented
15C2×D5×C4⋊C4—21no—
16C2×D5×C4⋊C4—21no—
17C2×D5×C4⋊C4C2211yescharacteristic
18C2×D5×C4⋊C4C2211yescharacteristic
19C2×#4036C2211yescharacteristic
20C2×#4036C2211yescharacteristic
21C2×#4035—21no—
22C2×#4035—21no—
23C2×C42×D5C2211yescharacteristic
24C2×#4016C2211yescharacteristic
25C2×C4×C5×C8C2211yescharacteristic
26C5×#382C2211yescharacteristic
27C2×#3952C2212yes—
28C2×#3946C2212yes—
29#65276C2212yes—
30C4⋊C4×Dic5C2212yes—
31#65225C2211yescharacteristic
32C2×C4×#168C2211yescharacteristic
33#64974—24no—
34#64955—21no—
35#64953—21no—
36#64940—21no—
37#64937—21no—
38C5×#340C2212yes—
39C5×#340C2212yes—
40#64771C2212yes—
41#64771C2212yes—
42#64749C2212yes—
43#64749C2212yes—
44#64749C2212yes—
45#64749C2212yes—
46#21836—51nomaximal, Sylow
47C22×C4×D5—21no—
48C22×C4×D5—21no—
49C22×C4×D5D411yescharacteristic
50C22×C4×D5D411yescharacteristic
51C22×C4×D5C2311yescharacteristic
52C22×C5×C8C2312yes—
53C5×#125—22no—
54C5×#125C2×C414yes—
55C2×C5×C4⋊C4—21no—
56C2×C5×C4⋊C4—21no—
57C2×C5×C4⋊C4C2312yes—
58C2×C5×C4⋊C4C2311yescharacteristic
59C2×C5×C4⋊C4C2311yescharacteristic
60C2×C42×C5C2311yescharacteristic
61C2×#685—22no—
62C2×C4⋊Dic5—21no—
63C2×C4⋊Dic5—21no—
64C2×C4⋊Dic5C2312yes—
65C2×C4⋊Dic5C2311yescharacteristic
66C2×C4⋊Dic5C2311yescharacteristic
67C2×#683—21no—
68C2×#683—21no—
69C2×#683—21no—
70C2×#683—21no—
71C2×#683—21no—
72C2×#683—21no—
73C2×C4×Dic5—22no—
74C2×C4×Dic5D411yescharacteristic
75C2×C4×Dic5D411yescharacteristic
76C2×C4×Dic5C2311yescharacteristic
77C22×#168C2312yes—
78D5×C4⋊C4—28no—
79D5×C4⋊C4—28no—
80D5×C4⋊C4—22no—
81D5×C4⋊C4—22no—
82D5×C4⋊C4C2×C414yes—
83D5×C4⋊C4C2×C414yes—
84#4036—22no—
85#4036—22no—
86#4036C2×C414yes—
87#4036C2×C414yes—
88#4035—28no—
89#4035—28no—
90C42×D5C2×C414yes—
91C42×D5D414yes—
92#4016—22no—
93#4016C2×C414yes—
94C4×C5×C8—22no—
95C5×#95—21no—
96C5×#95—21no—
97#3963—21no—
98#3963—21no—
99#3963—22no—
100#3963—22no—
101#3952—24no—
102#3946—24no—
103C4×#168—22no—
104C22×#125—51no—
105C2×#431—51no—
106#2283—51no—
107#1991—51no—
108#1991—51no—
109#1991—51no—
110#1991D511yescharacteristic, complemented
111#1989—52no—
112#1989—52no—
113#1824—52no—
114#1823—52no—
115C23×D5C2×D411yescharacteristic
116C22×C4×C5—21no—
117C22×C4×C5—21no—
118C22×C4×C5—22no—
119C22×C4×C5C2×D411yescharacteristic
120C22×C4×C5C2×D411yescharacteristic
121C22×C4×C5C2411yescharacteristic
122C22×Dic5—21no—
123C22×Dic5—21no—
124C22×Dic5—22no—
125C22×Dic5C2×D411yescharacteristic
126C22×Dic5C2×D411yescharacteristic
127C22×Dic5C2×D411yescharacteristic
128C2×C4×D5—24no—
129C2×C4×D5—22no—
130C2×C4×D5—22no—
131C2×C4×D5—24no—
132C2×C4×D5—24no—
133C2×C4×D5—42no—
134C2×C4×D5—44no—
135C2×C4×D5—44no—
136C2×C4×D5C22⋊C414yes—
137C2×C4×D5C22⋊C414yes—
138C2×C4×D5C22×C412yes—
139C2×C4×D5C2×D412yes—
140C2×C5×C8—22no—
141C2×C5×C8—22no—
142C2×C5×C8—22no—
143C5×C4⋊C4—24no—
144C5×C4⋊C4—24no—
145C5×C4⋊C4—21no—
146C5×C4⋊C4—21no—
147C5×C4⋊C4—24no—
148C5×C4⋊C4C22×C412yes—
149C5×C4⋊C4C22×C412yes—
150C42×C5C22×C412yes—
151C42×C5C2×D412yes—
152#685—44no—
153C4⋊Dic5—21no—
154C4⋊Dic5—21no—
155C4⋊Dic5—24no—
156C4⋊Dic5—24no—
157C4⋊Dic5—24no—
158C4⋊Dic5C22×C412yes—
159C4⋊Dic5C22×C412yes—
160#683—24no—
161#683—24no—
162#683—24no—
163#683—24no—
164#683—24no—
165#683—24no—
166C4×Dic5—44no—
167C4×Dic5C22⋊C414yes—
168C4×Dic5C22⋊C414yes—
169C4×Dic5C22×C412yes—
170C4×Dic5C2×D412yes—
171C2×#168—22no—
172C2×#168—22no—
173C2×#168—22no—
174C2×#125—58no—
175C2×#125—51no—
176C2×#125—51no—
177C2×#125—51no—
178C2×#125—101no—
179C2×#125—101no—
180C2×#125—104no—
181C2×#125C2×D511yescharacteristic
182C22×C4⋊C4—51no—
183C22×C4⋊C4—51no—
184C22×C4⋊C4—101no—
185C22×C4⋊C4—101no—
186C22×C42—51no—
187#431—104no—
188C2×C4⋊C8—52no—
189C2×C22⋊C8—52no—
190C2×C4×C8—51no—
191C2×C4×C8C2×D511yescharacteristic
192#383—101no—
193#382—51no—
194#382C2×D511yescharacteristic
195#381—101no—
196#380—52no—
197C4×C4⋊C4—52no—
198C4×C22⋊C4—101no—
199#376—101no—
200#340—52no—
201#340—52no—
202#340—52no—
203#340—52no—
204#340—52no—
205#340—52no—
206#340C2×D512yes—
207#340C2×D512yes—
208C23×C5C22×D411yescharacteristic
209C22×D5—21no—
210C22×D5—21no—
211C22×D5—22no—
212C22×D5C2×C22⋊C412yes—
213C22×D5#13514yes—
214C2×C4×C5—22no—
215C2×C4×C5—22no—
216C2×C4×C5—22no—
217C2×C4×C5—22no—
218C2×C4×C5—42no—
219C2×C4×C5—42no—
220C2×C4×C5—42no—
221C2×C4×C5—42no—
222C2×C4×C5—42no—
223C2×C4×C5C2×C22⋊C412yes—
224C2×C4×C5C2×C22⋊C412yes—
225C2×C4×C5C23×C411yescharacteristic
226C2×C4×C5C22×D411yescharacteristic
227C2×C4×C52−1+412yes—
228C2×C4×C52−1+412yes—
229C2×Dic5—21no—
230C2×Dic5—21no—
231C2×Dic5—22no—
232C2×Dic5—22no—
233C2×Dic5—22no—
234C2×Dic5—22no—
235C2×Dic5—42no—
236C2×Dic5—42no—
237C2×Dic5—42no—
238C2×Dic5—42no—
239C2×Dic5—42no—
240C2×Dic5C2×C22⋊C412yes—
241C2×Dic5C2×C22⋊C412yes—
242C2×Dic5C2×C22⋊C412yes—
243C4×D5—28no—
244C4×D5—24no—
245C4×D5—24no—
246C4×D5—44no—
247C4×D5—48no—
248C4×D5—48no—
249C5×C8—42no—
250#168—42no—
251C23×C4—51no—
252C23×C4—51no—
253C23×C4—51no—
254C23×C4—101no—
255C23×C4—101no—
256C22×C8—52no—
257C22×C8C22×D512yes—
258#125—22no—
259#125—54no—
260#125—54no—
261#125—54no—
262#125—108no—
263#125—108no—
264#125—102no—
265#125—102no—
266#125—102no—
267#125C4×D514yes—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—21no—
270C2×C4⋊C4—51no—
271C2×C4⋊C4—51no—
272C2×C4⋊C4—54no—
273C2×C4⋊C4—54no—
274C2×C4⋊C4—52no—
275C2×C4⋊C4—102no—
276C2×C4⋊C4—102no—
277C2×C4⋊C4—108no—
278C2×C4⋊C4—108no—
279C2×C4⋊C4—101no—
280C2×C4⋊C4—101no—
281C2×C4⋊C4—101no—
282C2×C4⋊C4—101no—
283C2×C4⋊C4—101no—
284C2×C4⋊C4—101no—
285C2×C4⋊C4—101no—
286C2×C4⋊C4—101no—
287C2×C4⋊C4C22×D512yes—
288C2×C4⋊C4C22×D511yescharacteristic
289C2×C4⋊C4C22×D511yescharacteristic
290C2×C22⋊C4—102no—
291C2×C42—51no—
292C2×C42—51no—
293C2×C42—51no—
294C2×C42—54no—
295C2×C42—54no—
296C2×C42—102no—
297C2×C42C22×D511yescharacteristic
298C4⋊C8—104no—
299C22⋊C8—104no—
300C4×C8—22no—
301C4×C8—102no—
302#95—21no—
303#95—21no—
304#95—102no—
305#95—102no—
306#95—101no—
307#95—101no—
308C22×C5C22×C22⋊C411yescharacteristic
309C22×C5#53611yescharacteristic
310C22×C5#53611yescharacteristic
311C22×C5C2×#13512yes—
312C22×C5#57512yes—
313C2×D5—22no—
314C2×D5—22no—
315C2×D5—24no—
316C2×D5—24no—
317C2×D5#41614yes—
318C4×C5—22no—
319C4×C5—22no—
320C4×C5—42no—
321C4×C5—42no—
322C4×C5—82no—
323C4×C5#51912yes—
324C4×C5#53612yes—
325Dic5—22no—
326Dic5—22no—
327Dic5—22no—
328Dic5—42no—
329Dic5—42no—
330Dic5—82no—
331C24—51no—
332C22×C4—21no—
333C22×C4—21no—
334C22×C4—22no—
335C22×C4—51no—
336C22×C4—51no—
337C22×C4—51no—
338C22×C4—52no—
339C22×C4—52no—
340C22×C4—54no—
341C22×C4—54no—
342C22×C4—104no—
343C22×C4—104no—
344C22×C4—104no—
345C22×C4—102no—
346C22×C4—102no—
347C22×C4—101no—
348C22×C4—101no—
349C22×C4—102no—
350C22×C4—202no—
351C22×C4—204no—
352C22×C4—204no—
353C22×C4D4×D511yescharacteristic
354C22×C4D4×D511yescharacteristic
355C22×C4C23×D511yescharacteristic
356C2×C8—22no—
357C2×C8—22no—
358C2×C8—22no—
359C2×C8—102no—
360C2×C8—102no—
361C2×C8—102no—
362C4⋊C4—21no—
363C4⋊C4—21no—
364C4⋊C4—24no—
365C4⋊C4—24no—
366C4⋊C4—24no—
367C4⋊C4—52no—
368C4⋊C4—52no—
369C4⋊C4—104no—
370C4⋊C4—104no—
371C4⋊C4—104no—
372C4⋊C4—104no—
373C4⋊C4—104no—
374C4⋊C4—104no—
375C4⋊C4—101no—
376C4⋊C4—101no—
377C4⋊C4—104no—
378C4⋊C4—104no—
379C4⋊C4—104no—
380C4⋊C4C2×C4×D512yes—
381C4⋊C4C2×C4×D512yes—
382C22⋊C4—204no—
383C42—52no—
384C42—52no—
385C42—54no—
386C42—54no—
387C42—204no—
388C42C2×C4×D512yes—
389C42D4×D512yes—
390C2×C5#231011yescharacteristic
391C2×C5C2×#41611yescharacteristic
392C2×C5#289611yescharacteristic
393C2×C5#323212yes—
394C2×C5#323212yes—
395D5—24no—
396C23—52no—
397C23—54no—
398C23—101no—
399C23—102no—
400C23—101no—
401C23C2×D4×D511yescharacteristic
402C2×C4—22no—
403C2×C4—22no—
404C2×C4—22no—
405C2×C4—22no—
406C2×C4—42no—
407C2×C4—42no—
408C2×C4—42no—
409C2×C4—42no—
410C2×C4—42no—
411C2×C4—52no—
412C2×C4—52no—
413C2×C4—52no—
414C2×C4—108no—
415C2×C4—101no—
416C2×C4—102no—
417C2×C4—102no—
418C2×C4—101no—
419C2×C4—104no—
420C2×C4—104no—
421C2×C4—102no—
422C2×C4—102no—
423C2×C4—204no—
424C2×C4—208no—
425C2×C4—208no—
426C2×C4—202no—
427C2×C4—202no—
428C2×C4—202no—
429C2×C4—202no—
430C2×C4—202no—
431C2×C4D5×C22⋊C412yes—
432C2×C4D5×C22⋊C412yes—
433C2×C4C22×C4×D511yescharacteristic
434C2×C4C2×D4×D511yescharacteristic
435C2×C4#414712yes—
436C2×C4#415012yes—
437C8—42no—
438C8—202no—
439C5#2183611yescharacteristic, complemented, Sylow
440C22—54no—
441C22—102no—
442C22—104no—
443C22—104no—
444C22—102no—
445C22C2×D5×C22⋊C411yescharacteristic
446C22#6600911yescharacteristic
447C22#6605811yescharacteristic
448C22D5×#13512yes—
449C22#6610212yes—
450C4—22no—
451C4—22no—
452C4—42no—
453C4—42no—
454C4—82no—
455C4—102no—
456C4—102no—
457C4—102no—
458C4—202no—
459C4—202no—
460C4—402no—
461C4#6590612yes—
462C4#6596212yes—
463C2—104no—
464C2#1060834111yescharacteristic
465C2D5×#41611yescharacteristic
466C2#1061056111yescharacteristic
467C2#1061337912yes—
468C2#1061365112yes—
subgroupG/H
centerC23C2×D4×D5
commutatorC2×C4×C5C23×C4
FrattiniC22×C4C23×D5
FittingC5×#1991C2
socleC23×C5C22×D4
prime radicalC23×D5C2×D4
cosocleC22×C4×C5C24
hypercenter#1991D5
hypocenterC5#21836
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1991

Complements

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

NH ≅ G/Ntype
4. C5×#1991C2semidirect
5. #10602533C2semidirect
6. #10600571C2semidirect
7. #10600347C2semidirect
10. #10599595C2semidirect
11. #10599594C2semidirect
14. D5×#125C4semidirect
110. #1991D5semidirect
439. C5#21836semidirect

Maximal subgroups

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

subgroupindex
C2×D5×#1252
C2×#649742
#106058782
C5×#19912
#106025332
#106005712
#106003472
#105996652
#105996642
#105995952
#105995942
#218365