Finite Group Databasebeta

← #12108828

Subgroups — #12108828

Order 1280.

1238 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D5×C4⋊Q8C211yesmaximal, characteristic
2C2×#65124C211yesmaximal, characteristic
3#10605483C211yesmaximal, characteristic
4C5×#1987C211yesmaximal, characteristic, complemented
5#10602572C211yesmaximal, characteristic, complemented
6#10601252C211yesmaximal, characteristic, complemented
7#10600282C211yesmaximal, characteristic, complemented
8#10599664C214yesmaximal
9#10599599C214yesmaximal, complemented
10C22×Q8×D5—21no—
11C2×C5×C4⋊Q8C2211yescharacteristic
12C2×#4090—21no—
13D5×C4⋊Q8—24no—
14D5×C4⋊Q8C418yescomplemented
15C2×D5×C4⋊C4—21no—
16C2×D5×C4⋊C4C2212yes—
17C2×#4034—21no—
18C2×#4034C2212yes—
19C2×C42×D5C2211yescharacteristic
20C2×#4015C2211yescharacteristic
21C2×C5×C4⋊C8C2211yescharacteristic
22C4×C5×C4⋊C4C2211yescharacteristic
23C2×#3952C2212yes—
24C2×#3947C2212yes—
25#65276C2212yes—
26#65266C2212yes—
27C4×#685—21no—
28C4×C4⋊Dic5C2211yescharacteristic
29#65221—21no—
30C2×C4⋊#168C2211yescharacteristic
31#65124—24no—
32#64953—21no—
33#64940—21no—
34C5×#340C2214yes—
35#64771C2214yes—
36#64749C2214yes—
37#64749C2214yes—
38#21840—51nomaximal, Sylow
39C22×C5×Q8—21no—
40C2×Q8×D5—28no—
41C2×Q8×D5—48no—
42C22×C4×D5—22no—
43C22×C4×D5D411yescharacteristic
44C22×C4×D5D411yescharacteristic
45C22×C4×D5C2311yescharacteristic
46C22×Dic10—21no—
47C22×Dic10—22no—
48C22×C5×C8C2312yes—
49C5×C4⋊Q8—22no—
50C5×C4⋊Q8C2×C414yes—
51C2×C5×C4⋊C4—21no—
52C2×C5×C4⋊C4C2312yes—
53C2×C5×C4⋊C4C2312yes—
54C2×C42×C5—21no—
55C2×C42×C5C2311yescharacteristic
56#4090—28no—
57C2×#685—22no—
58C2×C4⋊Dic5—21no—
59C2×C4⋊Dic5C2312yes—
60C2×C4⋊Dic5C2312yes—
61C2×#683—22no—
62C2×#683—22no—
63C2×C4×Dic5—21no—
64C2×C4×Dic5D411yescharacteristic
65C2×C4×Dic5D411yescharacteristic
66C2×C4×Dic5C2311yescharacteristic
67C22×#168C2312yes—
68D5×C4⋊C4—28no—
69D5×C4⋊C4—24no—
70D5×C4⋊C4C2×C418yes—
71#4034—28no—
72#4034—24no—
73#4034C2×C418yes—
74C42×D5C2×C414yes—
75C42×D5D414yes—
76#4015—22no—
77#4015C2×C414yes—
78C5×C4⋊C8—22no—
79C5×#95—21no—
80#3963—21no—
81#3963—22no—
82#3963—22no—
83#3963—22no—
84#3952—24no—
85#3947—24no—
86C4⋊#168—22no—
87C22×C4⋊Q8—51no—
88C2×#432—51no—
89#2283—51no—
90#1993—54no—
91#1987—51no—
92#1987—51no—
93#1987—51no—
94#1987D511yescharacteristic, complemented
95#1823—54no—
96C23×D5C2×D411yescharacteristic
97C2×C5×Q8—24no—
98C2×C5×Q8—44no—
99C22×C4×C5—22no—
100C22×C4×C5—22no—
101C22×C4×C5C2×D411yescharacteristic
102C22×C4×C5C2×D411yescharacteristic
103C22×C4×C5C2411yescharacteristic
104C22×Dic5—22no—
105C22×Dic5—22no—
106C22×Dic5C2×D411yescharacteristic
107C22×Dic5C2×D411yescharacteristic
108C22×Dic5C2×D411yescharacteristic
109Q8×D5—432no—
110C2×C4×D5—24no—
111C2×C4×D5—22no—
112C2×C4×D5—22no—
113C2×C4×D5—22no—
114C2×C4×D5—22no—
115C2×C4×D5—28no—
116C2×C4×D5—48no—
117C2×C4×D5C22⋊C414yes—
118C2×C4×D5C22⋊C414yes—
119C2×C4×D5C22×C412yes—
120C2×C4×D5C2×D412yes—
121C2×Dic10—24no—
122C2×Dic10—28no—
123C2×Dic10—48no—
124C2×Dic10—44no—
125C2×C5×C8—22no—
126C2×C5×C8—24no—
127C5×C4⋊C4—24no—
128C5×C4⋊C4—22no—
129C5×C4⋊C4—22no—
130C5×C4⋊C4—22no—
131C5×C4⋊C4C22×C414yes—
132C42×C5—42no—
133C42×C5C22×C412yes—
134C42×C5C2×D412yes—
135#685—44no—
136C4⋊Dic5—24no—
137C4⋊Dic5—22no—
138C4⋊Dic5—22no—
139C4⋊Dic5—22no—
140C4⋊Dic5C22×C414yes—
141#683—28no—
142#683—28no—
143C4×Dic5—42no—
144C4×Dic5C22⋊C414yes—
145C4×Dic5C22⋊C414yes—
146C4×Dic5C22×C412yes—
147C4×Dic5C2×D412yes—
148C2×#168—22no—
149C2×#168—24no—
150C23×Q8—101no—
151C2×C4⋊Q8—58no—
152C2×C4⋊Q8—52no—
153C2×C4⋊Q8—51no—
154C2×C4⋊Q8—101no—
155C2×C4⋊Q8—104no—
156C2×C4⋊Q8—101no—
157C2×C4⋊Q8C2×D511yescharacteristic
158C22×C4⋊C4—52no—
159C22×C4⋊C4—101no—
160C22×C42—51no—
161#432—104no—
162C2×C4⋊C8—51no—
163C2×C4⋊C8C2×D511yescharacteristic
164C2×C22⋊C8—52no—
165C2×#97—52no—
166#383—101no—
167#382—52no—
168#381—101no—
169#380—52no—
170C4×C4⋊C4—51no—
171C4×C4⋊C4C2×D511yescharacteristic
172C4×C22⋊C4—101no—
173#376—101no—
174#340—54no—
175#340—54no—
176#340—54no—
177#340C2×D514yes—
178C23×C5C22×D411yescharacteristic
179C22×D5—22no—
180C22×D5—21no—
181C22×D5—21no—
182C22×D5C2×C22⋊C412yes—
183C22×D5AGL(1,ℤ/8)14yes—
184C5×Q8—48no—
185C2×C4×C5—22no—
186C2×C4×C5—24no—
187C2×C4×C5—44no—
188C2×C4×C5—42no—
189C2×C4×C5—42no—
190C2×C4×C5—42no—
191C2×C4×C5C2×C22⋊C412yes—
192C2×C4×C5C2×C22⋊C412yes—
193C2×C4×C5#13712yes—
194C2×C4×C5#13712yes—
195C2×C4×C5C23×C411yescharacteristic
196C2×C4×C5C22×D411yescharacteristic
197C2×C4×C52−1+412yes—
198C2×C4×C52−1+412yes—
199C2×Dic5—22no—
200C2×Dic5—22no—
201C2×Dic5—21no—
202C2×Dic5—21no—
203C2×Dic5—24no—
204C2×Dic5—44no—
205C2×Dic5—42no—
206C2×Dic5—42no—
207C2×Dic5—42no—
208C2×Dic5C2×C22⋊C412yes—
209C2×Dic5C2×C22⋊C412yes—
210C2×Dic5C2×C22⋊C412yes—
211C4×D5—28no—
212C4×D5—24no—
213C4×D5—22no—
214C4×D5—22no—
215C4×D5—28no—
216C4×D5—416no—
217Dic10—416no—
218Dic10—48no—
219C5×C8—42no—
220#168—42no—
221C22×Q8—21no—
222C22×Q8—102no—
223C22×Q8—108no—
224C22×Q8—101no—
225C22×Q8—208no—
226C23×C4—51no—
227C23×C4—51no—
228C23×C4—51no—
229C23×C4—102no—
230C22×C8—52no—
231C22×C8C22×D512yes—
232C4⋊Q8—22no—
233C4⋊Q8—58no—
234C4⋊Q8—54no—
235C4⋊Q8—104no—
236C4⋊Q8—108no—
237C4⋊Q8—108no—
238C4⋊Q8—102no—
239C4⋊Q8C4×D514yes—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—52no—
242C2×C4⋊C4—58no—
243C2×C4⋊C4—52no—
244C2×C4⋊C4—104no—
245C2×C4⋊C4—108no—
246C2×C4⋊C4—102no—
247C2×C4⋊C4—102no—
248C2×C4⋊C4—101no—
249C2×C4⋊C4C22×D512yes—
250C2×C4⋊C4C22×D512yes—
251C2×C22⋊C4—102no—
252C2×C42—21no—
253C2×C42—51no—
254C2×C42—51no—
255C2×C42—51no—
256C2×C42—54no—
257C2×C42—54no—
258C2×C42—101no—
259C2×C42C22×D511yescharacteristic
260C4⋊C8—22no—
261C4⋊C8—102no—
262C22⋊C8—104no—
263#97—104no—
264#95—21no—
265#95—102no—
266#95—102no—
267#95—102no—
268#95—101no—
269C22×C5C22×C22⋊C411yescharacteristic
270C22×C5#53612yes—
271C22×C5C2×AGL(1,ℤ/8)12yes—
272C22×C5C2×#13711yescharacteristic
273C22×C5C2×#13711yescharacteristic
274C2×D5—22no—
275C2×D5—22no—
276C2×D5—24no—
277C2×D5—24no—
278C2×D5#41814yes—
279C4×C5—22no—
280C4×C5—44no—
281C4×C5—82no—
282C4×C5#41914yes—
283C4×C5#51912yes—
284C4×C5#53611yescharacteristic
285C4×C5#53611yescharacteristic
286Dic5—22no—
287Dic5—22no—
288Dic5—22no—
289Dic5—44no—
290Dic5—82no—
291C24—51no—
292C2×Q8—24no—
293C2×Q8—44no—
294C2×Q8—108no—
295C2×Q8—104no—
296C2×Q8—204no—
297C2×Q8—208no—
298C2×Q8—2032no—
299C22×C4—22no—
300C22×C4—22no—
301C22×C4—51no—
302C22×C4—51no—
303C22×C4—51no—
304C22×C4—52no—
305C22×C4—52no—
306C22×C4—54no—
307C22×C4—54no—
308C22×C4—104no—
309C22×C4—108no—
310C22×C4—102no—
311C22×C4—102no—
312C22×C4—102no—
313C22×C4—102no—
314C22×C4—102no—
315C22×C4—102no—
316C22×C4—208no—
317C22×C4D4×D511yescharacteristic
318C22×C4D4×D511yescharacteristic
319C22×C4C23×D511yescharacteristic
320C2×C8—22no—
321C2×C8—24no—
322C2×C8—102no—
323C2×C8—104no—
324C4⋊C4—22no—
325C4⋊C4—24no—
326C4⋊C4—22no—
327C4⋊C4—22no—
328C4⋊C4—54no—
329C4⋊C4—108no—
330C4⋊C4—108no—
331C4⋊C4—102no—
332C4⋊C4—104no—
333C4⋊C4—102no—
334C4⋊C4—102no—
335C4⋊C4C2×C4×D514yes—
336C22⋊C4—204no—
337C42—42no—
338C42—52no—
339C42—52no—
340C42—54no—
341C42—54no—
342C42—202no—
343C42C2×C4×D512yes—
344C42D4×D512yes—
345C2×C5#231011yescharacteristic
346C2×C5C2×#41811yescharacteristic
347C2×C5C2×#41911yescharacteristic
348C2×C5#323812yes—
349C2×C5#323812yes—
350D5—24no—
351C23—52no—
352C23—54no—
353C23—101no—
354C23—101no—
355C23—102no—
356C23C2×D4×D511yescharacteristic
357Q8—48no—
358Q8—208no—
359Q8—2016no—
360C2×C4—22no—
361C2×C4—24no—
362C2×C4—44no—
363C2×C4—42no—
364C2×C4—42no—
365C2×C4—42no—
366C2×C4—52no—
367C2×C4—52no—
368C2×C4—52no—
369C2×C4—108no—
370C2×C4—101no—
371C2×C4—101no—
372C2×C4—102no—
373C2×C4—102no—
374C2×C4—102no—
375C2×C4—108no—
376C2×C4—104no—
377C2×C4—102no—
378C2×C4—104no—
379C2×C4—2016no—
380C2×C4—204no—
381C2×C4—202no—
382C2×C4—202no—
383C2×C4—202no—
384C2×C4D5×C22⋊C412yes—
385C2×C4D5×C22⋊C412yes—
386C2×C4#406112yes—
387C2×C4#406412yes—
388C2×C4C22×C4×D511yescharacteristic
389C2×C4C2×D4×D511yescharacteristic
390C2×C4#414712yes—
391C2×C4#415012yes—
392C8—42no—
393C8—202no—
394C5#2184011yescharacteristic, complemented, Sylow
395C22—54no—
396C22—104no—
397C22—102no—
398C22—104no—
399C22—102no—
400C22C2×D5×C22⋊C411yescharacteristic
401C22#6596212yes—
402C22C2×#406111yescharacteristic
403C22C2×#406411yescharacteristic
404C22D5×AGL(1,ℤ/8)12yes—
405C4—22no—
406C4—44no—
407C4—82no—
408C4—102no—
409C4—102no—
410C4—102no—
411C4—204no—
412C4—402no—
413C4#6509114yes—
414C4#6590612yes—
415C4#6600911yescharacteristic
416C4#6605811yescharacteristic
417C2—104no—
418C2#1060834111yescharacteristic
419C2C2×#6509111yescharacteristic
420C2D5×#41811yescharacteristic
421C2#1061279812yes—
422C2#1061284612yes—
subgroupG/H
centerC23C2×D4×D5
commutatorC2×C4×C5C23×C4
FrattiniC22×C4C23×D5
FittingC5×#1987C2
socleC23×C5C22×D4
prime radicalC23×D5C2×D4
cosocleC22×C4×C5C24
hypercenter#1987D5
hypocenterC5#21840
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1987

Complements

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

NH ≅ G/Ntype
4. C5×#1987C2semidirect
5. #10602572C2semidirect
6. #10601252C2semidirect
7. #10600282C2semidirect
9. #10599599C2semidirect
14. D5×C4⋊Q8C4semidirect
94. #1987D5semidirect
394. C5#21840semidirect

Maximal subgroups

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

subgroupindex
C2×D5×C4⋊Q82
C2×#651242
#106054832
C5×#19872
#106025722
#106012522
#106002822
#105996642
#105995992
#218405