Finite Group Databasebeta

← #12108839

Subgroups — #12108839

Order 1280.

1010 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#66062C211yesmaximal, characteristic
2C2×#64994C211yesmaximal, characteristic
3#10605878C211yesmaximal, characteristic
4C5×#1993C211yesmaximal, characteristic, complemented
5#10602581C211yesmaximal, characteristic, complemented
6#10600621C211yesmaximal, characteristic, complemented
7#10600348C211yesmaximal, characteristic, complemented
8#10599606C214yesmaximal
9#10599595C214yesmaximal, complemented
10C2×C5×C4⋊Q8C2211yescharacteristic
11C2×#4092—21no—
12C2×Q8×Dic5—21no—
13#66062—24no—
14#66062C418yescomplemented
15C2×#4043—21no—
16C2×#4038C2212yes—
17C2×#4036C2212yes—
18C2×#4033—21no—
19C2×C42×D5C2211yescharacteristic
20C2×#4015C2211yescharacteristic
21C2×C5×#97C2211yescharacteristic
22C5×#382C2211yescharacteristic
23C2×#3952C2212yes—
24C2×#3946C2212yes—
25#65276C2212yes—
26C4⋊C4×Dic5C2212yes—
27#65225C2211yescharacteristic
28C2×#3935C2211yescharacteristic
29#64994—24no—
30#64955—21no—
31#64953—21no—
32#64940—21no—
33#64937—21no—
34C5×#340C2214yes—
35#64771C2214yes—
36#64749C2214yes—
37#64749C2214yes—
38#21842—51nomaximal, Sylow
39C22×C5×Q8—21no—
40C22×C4×D5D411yescharacteristic
41C22×C4×D5D411yescharacteristic
42C22×C4×D5C2311yescharacteristic
43C22×Dic10—21no—
44C22×C5×C8C2312yes—
45C5×C4⋊Q8—22no—
46C5×C4⋊Q8C2×C414yes—
47C2×C5×C4⋊C4—21no—
48C2×C5×C4⋊C4C2312yes—
49C2×C5×C4⋊C4C2312yes—
50C2×C42×C5C2311yescharacteristic
51#4092—28no—
52Q8×Dic5—28no—
53C2×#685—22no—
54C2×#685—22no—
55C2×C4⋊Dic5—21no—
56C2×C4⋊Dic5—22no—
57C2×C4⋊Dic5C2312yes—
58C2×C4⋊Dic5C2312yes—
59C2×#683—22no—
60C2×C4×Dic5—22no—
61C2×C4×Dic5—22no—
62C2×C4×Dic5D411yescharacteristic
63C2×C4×Dic5D411yescharacteristic
64C2×C4×Dic5C2311yescharacteristic
65C22×#168C2312yes—
66#4043—28no—
67#4038—24no—
68#4038C2×C418yes—
69#4036—24no—
70#4036C2×C418yes—
71#4033—28no—
72C42×D5C2×C414yes—
73C42×D5D414yes—
74#4015—22no—
75#4015C2×C414yes—
76C5×#97—22no—
77C5×#95—21no—
78C5×#95—21no—
79#3963—21no—
80#3963—21no—
81#3963—22no—
82#3963—22no—
83#3952—24no—
84#3946—24no—
85#3935—22no—
86C2×#533—51no—
87C2×#432—51no—
88#2283—51no—
89#1993—51no—
90#1993—51no—
91#1993—51no—
92#1993D511yescharacteristic, complemented
93#1989—54no—
94#1825—54no—
95C23×D5C2×D411yescharacteristic
96C2×C5×Q8—24no—
97C2×C5×Q8—44no—
98C22×C4×C5—22no—
99C22×C4×C5—22no—
100C22×C4×C5C2×D411yescharacteristic
101C22×C4×C5C2×D411yescharacteristic
102C22×C4×C5C2411yescharacteristic
103C22×Dic5—22no—
104C22×Dic5—22no—
105C22×Dic5C2×D411yescharacteristic
106C22×Dic5C2×D411yescharacteristic
107C22×Dic5C2×D411yescharacteristic
108C2×C4×D5—22no—
109C2×C4×D5—22no—
110C2×C4×D5—42no—
111C2×C4×D5—42no—
112C2×C4×D5C22⋊C414yes—
113C2×C4×D5C22⋊C414yes—
114C2×C4×D5C22×C412yes—
115C2×C4×D5C2×D412yes—
116C2×Dic10—24no—
117C2×Dic10—44no—
118C2×C5×C8—22no—
119C2×C5×C8—22no—
120C2×C5×C8—22no—
121C5×C4⋊C4—24no—
122C5×C4⋊C4—22no—
123C5×C4⋊C4—24no—
124C5×C4⋊C4C22×C414yes—
125C42×C5C22×C412yes—
126C42×C5C2×D412yes—
127#685—28no—
128#685—44no—
129C4⋊Dic5—24no—
130C4⋊Dic5—22no—
131C4⋊Dic5—28no—
132C4⋊Dic5—24no—
133C4⋊Dic5C22×C414yes—
134#683—28no—
135C4×Dic5—28no—
136C4×Dic5—44no—
137C4×Dic5C22⋊C414yes—
138C4×Dic5C22⋊C414yes—
139C4×Dic5C22×C412yes—
140C4×Dic5C2×D412yes—
141C2×#168—22no—
142C2×#168—22no—
143C2×#168—22no—
144#533—58no—
145#533—104no—
146C2×C4⋊Q8—51no—
147C2×C4⋊Q8C2×D511yescharacteristic
148C2×#125—52no—
149C2×C22⋊Q8—101no—
150C2×C22⋊Q8—101no—
151C2×C4×Q8—101no—
152C2×C4×Q8—101no—
153C2×#117—52no—
154C22×C42—51no—
155#432—104no—
156C2×C4⋊C8—52no—
157C2×C22⋊C8—52no—
158C2×#97—51no—
159C2×#97C2×D511yescharacteristic
160#383—101no—
161#382—51no—
162#382C2×D511yescharacteristic
163#381—101no—
164#380—52no—
165C4×C4⋊C4—52no—
166C4×C22⋊C4—101no—
167#376—101no—
168#340—54no—
169#340—54no—
170#340—54no—
171#340C2×D514yes—
172C23×C5C22×D411yescharacteristic
173C22×D5—21no—
174C22×D5—21no—
175C22×D5—22no—
176C22×D5—22no—
177C22×D5C2×C22⋊C412yes—
178C5×Q8—48no—
179C2×C4×C5—22no—
180C2×C4×C5—22no—
181C2×C4×C5—24no—
182C2×C4×C5—44no—
183C2×C4×C5—42no—
184C2×C4×C5—42no—
185C2×C4×C5—42no—
186C2×C4×C5C2×C22⋊C412yes—
187C2×C4×C5C2×C22⋊C412yes—
188C2×C4×C5C23×C411yescharacteristic
189C2×C4×C5C22×D411yescharacteristic
190C2×C4×C52−1+412yes—
191C2×C4×C52−1+412yes—
192C2×Dic5—21no—
193C2×Dic5—21no—
194C2×Dic5—22no—
195C2×Dic5—22no—
196C2×Dic5—24no—
197C2×Dic5—44no—
198C2×Dic5—42no—
199C2×Dic5—42no—
200C2×Dic5—42no—
201C2×Dic5C2×C22⋊C412yes—
202C2×Dic5C2×C22⋊C412yes—
203C2×Dic5C2×C22⋊C412yes—
204C4×D5—24no—
205C4×D5—24no—
206C4×D5—44no—
207C4×D5—44no—
208Dic10—48no—
209C5×C8—42no—
210#168—42no—
211C22×Q8—21no—
212C22×Q8—101no—
213C23×C4—51no—
214C23×C4—51no—
215C23×C4—51no—
216C22×C8—52no—
217C22×C8C22×D512yes—
218C4⋊Q8—22no—
219C4⋊Q8—54no—
220C4⋊Q8—102no—
221C4⋊Q8C4×D514yes—
222#125—58no—
223#125—104no—
224C22⋊Q8—108no—
225C22⋊Q8—108no—
226C4×Q8—108no—
227C4×Q8—108no—
228#117—58no—
229#117—104no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4—52no—
232C2×C4⋊C4—52no—
233C2×C4⋊C4—102no—
234C2×C4⋊C4—102no—
235C2×C4⋊C4—101no—
236C2×C4⋊C4C22×D512yes—
237C2×C4⋊C4C22×D512yes—
238C2×C22⋊C4—102no—
239C2×C22⋊C4—102no—
240C2×C42—51no—
241C2×C42—51no—
242C2×C42—51no—
243C2×C42—54no—
244C2×C42—54no—
245C2×C42—102no—
246C2×C42—102no—
247C2×C42C22×D511yescharacteristic
248C4⋊C8—104no—
249C22⋊C8—104no—
250#97—22no—
251#97—102no—
252#95—21no—
253#95—21no—
254#95—102no—
255#95—102no—
256#95—101no—
257#95—101no—
258C22×C5C22×C22⋊C411yescharacteristic
259C22×C5#53611yescharacteristic
260C22×C5#53611yescharacteristic
261C22×C5#57512yes—
262C22×C5#57512yes—
263C2×D5—22no—
264C2×D5—22no—
265C2×D5—22no—
266C2×D5—42no—
267C2×D5—42no—
268C4×C5—22no—
269C4×C5—22no—
270C4×C5—44no—
271C4×C5—82no—
272C4×C5#51912yes—
273C4×C5#53612yes—
274Dic5—22no—
275Dic5—22no—
276Dic5—22no—
277Dic5—44no—
278Dic5—82no—
279C24—51no—
280C2×Q8—24no—
281C2×Q8—44no—
282C2×Q8—104no—
283C2×Q8—204no—
284C22×C4—22no—
285C22×C4—22no—
286C22×C4—51no—
287C22×C4—51no—
288C22×C4—51no—
289C22×C4—52no—
290C22×C4—52no—
291C22×C4—54no—
292C22×C4—54no—
293C22×C4—102no—
294C22×C4—102no—
295C22×C4—102no—
296C22×C4—102no—
297C22×C4—202no—
298C22×C4—202no—
299C22×C4D4×D511yescharacteristic
300C22×C4D4×D511yescharacteristic
301C22×C4C23×D511yescharacteristic
302C2×C8—22no—
303C2×C8—22no—
304C2×C8—22no—
305C2×C8—102no—
306C2×C8—102no—
307C2×C8—102no—
308C4⋊C4—22no—
309C4⋊C4—24no—
310C4⋊C4—24no—
311C4⋊C4—54no—
312C4⋊C4—108no—
313C4⋊C4—108no—
314C4⋊C4—102no—
315C4⋊C4—104no—
316C4⋊C4—104no—
317C4⋊C4C2×C4×D514yes—
318C22⋊C4—108no—
319C22⋊C4—204no—
320C42—52no—
321C42—52no—
322C42—54no—
323C42—54no—
324C42—108no—
325C42—204no—
326C42C2×C4×D512yes—
327C42D4×D512yes—
328C2×C5#231011yescharacteristic
329C2×C5#289611yescharacteristic
330C2×C5#289611yescharacteristic
331C2×C5#324012yes—
332C2×C5#324012yes—
333D5—42no—
334C23—52no—
335C23—101no—
336C23—102no—
337C23—102no—
338C23—101no—
339C23C2×D4×D511yescharacteristic
340Q8—48no—
341Q8—208no—
342C2×C4—22no—
343C2×C4—22no—
344C2×C4—24no—
345C2×C4—44no—
346C2×C4—42no—
347C2×C4—42no—
348C2×C4—42no—
349C2×C4—52no—
350C2×C4—52no—
351C2×C4—52no—
352C2×C4—101no—
353C2×C4—102no—
354C2×C4—102no—
355C2×C4—101no—
356C2×C4—104no—
357C2×C4—104no—
358C2×C4—104no—
359C2×C4—204no—
360C2×C4—204no—
361C2×C4—204no—
362C2×C4—202no—
363C2×C4—202no—
364C2×C4—202no—
365C2×C4D5×C22⋊C412yes—
366C2×C4D5×C22⋊C412yes—
367C2×C4C22×C4×D511yescharacteristic
368C2×C4C2×D4×D511yescharacteristic
369C2×C4#414712yes—
370C2×C4#415012yes—
371C8—42no—
372C8—202no—
373C5#2184211yescharacteristic, complemented, Sylow
374C22—102no—
375C22—102no—
376C22—102no—
377C22—202no—
378C22—202no—
379C22C2×D5×C22⋊C411yescharacteristic
380C22#6600911yescharacteristic
381C22#6605811yescharacteristic
382C22#6610712yes—
383C22#6611112yes—
384C4—22no—
385C4—22no—
386C4—44no—
387C4—82no—
388C4—102no—
389C4—102no—
390C4—102no—
391C4—204no—
392C4—402no—
393C4#6590612yes—
394C4#6596212yes—
395C2—202no—
396C2#1060834111yescharacteristic
397C2#1061065511yescharacteristic
398C2#1061068711yescharacteristic
399C2#1061342412yes—
400C2#1061371612yes—
subgroupG/H
centerC23C2×D4×D5
commutatorC2×C4×C5C23×C4
FrattiniC22×C4C23×D5
FittingC5×#1993C2
socleC23×C5C22×D4
prime radicalC23×D5C2×D4
cosocleC22×C4×C5C24
hypercenter#1993D5
hypocenterC5#21842
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1993

Complements

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

NH ≅ G/Ntype
4. C5×#1993C2semidirect
5. #10602581C2semidirect
6. #10600621C2semidirect
7. #10600348C2semidirect
9. #10599595C2semidirect
14. #66062C4semidirect
92. #1993D5semidirect
373. C5#21842semidirect

Maximal subgroups

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

subgroupindex
C2×#660622
C2×#649942
#106058782
C5×#19932
#106025812
#106006212
#106003482
#105996062
#105995952
#218425