Finite Group Databasebeta

← #12108825

Subgroups — #12108825

Order 1280.

1238 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D5×C4⋊Q8C211yesmaximal, characteristic
2C2×#64994C211yesmaximal, characteristic
3#10605878C211yesmaximal, characteristic
4C5×#1993C211yesmaximal, characteristic, complemented
5#10602581C211yesmaximal, characteristic, complemented
6#10600621C211yesmaximal, characteristic, complemented
7#10600348C211yesmaximal, characteristic, complemented
8#10599664C214yesmaximal
9#10599592C214yesmaximal, 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×#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#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×C5C2311yescharacteristic
55#4090—28no—
56C2×#685—22no—
57C2×C4⋊Dic5—21no—
58C2×C4⋊Dic5C2312yes—
59C2×C4⋊Dic5C2312yes—
60C2×#683—22no—
61C2×#683—22no—
62C2×C4×Dic5—22no—
63C2×C4×Dic5D411yescharacteristic
64C2×C4×Dic5D411yescharacteristic
65C2×C4×Dic5C2311yescharacteristic
66C22×#168C2312yes—
67D5×C4⋊C4—28no—
68D5×C4⋊C4—24no—
69D5×C4⋊C4C2×C418yes—
70#4034—28no—
71#4034—24no—
72#4034C2×C418yes—
73C42×D5C2×C414yes—
74C42×D5D414yes—
75#4015—22no—
76#4015C2×C414yes—
77C5×#97—22no—
78C5×#95—21no—
79C5×#95—21no—
80#3963—21no—
81#3963—21no—
82#3963—22no—
83#3963—22no—
84#3952—24no—
85#3946—24no—
86#3935—22no—
87C22×C4⋊Q8—51no—
88C2×#432—51no—
89#2283—51no—
90#1993—51no—
91#1993—51no—
92#1993—51no—
93#1993D511yescharacteristic, complemented
94#1987—54no—
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—24no—
114C2×C4×D5—28no—
115C2×C4×D5—48no—
116C2×C4×D5C22⋊C414yes—
117C2×C4×D5C22⋊C414yes—
118C2×C4×D5C22×C412yes—
119C2×C4×D5C2×D412yes—
120C2×Dic10—24no—
121C2×Dic10—28no—
122C2×Dic10—48no—
123C2×Dic10—44no—
124C2×C5×C8—22no—
125C2×C5×C8—22no—
126C2×C5×C8—22no—
127C5×C4⋊C4—24no—
128C5×C4⋊C4—22no—
129C5×C4⋊C4—24no—
130C5×C4⋊C4C22×C414yes—
131C42×C5C22×C412yes—
132C42×C5C2×D412yes—
133#685—44no—
134C4⋊Dic5—24no—
135C4⋊Dic5—22no—
136C4⋊Dic5—24no—
137C4⋊Dic5C22×C414yes—
138#683—28no—
139#683—28no—
140C4×Dic5—44no—
141C4×Dic5C22⋊C414yes—
142C4×Dic5C22⋊C414yes—
143C4×Dic5C22×C412yes—
144C4×Dic5C2×D412yes—
145C2×#168—22no—
146C2×#168—22no—
147C2×#168—22no—
148C23×Q8—101no—
149C2×C4⋊Q8—58no—
150C2×C4⋊Q8—52no—
151C2×C4⋊Q8—51no—
152C2×C4⋊Q8—101no—
153C2×C4⋊Q8—104no—
154C2×C4⋊Q8—101no—
155C2×C4⋊Q8C2×D511yescharacteristic
156C22×C4⋊C4—52no—
157C22×C4⋊C4—101no—
158C22×C42—51no—
159#432—104no—
160C2×C4⋊C8—52no—
161C2×C22⋊C8—52no—
162C2×#97—51no—
163C2×#97C2×D511yescharacteristic
164#383—101no—
165#382—51no—
166#382C2×D511yescharacteristic
167#381—101no—
168#380—52no—
169C4×C4⋊C4—52no—
170C4×C22⋊C4—101no—
171#376—101no—
172#340—54no—
173#340—54no—
174#340—54no—
175#340C2×D514yes—
176C23×C5C22×D411yescharacteristic
177C22×D5—21no—
178C22×D5—21no—
179C22×D5—22no—
180C22×D5C2×C22⋊C412yes—
181C22×D5AGL(1,ℤ/8)14yes—
182C5×Q8—48no—
183C2×C4×C5—22no—
184C2×C4×C5—22no—
185C2×C4×C5—24no—
186C2×C4×C5—44no—
187C2×C4×C5—42no—
188C2×C4×C5—42no—
189C2×C4×C5—42no—
190C2×C4×C5C2×C22⋊C412yes—
191C2×C4×C5C2×C22⋊C412yes—
192C2×C4×C5C23×C411yescharacteristic
193C2×C4×C5C22×D411yescharacteristic
194C2×C4×C52−1+412yes—
195C2×C4×C52−1+412yes—
196C2×Dic5—21no—
197C2×Dic5—21no—
198C2×Dic5—22no—
199C2×Dic5—24no—
200C2×Dic5—44no—
201C2×Dic5—42no—
202C2×Dic5—42no—
203C2×Dic5—42no—
204C2×Dic5C2×C22⋊C412yes—
205C2×Dic5C2×C22⋊C412yes—
206C2×Dic5C2×C22⋊C412yes—
207C2×Dic5#13714yes—
208C4×D5—28no—
209C4×D5—24no—
210C4×D5—24no—
211C4×D5—28no—
212C4×D5—416no—
213Dic10—416no—
214Dic10—48no—
215C5×C8—42no—
216#168—42no—
217C22×Q8—21no—
218C22×Q8—102no—
219C22×Q8—108no—
220C22×Q8—101no—
221C22×Q8—208no—
222C23×C4—51no—
223C23×C4—51no—
224C23×C4—51no—
225C23×C4—102no—
226C22×C8—52no—
227C22×C8C22×D512yes—
228C4⋊Q8—22no—
229C4⋊Q8—58no—
230C4⋊Q8—54no—
231C4⋊Q8—104no—
232C4⋊Q8—108no—
233C4⋊Q8—108no—
234C4⋊Q8—102no—
235C4⋊Q8C4×D514yes—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—52no—
238C2×C4⋊C4—58no—
239C2×C4⋊C4—52no—
240C2×C4⋊C4—104no—
241C2×C4⋊C4—108no—
242C2×C4⋊C4—102no—
243C2×C4⋊C4—102no—
244C2×C4⋊C4—101no—
245C2×C4⋊C4C22×D512yes—
246C2×C4⋊C4C22×D512yes—
247C2×C22⋊C4—102no—
248C2×C42—51no—
249C2×C42—51no—
250C2×C42—51no—
251C2×C42—54no—
252C2×C42—54no—
253C2×C42—102no—
254C2×C42C22×D511yescharacteristic
255C4⋊C8—104no—
256C22⋊C8—104no—
257#97—22no—
258#97—102no—
259#95—21no—
260#95—21no—
261#95—102no—
262#95—102no—
263#95—101no—
264#95—101no—
265C22×C5C22×C22⋊C411yescharacteristic
266C22×C5#53611yescharacteristic
267C22×C5#53611yescharacteristic
268C22×C5C2×AGL(1,ℤ/8)12yes—
269C22×C5C2×#13712yes—
270C2×D5—22no—
271C2×D5—22no—
272C2×D5—24no—
273C2×D5—24no—
274C2×D5#41814yes—
275C4×C5—22no—
276C4×C5—22no—
277C4×C5—44no—
278C4×C5—82no—
279C4×C5#51912yes—
280C4×C5#53612yes—
281Dic5—22no—
282Dic5—22no—
283Dic5—44no—
284Dic5—82no—
285Dic5#41914yes—
286C24—51no—
287C2×Q8—24no—
288C2×Q8—44no—
289C2×Q8—108no—
290C2×Q8—104no—
291C2×Q8—204no—
292C2×Q8—208no—
293C2×Q8—2032no—
294C22×C4—22no—
295C22×C4—22no—
296C22×C4—51no—
297C22×C4—51no—
298C22×C4—51no—
299C22×C4—52no—
300C22×C4—52no—
301C22×C4—54no—
302C22×C4—54no—
303C22×C4—104no—
304C22×C4—104no—
305C22×C4—108no—
306C22×C4—102no—
307C22×C4—102no—
308C22×C4—102no—
309C22×C4—102no—
310C22×C4—208no—
311C22×C4D4×D511yescharacteristic
312C22×C4D4×D511yescharacteristic
313C22×C4C23×D511yescharacteristic
314C2×C8—22no—
315C2×C8—22no—
316C2×C8—22no—
317C2×C8—102no—
318C2×C8—102no—
319C2×C8—102no—
320C4⋊C4—22no—
321C4⋊C4—24no—
322C4⋊C4—24no—
323C4⋊C4—54no—
324C4⋊C4—108no—
325C4⋊C4—108no—
326C4⋊C4—102no—
327C4⋊C4—104no—
328C4⋊C4—104no—
329C4⋊C4C2×C4×D514yes—
330C22⋊C4—204no—
331C42—52no—
332C42—52no—
333C42—54no—
334C42—54no—
335C42—204no—
336C42C2×C4×D512yes—
337C42D4×D512yes—
338C2×C5#231011yescharacteristic
339C2×C5C2×#41811yescharacteristic
340C2×C5C2×#41911yescharacteristic
341C2×C5#323812yes—
342C2×C5#323812yes—
343D5—24no—
344C23—52no—
345C23—54no—
346C23—101no—
347C23—102no—
348C23—101no—
349C23C2×D4×D511yescharacteristic
350Q8—48no—
351Q8—208no—
352Q8—2016no—
353C2×C4—22no—
354C2×C4—22no—
355C2×C4—24no—
356C2×C4—44no—
357C2×C4—42no—
358C2×C4—42no—
359C2×C4—42no—
360C2×C4—52no—
361C2×C4—54no—
362C2×C4—52no—
363C2×C4—52no—
364C2×C4—108no—
365C2×C4—108no—
366C2×C4—101no—
367C2×C4—102no—
368C2×C4—101no—
369C2×C4—104no—
370C2×C4—104no—
371C2×C4—104no—
372C2×C4—2016no—
373C2×C4—204no—
374C2×C4—202no—
375C2×C4—202no—
376C2×C4—202no—
377C2×C4D5×C22⋊C412yes—
378C2×C4D5×C22⋊C412yes—
379C2×C4C22×C4×D511yescharacteristic
380C2×C4C2×D4×D511yescharacteristic
381C2×C4#414712yes—
382C2×C4#415012yes—
383C8—42no—
384C8—202no—
385C5#2184011yescharacteristic, complemented, Sylow
386C22—54no—
387C22—104no—
388C22—104no—
389C22—102no—
390C22—102no—
391C22C2×D5×C22⋊C411yescharacteristic
392C22#6600911yescharacteristic
393C22#6605811yescharacteristic
394C22D5×AGL(1,ℤ/8)12yes—
395C22D5×#13712yes—
396C4—22no—
397C4—22no—
398C4—44no—
399C4—54no—
400C4—82no—
401C4—102no—
402C4—102no—
403C4—204no—
404C4—402no—
405C4#6590612yes—
406C4#6596212yes—
407C2—104no—
408C2#1060834111yescharacteristic
409C2D5×#41811yescharacteristic
410C2D5×#41911yescharacteristic
411C2#1061342112yes—
412C2#1061371312yes—
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#21840
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. #10599592C2semidirect
14. D5×C4⋊Q8C4semidirect
93. #1993D5semidirect
385. 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×#649942
#106058782
C5×#19932
#106025812
#106006212
#106003482
#105996642
#105995922
#218405