Finite Group Databasebeta

← #12003525

Subgroups — #12003525

Order 1280.

490 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64983C211yesmaximal, characteristic
2C5×#1939C211yesmaximal, characteristic, complemented
3C2×#64701C211yesmaximal, characteristic, complemented
4C2×#64705C211yesmaximal, characteristic
5#10600282C211yesmaximal, characteristic, complemented
6#10600280C211yesmaximal, characteristic
7#10598145C211yesmaximal, characteristic, complemented
8C2×#4020C2211yescharacteristic
9C2×#4015C2211yescharacteristic
10C2×C5×C4⋊C8—21no—
11C2×C5×C4⋊C8C2211yescharacteristic
12C2×C4×C5×C8C2211yescharacteristic
13C4×C5×C4⋊C4C2211yescharacteristic
14C2×#3953—21no—
15C2×#3953—21no—
16C2×#3941—21no—
17C2×#3941—21no—
18C2×C4⋊#168C2211yescharacteristic
19C2×C4⋊#168C2211yescharacteristic
20#64983—22no—
21#64983—22no—
22C5×#336—21no—
23#64749—21no—
24#64749—21no—
25#64705—22no—
26#64701—22no—
27#10539—51nomaximal, Sylow
28C22×D20—21no—
29C22×D20—21no—
30C22×D20—21no—
31C22×Dic10—21no—
32C22×C5×C8—21no—
33C22×C5×C8D411yescharacteristic
34C22×C5×C8D411yescharacteristic
35C2×C5×C4⋊C4D411yescharacteristic
36C2×C5×C4⋊C4D411yescharacteristic
37C2×C42×C5—21no—
38C2×C42×C5C2311yescharacteristic
39C2×C4⋊Dic5—21no—
40C2×C4⋊Dic5—21no—
41C22×#168—21no—
42C22×#168—21no—
43#4020—21no—
44#4020—21no—
45#4020—21no—
46#4020D412yes—
47#4015—21no—
48#4015—21no—
49#4015—21no—
50#4015D412yes—
51C5×C4⋊C8—21no—
52C5×C4⋊C8—21no—
53C5×C4⋊C8—42no—
54C4×C5×C8—21no—
55C4×C5×C8—21no—
56C5×#95—21no—
57#3953—24no—
58#3953—24no—
59#3941—42no—
60#3941—42no—
61C4⋊#168—21no—
62C4⋊#168—21no—
63C4⋊#168—21no—
64C4⋊#168—21no—
65C2×#486—51no—
66#1987—51no—
67#1982—51no—
68#1939D511yescharacteristic, complemented
69C2×#333—51no—
70C2×#331—51no—
71#1277—51no—
72C23×D5—41no—
73C22×C4×C5—21no—
74C22×C4×C5—21no—
75C22×C4×C5C2×D411yescharacteristic
76C22×C4×C5C2×D411yescharacteristic
77C22×C4×C5#4111yescharacteristic
78C22×Dic5—41no—
79C2×D20—22no—
80C2×D20—22no—
81C2×D20—22no—
82C2×D20—41no—
83C2×D20—41no—
84C2×D20—41no—
85C2×D20—41no—
86C2×D20—41no—
87C2×D20—41no—
88C2×D20—41no—
89C2×D20—41no—
90C2×D20—41no—
91C2×D20—41no—
92C2×D20—41no—
93C2×D20—81no—
94C2×D20—81no—
95C2×Dic10—22no—
96C2×Dic10—41no—
97C2×Dic10—81no—
98C2×Dic10—81no—
99C2×C5×C8—21no—
100C2×C5×C8—21no—
101C2×C5×C8—21no—
102C2×C5×C8—21no—
103C2×C5×C8—21no—
104C2×C5×C8—21no—
105C2×C5×C8—41no—
106C2×C5×C8—41no—
107C2×C5×C8—41no—
108C5×C4⋊C4—21no—
109C5×C4⋊C4—21no—
110C5×C4⋊C4—21no—
111C5×C4⋊C4SD1612yes—
112C42×C5—41no—
113C42×C5—41no—
114C42×C5C2×D411yescharacteristic
115C42×C5C2×D411yescharacteristic
116C42×C5#4111yescharacteristic
117C42×C5#4111yescharacteristic
118C4⋊Dic5—22no—
119C4⋊Dic5—22no—
120C4⋊Dic5—41no—
121C4⋊Dic5—41no—
122C2×#168—41no—
123C2×#168—41no—
124C2×#168—41no—
125C2×#168—41no—
126C2×#168—41no—
127C2×#168—41no—
128C2×C4⋊Q8—51no—
129C2×#127—51no—
130#486—102no—
131#486—102no—
132C2×C4⋊C8—21no—
133C2×C4⋊C8—51no—
134C2×C4⋊C8—51no—
135C2×C4⋊C8C2×D511yescharacteristic
136C2×#102—101no—
137C2×#102—101no—
138C2×#102—101no—
139C2×#102—101no—
140C2×C4×C8C2×D511yescharacteristic
141C4×C4⋊C4C2×D511yescharacteristic
142#340—101no—
143#340—101no—
144#336—21no—
145#333—102no—
146#331—102no—
147C23×C5#12111yescharacteristic
148C22×D5—42no—
149C22×D5—81no—
150C22×D5—81no—
151C22×D5—81no—
152C22×D5—81no—
153C22×D5—81no—
154C22×D5—81no—
155C2×C4×C5—21no—
156C2×C4×C5—21no—
157C2×C4×C5—22no—
158C2×C4×C5—41no—
159C2×C4×C5—41no—
160C2×C4×C5—41no—
161C2×C4×C5—41no—
162C2×C4×C5—41no—
163C2×C4×C5#12011yescharacteristic
164C2×C4×C5#12111yescharacteristic
165C2×C4×C5#12111yescharacteristic
166C2×C4×C5#12311yescharacteristic
167C2×C4×C5#12311yescharacteristic
168C2×C4×C5#12411yescharacteristic
169C2×C4×C5C2×SD1611yescharacteristic
170C2×C4×C5#13511yescharacteristic
171C2×C4×C5#13511yescharacteristic
172C2×C4×C5#13511yescharacteristic
173C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
174C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
175C2×C4×C5#13711yescharacteristic
176C2×C4×C5#13711yescharacteristic
177C2×Dic5—42no—
178C2×Dic5—81no—
179C2×Dic5—81no—
180D20—42no—
181D20—42no—
182D20—42no—
183D20—42no—
184D20—82no—
185D20—82no—
186D20—81no—
187D20—81no—
188D20—81no—
189D20—81no—
190Dic10—82no—
191Dic10—82no—
192C5×C8—41no—
193C5×C8—41no—
194C5×C8—81no—
195#168—81no—
196#168—81no—
197C22×Q8—101no—
198C22×D4—101no—
199C22×D4—101no—
200C22×D4—101no—
201C22×C8—21no—
202C22×C8—101no—
203C22×C8—101no—
204C22×C8C22⋊D511yescharacteristic
205C22×C8C22⋊D511yescharacteristic
206C4⋊Q8—52no—
207C4⋊Q8—101no—
208C4⋊Q8—101no—
209C4⋊Q8—101no—
210#127—52no—
211#127—101no—
212#127—101no—
213#127—101no—
214C2×C4⋊C4—101no—
215C2×C4⋊C4—101no—
216C2×C4⋊C4D2011yescharacteristic
217C2×C4⋊C4D2011yescharacteristic
218C2×C42—21no—
219C2×C42C22×D511yescharacteristic
220C4⋊C8—21no—
221C4⋊C8—21no—
222C4⋊C8—42no—
223C4⋊C8—101no—
224C4⋊C8—101no—
225C4⋊C8—101no—
226C4⋊C8—101no—
227#102—104no—
228#102—104no—
229#102—202no—
230#102—202no—
231C4×C8—21no—
232C4×C8—21no—
233#95—21no—
234C22×C5#39411yescharacteristic
235C22×C5#46311yescharacteristic
236C22×C5#46411yescharacteristic
237C22×C5#46511yescharacteristic
238C22×C5#46811yescharacteristic
239C22×C5#47211yescharacteristic
240C22×C5#47211yescharacteristic
241C2×D5—82no—
242C2×D5—82no—
243C2×D5—82no—
244C2×D5—161no—
245C2×D5—161no—
246C2×D5—161no—
247C2×D5—161no—
248C4×C5—21no—
249C4×C5—21no—
250C4×C5—42no—
251C4×C5—81no—
252C4×C5#44911yescharacteristic
253C4×C5#45211yescharacteristic
254C4×C5#46011yescharacteristic
255C4×C5#46111yescharacteristic
256C4×C5#46311yescharacteristic
257C4×C5#46411yescharacteristic
258C4×C5#48811yescharacteristic
259C4×C5#48911yescharacteristic
260Dic5—82no—
261C24—201no—
262C2×Q8—102no—
263C2×Q8—201no—
264C2×Q8—401no—
265C2×Q8—401no—
266C2×D4—102no—
267C2×D4—102no—
268C2×D4—102no—
269C2×D4—201no—
270C2×D4—201no—
271C2×D4—201no—
272C2×D4—201no—
273C2×D4—201no—
274C2×D4—201no—
275C2×D4—201no—
276C2×D4—201no—
277C2×D4—201no—
278C2×D4—201no—
279C2×D4—201no—
280C2×D4—401no—
281C2×D4—401no—
282C22×C4—21no—
283C22×C4—21no—
284C22×C4—201no—
285C22×C4C2×D2011yescharacteristic
286C22×C4#70911yescharacteristic
287C22×C4C2×C22⋊D511yescharacteristic
288C2×C8—21no—
289C2×C8—21no—
290C2×C8—21no—
291C2×C8—21no—
292C2×C8—21no—
293C2×C8—21no—
294C2×C8—41no—
295C2×C8—41no—
296C2×C8—41no—
297C2×C8—201no—
298C2×C8—201no—
299C2×C8—201no—
300C2×C8—201no—
301C2×C8—201no—
302C2×C8—201no—
303C4⋊C4—21no—
304C4⋊C4—21no—
305C4⋊C4—21no—
306C4⋊C4—102no—
307C4⋊C4—102no—
308C4⋊C4—201no—
309C4⋊C4—201no—
310C4⋊C4#67712yes—
311C42—41no—
312C42—41no—
313C42D4×D511yescharacteristic
314C42D4×D511yescharacteristic
315C42#71311yescharacteristic
316C42#71311yescharacteristic
317C2×C5#167711yescharacteristic
318C2×C5#167811yescharacteristic
319C2×C5#169711yescharacteristic
320C2×C5#169811yescharacteristic
321C2×C5#204211yescharacteristic
322C2×C5#204511yescharacteristic
323C2×C5#205511yescharacteristic
324D5—162no—
325C23—202no—
326C23—401no—
327C23—401no—
328C23—401no—
329C23—401no—
330C23—401no—
331C23—401no—
332C23#407611yescharacteristic
333Q8—402no—
334Q8—402no—
335D4—202no—
336D4—202no—
337D4—202no—
338D4—202no—
339D4—402no—
340D4—402no—
341D4—401no—
342D4—401no—
343D4—401no—
344D4—401no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—22no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—202no—
354C2×C4—401no—
355C2×C4—401no—
356C2×C4#404011yescharacteristic
357C2×C4#404011yescharacteristic
358C2×C4#404111yescharacteristic
359C2×C4#404111yescharacteristic
360C2×C4C2×#67711yescharacteristic
361C2×C4#405011yescharacteristic
362C2×C4#405411yescharacteristic
363C2×C4#405511yescharacteristic
364C2×C4#407811yescharacteristic
365C2×C4#408311yescharacteristic
366C2×C4#408811yescharacteristic
367C2×C4#409311yescharacteristic
368C2×C4#409611yescharacteristic
369C2×C4#409611yescharacteristic
370C8—41no—
371C8—41no—
372C8—81no—
373C8—401no—
374C8—401no—
375C5#1053911yescharacteristic, complemented, Sylow
376C22—402no—
377C22—402no—
378C22—402no—
379C22—801no—
380C22—801no—
381C22—801no—
382C22—801no—
383C22#6528011yescharacteristic
384C22#6530511yescharacteristic
385C22#6531711yescharacteristic
386C22#6540311yescharacteristic
387C22#6542311yescharacteristic
388C22#6543111yescharacteristic
389C22#6543111yescharacteristic
390C4—21no—
391C4—21no—
392C4—42no—
393C4—81no—
394C4—402no—
395C4#6513011yescharacteristic
396C4#6513311yescharacteristic
397C4#6513411yescharacteristic
398C4#6513711yescharacteristic
399C4#6532611yescharacteristic
400C4#6533611yescharacteristic
401C4#6535711yescharacteristic
402C4#6537811yescharacteristic
403C2—802no—
404C2#1060042111yescharacteristic
405C2#1060127511yescharacteristic
406C2#1060133311yescharacteristic
407C2#1060164111yescharacteristic
408C2#1060166211yescharacteristic
409C2#1060173311yescharacteristic
410C2#1060175311yescharacteristic
subgroupG/H
centerC23#4076
commutator, cosocleC2×C42×C5C23
FrattiniC2×C42C22×D5
FittingC5×#1939C2
socleC23×C5#121
prime radicalC2×#4020C22
hypercenter#1939D5
hypocenterC5#10539
LCSG ▷ C2×C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1939

Complements

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

NH ≅ G/Ntype
2. C5×#1939C2semidirect
3. C2×#64701C2semidirect
5. #10600282C2semidirect
7. #10598145C2semidirect
68. #1939D5semidirect
375. C5#10539semidirect

Maximal subgroups

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

subgroupindex
C2×#649832
C5×#19392
C2×#647012
C2×#647052
#106002822
#106002802
#105981452
#105395