Finite Group Databasebeta

← #12003522

Subgroups — #12003522

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×#65377C211yesmaximal, characteristic
2C5×#1987C211yesmaximal, characteristic, complemented
3C2×#64766C211yesmaximal, characteristic, complemented
4C2×#64705C211yesmaximal, characteristic
5#10600280C211yesmaximal, characteristic
6#10600277C211yesmaximal, characteristic, complemented
7#10598194C211yesmaximal, characteristic, complemented
8C2×C5×C4⋊Q8C2211yescharacteristic
9C2×#4020C2211yescharacteristic
10C2×C5×C4⋊C8C2211yescharacteristic
11C4×C5×C4⋊C4C2211yescharacteristic
12#65377—22no—
13#65377—22no—
14C2×#3941—21no—
15C2×#3941—21no—
16C2×#3941—21no—
17C2×#3941—21no—
18C2×C4⋊#168—21no—
19C2×C4⋊#168C2211yescharacteristic
20C2×C4⋊#168C2211yescharacteristic
21C2×C4×#168C2211yescharacteristic
22C5×#340—21no—
23C5×#340—21no—
24#64766—22no—
25#64744—21no—
26#64705—22no—
27#10539—51nomaximal, Sylow
28C22×C5×Q8—21no—
29C22×D20—21no—
30C22×D20—21no—
31C22×D20—21no—
32C22×C5×C8—21no—
33C5×C4⋊Q8—21no—
34C5×C4⋊Q8—21no—
35C5×C4⋊Q8—21no—
36C5×C4⋊Q8D412yes—
37C2×C5×C4⋊C4—21no—
38C2×C5×C4⋊C4—21no—
39C2×C5×C4⋊C4D411yescharacteristic
40C2×C5×C4⋊C4D411yescharacteristic
41C2×C42×C5—21no—
42C2×C42×C5C2311yescharacteristic
43C22×#168—21no—
44C22×#168—21no—
45C22×#168D411yescharacteristic
46C22×#168D411yescharacteristic
47#4020—21no—
48#4020—21no—
49#4020—21no—
50#4020D412yes—
51C5×C4⋊C8—21no—
52C5×C4⋊C8—21no—
53C5×#95—21no—
54#3941—24no—
55#3941—24no—
56#3941—42no—
57#3941—42no—
58C4⋊#168—21no—
59C4⋊#168—21no—
60C4⋊#168—21no—
61C4⋊#168—21no—
62C4⋊#168—42no—
63C4×#168—21no—
64C4×#168—21no—
65C2×#486—51no—
66#1987D511yescharacteristic, complemented
67#1982—51no—
68#1939—51no—
69C2×#333—51no—
70C2×#331—51no—
71#1277—51no—
72C23×D5—41no—
73C2×C5×Q8—22no—
74C2×C5×Q8—41no—
75C2×C5×Q8—81no—
76C2×C5×Q8—81no—
77C22×C4×C5—21no—
78C22×C4×C5—21no—
79C22×C4×C5—41no—
80C22×C4×C5C2×D411yescharacteristic
81C22×C4×C5C2×D411yescharacteristic
82C22×C4×C5#4111yescharacteristic
83C2×D20—22no—
84C2×D20—22no—
85C2×D20—22no—
86C2×D20—41no—
87C2×D20—41no—
88C2×D20—41no—
89C2×D20—41no—
90C2×D20—41no—
91C2×D20—41no—
92C2×D20—41no—
93C2×D20—41no—
94C2×D20—41no—
95C2×D20—41no—
96C2×D20—41no—
97C2×D20—81no—
98C2×D20—81no—
99C2×C5×C8—41no—
100C2×C5×C8—41no—
101C2×C5×C8—41no—
102C5×C4⋊C4—21no—
103C5×C4⋊C4—22no—
104C5×C4⋊C4—22no—
105C5×C4⋊C4—21no—
106C5×C4⋊C4—21no—
107C5×C4⋊C4—41no—
108C5×C4⋊C4—41no—
109C5×C4⋊C4SD1612yes—
110C42×C5—41no—
111C42×C5—41no—
112C42×C5C2×D411yescharacteristic
113C42×C5C2×D411yescharacteristic
114C42×C5#4111yescharacteristic
115C42×C5#4111yescharacteristic
116C2×#168—21no—
117C2×#168—21no—
118C2×#168—21no—
119C2×#168—21no—
120C2×#168—21no—
121C2×#168—21no—
122C2×#168—41no—
123C2×#168—41no—
124C2×#168—41no—
125C2×#168—41no—
126C2×#168—41no—
127C2×#168—41no—
128C2×C4⋊Q8C2×D511yescharacteristic
129C2×#127—51no—
130#486—102no—
131#486—102no—
132C2×C4⋊C8—51no—
133C2×C4⋊C8—51no—
134C2×C4⋊C8—101no—
135C2×C4⋊C8C2×D511yescharacteristic
136C2×#102—101no—
137C2×#102—101no—
138C2×#102—101no—
139C2×#102—101no—
140C2×C4×C8—51no—
141C4×C4⋊C4C2×D511yescharacteristic
142#340—21no—
143#340—21no—
144#336—101no—
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—
155C5×Q8—82no—
156C5×Q8—82no—
157C2×C4×C5—21no—
158C2×C4×C5—21no—
159C2×C4×C5—22no—
160C2×C4×C5—41no—
161C2×C4×C5—41no—
162C2×C4×C5—42no—
163C2×C4×C5—41no—
164C2×C4×C5—41no—
165C2×C4×C5—41no—
166C2×C4×C5—81no—
167C2×C4×C5—81no—
168C2×C4×C5#12011yescharacteristic
169C2×C4×C5#12111yescharacteristic
170C2×C4×C5#12111yescharacteristic
171C2×C4×C5#12311yescharacteristic
172C2×C4×C5#12311yescharacteristic
173C2×C4×C5#12411yescharacteristic
174C2×C4×C5C2×SD1611yescharacteristic
175C2×C4×C5#13511yescharacteristic
176C2×C4×C5#13511yescharacteristic
177C2×C4×C5#13511yescharacteristic
178C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
179C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
180C2×C4×C5#13711yescharacteristic
181C2×C4×C5#13711yescharacteristic
182D20—42no—
183D20—42no—
184D20—42no—
185D20—42no—
186D20—82no—
187D20—82no—
188D20—81no—
189D20—81no—
190D20—81no—
191D20—81no—
192C5×C8—81no—
193#168—41no—
194#168—41no—
195#168—81no—
196#168—81no—
197C22×Q8—21no—
198C22×D4—101no—
199C22×D4—101no—
200C22×D4—101no—
201C22×C8—21no—
202C22×C8—51no—
203C22×C8—51no—
204C22×C8—101no—
205C22×C8—101no—
206C4⋊Q8—21no—
207C4⋊Q8—21no—
208C4⋊Q8—21no—
209C4⋊Q8D2012yes—
210#127—52no—
211#127—101no—
212#127—101no—
213#127—101no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—21no—
216C2×C4⋊C4C22⋊D511yescharacteristic
217C2×C4⋊C4C22⋊D511yescharacteristic
218C2×C42—21no—
219C2×C42C22×D511yescharacteristic
220C4⋊C8—21no—
221C4⋊C8—21no—
222C4⋊C8—101no—
223C4⋊C8—101no—
224C4⋊C8—101no—
225C4⋊C8—101no—
226C4⋊C8—202no—
227#102—104no—
228#102—104no—
229#102—202no—
230#102—202no—
231C4×C8—101no—
232C4×C8—101no—
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—82no—
253C4×C5#44911yescharacteristic
254C4×C5#45211yescharacteristic
255C4×C5#46011yescharacteristic
256C4×C5#46111yescharacteristic
257C4×C5#46311yescharacteristic
258C4×C5#46411yescharacteristic
259C4×C5#48811yescharacteristic
260C4×C5#48911yescharacteristic
261C24—201no—
262C2×Q8—22no—
263C2×Q8—41no—
264C2×Q8—81no—
265C2×Q8—81no—
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—41no—
285C22×C4D4×D511yescharacteristic
286C22×C4#71111yescharacteristic
287C22×C4C2×C22⋊D511yescharacteristic
288C2×C8—41no—
289C2×C8—41no—
290C2×C8—41no—
291C2×C8—101no—
292C2×C8—101no—
293C2×C8—101no—
294C2×C8—101no—
295C2×C8—101no—
296C2×C8—101no—
297C2×C8—201no—
298C2×C8—201no—
299C2×C8—201no—
300C2×C8—201no—
301C2×C8—201no—
302C2×C8—201no—
303C4⋊C4—21no—
304C4⋊C4—22no—
305C4⋊C4—22no—
306C4⋊C4—21no—
307C4⋊C4—21no—
308C4⋊C4—41no—
309C4⋊C4—41no—
310C4⋊C4#68812yes—
311C42—41no—
312C42—41no—
313C42C2×D2011yescharacteristic
314C42#70911yescharacteristic
315C42D4×D511yescharacteristic
316C42#71111yescharacteristic
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#408511yescharacteristic
333Q8—82no—
334Q8—82no—
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—42no—
354C2×C4—81no—
355C2×C4—81no—
356C2×C4#402811yescharacteristic
357C2×C4#402911yescharacteristic
358C2×C4#403111yescharacteristic
359C2×C4#403211yescharacteristic
360C2×C4#406011yescharacteristic
361C2×C4#406211yescharacteristic
362C2×C4#406411yescharacteristic
363C2×C4#406511yescharacteristic
364C2×C4#407611yescharacteristic
365C2×C4#408411yescharacteristic
366C2×C4C2×#68811yescharacteristic
367C2×C4#408811yescharacteristic
368C2×C4#409511yescharacteristic
369C2×C4#409611yescharacteristic
370C8—81no—
371C8—201no—
372C8—201no—
373C8—401no—
374C8—401no—
375C5#1053911yescharacteristic, complemented, Sylow
376C22—402no—
377C22—402no—
378C22—402no—
379C22—801no—
380C22—801no—
381C22—801no—
382C22—801no—
383C22#6525011yescharacteristic
384C22#6533711yescharacteristic
385C22#6533811yescharacteristic
386C22#6545411yescharacteristic
387C22#6547411yescharacteristic
388C22#6548811yescharacteristic
389C22#6548811yescharacteristic
390C4—21no—
391C4—21no—
392C4—42no—
393C4—82no—
394C4—81no—
395C4#6508411yescharacteristic
396C4#6508911yescharacteristic
397C4#6509911yescharacteristic
398C4#6510011yescharacteristic
399C4#6531611yescharacteristic
400C4#6531711yescharacteristic
401C4#6534611yescharacteristic
402C4#6537211yescharacteristic
403C2—802no—
404C2#1060047311yescharacteristic
405C2#1060103811yescharacteristic
406C2#1060111211yescharacteristic
407C2#1060192711yescharacteristic
408C2#1060193111yescharacteristic
409C2#1060194311yescharacteristic
410C2#1060194711yescharacteristic
subgroupG/H
centerC23#4085
commutator, cosocleC2×C42×C5C23
FrattiniC2×C42C22×D5
FittingC5×#1987C2
socleC23×C5#121
prime radicalC2×#4020C22
hypercenter#1987D5
hypocenterC5#10539
LCSG ▷ C2×C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1987

Complements

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

NH ≅ G/Ntype
2. C5×#1987C2semidirect
3. C2×#64766C2semidirect
6. #10600277C2semidirect
7. #10598194C2semidirect
66. #1987D5semidirect
375. C5#10539semidirect

Maximal subgroups

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

subgroupindex
C2×#653772
C5×#19872
C2×#647662
C2×#647052
#106002802
#106002772
#105981942
#105395