Finite Group Databasebeta

← #11998188

Subgroups — #11998188

Order 1280.

534 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#688C211yesmaximal, characteristic
2C5×#1984C211yesmaximal, characteristic, complemented
3C2×Q8⋊#168C211yesmaximal, characteristic, complemented
4C2×#64703C211yesmaximal, characteristic
5C2×#64700C211yesmaximal, characteristic, complemented
6#10600580C211yesmaximal, characteristic
7C2×#64675C211yesmaximal, characteristic, complemented
8C2×C4×C5×Q8C2211yescharacteristic
9C22×#688C411yescharacteristic
10C2×C4×D20C2211yescharacteristic
11C2×C5×C4⋊C8C2211yescharacteristic
12C2×C4×C5×C8C2211yescharacteristic
13C2×#3967C411yescharacteristic
14C2×#3952—22no—
15C4×#688—22no—
16C4×#688—22no—
17C2×#3941C411yescharacteristic
18C2×#3940C411yescharacteristic
19C2×C4⋊#168C2211yescharacteristic
20C2×C4×#168C2211yescharacteristic
21C2×C4×#168C2211yescharacteristic
22C5×#336—22no—
23Q8⋊#168—22no—
24#64703—22no—
25#64700—22no—
26#64675—22no—
27#9661—51nomaximal, Sylow
28C22×C5×Q8C2×C411yescharacteristic
29C22×D20C2×C411yescharacteristic
30C22×C4×D5—21no—
31C22×C5×C8—21no—
32C22×C5×C8D412yes—
33C4×C5×Q8—21no—
34C4×C5×Q8—21no—
35C4×C5×Q8—21no—
36C4×C5×Q8—21no—
37C2×C5×C4⋊C4—21no—
38C2×C5×C4⋊C4C2×C411yescharacteristic
39C2×C42×C5—21no—
40C2×C42×C5C2311yescharacteristic
41C2×#688—22no—
42C2×#688—22no—
43C2×#688—22no—
44C2×#685—21no—
45C2×C4⋊Dic5C2×C411yescharacteristic
46C22×#168—21no—
47C22×#168—21no—
48C22×#168C2×C411yescharacteristic
49C22×#168C2×C411yescharacteristic
50C4×D20—21no—
51C4×D20—21no—
52C4×D20—21no—
53C4×D20—21no—
54C5×C4⋊C8—21no—
55C5×C4⋊C8—21no—
56C4×C5×C8—21no—
57C4×C5×C8—21no—
58#3967—22no—
59#3952—44no—
60#3941—22no—
61#3940—22no—
62C4⋊#168—21no—
63C4⋊#168—21no—
64C4×#168—21no—
65C4×#168D412yes—
66C4×#168D412yes—
67C4×#168D412yes—
68C2×C4×SD16—51no—
69#1984D511yescharacteristic, complemented
70#1954—51no—
71C2×#334—51no—
72C2×Q8⋊C8—51no—
73C2×D4⋊C8—51no—
74C2×#322—51no—
75C23×D5—21no—
76C2×C5×Q8—21no—
77C2×C5×Q8—21no—
78C2×C5×Q8—21no—
79C2×C5×Q8—21no—
80C2×C5×Q8—21no—
81C2×C5×Q8M1612yes—
82C22×C4×C5—21no—
83C22×C4×C5—21no—
84C22×C4×C5C22×C411yescharacteristic
85C22×C4×C5C2×D411yescharacteristic
86C22×C4×C5#4111yescharacteristic
87C22×Dic5—21no—
88C2×D20—21no—
89C2×D20—21no—
90C2×D20—21no—
91C2×D20—21no—
92C2×D20—21no—
93C2×D20M1612yes—
94C2×C4×D5—41no—
95C2×C4×D5—41no—
96C2×C4×D5—42no—
97C2×C4×D5—42no—
98C2×C5×C8—22no—
99C2×C5×C8—22no—
100C2×C5×C8—41no—
101C2×C5×C8—42no—
102C2×C5×C8SD1614yescomplemented
103C5×C4⋊C4—21no—
104C5×C4⋊C4—21no—
105C5×C4⋊C4—41no—
106C5×C4⋊C4—41no—
107C42×C5—41no—
108C42×C5—41no—
109C42×C5C2×D411yescharacteristic
110C42×C5C2×D411yescharacteristic
111C42×C5C2×D411yescharacteristic
112C42×C5#4111yescharacteristic
113#688—28no—
114#685—41no—
115#685—41no—
116C4⋊Dic5—21no—
117C4⋊Dic5—21no—
118C2×#168—21no—
119C2×#168—21no—
120C2×#168—21no—
121C2×#168—21no—
122C2×#168—22no—
123C2×#168—42no—
124C2×#168—41no—
125C2×#168—42no—
126C2×#168C22⋊C412yes—
127C2×#168C22⋊C412yes—
128C22×SD16—51no—
129C2×C4×Q8C2×D511yescharacteristic
130C2×C4×D4—51no—
131C4×SD16—102no—
132C4×SD16—102no—
133C2×#106—51no—
134C2×C4⋊C8—51no—
135C2×C4⋊C8C2×D511yescharacteristic
136C2×#103—51no—
137C2×#102—51no—
138C2×C22⋊C8—102no—
139C2×C4×C8—51no—
140C2×C4×C8—51no—
141C2×C4×C8C2×D511yescharacteristic
142#336—22no—
143#334—102no—
144Q8⋊C8—102no—
145D4⋊C8—102no—
146#322—102no—
147C23×C5C4×D411yescharacteristic
148C22×D5—22no—
149C22×D5—41no—
150C22×D5—41no—
151C22×D5—42no—
152C22×D5—42no—
153C5×Q8—22no—
154C5×Q8—22no—
155C5×Q8—41no—
156C5×Q8—41no—
157C2×C4×C5—22no—
158C2×C4×C5—22no—
159C2×C4×C5—41no—
160C2×C4×C5—41no—
161C2×C4×C5—41no—
162C2×C4×C5—42no—
163C2×C4×C5C2×C22⋊C411yescharacteristic
164C2×C4×C5C4×D411yescharacteristic
165C2×C4×C5#12111yescharacteristic
166C2×C4×C5#12111yescharacteristic
167C2×C4×C5#12411yescharacteristic
168C2×C4×C5#12711yescharacteristic
169C2×C4×C5C2×M1611yescharacteristic
170C2×C4×C5C2×M1611yescharacteristic
171C2×C4×C5#13111yescharacteristic
172C2×C4×C5#13111yescharacteristic
173C2×C4×C5C2×SD1612yes—
174C2×C4×C5#13512yes—
175C2×Dic5—41no—
176C2×Dic5—42no—
177D20—22no—
178D20—22no—
179D20—41no—
180D20—41no—
181C4×D5—82no—
182C4×D5—81no—
183C4×D5—81no—
184C5×C8—24no—
185C5×C8—81no—
186#168—22no—
187#168—22no—
188#168—42no—
189#168—81no—
190C22×Q8C4×D511yescharacteristic
191C22×D4—51no—
192C23×C4—101no—
193C2×SD16—102no—
194C2×SD16—102no—
195C2×SD16—102no—
196C22×C8—21no—
197C22×C8—51no—
198C22×C8—51no—
199C22×C8—101no—
200C22×C8—101no—
201C22×C8C22⋊D512yes—
202C4×Q8—21no—
203C4×Q8—21no—
204C4×Q8—21no—
205C4×Q8—21no—
206C4×D4—101no—
207C4×D4—101no—
208C4×D4—101no—
209C4×D4—101no—
210C2×C4⋊C4—21no—
211C2×C4⋊C4—51no—
212C2×C4⋊C4C4×D511yescharacteristic
213C2×C22⋊C4—101no—
214C2×C42—21no—
215C2×C42C22×D511yescharacteristic
216#106—102no—
217C4⋊C8—21no—
218C4⋊C8—21no—
219C4⋊C8—101no—
220C4⋊C8—101no—
221#103—102no—
222#102—102no—
223C22⋊C8—204no—
224C4×C8—21no—
225C4×C8—21no—
226C4×C8—52no—
227C4×C8—52no—
228C4×C8—52no—
229C4×C8—101no—
230C22×C5#39011yescharacteristic
231C22×C5#43511yescharacteristic
232C22×C5#43511yescharacteristic
233C22×C5C4×SD1612yes—
234C22×C5#44412yes—
235C2×D5—44no—
236C2×D5—42no—
237C2×D5—82no—
238C2×D5—81no—
239C2×D5—81no—
240C4×C5—21no—
241C4×C5—21no—
242C4×C5—42no—
243C4×C5—81no—
244C4×C5#40711yescharacteristic
245C4×C5#40811yescharacteristic
246C4×C5#43511yescharacteristic
247C4×C5#43511yescharacteristic
248C4×C5#46512yes—
249C4×C5#49211yescharacteristic
250C4×C5#49511yescharacteristic
251Dic5—81no—
252C24—101no—
253C2×Q8—21no—
254C2×Q8—21no—
255C2×Q8—21no—
256C2×Q8—21no—
257C2×Q8—21no—
258C2×Q8#67612yes—
259C2×D4—52no—
260C2×D4—101no—
261C2×D4—101no—
262C2×D4—101no—
263C2×D4—101no—
264C2×D4—101no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—101no—
268C22×C4—202no—
269C22×C4—201no—
270C22×C4—201no—
271C22×C4—202no—
272C22×C4C2×C4×D511yescharacteristic
273C22×C4#70911yescharacteristic
274C22×C4C2×C22⋊D511yescharacteristic
275SD16—108no—
276C2×C8—22no—
277C2×C8—22no—
278C2×C8—42no—
279C2×C8—41no—
280C2×C8—52no—
281C2×C8—52no—
282C2×C8—101no—
283C2×C8—101no—
284C2×C8—101no—
285C2×C8—101no—
286C2×C8—102no—
287C2×C8—202no—
288C2×C8—201no—
289C2×C8—202no—
290C2×C8#68814yescomplemented
291C4⋊C4—21no—
292C4⋊C4—21no—
293C4⋊C4—41no—
294C4⋊C4—41no—
295C4⋊C4—101no—
296C4⋊C4—101no—
297C22⋊C4—201no—
298C22⋊C4—201no—
299C42—41no—
300C42—41no—
301C42D4×D511yescharacteristic
302C42D4×D511yescharacteristic
303C42D4×D511yescharacteristic
304C42#71111yescharacteristic
305C2×C5#158212yes—
306C2×C5#158312yes—
307C2×C5#195511yescharacteristic
308C2×C5#196811yescharacteristic
309C2×C5#197511yescharacteristic
310D5—82no—
311C23—102no—
312C23—202no—
313C23—201no—
314C23—202no—
315C23—201no—
316C23C4×C22⋊D511yescharacteristic
317Q8—22no—
318Q8—22no—
319Q8—41no—
320Q8—41no—
321D4—102no—
322D4—102no—
323D4—201no—
324D4—201no—
325C2×C4—22no—
326C2×C4—22no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—42no—
330C2×C4—41no—
331C2×C4—202no—
332C2×C4—201no—
333C2×C4—402no—
334C2×C4—401no—
335C2×C4—401no—
336C2×C4D5×C22⋊C411yescharacteristic
337C2×C4#402711yescharacteristic
338C2×C4#403011yescharacteristic
339C2×C4#403111yescharacteristic
340C2×C4C2×#67611yescharacteristic
341C2×C4#404711yescharacteristic
342C2×C4D5×M1611yescharacteristic
343C2×C4#405311yescharacteristic
344C2×C4#408511yescharacteristic
345C2×C4#408611yescharacteristic
346C2×C4C2×#68812yes—
347C2×C4#409612yes—
348C8—24no—
349C8—81no—
350C8—102no—
351C8—102no—
352C8—202no—
353C8—401no—
354C5#966111yescharacteristic, complemented, Sylow
355C22—202no—
356C22—204no—
357C22—401no—
358C22—401no—
359C22—402no—
360C22#6524611yescharacteristic
361C22C4×#68812yes—
362C22#6540011yescharacteristic
363C22#6541611yescharacteristic
364C22#6543412yes—
365C4—21no—
366C4—21no—
367C4—42no—
368C4—81no—
369C4—401no—
370C4#6501511yescharacteristic
371C4#6501611yescharacteristic
372C4#6501711yescharacteristic
373C4#6501911yescharacteristic
374C4#6533712yes—
375C4#6534811yescharacteristic
376C4#6537411yescharacteristic
377C2—402no—
378C2#1060046911yescharacteristic
379C2#1060071011yescharacteristic
380C2#1060079311yescharacteristic
381C2#1060172612yes—
382C2#1060174612yes—
subgroupG/H
centerC22×C4C2×C22⋊D5
commutatorC22×C4×C5C22×C4
FrattiniC2×C42C22×D5
FittingC5×#1984C2
socleC23×C5C4×D4
prime radicalC22×D20C2×C4
cosocleC2×C42×C5C23
hypercenter#1984D5
hypocenterC5#9661
LCSG ▷ C22×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C4 ◁ C2×C4×C8 ◁ #1984

Complements

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

NH ≅ G/Ntype
2. C5×#1984C2semidirect
3. C2×Q8⋊#168C2semidirect
5. C2×#64700C2semidirect
7. C2×#64675C2semidirect
69. #1984D5semidirect
102. C2×C5×C8SD16semidirect
290. C2×C8#688semidirect
354. C5#9661semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#6882
C5×#19842
C2×Q8⋊#1682
C2×#647032
C2×#647002
#106005802
C2×#646752
#96615