Finite Group Databasebeta

← #11990107

Subgroups — #11990107

Order 1280.

570 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×#168C211yesmaximal, characteristic
2C4×C5×#102C211yesmaximal, characteristic
3C2×D4⋊#168C211yesmaximal, characteristic
4C2×#64674C211yesmaximal, characteristic, complemented
5#10600270C211yesmaximal, characteristic, complemented
6#10598145C211yesmaximal, characteristic, complemented
7#10598110C211yesmaximal, characteristic, complemented
8C2×C4×C5×D4C2211yescharacteristic
9C23×#168—21no—
10C2×C5×#102C412yes—
11C2×C4×C5×C8C2211yescharacteristic
12C4×C5×C4⋊C4C2211yescharacteristic
13C2×C22⋊#168—21no—
14D4×#168—22no—
15D4×#168C414yescomplemented
16C2×C4⋊#168C2211yescharacteristic
17C2×C4⋊#168C2211yescharacteristic
18C2×#3935—21no—
19C2×C4×#168C2211yescharacteristic
20C2×C4×#168C2211yescharacteristic
21C5×#340C412yes—
22D4⋊#168C414yescomplemented
23#64744—21no—
24#64674—22no—
25#8204—51nomaximal, Sylow
26C22×C5×D4C2×C411yescharacteristic
27C23×C4×C5—21no—
28C22×C5×C8C2×C412yes—
29C4×C5×D4—21no—
30C4×C5×D4—21no—
31C4×C5×D4C2×C412yes—
32C4×C5×D4C2×C412yes—
33C2×C5×C4⋊C4C2×C412yes—
34C2×C5×C4⋊C4C2×C411yescharacteristic
35C2×C5×C22⋊C4—21no—
36C2×C42×C5—21no—
37C2×C42×C5C2311yescharacteristic
38C22×#168—21no—
39C22×#168—21no—
40C22×#168—21no—
41C22×#168—24no—
42C22×#168—42no—
43C22×#168—42no—
44C22×#168D411yescharacteristic
45C22×#168D411yescharacteristic
46C5×#102—24no—
47C4×C5×C8—21no—
48C4×C5×C8—21no—
49C5×#95—21no—
50C22⋊#168—24no—
51C4⋊#168—21no—
52C4⋊#168—21no—
53C4⋊#168C2×C412yes—
54C4⋊#168C2×C412yes—
55#3935—42no—
56C4×#168—21no—
57C4×#168C2×C412yes—
58C4×#168C2×C412yes—
59C4×#168D412yes—
60C2×C8×D4—51no—
61#1770—51no—
62C4×#102D511yescharacteristic
63C2×D4⋊C8—51no—
64C2×#322—51no—
65#1279—51no—
66#1277—51no—
67C24×C5—21no—
68C2×C5×D4—21no—
69C2×C5×D4—22no—
70C2×C5×D4C4212yes—
71C2×C5×D4M1614yes—
72C22×C4×C5—21no—
73C22×C4×C5—22no—
74C22×C4×C5—22no—
75C22×C4×C5—22no—
76C22×C4×C5—41no—
77C22×C4×C5—41no—
78C22×C4×C5—41no—
79C22×C4×C5—41no—
80C22×C4×C5C22×C411yescharacteristic
81C22×C4×C5C2×D411yescharacteristic
82C22×C4×C5#4111yescharacteristic
83C2×C5×C8—22no—
84C2×C5×C8—22no—
85C2×C5×C8—22no—
86C5×C4⋊C4—21no—
87C5×C4⋊C4—22no—
88C5×C4⋊C4—22no—
89C5×C4⋊C4C4212yes—
90C5×C22⋊C4—22no—
91C5×C22⋊C4—22no—
92C42×C5—41no—
93C42×C5—41no—
94C42×C5C22×C411yescharacteristic
95C42×C5C22×C411yescharacteristic
96C42×C5C2×D411yescharacteristic
97C42×C5#4111yescharacteristic
98C2×#168—24no—
99C2×#168—22no—
100C2×#168—21no—
101C2×#168—21no—
102C2×#168—21no—
103C2×#168—21no—
104C2×#168—22no—
105C2×#168—22no—
106C2×#168—48no—
107C2×#168—41no—
108C2×#168—41no—
109C2×#168—41no—
110C2×#168—41no—
111C2×#168C22⋊C412yes—
112C2×#168C22⋊C412yes—
113C23×C8—101no—
114C2×C4×D4C2×D511yescharacteristic
115C8×D4—54no—
116C8×D4—102no—
117C2×C4⋊C8—51no—
118C2×C4⋊C8—51no—
119C2×#102Dic512yes—
120C2×C22⋊C8—101no—
121C2×#97—101no—
122C2×C4×C8—51no—
123C2×C4×C8—51no—
124C2×C4×C8C2×D511yescharacteristic
125C4×C4⋊C4C2×D511yescharacteristic
126#340Dic512yes—
127#336—101no—
128D4⋊C8—54no—
129#322—102no—
130C23×C5—22no—
131C23×C5—24no—
132C23×C5—41no—
133C23×C5—41no—
134C23×C5—42no—
135C23×C5C4×D411yescharacteristic
136C5×D4—22no—
137C5×D4—24no—
138C5×D4#9714yescomplemented
139C2×C4×C5—22no—
140C2×C4×C5—22no—
141C2×C4×C5—41no—
142C2×C4×C5—41no—
143C2×C4×C5—42no—
144C2×C4×C5—42no—
145C2×C4×C5—42no—
146C2×C4×C5—42no—
147C2×C4×C5—42no—
148C2×C4×C5—42no—
149C2×C4×C5—42no—
150C2×C4×C5C2×C4211yescharacteristic
151C2×C4×C5C2×C22⋊C411yescharacteristic
152C2×C4×C5#11711yescharacteristic
153C2×C4×C5C4×D411yescharacteristic
154C2×C4×C5C4×D411yescharacteristic
155C2×C4×C5C4×D411yescharacteristic
156C2×C4×C5C2×M1612yes—
157C2×C4×C5#13112yes—
158C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
159C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
160C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
161C2×C4×C5#13711yescharacteristic
162C5×C8—42no—
163#168—24no—
164#168—22no—
165#168—22no—
166#168—42no—
167#168—42no—
168C22×D4C2×Dic511yescharacteristic
169C23×C4—21no—
170C22×C8—51no—
171C22×C8—51no—
172C22×C8—104no—
173C22×C8—101no—
174C22×C8—101no—
175C22×C8—101no—
176C22×C8—202no—
177C22×C8—202no—
178C22×C8C2×Dic512yes—
179C4×D4—21no—
180C4×D4—21no—
181C4×D4C4×D512yes—
182C4×D4C4×D512yes—
183C2×C4⋊C4C2×Dic512yes—
184C2×C4⋊C4C2×Dic511yescharacteristic
185C2×C22⋊C4—21no—
186C2×C42—21no—
187C2×C42C22×D511yescharacteristic
188C4⋊C8—52no—
189C4⋊C8—52no—
190C4⋊C8—101no—
191C4⋊C8—101no—
192#102—24no—
193C22⋊C8—104no—
194#97—202no—
195C4×C8—21no—
196C4×C8—21no—
197C4×C8—52no—
198C4×C8—52no—
199C4×C8—52no—
200C4×C8—101no—
201#95—21no—
202C22×C5—24no—
203C22×C5—44no—
204C22×C5—44no—
205C22×C5—42no—
206C22×C5—42no—
207C22×C5C4×C22⋊C411yescharacteristic
208C22×C5#43512yes—
209C22×C5#44011yescharacteristic
210C22×C5#44211yescharacteristic
211C22×C5#44312yes—
212C4×C5—21no—
213C4×C5—21no—
214C4×C5—42no—
215C4×C5—82no—
216C4×C5C2×#9711yescharacteristic
217C4×C5#40511yescharacteristic
218C4×C5#41711yescharacteristic
219C4×C5#41811yescharacteristic
220C4×C5#43512yes—
221C4×C5#44011yescharacteristic
222C4×C5#44211yescharacteristic
223C24—21no—
224C2×D4—21no—
225C2×D4—22no—
226C2×D4#68114yes—
227C2×D4C4×Dic512yes—
228C22×C4—21no—
229C22×C4—22no—
230C22×C4—22no—
231C22×C4—22no—
232C22×C4—41no—
233C22×C4—41no—
234C22×C4—41no—
235C22×C4—41no—
236C22×C4D4×D511yescharacteristic
237C22×C4#71111yescharacteristic
238C22×C4C22×Dic511yescharacteristic
239C2×C8—22no—
240C2×C8—22no—
241C2×C8—22no—
242C2×C8—52no—
243C2×C8—52no—
244C2×C8—104no—
245C2×C8—102no—
246C2×C8—101no—
247C2×C8—101no—
248C2×C8—101no—
249C2×C8—101no—
250C2×C8—102no—
251C2×C8—102no—
252C2×C8—208no—
253C2×C8—201no—
254C2×C8—201no—
255C2×C8—201no—
256C2×C8—201no—
257C4⋊C4—21no—
258C4⋊C4—22no—
259C4⋊C4—22no—
260C4⋊C4C4×Dic512yes—
261C22⋊C4—22no—
262C22⋊C4—22no—
263C42—41no—
264C42—41no—
265C42C2×C4×D511yescharacteristic
266C42C2×C4×D511yescharacteristic
267C42D4×D511yescharacteristic
268C42#71111yescharacteristic
269C2×C5—44no—
270C2×C5#158512yes—
271C2×C5#158612yes—
272C2×C5#175211yescharacteristic
273C2×C5#176211yescharacteristic
274C2×C5#176411yescharacteristic
275C23—24no—
276C23—22no—
277C23—41no—
278C23—41no—
279C23—42no—
280C23D4×Dic511yescharacteristic
281D4—22no—
282D4—24no—
283D4#393514yescomplemented
284C2×C4—22no—
285C2×C4—22no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—42no—
289C2×C4—42no—
290C2×C4—42no—
291C2×C4—42no—
292C2×C4—42no—
293C2×C4—42no—
294C2×C4—42no—
295C2×C4#402311yescharacteristic
296C2×C4D5×C22⋊C411yescharacteristic
297C2×C4#402711yescharacteristic
298C2×C4#402711yescharacteristic
299C2×C4#405711yescharacteristic
300C2×C4#405711yescharacteristic
301C2×C4#406011yescharacteristic
302C2×C4#406111yescharacteristic
303C2×C4C2×#68112yes—
304C2×C4C2×C4×Dic511yescharacteristic
305C2×C4D4×Dic511yescharacteristic
306C2×C4#409412yes—
307C8—42no—
308C8—104no—
309C8—102no—
310C8—102no—
311C8—202no—
312C8—202no—
313C5#820411yescharacteristic, complemented, Sylow
314C22—24no—
315C22—42no—
316C22—44no—
317C22—44no—
318C22—42no—
319C22C22⋊C4×Dic511yescharacteristic
320C22#6530012yes—
321C22#6544111yescharacteristic
322C22#6545311yescharacteristic
323C22#6548512yes—
324C4—21no—
325C4—21no—
326C4—42no—
327C4—82no—
328C4#6504611yescharacteristic
329C4#6505911yescharacteristic
330C4#6506011yescharacteristic
331C4#6507411yescharacteristic
332C4C2×#393511yescharacteristic
333C4#6528611yescharacteristic
334C4#6530012yes—
335C2—44no—
336C2#1060024011yescharacteristic
337C2#1060094511yescharacteristic
338C2#1060108211yescharacteristic
339C2#1060167312yes—
340C2#1060169012yes—
subgroupG/H
centerC22×C4D4×D5
commutatorC2×C4×C5C2×C42
FrattiniC2×C42C22×D5
FittingC4×C5×#102C2
socleC23×C5C4×D4
prime radicalC22×C5×D4C2×C4
cosocleC2×C42×C5C23
hypercenterC4×#102D5
hypocenterC5#8204
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C4×#102

Complements

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

NH ≅ G/Ntype
4. C2×#64674C2semidirect
5. #10600270C2semidirect
6. #10598145C2semidirect
7. #10598110C2semidirect
15. D4×#168C4semidirect
22. D4⋊#168C4semidirect
138. C5×D4#97semidirect
283. D4#3935semidirect
313. C5#8204semidirect

Maximal subgroups

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

subgroupindex
C2×D4×#1682
C4×C5×#1022
C2×D4⋊#1682
C2×#646742
#106002702
#105981452
#105981102
#82045