Finite Group Databasebeta

← #12009679

Subgroups — #12009679

Order 1280.

402 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 95 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2399C211yesmaximal, characteristic
2C4×#3968C211yesmaximal, characteristic
3#10602417C211yesmaximal, characteristic
4#10598141C212yesmaximal
5#10598139C212yesmaximal
6C2×C4×C5×Q8C411yescharacteristic
7C2×C4×C5×Q8C2211yescharacteristic
8C5×#398—21no—
9C5×#398C411yescharacteristic
10C5×#398C2211yescharacteristic
11C5×#395—21no—
12C5×#395C411yescharacteristic
13C5×#395C2211yescharacteristic
14C4×C5×C4⋊C4—21no—
15C4×C5×C4⋊C4—21no—
16C5×#376C411yescharacteristic
17C2×#3968—21no—
18#65214—21no—
19C4×#681—21no—
20#64750C2212yes—
21#64748—21no—
22#64748C2212yes—
23#11736—51nomaximal, Sylow
24C22×C5×Q8C2×C411yescharacteristic
25C22×C5×Q8D411yescharacteristic
26C4×C5×Q8—41no—
27C4×C5×Q8—41no—
28C4×C5×Q8—41no—
29C4×C5×Q8—41no—
30C2×C5×C4⋊C4—21no—
31C2×C5×C4⋊C4—21no—
32C2×C5×C4⋊C4—21no—
33C2×C5×C4⋊C4—21no—
34C2×C5×C4⋊C4—21no—
35C2×C5×C4⋊C4C2×C411yescharacteristic
36C2×C5×C4⋊C4C2×C411yescharacteristic
37C2×C5×C4⋊C4D411yescharacteristic
38C2×C5×C4⋊C4C2311yescharacteristic
39C2×C42×C5—21no—
40C2×C42×C5—21no—
41C2×C42×C5C2×C411yescharacteristic
42C2×C42×C5D411yescharacteristic
43C2×C42×C5D411yescharacteristic
44C2×#681—22no—
45C5×#95—21no—
46C5×#95—21no—
47C5×#95—21no—
48C5×#95—21no—
49C5×#95—21no—
50C5×#95C2×C411yescharacteristic
51C5×#95C2×C411yescharacteristic
52#3968—24no—
53C22⋊#168—22no—
54C4⋊#168—41no—
55#3935—41no—
56C4×#168—41no—
57C4×#168—41no—
58#2399D511yescharacteristic
59C4×#101—51no—
60#1461—51no—
61#1354—52no—
62#1346—52no—
63C2×C5×Q8—22no—
64C2×C5×Q8—22no—
65C2×C5×Q8—41no—
66C2×C5×Q8—42no—
67C2×C5×Q8—41no—
68C22×C4×C5—21no—
69C22×C4×C5—21no—
70C22×C4×C5—21no—
71C22×C4×C5—21no—
72C22×C4×C5C22⋊C411yescharacteristic
73C22×C4×C5C22⋊C411yescharacteristic
74C22×C4×C5C22⋊C411yescharacteristic
75C22×C4×C5C22⋊C411yescharacteristic
76C22×C4×C5C22×C411yescharacteristic
77C22×C4×C5C2×D411yescharacteristic
78C22×C4×C5C2×D411yescharacteristic
79C5×C4⋊C4—41no—
80C5×C4⋊C4—41no—
81C5×C4⋊C4—41no—
82C5×C4⋊C4—41no—
83C5×C4⋊C4—42no—
84C5×C4⋊C4—42no—
85C5×C4⋊C4—42no—
86C5×C4⋊C4—42no—
87C5×C4⋊C4—42no—
88C42×C5—24no—
89C42×C5—21no—
90C42×C5—21no—
91C42×C5—21no—
92C42×C5—21no—
93C42×C5—21no—
94C42×C5—21no—
95C42×C5—41no—
96C42×C5—41no—
97#681—24no—
98#681—42no—
99C2×#168—42no—
100C2×#168—42no—
101C2×C4×Q8Dic511yescharacteristic
102C2×C4×Q8C2×D511yescharacteristic
103#431—101no—
104C2×#101—101no—
105C4×M16—101no—
106#398—21no—
107#398Dic511yescharacteristic
108#398C2×D511yescharacteristic
109#395—21no—
110#395Dic511yescharacteristic
111#395C2×D511yescharacteristic
112C4×C4⋊C4—21no—
113C4×C4⋊C4—21no—
114#376Dic511yescharacteristic
115#343—52no—
116#324—52no—
117#324—101no—
118C23×C5C2×C22⋊C411yescharacteristic
119C5×Q8—44no—
120C5×Q8—42no—
121C5×Q8—42no—
122C2×C4×C5—21no—
123C2×C4×C5—21no—
124C2×C4×C5—21no—
125C2×C4×C5—21no—
126C2×C4×C5—22no—
127C2×C4×C5—22no—
128C2×C4×C5—22no—
129C2×C4×C5—22no—
130C2×C4×C5—21no—
131C2×C4×C5—21no—
132C2×C4×C5—21no—
133C2×C4×C5—21no—
134C2×C4×C5—21no—
135C2×C4×C5—21no—
136C2×C4×C5—41no—
137C2×C4×C5—41no—
138C2×C4×C5—41no—
139C2×C4×C5—41no—
140C2×C4×C5—41no—
141C2×C4×C5—41no—
142C2×C4×C5—41no—
143C2×C4×C5—41no—
144C2×C4×C5—41no—
145C2×C4×C5—41no—
146C2×C4×C5—41no—
147C2×C4×C5—41no—
148C2×C4×C5#9911yescharacteristic
149C2×C4×C5#9911yescharacteristic
150C2×C4×C5#10412yes—
151C2×C4×C5#13512yes—
152#168—44no—
153#168—82no—
154C22×Q8C2×Dic511yescharacteristic
155C22×Q8C22⋊D511yescharacteristic
156C2×M16—102no—
157C4×Q8—41no—
158C4×Q8—41no—
159C4×Q8—41no—
160C4×Q8—41no—
161C2×C4⋊C4—21no—
162C2×C4⋊C4—21no—
163C2×C4⋊C4—21no—
164C2×C4⋊C4—21no—
165C2×C4⋊C4—21no—
166C2×C4⋊C4C2×Dic511yescharacteristic
167C2×C4⋊C4C2×Dic511yescharacteristic
168C2×C4⋊C4C22⋊D511yescharacteristic
169C2×C4⋊C4C22×D511yescharacteristic
170C2×C42—21no—
171C2×C42—21no—
172C2×C42C2×Dic511yescharacteristic
173C2×C42C22⋊D511yescharacteristic
174C2×C42C22⋊D511yescharacteristic
175C4⋊C8—201no—
176#101—104no—
177C22⋊C8—102no—
178#97—201no—
179C4×C8—201no—
180C4×C8—201no—
181#95—21no—
182#95—21no—
183#95—21no—
184#95—21no—
185#95—21no—
186#95C2×Dic511yescharacteristic
187#95C2×Dic511yescharacteristic
188C22×C5—21no—
189C22×C5—21no—
190C22×C5C2×#9911yescharacteristic
191C22×C5#41611yescharacteristic
192C22×C5C2×#10411yescharacteristic
193C4×C5—21no—
194C4×C5—22no—
195C4×C5—22no—
196C4×C5—42no—
197C4×C5—42no—
198C4×C5—41no—
199C4×C5—41no—
200C4×C5—42no—
201C4×C5—41no—
202C4×C5—41no—
203C4×C5—81no—
204C4×C5#35612yes—
205C2×Q8—22no—
206C2×Q8—22no—
207C2×Q8—41no—
208C2×Q8—42no—
209C2×Q8—41no—
210C22×C4—21no—
211C22×C4—21no—
212C22×C4—21no—
213C22×C4—21no—
214C22×C4C22⋊Dic511yescharacteristic
215C22×C4C22⋊Dic511yescharacteristic
216C22×C4C22⋊Dic511yescharacteristic
217C22×C4C22⋊Dic511yescharacteristic
218C22×C4C22×Dic511yescharacteristic
219C22×C4C2×C22⋊D511yescharacteristic
220C22×C4C2×C22⋊D511yescharacteristic
221M16—104no—
222M16—202no—
223C2×C8—202no—
224C2×C8—202no—
225C4⋊C4—41no—
226C4⋊C4—41no—
227C4⋊C4—41no—
228C4⋊C4—41no—
229C4⋊C4—42no—
230C4⋊C4—42no—
231C4⋊C4—42no—
232C4⋊C4—42no—
233C4⋊C4—42no—
234C42—24no—
235C42—21no—
236C42—21no—
237C42—21no—
238C42—21no—
239C42—21no—
240C42—21no—
241C42—41no—
242C42—41no—
243C2×C5—21no—
244C2×C5—21no—
245C2×C5#150111yescharacteristic
246C2×C5#212011yescharacteristic
247C2×C5C2×#35611yescharacteristic
248C23C2×C22⋊Dic511yescharacteristic
249Q8—44no—
250Q8—42no—
251Q8—42no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—22no—
257C2×C4—22no—
258C2×C4—22no—
259C2×C4—22no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4#396611yescharacteristic
279C2×C4#396611yescharacteristic
280C2×C4#396912yes—
281C2×C4#409612yes—
282C8—204no—
283C8—402no—
284C5#1173611yescharacteristic, complemented, Sylow
285C22—21no—
286C22—21no—
287C22C2×#396611yescharacteristic
288C22#6552211yescharacteristic
289C22C2×#396911yescharacteristic
290C4—22no—
291C4—22no—
292C4—21no—
293C4—42no—
294C4—42no—
295C4—41no—
296C4—41no—
297C4—42no—
298C4—41no—
299C4—41no—
300C4—81no—
301C4#6476812yes—
302C2—21no—
303C2—21no—
304C2#1060250011yescharacteristic
305C2#1060250911yescharacteristic
306C2C2×#6476811yescharacteristic
subgroupG/H
centerC2×C4#3966
commutatorC22×C4×C5C22×C4
FrattiniC2×C4⋊C4C22×D5
FittingC5×#2399C2
socleC22×C5C2×#99
prime radicalC23×C5C2×C22⋊C4
cosocleC2×C5×C4⋊C4C23
hypercenter#2399D5
hypocenterC5#11736
LCSG ▷ C22×C4×C5 ▷ C23×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #2399

Complements

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

NH ≅ G/Ntype
284. C5#11736semidirect

Maximal subgroups

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

subgroupindex
C5×#23992
C4×#39682
#106024172
#105981412
#105981392
#117365