Finite Group Databasebeta

← #12009951

Subgroups — #12009951

Order 1280.

394 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 87 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
1#10614209C211yesmaximal, characteristic
2C4×C5×#101C211yesmaximal, characteristic
3#10602418C211yesmaximal, characteristic
4#10597985C214yesmaximal
5C2×C4×C5×Q8C2211yescharacteristic
6C2×#4015C411yescharacteristic
7C2×C5×#101—21no—
8C4×C5×M16—21no—
9#65519—21no—
10#65268C412yes—
11#65268C2212yes—
12#65265—21no—
13C4×C4⋊Dic5C411yescharacteristic
14#65217—21no—
15#65217—21no—
16#65215—21no—
17C5×#343C2212yes—
18#64748—21no—
19#64748C2212yes—
20#11795—51nomaximal, Sylow
21C22×C5×Q8D411yescharacteristic
22C22×Dic10C2×C412yes—
23C2×C5×M16—22no—
24C4×C5×Q8—41no—
25C4×C5×Q8—41no—
26C2×C5×C4⋊C4C2×C411yescharacteristic
27C2×C5×C4⋊C4D411yescharacteristic
28C2×C5×C4⋊C4C2311yescharacteristic
29C2×C42×C5C2×C411yescharacteristic
30C2×C42×C5D411yescharacteristic
31C2×C42×C5D411yescharacteristic
32C2×C4⋊Dic5—21no—
33C2×C4⋊Dic5—21no—
34C2×C4⋊Dic5—21no—
35C2×#683—22no—
36C2×#683—22no—
37C2×C4×Dic5—21no—
38#4015—41no—
39#4015—41no—
40C5×#101—24no—
41C5×#97—41no—
42C4×C5×C8—41no—
43#3963—22no—
44#3963—22no—
45#3963C2×C412yes—
46C22⋊#168—22no—
47C4⋊#168—41no—
48#3935—41no—
49#2567—51no—
50C4×#101D511yescharacteristic
51#1467—51no—
52#1354—54no—
53C2×C5×Q8—22no—
54C2×C5×Q8—22no—
55C2×C5×Q8—41no—
56C22×C4×C5C22⋊C411yescharacteristic
57C22×C4×C5C22⋊C411yescharacteristic
58C22×C4×C5C22⋊C411yescharacteristic
59C22×C4×C5C22⋊C411yescharacteristic
60C22×C4×C5C22×C411yescharacteristic
61C22×C4×C5C2×D411yescharacteristic
62C22×C4×C5C2×D411yescharacteristic
63C22×Dic5—22no—
64C22×Dic5—22no—
65C2×Dic10—42no—
66C2×Dic10—82no—
67C5×M16—24no—
68C5×M16—42no—
69C2×C5×C8—42no—
70C5×C4⋊C4—41no—
71C5×C4⋊C4—41no—
72C5×C4⋊C4—41no—
73C42×C5—21no—
74C42×C5—21no—
75C42×C5—21no—
76C42×C5—21no—
77C42×C5—21no—
78C42×C5—21no—
79C4⋊Dic5—24no—
80C4⋊Dic5—42no—
81C4⋊Dic5—41no—
82C4⋊Dic5—41no—
83#683—82no—
84#683—82no—
85C4×Dic5—42no—
86C2×#168—42no—
87C2×C4⋊Q8—51no—
88C2×C4×Q8C2×D511yescharacteristic
89#432—101no—
90C2×#101—21no—
91C4×M16—21no—
92#395—52no—
93#395—52no—
94#391—101no—
95#389—101no—
96#389—101no—
97#384—101no—
98C4×C4⋊C4—51no—
99#343C2×D512yes—
100#324—52no—
101#324—101no—
102C23×C5C2×C22⋊C411yescharacteristic
103C5×Q8—44no—
104C2×C4×C5—21no—
105C2×C4×C5—21no—
106C2×C4×C5—21no—
107C2×C4×C5—21no—
108C2×C4×C5—22no—
109C2×C4×C5—21no—
110C2×C4×C5—21no—
111C2×C4×C5—21no—
112C2×C4×C5—21no—
113C2×C4×C5—21no—
114C2×C4×C5—21no—
115C2×C4×C5—41no—
116C2×C4×C5—41no—
117C2×C4×C5—41no—
118C2×C4×C5#9911yescharacteristic
119C2×C4×C5#9911yescharacteristic
120C2×C4×C5#10412yes—
121C2×C4×C5#13712yes—
122C2×Dic5—24no—
123C2×Dic5—42no—
124C2×Dic5—42no—
125C2×Dic5—42no—
126C2×Dic5—42no—
127C2×Dic5—42no—
128Dic10—84no—
129C5×C8—44no—
130#168—82no—
131C22×Q8—52no—
132C22×Q8C22⋊D511yescharacteristic
133C2×M16—22no—
134C4⋊Q8—201no—
135C4⋊Q8—201no—
136C4×Q8—41no—
137C4×Q8—41no—
138C2×C4⋊C4—101no—
139C2×C4⋊C4—101no—
140C2×C4⋊C4—101no—
141C2×C4⋊C4—102no—
142C2×C4⋊C4—102no—
143C2×C4⋊C4C4×D511yescharacteristic
144C2×C4⋊C4D2011yescharacteristic
145C2×C4⋊C4C22×D511yescharacteristic
146C2×C42—101no—
147C2×C42C4×D511yescharacteristic
148C2×C42D2011yescharacteristic
149C2×C42C22⋊D511yescharacteristic
150C4⋊C8—201no—
151#101—24no—
152C22⋊C8—102no—
153#97—41no—
154#97—201no—
155C4×C8—41no—
156#95—52no—
157#95—102no—
158#95—102no—
159C22×C5—21no—
160C22×C5—21no—
161C22×C5C2×#9911yescharacteristic
162C22×C5#41911yescharacteristic
163C22×C5C2×#10411yescharacteristic
164C4×C5—21no—
165C4×C5—22no—
166C4×C5—22no—
167C4×C5—41no—
168C4×C5—41no—
169C4×C5—41no—
170C4×C5—41no—
171C4×C5#35612yes—
172Dic5—44no—
173Dic5—82no—
174C2×Q8—22no—
175C2×Q8—22no—
176C2×Q8—41no—
177C2×Q8—202no—
178C2×Q8—402no—
179C22×C4—102no—
180C22×C4—102no—
181C22×C4#68511yescharacteristic
182C22×C4#68511yescharacteristic
183C22×C4#68511yescharacteristic
184C22×C4#68511yescharacteristic
185C22×C4C2×C4×D511yescharacteristic
186C22×C4C2×D2011yescharacteristic
187C22×C4C2×C22⋊D511yescharacteristic
188M16—24no—
189M16—42no—
190C2×C8—42no—
191C2×C8—202no—
192C4⋊C4—41no—
193C4⋊C4—41no—
194C4⋊C4—41no—
195C4⋊C4—104no—
196C4⋊C4—202no—
197C4⋊C4—201no—
198C4⋊C4—201no—
199C4⋊C4—402no—
200C4⋊C4—402no—
201C42—21no—
202C42—21no—
203C42—21no—
204C42—21no—
205C42—21no—
206C42—21no—
207C42—202no—
208C2×C5—21no—
209C2×C5—21no—
210C2×C5#150811yescharacteristic
211C2×C5#212211yescharacteristic
212C2×C5C2×#35611yescharacteristic
213C23C2×#68511yescharacteristic
214Q8—44no—
215Q8—404no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—22no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—41no—
228C2×C4—41no—
229C2×C4—41no—
230C2×C4—104no—
231C2×C4—202no—
232C2×C4—202no—
233C2×C4—202no—
234C2×C4—202no—
235C2×C4—202no—
236C2×C4#393712yes—
237C2×C4#393811yescharacteristic
238C2×C4#393811yescharacteristic
239C2×C4#409712yes—
240C8—44no—
241C8—402no—
242C5#1179511yescharacteristic, complemented, Sylow
243C22—21no—
244C22—21no—
245C22C2×#393711yescharacteristic
246C22C2×#393811yescharacteristic
247C22#6529311yescharacteristic
248C4—22no—
249C4—22no—
250C4—21no—
251C4—41no—
252C4—41no—
253C4—41no—
254C4—41no—
255C4—204no—
256C4—402no—
257C4#6469812yes—
258C2—21no—
259C2—21no—
260C2#1060023811yescharacteristic
261C2C2×#6469811yescharacteristic
262C2#1060093911yescharacteristic
subgroupG/H
centerC22C2×#3938
commutatorC22×C4×C5C22×C4
FrattiniC2×C4⋊C4C22×D5
FittingC4×C5×#101C2
socleC22×C5C2×#99
prime radicalC23×C5C2×C22⋊C4
cosocleC2×C5×C4⋊C4C23
hypercenterC4×#101D5
hypocenterC5#11795
LCSG ▷ C22×C4×C5 ▷ C23×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ C4×#101

Complements

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

NH ≅ G/Ntype
242. C5#11795semidirect

Maximal subgroups

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

subgroupindex
#106142092
C4×C5×#1012
#106024182
#105979852
#117955