Finite Group Databasebeta

← #11987570

Subgroups — #11987570

Order 1280.

468 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 127 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
1C4×C5×C4⋊Q8C211yesmaximal, characteristic
2#10600182C211yesmaximal, characteristic
3#10600182C211yesmaximal, characteristic
4#10598129C214yesmaximal
5C2×C5×C4⋊Q8C411yescharacteristic
6C2×C4×C5×Q8—21no—
7C5×#391—21no—
8C5×#389—21no—
9C5×#389C2212yes—
10C5×#384C411yescharacteristic
11C4×C5×C4⋊C4—21no—
12C4×C5×C4⋊C4C412yes—
13C43×C5C2211yescharacteristic
14C2×#3935—21no—
15C2×#3935—21no—
16#64744—21no—
17#64744—21no—
18#64744C2212yes—
19#64744C2212yes—
20#7638—51nomaximal, Sylow
21C22×C5×Q8—21no—
22C5×C4⋊Q8—24no—
23C4×C5×Q8—44no—
24C2×C5×C4⋊C4—21no—
25C2×C5×C4⋊C4—21no—
26C2×C5×C4⋊C4—21no—
27C2×C5×C4⋊C4—22no—
28C2×C5×C4⋊C4C2×C412yes—
29C2×C5×C4⋊C4C2×C412yes—
30C2×C42×C5—22no—
31C2×C42×C5C2×C411yescharacteristic
32C2×C42×C5C2×C411yescharacteristic
33C2×C42×C5D411yescharacteristic
34C2×C42×C5D411yescharacteristic
35C2×C42×C5D411yescharacteristic
36C2×C42×C5D411yescharacteristic
37C2×C42×C5C2311yescharacteristic
38C22×#168—22no—
39C22×#168—22no—
40C5×#95—22no—
41C5×#95—22no—
42#3935—24no—
43#3935—24no—
44C4×C4⋊Q8D511yescharacteristic
45#1745—51no—
46#1745—51no—
47#1271—54no—
48C2×C5×Q8—24no—
49C2×C5×Q8—42no—
50C2×C5×Q8—42no—
51C22×C4×C5—22no—
52C22×C4×C5—22no—
53C22×C4×C5C22⋊C411yescharacteristic
54C22×C4×C5C22⋊C411yescharacteristic
55C22×C4×C5C22⋊C411yescharacteristic
56C22×C4×C5C22⋊C411yescharacteristic
57C22×C4×C5C22×C411yescharacteristic
58C22×C4×C5C2×D411yescharacteristic
59C22×C4×C5C2×D411yescharacteristic
60C5×C4⋊C4—24no—
61C5×C4⋊C4—22no—
62C5×C4⋊C4—42no—
63C5×C4⋊C4—42no—
64C5×C4⋊C4—42no—
65C5×C4⋊C4—44no—
66C5×C4⋊C4M1614yes—
67C42×C5—22no—
68C42×C5—22no—
69C42×C5—22no—
70C42×C5—22no—
71C42×C5—22no—
72C42×C5—22no—
73C42×C5—41no—
74C42×C5—44no—
75C2×#168—24no—
76C2×#168—24no—
77C2×#168—42no—
78C2×#168—42no—
79C2×#168—42no—
80C2×#168—42no—
81C2×C4⋊Q8Dic511yescharacteristic
82C2×C4×Q8—21no—
83C2×#97—101no—
84C2×#97—101no—
85#391—21no—
86#389—21no—
87#389C2×D512yes—
88#384Dic511yescharacteristic
89C4×C4⋊C4—21no—
90C4×C4⋊C4Dic512yes—
91C43C2×D511yescharacteristic
92#336—52no—
93#336—52no—
94#336—101no—
95#336—101no—
96C23×C5C2×C22⋊C411yescharacteristic
97C5×Q8—48no—
98C2×C4×C5—21no—
99C2×C4×C5—21no—
100C2×C4×C5—21no—
101C2×C4×C5—21no—
102C2×C4×C5—21no—
103C2×C4×C5—21no—
104C2×C4×C5—21no—
105C2×C4×C5—21no—
106C2×C4×C5—21no—
107C2×C4×C5—21no—
108C2×C4×C5—21no—
109C2×C4×C5—21no—
110C2×C4×C5—24no—
111C2×C4×C5—21no—
112C2×C4×C5—21no—
113C2×C4×C5—21no—
114C2×C4×C5—42no—
115C2×C4×C5—42no—
116C2×C4×C5—42no—
117C2×C4×C5—42no—
118C2×C4×C5—42no—
119C2×C4×C5#10112yes—
120C2×C4×C5#10412yes—
121C2×C4×C5#10412yes—
122C2×C4×C5C2×M1612yes—
123C2×C4×C5AGL(1,ℤ/8)12yes—
124C2×C4×C5#13712yes—
125#168—44no—
126#168—44no—
127C22×Q8—21no—
128C22×C8—102no—
129C22×C8—102no—
130C4⋊Q8—24no—
131C4×Q8—44no—
132C2×C4⋊C4—21no—
133C2×C4⋊C4—21no—
134C2×C4⋊C4—21no—
135C2×C4⋊C4—22no—
136C2×C4⋊C4C2×Dic512yes—
137C2×C4⋊C4C2×Dic512yes—
138C2×C42—22no—
139C2×C42C2×Dic511yescharacteristic
140C2×C42C2×Dic511yescharacteristic
141C2×C42C22⋊D511yescharacteristic
142C2×C42C22⋊D511yescharacteristic
143C2×C42C22⋊D511yescharacteristic
144C2×C42C22⋊D511yescharacteristic
145C2×C42C22×D511yescharacteristic
146#97—104no—
147#97—104no—
148#95—22no—
149#95—22no—
150C22×C5#40711yescharacteristic
151C22×C5#41011yescharacteristic
152C22×C5C2×#10111yescharacteristic
153C22×C5#41811yescharacteristic
154C22×C5#41911yescharacteristic
155C22×C5C2×#10411yescharacteristic
156C22×C5C2×#10411yescharacteristic
157C4×C5—22no—
158C4×C5—22no—
159C4×C5—22no—
160C4×C5—22no—
161C4×C5—22no—
162C4×C5—22no—
163C4×C5—44no—
164C4×C5—41no—
165C4×C5—82no—
166C2×Q8—24no—
167C2×Q8—42no—
168C2×Q8—42no—
169C22×C4—22no—
170C22×C4—22no—
171C22×C4C22⋊Dic511yescharacteristic
172C22×C4C22⋊Dic511yescharacteristic
173C22×C4C22⋊Dic511yescharacteristic
174C22×C4C22⋊Dic511yescharacteristic
175C22×C4C22×Dic511yescharacteristic
176C22×C4C2×C22⋊D511yescharacteristic
177C22×C4C2×C22⋊D511yescharacteristic
178C2×C8—104no—
179C2×C8—104no—
180C2×C8—202no—
181C2×C8—202no—
182C2×C8—202no—
183C2×C8—202no—
184C4⋊C4—24no—
185C4⋊C4—22no—
186C4⋊C4—42no—
187C4⋊C4—42no—
188C4⋊C4—42no—
189C4⋊C4—44no—
190C4⋊C4#68114yes—
191C42—22no—
192C42—22no—
193C42—22no—
194C42—22no—
195C42—22no—
196C42—22no—
197C42—41no—
198C42—44no—
199C2×C5#146711yescharacteristic
200C2×C5#149011yescharacteristic
201C2×C5#149111yescharacteristic
202C2×C5#150511yescharacteristic
203C2×C5#150611yescharacteristic
204C2×C5#152611yescharacteristic
205C2×C5#155611yescharacteristic
206C23C2×C22⋊Dic511yescharacteristic
207Q8—48no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—24no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—42no—
225C2×C4—42no—
226C2×C4—42no—
227C2×C4—42no—
228C2×C4—42no—
229C2×C4#396812yes—
230C2×C4#396912yes—
231C2×C4#396912yes—
232C2×C4C2×#68112yes—
233C2×C4#407812yes—
234C2×C4#408812yes—
235C8—204no—
236C8—204no—
237C5#763811yescharacteristic, complemented, Sylow
238C22#6549611yescharacteristic
239C22#6550411yescharacteristic
240C22#6551411yescharacteristic
241C22C2×#396811yescharacteristic
242C22C2×#396911yescharacteristic
243C22C2×#396911yescharacteristic
244C22#6552911yescharacteristic
245C4—22no—
246C4—22no—
247C4—22no—
248C4—22no—
249C4—22no—
250C4—22no—
251C4—41no—
252C4—44no—
253C4—82no—
254C2#1060239211yescharacteristic
255C2#1060241611yescharacteristic
256C2#1060241811yescharacteristic
257C2#1060256911yescharacteristic
258C2#1060260511yescharacteristic
259C2#1060261411yescharacteristic
260C2#1060262911yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic5
commutatorC22×C4×C5C22×C4
FrattiniC2×C42C22×D5
FittingC4×C5×C4⋊Q8C2
socle, prime radicalC23×C5C2×C22⋊C4
cosocleC2×C42×C5C23
hypercenterC4×C4⋊Q8D5
hypocenterC5#7638
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C43 ◁ C4×C4⋊Q8

Complements

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

NH ≅ G/Ntype
237. C5#7638semidirect

Maximal subgroups

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

subgroupindex
C4×C5×C4⋊Q82
#106001822
#105981292
#76385