Finite Group Databasebeta

← #13014777

Subgroups — #13014777

Order 1280.

440 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 106 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×#4090C211yesmaximal, characteristic
2#10604189C212yesmaximal
3#10598828C212yesmaximal
4#10598715C212yesmaximal
5C2×C4×C5×Q8C411yescharacteristic
6C2×#4090C411yescharacteristic
7C2×C4×Dic10C411yescharacteristic
8#65519C2211yescharacteristic
9#65265C411yescharacteristic
10#65263C2211yescharacteristic
11#65261—22no—
12C4×#683—22no—
13C42×Dic5C2211yescharacteristic
14#64918—22no—
15#64918—22no—
16#64918C2214yes—
17#7605—51nomaximal, Sylow
18C22×C5×Q8C2×C411yescharacteristic
19C22×Dic10C2×C411yescharacteristic
20C22×#170—24no—
21C4×C5×Q8—42no—
22C2×C5×C4⋊C4—21no—
23C2×C5×C4⋊C4C2×C411yescharacteristic
24C2×C42×C5—21no—
25C2×C42×C5C2×C411yescharacteristic
26#4090—22no—
27#4090C814yescomplemented
28C2×C4⋊Dic5C2×C411yescharacteristic
29C2×#683—22no—
30C2×#683—21no—
31C2×#683—22no—
32C2×C4×Dic5—21no—
33C2×C4×Dic5C2×C411yescharacteristic
34C2×C4×Dic5D412yes—
35C2×C4×Dic5D412yes—
36C2×C4×Dic5C2311yescharacteristic
37C4×Dic10—42no—
38#3963—22no—
39#3963—22no—
40C4×C4⋊Q8—51no—
41#1839—52no—
42#1272—52no—
43#1272—52no—
44C2×C5×Q8—21no—
45C2×C5×Q8—41no—
46C2×C5×Q8—41no—
47C2×C5×Q8C2×C812yes—
48C22×C4×C5—21no—
49C22×C4×C5—21no—
50C22×C4×C5C22⋊C411yescharacteristic
51C22×C4×C5C22⋊C411yescharacteristic
52C22×C4×C5C22×C411yescharacteristic
53C22×Dic5—21no—
54C22×Dic5—21no—
55C22×Dic5C22⋊C412yes—
56C22×Dic5C2×D412yes—
57C2×Dic10—21no—
58C2×Dic10—41no—
59C2×Dic10—41no—
60C2×Dic10C2×C812yes—
61C2×#170—44no—
62C2×#170—44no—
63C2×#170—44no—
64C5×C4⋊C4—41no—
65C5×C4⋊C4—42no—
66C42×C5—22no—
67C42×C5—42no—
68C4⋊Dic5—41no—
69#683—28no—
70#683—44no—
71#683—42no—
72C4×Dic5—24no—
73C4×Dic5—42no—
74C4×Dic5—41no—
75C4×Dic5—42no—
76C4×Dic5C2×C812yes—
77C4×Dic5M1612yes—
78C2×C4⋊Q8—51no—
79C2×C4×Q8—51no—
80C2×C4×Q8AGL(1,𝔽5)11yescharacteristic
81#391—51no—
82#391—51no—
83#389—102no—
84#384—51no—
85C4×C4⋊C4—102no—
86C43—51no—
87#336—54no—
88#336—102no—
89#336—102no—
90C23×C5C2×C22⋊C411yescharacteristic
91C5×Q8—42no—
92C5×Q8—42no—
93C2×C4×C5—21no—
94C2×C4×C5—21no—
95C2×C4×C5—22no—
96C2×C4×C5—22no—
97C2×C4×C5—21no—
98C2×C4×C5—22no—
99C2×C4×C5—41no—
100C2×C4×C5—41no—
101C2×C4×C5—41no—
102C2×C4×C5—42no—
103C2×C4×C5#10012yes—
104C2×C4×C5C22×C811yescharacteristic
105C2×C4×C5C2×M1611yescharacteristic
106C2×Dic5—22no—
107C2×Dic5—22no—
108C2×Dic5—22no—
109C2×Dic5—22no—
110C2×Dic5—22no—
111C2×Dic5—41no—
112C2×Dic5—41no—
113C2×Dic5—41no—
114C2×Dic5—42no—
115C2×Dic5C22⋊C814yes—
116C2×Dic5#13714yes—
117Dic10—42no—
118Dic10—42no—
119#170—84no—
120C22×Q8—51no—
121C22×Q8C2×AGL(1,𝔽5)11yescharacteristic
122C22×C8—104no—
123C4⋊Q8—54no—
124C4⋊Q8—102no—
125C4×Q8—42no—
126C4×Q8—202no—
127C2×C4⋊C4—21no—
128C2×C4⋊C4—51no—
129C2×C4⋊C4—102no—
130C2×C4⋊C4—102no—
131C2×C4⋊C4—101no—
132C2×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
133C2×C42—21no—
134C2×C42—51no—
135C2×C42—52no—
136C2×C42—52no—
137C2×C42—51no—
138C2×C42—101no—
139C2×C42C2×AGL(1,𝔽5)11yescharacteristic
140#95—102no—
141#95—102no—
142C22×C5C2×C22⋊C811yescharacteristic
143C22×C5#41011yescharacteristic
144C22×C5C2×#10011yescharacteristic
145C22×C5#41912yes—
146C22×C5#42112yes—
147C4×C5—22no—
148C4×C5—21no—
149C4×C5—21no—
150C4×C5—41no—
151C4×C5—42no—
152C4×C5—81no—
153Dic5—24no—
154Dic5—24no—
155Dic5—42no—
156Dic5—81no—
157C2×Q8—21no—
158C2×Q8—41no—
159C2×Q8—41no—
160C2×Q8—52no—
161C2×Q8—101no—
162C2×Q8—201no—
163C2×Q8—201no—
164C2×Q8D5⋊C812yes—
165C22×C4—21no—
166C22×C4—21no—
167C22×C4—52no—
168C22×C4—52no—
169C22×C4—101no—
170C22×C4—101no—
171C22×C4C22⋊AGL(1,𝔽5)11yescharacteristic
172C22×C4C22⋊AGL(1,𝔽5)11yescharacteristic
173C22×C4C22×AGL(1,𝔽5)11yescharacteristic
174C2×C8—204no—
175C2×C8—204no—
176C2×C8—204no—
177C4⋊C4—41no—
178C4⋊C4—42no—
179C4⋊C4—108no—
180C4⋊C4—201no—
181C4⋊C4—202no—
182C4⋊C4—204no—
183C42—22no—
184C42—42no—
185C42—52no—
186C42—52no—
187C42—104no—
188C42—201no—
189C42—202no—
190C42—202no—
191C2×C5#146011yescharacteristic
192C2×C5#147912yes—
193C2×C5#151512yes—
194C2×C5#153611yescharacteristic
195C2×C5#155811yescharacteristic
196C23C2×C22⋊AGL(1,𝔽5)11yescharacteristic
197Q8—42no—
198Q8—42no—
199Q8—202no—
200Q8—202no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—21no—
206C2×C4—22no—
207C2×C4—41no—
208C2×C4—41no—
209C2×C4—42no—
210C2×C4—41no—
211C2×C4—54no—
212C2×C4—54no—
213C2×C4—102no—
214C2×C4—102no—
215C2×C4—102no—
216C2×C4—102no—
217C2×C4—102no—
218C2×C4—201no—
219C2×C4—201no—
220C2×C4—202no—
221C2×C4—201no—
222C2×C4#401312yes—
223C2×C4C2×D5⋊C811yescharacteristic
224C2×C4D5⋊M1611yescharacteristic
225C8—404no—
226C5#760511yescharacteristic, complemented, Sylow
227C22#6574511yescharacteristic
228C22D5⋊(C22⋊C8)11yescharacteristic
229C22#6578212yes—
230C22#6579512yes—
231C22C2×#401311yescharacteristic
232C4—21no—
233C4—21no—
234C4—22no—
235C4—42no—
236C4—41no—
237C4—81no—
238C4—104no—
239C4—104no—
240C4—202no—
241C4—401no—
242C2#1060442812yes—
243C2#1060443812yes—
244C2#1060487911yescharacteristic
245C2#1060497211yescharacteristic
246C2#1060499511yescharacteristic
subgroupG/H
centerC23C2×C22⋊AGL(1,𝔽5)
commutatorC2×C4×C5C22×C8
FrattiniC22×C4C22×AGL(1,𝔽5)
FittingC2×C4×C5×Q8C4
socle, prime radicalC23×C5C2×C22⋊C4
cosocleC2×C4×Dic5C23
hypercenterC2×C4×Q8AGL(1,𝔽5)
hypocenterC5#7605
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
27. #4090C8semidirect
226. C5#7605semidirect

Maximal subgroups

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

subgroupindex
C4×#40902
#106041892
#105988282
#105987152
#76055