Finite Group Databasebeta

← #13014945

Subgroups — #13014945

Order 1280.

456 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 122 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#10604187C212yesmaximal
3#10598828C212yesmaximal
4#10598715C212yesmaximal
5C2×C4×C5×Q8C411yescharacteristic
6C2×#4090C411yescharacteristic
7C2×C4×Dic10C411yescharacteristic
8C2×C4⋊#170—22no—
9#65519C2211yescharacteristic
10#65265C411yescharacteristic
11#65263C2211yescharacteristic
12#65261—22no—
13C4×#683—22no—
14C42×Dic5C2211yescharacteristic
15#64918—22no—
16#64918C2214yes—
17#7653—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#4090—22no—
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—
38C4⋊#170—44no—
39#3963—22no—
40#3963—22no—
41C4×C4⋊Q8—51no—
42#1831—52no—
43#1272—52no—
44#1272—52no—
45C2×C5×Q8—21no—
46C2×C5×Q8—41no—
47C2×C5×Q8—41no—
48C2×C5×Q8M1612yes—
49C22×C4×C5—21no—
50C22×C4×C5—21no—
51C22×C4×C5C22⋊C411yescharacteristic
52C22×C4×C5C22⋊C411yescharacteristic
53C22×C4×C5C22×C411yescharacteristic
54C22×Dic5—21no—
55C22×Dic5—21no—
56C22×Dic5C22⋊C412yes—
57C22×Dic5C2×D412yes—
58C2×Dic10—21no—
59C2×Dic10—41no—
60C2×Dic10—41no—
61C2×Dic10M1612yes—
62C2×#170—44no—
63C2×#170—44no—
64C2×#170—44no—
65C5×C4⋊C4—41no—
66C5×C4⋊C4—42no—
67C42×C5—22no—
68C42×C5—42no—
69C4⋊Dic5—41no—
70#683—28no—
71#683—44no—
72#683—42no—
73C4×Dic5—21no—
74C4×Dic5—21no—
75C4×Dic5—42no—
76C4×Dic5—41no—
77C4×Dic5—42no—
78C4×Dic5SD1614yes—
79C4×Dic5Q1614yes—
80C2×C4⋊Q8—51no—
81C2×C4×Q8—51no—
82C2×C4×Q8AGL(1,𝔽5)11yescharacteristic
83C2×C4⋊C8—102no—
84#391—51no—
85#391—51no—
86#389—102no—
87#384—51no—
88C4×C4⋊C4—102no—
89C43—51no—
90#336—54no—
91#336—102no—
92C23×C5C2×C22⋊C411yescharacteristic
93C5×Q8—42no—
94C5×Q8—42no—
95C2×C4×C5—21no—
96C2×C4×C5—21no—
97C2×C4×C5—22no—
98C2×C4×C5—21no—
99C2×C4×C5—22no—
100C2×C4×C5—41no—
101C2×C4×C5—41no—
102C2×C4×C5—41no—
103C2×C4×C5—42no—
104C2×C4×C5#10012yes—
105C2×C4×C5#10314yes—
106C2×C4×C5C2×M1611yescharacteristic
107C2×C4×C5C2×M1611yescharacteristic
108C2×Dic5—22no—
109C2×Dic5—22no—
110C2×Dic5—22no—
111C2×Dic5—22no—
112C2×Dic5—22no—
113C2×Dic5—41no—
114C2×Dic5—41no—
115C2×Dic5—41no—
116C2×Dic5—42no—
117C2×Dic5#10314yes—
118C2×Dic5C2×SD1612yes—
119C2×Dic5C2×Q1612yes—
120Dic10—42no—
121Dic10—42no—
122#170—84no—
123C22×Q8—51no—
124C22×Q8C2×AGL(1,𝔽5)11yescharacteristic
125C22×C8—104no—
126C4⋊Q8—102no—
127C4⋊Q8—102no—
128C4×Q8—42no—
129C4×Q8—202no—
130C2×C4⋊C4—21no—
131C2×C4⋊C4—51no—
132C2×C4⋊C4—102no—
133C2×C4⋊C4—102no—
134C2×C4⋊C4—101no—
135C2×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
136C2×C42—21no—
137C2×C42—52no—
138C2×C42—51no—
139C2×C42—52no—
140C2×C42—51no—
141C2×C42—101no—
142C2×C42C2×AGL(1,𝔽5)11yescharacteristic
143C4⋊C8—204no—
144#95—102no—
145#95—102no—
146C22×C5#40711yescharacteristic
147C22×C5#41011yescharacteristic
148C22×C5C2×#10011yescharacteristic
149C22×C5C2×#10312yes—
150C22×C5#42112yes—
151C4×C5—21no—
152C4×C5—21no—
153C4×C5—41no—
154C4×C5—42no—
155C4×C5—81no—
156C4×C5#33314yes—
157Dic5—24no—
158Dic5—22no—
159Dic5—22no—
160Dic5—42no—
161Dic5—81no—
162C2×Q8—21no—
163C2×Q8—41no—
164C2×Q8—41no—
165C2×Q8—52no—
166C2×Q8—101no—
167C2×Q8—201no—
168C2×Q8—201no—
169C2×Q8#70012yes—
170C22×C4—21no—
171C22×C4—21no—
172C22×C4—52no—
173C22×C4—52no—
174C22×C4—101no—
175C22×C4—101no—
176C22×C4C22⋊AGL(1,𝔽5)11yescharacteristic
177C22×C4C22⋊AGL(1,𝔽5)11yescharacteristic
178C22×C4C22×AGL(1,𝔽5)11yescharacteristic
179C2×C8—204no—
180C2×C8—204no—
181C2×C8—204no—
182C4⋊C4—41no—
183C4⋊C4—42no—
184C4⋊C4—108no—
185C4⋊C4—201no—
186C4⋊C4—202no—
187C4⋊C4—204no—
188C42—22no—
189C42—42no—
190C42—54no—
191C42—54no—
192C42—101no—
193C42—101no—
194C42—201no—
195C42—202no—
196C42—202no—
197C2×C5#146611yescharacteristic
198C2×C5#148712yes—
199C2×C5#151812yes—
200C2×C5#153611yescharacteristic
201C2×C5C2×#33311yescharacteristic
202C23C2×C22⋊AGL(1,𝔽5)11yescharacteristic
203Q8—42no—
204Q8—42no—
205Q8—202no—
206Q8—202no—
207C2×C4—21no—
208C2×C4—21no—
209C2×C4—22no—
210C2×C4—21no—
211C2×C4—22no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—42no—
215C2×C4—41no—
216C2×C4—52no—
217C2×C4—54no—
218C2×C4—52no—
219C2×C4—102no—
220C2×C4—102no—
221C2×C4—102no—
222C2×C4—102no—
223C2×C4—102no—
224C2×C4—201no—
225C2×C4—201no—
226C2×C4—202no—
227C2×C4—201no—
228C2×C4#400914yes—
229C2×C4#401312yes—
230C2×C4C2×#70011yescharacteristic
231C2×C4D5⋊M1611yescharacteristic
232C8—404no—
233C5#765311yescharacteristic, complemented, Sylow
234C22#6574511yescharacteristic
235C22#6575611yescharacteristic
236C22C2×#400912yes—
237C22#6579512yes—
238C22C2×#401311yescharacteristic
239C4—21no—
240C4—21no—
241C4—42no—
242C4—41no—
243C4—81no—
244C4—102no—
245C4—102no—
246C4—104no—
247C4—202no—
248C4—401no—
249C4#6493114yes—
250C2#1060442912yes—
251C2#1060443912yes—
252C2#1060488511yescharacteristic
253C2C2×#6493111yescharacteristic
254C2#1060499511yescharacteristic
subgroupG/H
centerC23C2×C22⋊AGL(1,𝔽5)
commutatorC22×C4×C5C22×C4
FrattiniC22×C4C22×AGL(1,𝔽5)
FittingC2×C4×C5×Q8C4
socle, prime radicalC23×C5C2×C22⋊C4
cosocleC2×C4×Dic5C23
hypercenterC2×C4×Q8AGL(1,𝔽5)
hypocenterC5#7653
LCSG ▷ C22×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
233. C5#7653semidirect

Maximal subgroups

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

subgroupindex
C4×#40902
#106041872
#105988282
#105987152
#76535